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Rep:Mod:S1R9J9S3

2014-03-21T22:10:30Z

Srs11: /* Spectroscopic Simulation using Quantum Mechanics */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>. Although, by altering the temperature and pressure of the reaction, it is possible to favour the thermodynamic product in an equilibrium situation.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation. Likewise, as with the previous example, the concentrations of products obtained can be altered by changing the reaction conditions, notably the temperature and pressure.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised in Avogadro, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6 - Thermodynamic Parameters of Molecule 18
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

Finally, the properties for Molecule 17 were also calculated<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28068}}]</ref> and by comparing the output files from the HPC computation, it is apparent that Molecule 18 is the thermodynamically more stable isomer, and the increase in energy when analysing Molecule 17 s a result of the torsional strain experienced by the carbonyl when rotating, particularly when approaching the bridging group.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is surprisingly consistent with reported literature values<ref>[David K. Romney and Scott J. Miller, ''Org. Lett.'', 2012, '''14''', S17]</ref> for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

===Assigning the Absolute Configuration of the Products===

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

In order to calculate the enantiomeric excess from the transition state data provided, the lowest energy S and R (or SS and RR) transition state (reported in Hartrees and converted to KJmol<sup>-1</sup>) were compared to obtain the value for ΔG, which using the thermodynamic equilibrium constant K was obtained by rearranging the equation ΔG=-RTlnK. K=[Products]/[Reactants] was the relationship then used, yet insetead of using concentrations of products and reactants, mole fractions of the relative proportion of transition state were used to determine the enantiomeric excess via: Enantiomeric Excess = 100(|y-x|), where x and y are the mole fractions. The results presented below have been determined based on the relative energies of each transition state.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, for example being reported as 23.68°<ref>[Yuan Ching P. Chiang, Michael N. Chang, Shu Shu Yang, John C. Chabala and James V. Heck, ''J. Org. Chem.'', 1988, '''53''', 4599-4603]</ref> in one reference, yet 10.8° in another<ref>[Hideaki Muratake and Mitsutaka Natsume, ''Tetrahedron Lett.'', 1989, '''30''', 5771-5772]</ref>, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T22:06:26Z

Srs11: /* Suggestions for New Calculations */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>. Although, by altering the temperature and pressure of the reaction, it is possible to favour the thermodynamic product in an equilibrium situation.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation. Likewise, as with the previous example, the concentrations of products obtained can be altered by changing the reaction conditions, notably the temperature and pressure.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised in Avogadro, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6 - Thermodynamic Parameters of Molecule 18
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

Finally, the properties for Molecule 17 were also calculated<ref>[{Samuel Spreadbury, 2014, DOI|10042/28068}]</ref> and by comparing the output files from the HPC computation, it is apparent that Molecule 18 is the thermodynamically more stable isomer, and the increase in energy when analysing Molecule 17 s a result of the torsional strain experienced by the carbonyl when rotating, particularly when approaching the bridging group.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is surprisingly consistent with reported literature values<ref>[David K. Romney and Scott J. Miller, ''Org. Lett.'', 2012, '''14''', S17]</ref> for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

===Assigning the Absolute Configuration of the Products===

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

In order to calculate the enantiomeric excess from the transition state data provided, the lowest energy S and R (or SS and RR) transition state (reported in Hartrees and converted to KJmol<sup>-1</sup>) were compared to obtain the value for ΔG, which using the thermodynamic equilibrium constant K was obtained by rearranging the equation ΔG=-RTlnK. K=[Products]/[Reactants] was the relationship then used, yet insetead of using concentrations of products and reactants, mole fractions of the relative proportion of transition state were used to determine the enantiomeric excess via: Enantiomeric Excess = 100(|y-x|), where x and y are the mole fractions. The results presented below have been determined based on the relative energies of each transition state.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, for example being reported as 23.68°<ref>[Yuan Ching P. Chiang, Michael N. Chang, Shu Shu Yang, John C. Chabala and James V. Heck, ''J. Org. Chem.'', 1988, '''53''', 4599-4603]</ref> in one reference, yet 10.8° in another<ref>[Hideaki Muratake and Mitsutaka Natsume, ''Tetrahedron Lett.'', 1989, '''30''', 5771-5772]</ref>, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T21:51:21Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>. Although, by altering the temperature and pressure of the reaction, it is possible to favour the thermodynamic product in an equilibrium situation.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation. Likewise, as with the previous example, the concentrations of products obtained can be altered by changing the reaction conditions, notably the temperature and pressure.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised in Avogadro, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6 - Thermodynamic Parameters of Molecule 18
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

Finally, the properties for Molecule 17 were also calculated<ref>[{Samuel Spreadbury, 2014, DOI|10042/28068}]</ref> and by comparing the output files from the HPC computation, it is apparent that Molecule 18 is the thermodynamically more stable isomer, and the increase in energy when analysing Molecule 17 s a result of the torsional strain experienced by the carbonyl when rotating, particularly when approaching the bridging group.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is surprisingly consistent with reported literature values<ref>[David K. Romney and Scott J. Miller, ''Org. Lett.'', 2012, '''14''', S17]</ref> for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

===Assigning the Absolute Configuration of the Products===

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

In order to calculate the enantiomeric excess from the transition state data provided, the lowest energy S and R (or SS and RR) transition state (reported in Hartrees and converted to KJmol<sup>-1</sup>) were compared to obtain the value for ΔG, which using the thermodynamic equilibrium constant K was obtained by rearranging the equation ΔG=-RTlnK. K=[Products]/[Reactants] was the relationship then used, yet insetead of using concentrations of products and reactants, mole fractions of the relative proportion of transition state were used to determine the enantiomeric excess via: Enantiomeric Excess = 100(|y-x|), where x and y are the mole fractions. The results presented below have been determined based on the relative energies of each transition state.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T21:31:51Z

Srs11: /* The Hydrogenation of Cyclopentadiene Dimer */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>. Although, by altering the temperature and pressure of the reaction, it is possible to favour the thermodynamic product in an equilibrium situation.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation. Likewise, as with the previous example, the concentrations of products obtained can be altered by changing the reaction conditions, notably the temperature and pressure.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised in Avogadro, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6 - Thermodynamic Parameters of Molecule 18
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

Finally, the properties for Molecule 17 were also calculated<ref>[{Samuel Spreadbury, 2014, DOI|10042/28068}]</ref> and by comparing the output files from the HPC computation, it is apparent that Molecule 18 is the thermodynamically more stable isomer, and the increase in energy when analysing Molecule 17 s a result of the torsional strain experienced by the carbonyl when rotating, particularly when approaching the bridging group.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is surprisingly consistent with reported literature values<ref>[David K. Romney and Scott J. Miller, ''Org. Lett.'', 2012, '''14''', S17]</ref> for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

In order to calculate the enantiomeric excess from the transition state data provided, the lowest energy S and R (or SS and RR) transition state were compared to obtain the value for ΔG, which using the thermodynamic equilibrium constant K was obtained by rearranging the equation ΔG=-RTlnK. From this value, and considering mole fractions, the enantiomeric excess of the specific alkenes were obtained, based on the relative energies of each transition state.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T20:18:25Z

