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2013-11-22T11:11:25Z

Jp1611: /* Crystal Structure of Shi and Jacobsen Catalysts */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one peak, but computationally shown as a number