Srs11: /* Spectroscopic Simulation using Quantum Mechanics */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised in Avogadro, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6 - Thermodynamic Parameters of Molecule 18
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

Finally, the properties for Molecule 17 were also calculated<ref>[{Samuel Spreadbury, 2014, DOI|10042/28068}]</ref> and by comparing the output files from the HPC computation, it is apparent that Molecule 18 is the thermodynamically more stable isomer, and the increase in energy when analysing Molecule 17 s a result of the torsional strain experienced by the carbonyl when rotating, particularly when approaching the bridging group.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is surprisingly consistent with reported literature values<ref>[David K. Romney and Scott J. Miller, ''Org. Lett.'', 2012, '''14''', S17]</ref> for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

In order to calculate the enantiomeric excess from the transition state data provided, the lowest energy S and R (or SS and RR) transition state were compared to obtain the value for ΔG, which using the thermodynamic equilibrium constant K was obtained by rearranging the equation ΔG=-RTlnK. From this value, and considering mole fractions, the enantiomeric excess of the specific alkenes were obtained, based on the relative energies of each transition state.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T20:08:29Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

Finally, the properties for Molecule 17 were also calculated<ref>[{Samuel Spreadbury, 2014, DOI|10042/28068}]</ref> and by comparing the output files from the HPC computation, it is apparent that Molecule 18 is the thermodynamically more stable isomer, and the increase in energy when analysing Molecule 17 s a result of the torsional strain experienced by the carbonyl when rotating, particularly when approaching the bridging group.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is surprisingly consistent with reported literature values<ref>[David K. Romney and Scott J. Miller, ''Org. Lett.'', 2012, '''14''', S17]</ref> for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

In order to calculate the enantiomeric excess from the transition state data provided, the lowest energy S and R (or SS and RR) transition state were compared to obtain the value for ΔG, which using the thermodynamic equilibrium constant K was obtained by rearranging the equation ΔG=-RTlnK. From this value, and considering mole fractions, the enantiomeric excess of the specific alkenes were obtained, based on the relative energies of each transition state.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T20:03:08Z

Srs11: /* NMR Properties of Epoxidised Alkenes */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

Finally, the properties for Molecule 17 were also calculated<ref>[{Samuel Spreadbury, 2014, DOI|10042/28068}]</ref> and by comparing the output files from the HPC computation, it is apparent that Molecule 18 is the thermodynamically more stable isomer, and the increase in energy when analysing Molecule 17 s a result of the torsional strain experienced by the carbonyl when rotating, particularly when approaching the bridging group.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is surprisingly consistent with reported literature values<ref>[David K. Romney and Scott J. Miller, ''Org. Lett.'', 2012, '''14''', S17]</ref> for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T19:56:08Z

Srs11: /* Spectroscopic Simulation using Quantum Mechanics */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

Finally, the properties for Molecule 17 were also calculated<ref>[{Samuel Spreadbury, 2014, DOI|10042/28068}]</ref> and by comparing the output files from the HPC computation, it is apparent that Molecule 18 is the thermodynamically more stable isomer, and the increase in energy when analysing Molecule 17 s a result of the torsional strain experienced by the carbonyl when rotating, particularly when approaching the bridging group.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T19:54:14Z

Srs11: /* Spectroscopic Simulation using Quantum Mechanics */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

Finally, the properties for Molecule 17 were also calculated<ref>[{{DOI:10042/28068}}]</ref> and by comparing the output files from the HPC computation, it is apparent that Molecule 18 is the thermodynamically more stable isomer, and the increase in energy when analysing Molecule 17 s a result of the torsional strain experienced by the carbonyl when rotating, particularly when approaching the bridging group.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T19:44:36Z

Srs11: /* Atropisomerism in a Taxol Intermediate */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T19:43:21Z

Srs11: /* Atropisomerism in a Taxol Intermediate */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.75903
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|19.02387
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.71043
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|35.03588
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-0.06548
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>66.28650</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

File:SRJS Molecule10 twist Boat.cml

2014-03-21T19:39:35Z

Srs11: uploaded a new version of "File:SRJS Molecule10 twist Boat.cml"

Rep:Mod:S1R9J9S3

2014-03-21T19:36:19Z

Srs11: /* Atropisomerism in a Taxol Intermediate */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 10 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule10 Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 10 Twist</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Molecule10 twist Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

File:SRJS Molecule10 twist Boat.cml

2014-03-21T19:32:43Z

Srs11:

Rep:Mod:S1R9J9S3

2014-03-21T19:22:00Z

Srs11: /* Atropisomerism in a Taxol Intermediate */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T19:16:09Z

Srs11: /* Transition State Analysis */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

[[File:SRJS_Topology_Image.png|thumb|Electron Topology of Shi Epoxidation]]The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly. The position of the yellow point, representing the mean electron density within a bond, or an interaction in terms of the transition state, is located directly in between the alkene and the dioxirane oxygen, indicating that there is a build up of electron density as the bond is forming. Furthermore, it is visible that the position of this point is not always at the centre of the bond, particularly when a polar covalent bond is formed, such as those present in the anomeric carbons of the catalyst.

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

File:SRJS Topology Image.png

2014-03-21T19:10:58Z

Srs11:

Rep:Mod:S1R9J9S3

2014-03-21T19:08:40Z

Srs11: /* Suggestions for New Calculations */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
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The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

[[File:SRJS_Final_Suggestion.png|thumb|R-(+)-Pulegone Epoxidation]]R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess. Furthermore, the literature reported enantiomeric excess is particularly varied, even when identical/extremely similar measurement conditions have been reported, therefore, computational analysis would be useful for identifying misleading literature reports.

==References==
<references/>

File:SRJS Final Suggestion.png

2014-03-21T19:06:46Z

Srs11:

Rep:Mod:S1R9J9S3

2014-03-21T18:59:16Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
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<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Shi Catalyst S 4.cml</uploadedFileContents>
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|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SSB-methyl styrene RR 4 Shi Catalyst.cml</uploadedFileContents>
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|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Jacobsen S 1.cml </uploadedFileContents>
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|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-methyl styrene SS 1 Jacobsen.cml</uploadedFileContents>
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|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
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The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

File:SSB-methyl styrene RR 4 Shi Catalyst.cml

2014-03-21T18:58:45Z

Srs11:

Rep:Mod:S1R9J9S3

2014-03-21T18:54:08Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|3D Visualisation
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|[[File:SRJS Styrene Shi Catalyst S 4.cml]]
|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|
|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|
|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|
|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
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<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
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The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

File:SRJS Styrene Shi Catalyst S 4.cml

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Srs11:

File:SRJS Styrene Jacobsen S 1.cml

2014-03-21T18:50:09Z

Srs11:

File:SRJS B-methyl styrene SS 1 Jacobsen.cml

2014-03-21T18:50:08Z

Srs11:

Rep:Mod:S1R9J9S3

2014-03-21T18:45:55Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.88
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As all of the systems reported are the lowest energy transition state, it can be assumed that the reaction is under kinetic control, as the lowest energy pathway is utilised in the formation of the product. As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity. The match to literature value is quite poor, however, this may be as a result of different experimental conditions undertaken, compared to the computed model.

For the Jacobsen catalyst, Styrene Oxide primary forms the RR enantiomer and the literature is in good agreement with the computed data. From the transition state, it is visible that the aromatic π system of the alkene overlays with a phenyl ring on the catalyst and these favourable π stacking interactions could lead to the minimisation of the transition state energy (indicating that this transition state is endo), which would not be possible on the approach to form the RR enantiomer.

Once again, the agreement with literature is fairly good for the Shi catalysis of trans-β-methyl Styrene Oxide and it can be observed in the transition state that the face approached by the substrate avoids repulsive interactions between Oxygen lone pairs and the aromatic system, if the opposite face were to be approached (this is reflected in the significantly higher energy of the corresponding SS transition state).

Finally, the Jacobsen catalysis forming trans-β-methyl Styrene Oxide, again, the aromatic π system of the alkene overlays with a phenyl ring on the catalyst, however there are additional interactions present between the methyl protons on the substrate and the protons on the cyclohexane ring, which are within 2 Van der Waal's radii, forming attractive interactions, which promote the formation of the SS isomer. If the RR isomer we to form, the phenyl group on the alkene would have to come into close contact with the cyclohexane ring of the Jacobsen catalyst, leading to repulsive interactions, therefore a higher energy, therefore, a high enantiomeric excess is obtained.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
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The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T18:17:43Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.65
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

As seen from the table above, the Shi catalysis of Styrene yielding Styrene Oxide has a transition state which yields the S enantiomer as the lowest energy transition state. Despite this, an R transition state is only 1 KJ mol<sup>-1</sup> higher in energy than the S transition state, therefore, even at ambient temperatures, this energy barrier can be overcome, leading to both enantiomers forming, resulting in the computed and literature reported ee values being particularly low. Furthermore, there is no steric encumberment to the approach from either face, again leading to low S selectivity.

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T18:02:23Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.65
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|98
|}

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T17:47:50Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.65
|style="text-align: center;"|92<ref>[Filippo Minutolo, Dario Pini, Piero Salvadori; ''Tetrahedron Lett.'', 1996, '''37'''', 3376]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|
|}

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T17:25:13Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|98<ref>[Yian Shi; ''US Patent: US6348608 B1'', 2002]</ref>
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.65
|style="text-align: center;"|
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|
|}

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T17:09:46Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85
|style="text-align: center;"|48<ref>[John Hanson; ''J. Chem. Educ.'', 2001, '''78''', S18]</ref>
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94
|style="text-align: center;"|
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.65
|style="text-align: center;"|
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96
|style="text-align: center;"|
|}

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T17:02:44Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
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===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
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<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
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|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
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|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
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<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align: center;"|Catalyst
|style="text-align: center;"|Epoxide
|style="text-align: center;"|Most Stable Transition State Configuration
|style="text-align: center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align: center;"|K
|style="text-align: center;"|Enantiomeric Excess (%)
|style="text-align: center;"|Literature EE (%)
|-
|rowspan="2" style="text-align: center;"|Shi
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-1.2051
|style="text-align: center;"|1.626459
|style="text-align: center;"|23.85186
|style="text-align: center;"|
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|RR
|style="text-align: center;"|-20.219
|style="text-align: center;"|3500.995
|style="text-align: center;"|99.94289
|style="text-align: center;"|
|-
|rowspan="2" style="text-align: center;"|Jacobsen
|style="text-align: center;"|Styrene Oxide
|style="text-align: center;"|S
|style="text-align: center;"|-15.7688
|style="text-align: center;"|580.912
|style="text-align: center;"|99.65631
|style="text-align: center;"|
|-
|style="text-align: center;"|Trans-β-methyl Styrene Oxide
|style="text-align: center;"|SS
|style="text-align: center;"|-21.3637
|style="text-align: center;"|5557.116
|style="text-align: center;"|99.96402
|style="text-align: center;"|
|}

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

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</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T16:59:56Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align; center;"|Catalyst
|style="text-align; center;"|Epoxide
|style="text-align; center;"|Most Stable Transition State Configuration
|style="text-align; center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align; center;"|K
|style="text-align; center;"|Enantiomeric Excess (%)
|style="text-align; center;"|Literature EE (%)
|-
|rowspan="6" style="text-align; center;"|Shi
|style="text-align; center;"|Styrene Oxide
|style="text-align; center;"|S
|style="text-align; center;"|-1.2051
|style="text-align; center;"|1.626459
|style="text-align; center;"|23.85186
|style="text-align; center;"|
|-
|style="text-align; center;"|Trans-β-methyl Styrene Oxide
|style="text-align; center;"|RR
|style="text-align; center;"|-20.219
|style="text-align; center;"|3500.995
|style="text-align; center;"|99.94289
|style="text-align; center;"|
|-
|rowspan="6" style="text-align; center;"|Jacobsen
|style="text-align; center;"|Styrene Oxide
|style="text-align; center;"|S
|style="text-align; center;"|-15.7688
|style="text-align; center;"|580.912
|style="text-align; center;"|99.65631
|style="text-align; center;"|
|-
|style="text-align; center;"|Trans-β-methyl Styrene Oxide
|style="text-align; center;"|SS
|style="text-align; center;"|-21.3637
|style="text-align; center;"|5557.116
|style="text-align; center;"|99.96402
|style="text-align; center;"|
|}

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
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The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T16:53:26Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 12 - Computed and Literature Enantiomeric Excess for Analysed Epoxides
|-
|style="text-align; center;"|Catalyst
|rowspan="6" style="text-align; center;"|Shi
|rowspan="6" style="text-align; center;"|Jacobsen
|-
|style="text-align; center;"|Epoxide
|style="text-align; center;"|Styrene Oxide
|style="text-align; center;"|Trans-β-methyl Styrene Oxide
|style="text-align; center;"|Styrene Oxide
|style="text-align; center;"|Trans-β-methyl Styrene Oxide
|-
|style="text-align; center;"|Most Stable Transition State Configuration
|style="text-align; center;"|S
|style="text-align; center;"|RR
|style="text-align; center;"|S
|style="text-align; center;"|SS
|-
|style="text-align; center;"|ΔG (KJ mol<sup>-1</sup>
|style="text-align; center;"|-1.2051
|style="text-align; center;"|-20.219
|style="text-align; center;"|-15.7688
|style="text-align; center;"|-21.3637
|-
|style="text-align; center;"|K
|style="text-align; center;"|1.626459
|style="text-align; center;"|3500.995
|style="text-align; center;"|580.912
|style="text-align; center;"|5557.116
|-
|style="text-align; center;"|Enantiomeric Excess (%)
|style="text-align; center;"|23.85186
|style="text-align; center;"|99.94289
|style="text-align; center;"|99.65631
|style="text-align; center;"|99.96402
|-
|style="text-align; center;"|Literature EE (%)
|style="text-align; center;"|
|style="text-align; center;"|
|style="text-align; center;"|
|style="text-align; center;"|
|}

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T16:09:22Z

Srs11: /* Analysis of Crystal Structures of Jacobsen and Shi Catalyst */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>400</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T15:59:47Z

Srs11: /* Assigning the Absolute Configuration of the Products */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 11.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 11 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T15:59:00Z

Srs11: /* NMR Properties of Epoxidised Alkenes */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T15:58:11Z

Srs11: /* Analysis of Crystal Structures of Jacobsen and Shi Catalyst */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 9 - 3D Structure of Catalysts
|-
|style="text-align: center;"|Shi Catalyst
|style="text-align: center;"|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 9.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 9 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
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The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T15:55:40Z

Srs11: /* Analysis of Crystal Structures of Jacobsen and Shi Catalyst */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

The tertiary butyl groups bonded to the aromatic rings within the Jacobsen catalyst display multiple short contact interactions with adjacent molecules, particularly between adjacent tertiary butyl groups. The measured distance between such atoms in the crystal structure<ref>[J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin; ''Cryst. Struct. Commun.'', 1999, '''55''', 1766]</ref> is reported as 2.351 Å, which is slightly shorter than two times the reported literature Van der Waals radii of a hydrogen atom (2.4 Å<ref>[Roger A. Klein; ''Chem. Phys. Lett.'', 2006, '''425''', 129]</ref>). This observed close range interaction results from an attractive force between the two atoms, which results in a stabilisation of the crystal structure, minimising the overall energy. Moreover, additional short range interactions are present in the crystal structure, for example, between the cyclohexane ring of one molecule and the coordinated chlorine atom in a subsequent molecule in the crystal (2.76 Å); again, this value is less than two Van der Waal's radii of chlorine and hydrogen, further indicating that short range interactions are playing a key role in the overall stabilisation of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|-
|Shi Catalyst
|Jacobsen Catalyst
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
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|<jmol><jmolApplet><title>Jacobsen Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Jacobsen_Catalyst_3D.mol</uploadedFileContents>
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|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 9.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 9 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
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The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

File:SRJS Jacobsen Catalyst 3D.mol

2014-03-21T15:54:16Z

Srs11:

Rep:Mod:S1R9J9S3

2014-03-21T15:28:48Z

Srs11: /* Analysis of Crystal Structures of Jacobsen and Shi Catalyst */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
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|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

Bond lengths of the c-o in Shi and then the approach of the tBu groups in the Jacobson

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 9.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 9 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T15:26:48Z

Srs11: /* Analysis of Crystal Structures of Jacobsen and Shi Catalyst */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

Bond lengths of the c-o in Shi and then the approach of the tBu groups in the Jacobson

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|-
|<jmol><jmolApplet><title>Shi Catalyst</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents> File:SRJS Shi Catalyst 3D.cif</uploadedFileContents>
</jmolApplet></jmol>
|}

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 9.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 9 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/7/7a/SRJS_RR_Checkpoint_den.cub.jvxl" translucent;</script>
<uploadedFileContents>SRJS_RR_Checkpoint_den.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
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The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>

Rep:Mod:S1R9J9S3

2014-03-21T15:23:43Z

Srs11: /* Analysis of Crystal Structures of Jacobsen and Shi Catalyst */

==1S Computational Chemistry Module==

===The Hydrogenation of Cyclopentadiene Dimer===

The following calculations were undertaken in Avogadro yielding the following energy results:

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Cyclopentadiene Dimer'''
| style="text-align: center;"|'''Isomer 1'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Isomer 2'''
[[File:SRJSIsomer2.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule1_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Cylopentadiene Dimer Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule2_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.54301
|style="text-align: center;"|3.46740
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.77268
|style="text-align: center;"|33.19125
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-2.73103
|style="text-align: center;"|-2.94946
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|12.80164
|style="text-align: center;"|12.35740
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.01367
|style="text-align: center;"|14.18430
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|55.37344
|style="text-align: center;"|58.19070
|}

[[File:SRJS Mechanism of Formation Part 1.png|center|500px|thumb|Figure 1: Cyclodimerisation of two cyclopentadiene units]]

From the above calculations,it is apparent that the exo dimer is thermodynamically more stable that the endo product. Therefore, in order to explain the specific formation of the endo dimer, the mechanisms of formation and transition states for the two dimers need to be considered. This [4+2] Diels Alder cycloaddition can proceed via either an exo or an endo transition state, figure 1 below. The endo transition state illustrates a through space orbital contribution to the stability; the HOMO π-orbitals at the C2 and C3 positions on the diene (involved in the formation of a new π-bond) are aligned correctly and are the correct symmetry in order to form favourable interactions with the LUMO π*-orbital of the alkene not involved in the cycloaddition<ref>[Kenneth L. Williamson and Yuan-Fang Li Hsu, ''J. Am. Chem. Soc.,'' 1970, '''92''', 7385]</ref>.

[[File:SRJS Endo TS Molecule 2.png|center|500px|thumb|Figure 2: HOMO/LUMO overlap in Endo Transition State]]

This interaction is not present in the exo transition state, which results in the reduction in energy of the transition state pathway for endo product formation, resulting in the kinetic product, the endo dimer, forming predominantly. Furthermore, the stability of the exo product can be rationalised by considering the structure of the 2 dimers. Both dimers contain a one-carbon-bridge and a two-carbon-bridge across the ends of the newly formed bonds, and from this, it can be easily understood that there is a greater steric interaction between the two-carbon-bridge and the bonded cyclopentene ring apparent in the endo dimer, compared to a smaller steric interaction between the one-carbon-bridge and the cyclopentene ring<ref>[Jonathan Clayden, Nick Greeves, Stuart Warren and Peter Worthers, ''Organic Chemistry'', 1<sup>st</sup> Ed. Oxford, Oxford University Press, 2001, 912]</ref>.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table representing Relative Energies of Mono-hydrogenated Cyclopentadiene Dimers
|-
| style="text-align: center;"|'''Hydrogenation Product'''
| style="text-align: center;"|'''Molecule 3'''
[[File:SRJSMolecule3.jpg|100px]]
| style="text-align: center;"|'''Molecule 4'''
[[File:SRJSMolecule4.jpg|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Monohydrogenated Isomer 1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule3_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>Monohydrogenated Isomer 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJSMolecule4_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.30774
|style="text-align: center;"|2.82303
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.86144
|style="text-align: center;"|24.68590
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.06524
|style="text-align: center;"|-0.37823
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.27850
|style="text-align: center;"|10.63664
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|5.12098
|style="text-align: center;"|5.14702
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|50.72283
|style="text-align: center;"|41.25749
|}

The thermodynamic parameters calculated for the minimum energy structures of molecules 3 and 4 above indicate that molecule 4 is more thermodynamically stable, as it displays the lowest total energy, indicating that the double bond in the norbornene ring is hydrogenated first. This has been confirmed by literature<ref>[D. Skàla and J. Hanika, ''Petroleum and Coal'', 2003, '''45''', 105]</ref> which indicates that this particular double bond experiences a higher degree of angle strain compared to the double bond located in the cyclopentane ring, as it is bent away from 120° (the preferred sp<sup>2</sup> configuration); this is indicated in the above table which shows that molecule 3 has a higher angle bending energy than molecule 4. Furthermore, the data displayed in the table above indicates that molecule 4 is most thermodynamically stable in nearly all aspects. Moreover, literature computational models of these isomers modelled with a B3LYP/6-31G<sup>*</sup> basis set illustrates that the HOMO-LUMO gap of the norbornene double bond is lower than the energy gap corresponding to the cyclopentane ring double bond, indicating that there is a lower energy pathway to form this hydrogenation intermediate<ref>[Ji-Jun Zou, Xiangwen Zhang, Jing Kong and Li Wang, ''Fuel'', 2008, '''87''', 3657]</ref>, which would indicate that it is the kinetic and thermodynamic product of mono-hydrogenation.

===Atropisomerism in a Taxol Intermediate===

Paquette was able to synthesise stereoisomers 9 and 10 via an oxy-cope rearrangement<ref>[Steven W. Elmore and Leo A. Paquette, ''Tetrahedron Lett.'' 1991, '''32''', 319]</ref> which either have the carbonyl group pointing up or down. Table 3, below, illustrates the calculated thermodynamic parameters for molecule 9 and table 4, also below, depicts the computed parameters for molecule 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 3 - Computed Thermodynamic Parameters of conformers of Molecule 9
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
<jmol><jmolApplet><title>Molecule 9 Chair</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Boat'''
<jmol><jmolApplet><title>Molecule 9 Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat.cml</uploadedFileContents>
</jmolApplet></jmol>
|style="text-align: center;"|'''Twist Boat 2'''
<jmol><jmolApplet><title>Molecule 9 Twist Boat 2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule9_Twist_boat_High.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.69641
|style="text-align: center;"|7.92850
|style="text-align: center;"|8.00892
|style="text-align: center;"|7.95185
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.37502
|style="text-align: center;"|29.86372
|style="text-align: center;"|30.20657
|style="text-align: center;"|29.74044
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.11482
|style="text-align: center;"|3.38529
|style="text-align: center;"|2.70592
|style="text-align: center;"|2.57221
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.16287
|style="text-align: center;"|35.49668
|style="text-align: center;"|35.79287
|style="text-align: center;"|34.66560
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.30583
|style="text-align: center;"|0.29174
|style="text-align: center;"|0.29456
|style="text-align: center;"|0.32263
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.53691</u>'''
|style="text-align: center;"|'''<u>77.92964</u>'''
|style="text-align: center;"|'''<u>77.91565</u>'''
|style="text-align: center;"|'''<u>76.29289</u>'''
|}

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 4 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Chair'''
[[File:SRJSMolecule1.jpg|100px]]
| style="text-align: center;"|'''Boat'''
[[File:SRJSIsomer2.jpg|100px]]
|style="text-align: center;"|'''Twist Boat'''
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|7.78087
|style="text-align: center;"|7.59358
|
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|28.29809
|style="text-align: center;"|18.80119
|
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.03087
|style="text-align: center;"|0.23888
|
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|33.26364
|style="text-align: center;"|33.26548
|
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.29630
|style="text-align: center;"|-0.05334
|
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>70.55869</u>'''
|style="text-align: center;"|'''<u>60.55108</u>'''
|
|}

'''Include 3D diagrams and descriptions of data.'''

As visible from the tables above, the chair conformer of molecules 9 and 10 is thermodynamically most stable. Molecules 9 and 10 are isomers, exhibiting atropisomerism, which originates from the restricted rotation of the carbonyl group due to steric hindrance from the neighbouring bridging group which contains 2 methyl substituents. This results in a high rotational energy and yields stereoisomers<ref>[Gerhard Bringmann, Anne J. Price Mortimer, Paul A. Keller, Mary J. Gresser, James Garner and Matthias Breuning, ''Angew. Chem. Int. Edit.'' 2005, '''44''', 5384]</ref>. These chair structure shall now be the basis for an energy minimisation and calculation for the hydrogenated equivalents of molecules 9 and 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 5 - Computed Thermodynamic Parameters of Molecule 10
|-
| style="text-align: center;"|'''Intermediate'''
| style="text-align: center;"|'''Hydrogenated 9'''
<jmol><jmolApplet><title>Molecule 9 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script><uploadedFileContents>SRJS_Molecule9_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
| style="text-align: center;"|'''Hydrogenated 10'''
<jmol><jmolApplet><title>Molecule 10 Chair Hydrogenated</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule10_Hydrogenated.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|6.98206
|style="text-align: center;"|6.59705
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.05804
|style="text-align: center;"|24.77066
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.45780
|style="text-align: center;"|8.37750
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|32.70064
|style="text-align: center;"|31.19723
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|0.00000
|style="text-align: center;"|0.00000
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>81.75918</u>'''
|style="text-align: center;"|'''<u>71.44174</u>'''
|}

In order to predict the reactivity of molecules 9 and 10, it needs to be discovered if the alkenes are hyperstable and resistant to alkene functionalisation reactions. Hyperstable alkenes are less strained that the equivalent hydrogenated compound, which leads to a decreased reactivity<ref>[Wilhelm F. Maier and Paul von RaguC Schleyer, ''J. Am. Chem. Soc.'' 1981, '''103''', 1892]</ref>. To determine whether these compounds are hyperstable alkenes, the olefin strain (OS) energy must be determined, which can be calculated by comparing the difference between total strain energies (the sum of the total torsional energy and total angle bending energy) of the alkane and alkene equivalent.

OS Energy (Molecule 9) = (32.05804 + 9.45780) - (28.37502 + 0.11482) = <u>13.026 Kcal mol<sup>-1</sup></u>

OS Energy (Molecule 10) = (24.77066 + 8.37750) - (18.80119 + 0.23888) = <u>14.10809 Kcal mol<sup>-1</sup></u>

The above calculated olefin strain energies indicate that the unsaturated compounds 9 and 10 are more stable that their hydrogenated equivalents, therefore would appear to be resistant towards alkene functionalisation, such as hydrogenation of halogenation.

===Spectroscopic Simulation using Quantum Mechanics===

Molecule 18, displayed in the table below, is a derivative of the lowest energy conformer (the chair conformer) of molecule 10. This compound has been energetically minimised, to which, again, the lowest energy conformer is in the chair conformation. The results from this optimisation is presented below in table 6.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 6
|-
| style="text-align: center;"|'''Molecule 18'''
| style="text-align: center;"|[[File:SRSJ_Molecule_18.png|100px]]
|-
|style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>Molecule 18 Optimised</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS_Molecule18_Pre_Optimised.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|15.06291
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|30.73757
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|9.73173
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|49.53373
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|-6.08258
|-
|style="text-align: center;"|'''<u>Total Energy (Kcal mol<sup>-1</sup>)</u>'''
|style="text-align: center;"|'''<u>100.52696</u>'''
|}

This structure was submitted to the HPC to predict both the <sup>1</sup>H and <sup>13</sup>C NMR spectra, in order to analyse the effectiveness of computational NMR prediction. The results from this computational analysis is presented below in table 7.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 7 - Tabulated <sup>1</sup>H NMR Comparison for Molecule 18<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28067}}]</ref>
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled.png|400px]]
|colspan="3" align="center"|[[File:SRJSH-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|26
|colspan="2" style="text-align: center;"|0.91
|colspan="2" rowspan="3" style="text-align: center;"|1.03
|-
|colspan="2" style="text-align: center;"|27
|colspan="2" style="text-align: center;"|0.918
|-
|colspan="2" style="text-align: center;"|28
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|29
|colspan="2" style="text-align: center;"|0.96
|colspan="2" rowspan="3" style="text-align: center;"|1.07
|-
|colspan="2" style="text-align: center;"|30
|colspan="2" style="text-align: center;"|1.62
|-
|colspan="2" style="text-align: center;"|31
|colspan="2" style="text-align: center;"|1.20
|-
|colspan="2" style="text-align: center;"|43
|colspan="2" style="text-align: center;"|1.27
|colspan="2" rowspan="3" style="text-align: center;"|1.10
|-
|colspan="2" style="text-align: center;"|44
|colspan="2" style="text-align: center;"|0.61
|-
|colspan="2" style="text-align: center;"|45
|colspan="2" style="text-align: center;"|2.33
|-
|colspan="2" style="text-align: center;"|25
|colspan="2" style="text-align: center;"|1.97
|colspan="2" rowspan="3" style="text-align: center;"|1.50 - 1.20
|-
|colspan="2" style="text-align: center;"|36
|colspan="2" style="text-align: center;"|1.52
|-
|colspan="2" style="text-align: center;"|37
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|19
|colspan="2" style="text-align: center;"|2.40
|colspan="2" style="text-align: center;"|1.58
|-
|colspan="2" style="text-align: center;"|21
|colspan="2" style="text-align: center;"|2.58
|colspan="2" rowspan="6" style="text-align: center;"|2.20 - 1.70
|-
|colspan="2" style="text-align: center;"|22
|colspan="2" style="text-align: center;"|1.82
|-
|colspan="2" style="text-align: center;"|38
|colspan="2" style="text-align: center;"|2.49
|-
|colspan="2" style="text-align: center;"|39
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|40
|colspan="2" style="text-align: center;"|2.31
|-
|colspan="2" style="text-align: center;"|41
|colspan="2" style="text-align: center;"|1.23
|-
|colspan="2" style="text-align: center;"|23
|colspan="2" style="text-align: center;"|2.81
|colspan="2" rowspan="4" style="text-align: center;"|2.70 - 2.35
|-
|colspan="2" style="text-align: center;"|24
|colspan="2" style="text-align: center;"|2.00
|-
|colspan="2" style="text-align: center;"|34
|colspan="2" style="text-align: center;"|2.67
|-
|colspan="2" style="text-align: center;"|35
|colspan="2" style="text-align: center;"|2.80
|-
|colspan="2" style="text-align: center;"|32
|colspan="2" style="text-align: center;"|1.58
|colspan="2" rowspan="6" style="text-align: center;"|3.00 - 2.70
|-
|colspan="2" style="text-align: center;"|33
|colspan="2" style="text-align: center;"|2.77
|-
|colspan="2" style="text-align: center;"|50
|colspan="2" style="text-align: center;"|2.91
|-
|colspan="2" style="text-align: center;"|51
|colspan="2" style="text-align: center;"|3.18
|-
|colspan="2" style="text-align: center;"|52
|colspan="2" style="text-align: center;"|3.02
|-
|colspan="2" style="text-align: center;"|53
|colspan="2" style="text-align: center;"|3.17
|-
|colspan="2" style="text-align: center;"|20
|colspan="2" style="text-align: center;"|5.95
|colspan="2" style="text-align: center;"|5.21
|}

Assigning particular atoms to the literature reported chemical shifts was more difficult for some protons in molecule 18 than others. The easiest and most obviously assigned peak is the sole alkene proton appearing in the molecule, who's chemical shift deviates by 0.74 ppm. Further to this, the literature originally reported a multiplet containing 6 protons appearing between 3.00 - 2.70 ppm, which has been assigned to the four protons on the thio-ether section of the molecule and the two alkane protons adjacent to the carbonyl group; this was assigned mainly due to both Sulfer and Oxygen being particularly electronegative, therefore would deshield nearby protons. Moreover, as the literature had specified three singlets that were shielded, all appearing to possess an integration of three, these can be assigned to the methyl protons, which cannot couple to any other protons in the molecule, and the basis of the particular assignment of methyl groups was based on proximity to electron withdrawing centres, however this is only a qualitative assignment, hence the NMR properties of molecule 18 would have to be further explored, possibly by using selectively deuterated methyl group, which would aid identification.

It is visible from the above table that there are significant differences between the computed chemical shifts and the interpreted literature chemical shifts. This has been previously mentioned, specifically by the 0.74 ppm difference in the computed and experimental NMR shifts for the alkene proton (atom 20) and is again illustrated by a 0.82 ppm difference between calculated and experimental shifts for atom 19. The high difference in chemical shift values could be a result of limitations with the calculation, which has made certain assumptions about the molecular framework, such as bonds lengths. A more likely explanation for this difference in chemical shift would be that the calculation has generated an NMR spectrum from a static, energetically optimised molecule. This molecule has not been permitted to vibrate, as it would in reality, which has resulted in the fixed atomic positions generating chemical shifts based on proximity to other groups within the molecule, with electronegative groups having a greater influence on the calculated electronegativity. This is particularly apparent for the methyl protons 29, 30 and 31, which in reality would be equivalent due to rotation about the carbon bond, however the calculated static NMR has assigned each of these atoms to a different chemical environment.

Likewise, the calculated carbon NMR was calculated and is displayed below in table 8.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+ Table 8 - Tabulated <sup>13</sup>C NMR Comparison for Molecule 18
|-
|colspan="3" align="center"|[[File:SRJS_Molecule_18_Labled_Carbons.png|400px]]
|colspan="3" align="center"|[[File:SRJSC-NMR-18.png|400px]]
|-
| colspan="2" style="text-align: center;"|'''Atom Number'''
| colspan="2" style="text-align: center;"|'''Computed NMR Shift (ppm)'''
| colspan="2" style="text-align: center;"|'''Literature NMR Shift (ppm)'''
|-
|colspan="2" style="text-align: center;"|11
|colspan="2" style="text-align: center;"|211.06
|colspan="2" style="text-align: center;"|211.49
|-
|colspan="2" style="text-align: center;"|3
|colspan="2" style="text-align: center;"|147.93
|colspan="2" style="text-align: center;"|148.72
|-
|colspan="2" style="text-align: center;"|8
|colspan="2" style="text-align: center;"|120.04
|colspan="2" style="text-align: center;"|120.9
|-
|colspan="2" style="text-align: center;"|14
|colspan="2" style="text-align: center;"|93.64
|colspan="2" style="text-align: center;"|74.61
|-
|colspan="2" style="text-align: center;"|13
|colspan="2" style="text-align: center;"|60.46
|colspan="2" style="text-align: center;"|60.53
|-
|colspan="2" style="text-align: center;"|4
|colspan="2" style="text-align: center;"|54.77
|colspan="2" style="text-align: center;"|51.30
|-
|colspan="2" style="text-align: center;"|12
|colspan="2" style="text-align: center;"|53.94
|colspan="2" style="text-align: center;"|50.94
|-
|colspan="2" style="text-align: center;"|5
|colspan="2" style="text-align: center;"|49.54
|colspan="2" style="text-align: center;"|45.53
|-
|colspan="2" style="text-align: center;"|16
|colspan="2" style="text-align: center;"|49.15
|colspan="2" style="text-align: center;"|43.28
|-
|colspan="2" style="text-align: center;"|48
|colspan="2" style="text-align: center;"|46.66
|colspan="2" style="text-align: center;"|40.82
|-
|colspan="2" style="text-align: center;"|15
|colspan="2" style="text-align: center;"|41.90
|colspan="2" style="text-align: center;"|38.73
|-
|colspan="2" style="text-align: center;"|49
|colspan="2" style="text-align: center;"|41.73
|colspan="2" style="text-align: center;"|36.78
|-
|colspan="2" style="text-align: center;"|9
|colspan="2" style="text-align: center;"|38.53
|colspan="2" style="text-align: center;"|35.47
|-
|colspan="2" style="text-align: center;"|10
|colspan="2" style="text-align: center;"|34.05
|colspan="2" style="text-align: center;"|30.84
|-
|colspan="2" style="text-align: center;"|42
|colspan="2" style="text-align: center;"|33.61
|colspan="2" style="text-align: center;"|30.00
|-
|colspan="2" style="text-align: center;"|2
|colspan="2" style="text-align: center;"|28.09
|colspan="2" style="text-align: center;"|25.56
|-
|colspan="2" style="text-align: center;"|6
|colspan="2" style="text-align: center;"|26.45
|colspan="2" style="text-align: center;"|25.35
|-
|colspan="2" style="text-align: center;"|1
|colspan="2" style="text-align: center;"|24.40
|colspan="2" style="text-align: center;"|22.21
|-
|colspan="2" style="text-align: center;"|7
|colspan="2" style="text-align: center;"|22.62
|colspan="2" style="text-align: center;"|21.39
|-
|colspan="2" style="text-align: center;"|17
|colspan="2" style="text-align: center;"|21.57
|colspan="2" style="text-align: center;"|19.83
|}

As previously, as the computed NMR has been calculated from the perspective of a static molecule, there is some deviation between literature values, however, only one peak in the <sup>13</sup>C NMR can be assigned with certainty (Atom 11, the carbonyl carbon) whereas the other two easily identifiable groups (sp<sup>2</sup> alkene carbons) can't be assigned definitely, but match well with literature<ref>[Leo A. Paquette, Neil A. Pegg, Dana Toops, George D. Maynard, Robin D. Rogers; ''J. Am. Chem. Soc.'', 1990, '''112''', 283]</ref>.

===Analysis of Crystal Structures of Jacobsen and Shi Catalyst===

Bond lengths of the c-o in Shi and then the approach of the tBu groups in the Jacobson

The Shi Catalyst, whose crystal structure is displayed below<ref>[Zhi-Xian Wang, Susie M. Miller, Oren P. Anderson and Yian Shi; ''J. Org. Chem.'', 2001, '''66''', S5]</ref>, has adopted a structure which minimises the overall energy and maximises the number and strength of favourable interactions occuring. A expected, the pyranose ring adopts the chair conformation, which as illustrated in previous computational exercises, is the minimum energy structure for a six-membered ring. Furthermore, the catalyst has adopted a structure to maximise the anomeric effect, whereby a C-O bond located α to the Oxygen atom of the pyranose ring is axial in relation to the lone pair located on the Oxygen atom. This arrangement of atoms allows for the best overlap of the lone pair electrons into the σ* orbital of the C-O bond, resulting in additional stabilisation of the compound. The analysed crystal structure shows a distinct anomeric effect, with the shortening of the ring internal C-O bond length (1.41 Å) compared to the literature standard C-O bond length for D-Fructose<ref>[Medhat Ibrahim, Moussa Alaam, Hanan El-Haes, Abraham F. Jalbout and Aned de Leon; ''Ecelt. Quim.'', 2006, '''31''', 18]</ref>, the molecular basis for this catalyst. A further significant anomeric effect is observed at a ketal centre, with the bond lengths reported as 1.44 Å and 1.38 Å, indicating that stereoelectronic interactions are contributing significantly to the overall stability of the molecule. Another notable observation from the crystal structure was that the bond angles within the pyranose ring are not all equal, with the C-O-C angle (106°) being slightly shorter than the ideal sp<sup>2</sup> hybridised angle (109.5°). Moreover, the second ketal centre in the catalyst again demonstrates the anomeric effect occuring, however, to a lesser extent than the previously mentioned ketal centre(located near the pyranose anomeric centre). These observations could be rationalised by crystal packing forces acting upon the molecules, which would not be present when the catalyst is in solution and in its active form. Finally, it can be observed that hydrogen bonding is present between molecules within the crystal, possibly contributing to the overall structure of the crystal.

===NMR Properties of Epoxidised Alkenes===

For the alkenes assigned, the structures were energetically minimised in Avogadro and their NMR spectra (<sup>1</sup>H and <sup>13</sup>C) were computed on the HPC. The results and spectra are displayed below in table 9.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 9 - Computed Thermodynamic Parameters of Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28118}}]</ref>
[[File:SRJS R-Styrene.png|100px]]
| style="text-align: center;"|'''S-Styrene Oxide'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28119}}]</ref>
[[File:SRJS S-Styrene.png|100px]]
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28120}}]</ref>
[[File:SRJS R-b-methyl styrene.png|100px]]
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28121}}]</ref>
[[File:SRJS S-b-methyl styrene.png|100px]]
|-
| style="text-align: center;"|'''3D Visualisation'''
|<jmol><jmolApplet><title>R-Styrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide R.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>-SStyrene Oxide</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2R,3R)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide R.cml </uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>(2S,3S)-trans-β-methyl Styrene</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>SRJS B-Methyl-Styrene Oxide S.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
|style="text-align: center;"|'''Total Bond stretching Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.84104
|style="text-align: center;"|1.84204
|style="text-align: center;"|1.88697
|style="text-align: center;"|1.88601
|-
|style="text-align: center;"|'''Total Angle Bending Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|1.42453
|style="text-align: center;"|1.42456
|style="text-align: center;"|1.73727
|style="text-align: center;"|1.73620
|-
|style="text-align: center;"|'''Total Torsional Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|2.34615
|style="text-align: center;"|2.34611
|style="text-align: center;"|2.89538
|style="text-align: center;"|2.89554
|-
|style="text-align: center;"|'''Total Van der Waals Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|13.66822
|style="text-align: center;"|13.67332
|style="text-align: center;"|14.32733
|style="text-align: center;"|14.32381
|-
|style="text-align: center;"|'''Total Electrostatic Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|3.07979
|style="text-align: center;"|3.07406
|style="text-align: center;"|3.03625
|style="text-align: center;"|3.04125
|-
|style="text-align: center;"|'''Total Energy (Kcal mol<sup>-1</sup>)'''
|style="text-align: center;"|'''<u>21.61510</u>'''
|style="text-align: center;"|'''<u>21.61505</u>'''
|style="text-align: center;"|'''<u>23.12036</u>'''
|style="text-align: center;"|'''<u>23.12033 </u>'''
|-
|style="text-align: center;"|'''<sup>1</sup>H NMR Spectra'''
|[[File:SRJS Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S NMR.png|150px|center]]
|-
|style="text-align: center;"|'''<sup>13</sup>C NMR Spectra'''
|[[File:SRJS Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS Styrene Oxide S C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide R C NMR.png|150px|center]]
|[[File:SRJS B-Methyl-Styrene Oxide S C NMR.png|150px|center]]
|}

The calculations above yielded NMR spectra that is consistent with reported literature values for both of the studied epoxides and as expected, both the R and S enantiomers (or RR and SS enantiomers for trans-β-methyl styrene) display exactly the same spectrum, therefore, assigning the absolute configuration of the epoxides is impossible from this computed data alone.

'''LITERATURE REFERENCE NEEDED SAM'''

http://pubs.acs.org/doi/suppl/10.1021/ol3000712/suppl_file/ol3000712_si_001.pdf ss b

===Assigning the Absolute Configuration of the Products===

Energies of transition states and working out K values, discussing the predicted values with actual literature results, and subsequently discuss the flaws with the calculation ie. what it doesn't consider.

The above pre-optimised structures for the four assigned epoxides were submitted to the HPC for further computation, specifically to calculate the optical rotation at a wavelength of 589nm, the results of which and literature comparison are displayed below in table 10.

{|class="wikitable" border="1" style="margin: 1em auto 1em auto;"
|+Table 10 - Computed and Literature Optical Rotations for the Analysed Epoxides
|-
| style="text-align: center;"|'''Epoxide'''
| style="text-align: center;"|'''R-Styrene Oxide'''
| style="text-align: center;"|'''S-Styrene Oxide'''
|style="text-align: center;"|'''(2R,3R)-trans-β-methyl Styrene'''
|style="text-align: center;"|'''(2S,3S)-trans-β-methyl Styrene'''
|-
|style="text-align: center;"|'''Computed Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-30.15<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28128}}]</ref>
|style="text-align: center;"|30.41<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28131}}]</ref>
|style="text-align: center;"|46.78<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28129}}]</ref>
|style="text-align: center;"|-46.77<ref>[Samuel Spreadbury, 2014, {{DOI|10042/28130}}]</ref>
|-
|style="text-align: center;"|'''Literature Optical Rotation [α]<sub>D</sub>'''
|style="text-align: center;"|-19.5<ref>Wolfgang Kroutil, Joerg H.chrittwieser, Ivan Lavandera, Barbara Mautner, Birgit Seisser, Jeffrey H. Lutje Spelberg; ''Tetrahedron Asymmetr'', 2009 , '''20''', 483-488</ref>
|style="text-align: center;"|32.1<ref>Hui Lin, Yan Liu, Jing Qiao, Zhong-Liu Wu; ''J. Mol. Catal. B-Enzym.'', 2010 , '''67''', 236-241</ref>
|style="text-align: center;"|47<ref>Fuganti Fronza, Mele Grasselli; ''J. Org. Chem.'', 1991 , '''56''', 6019-6023</ref>
|style="text-align: center;"|-43.6<ref>Tsutomu Katsuki, Shota Koya, Hirotaka Mizoguchi, Yota Nishioka, Tatsuya Uchida; ''Angew. Chem. Int. Edit.'', 2012, '''51''', 8243-8246</ref>
|}

The above table clearly indicates a good general agreement and correlation with the literature reported optical rotations, obviously indicating that using a better basis set (in this case, the B3LYP/6-311++g(2df,p) set, as opposed to the standard B3LYP/6-311(d,p) basis set) improves the accuracy of the calculation, although this does impose additional calculation time. However, throughout the literature, multiple values are reported for the optical rotations, mainly due to the parameter's dependence on the temperature and concentration. This makes accurate comparison between experiment and computational studies difficult, particularly because it is not know what temperature and concentration the calculation was computed for. Additionally, as a particular stereochemistry was specified in the computation, it can be assumed that the enantiomeric excess (ee) is 100%, yet often in experimental results, the ee is not specified, leading to a loss of information and and increase in the uncertainty of accuracy when comparing these values.

'''Transition State Stuff'''

===Transition State Analysis===

The diagrams below indicate the non-covalent interactions present between the lowest energy transition state of the epoxidation of β-methyl styrene using the Shi catalyst. From the below diagrams, it can be easily seen that there are many attractive non-covalent interactions present between the active Shi catalyst and the β-methyl styrene unit (indicated by the many areas of green present between the molecules). The attractive interactions occur mostly between hydrogen and oxygen units interacting, possibly indicating the formation of hydrogen bonds between the catalyst and the substrate, which could contribute to the overall stability of the transition state. An additional area of attractive interactions appearing between the aromatic ring of the substrate and an oxygen on the catalyst forming the ketal, visible in the second diagram of the transition state (the reverse face to the first). This type of interaction is known as polar π interaction, which has previously been reported in proteins and other fundamental biological molecules, actively contributing the the stability of the molecule<ref>[Qi-Shi Du, Qing-Yan Wang, Li-Qin Du, Dong Chen, Ri-Bo Huang, ''Chemistry Central Journal'' 2013, '''7''', 1]</ref>. Additionally, when considering the active catalyst, there are multiple non covalent interactions, which indicates further stability of the catalyst, and if the non covalent interactions of the active Shi catalyst was calculated and compared, this could further elude to conformational changes in the catalyst upon coordinating with the alkene substrate, forming the transition state.

{| class="wikitable" border="1"
|
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The electronic topology calculations of the transition state indicates that there are 7 areas of increased electron density in the transition state, including notably build up of electron density between one of the oxygen atoms of the dioxyrane section of the Shi catalyst, and one of the sp<sup>2</sup> carbons (the alkene), which in the non covalent interactions diagram, showed the topology of a bond forming. Also, areas where the non covalent interactions were particularly attractive further indicate a build up of electron density in multiple areas of the molecule, which could contribute to the overall stabilisation of the transition state. This could be further investigated by making comparisons between additional transition states, only qualitatively, to determine particular intermolecular forces contributing to a minimisation of the energy, leading to a specific enantiomer forming predominantly.

Insert Picture of Topology and talk about position

[[File:SRJS NCI RR4 1.png|center]]

[[File:SRJS NCI RR4 2.png|center]]

===Suggestions for New Calculations===

R-Pulegone is an available alkene from Sigma Aldrich, which has a cyclic ketone α to the alkene. This compound would be of particular interest to perform either Jacobsen or Shi catalysis, mainly due to the presence of the ketone functionality, which could be computationally explored to understand the particular non-covalent interactions present in the transition state, which could result in a particularly high enantiomeric excess.

==References==
<references/>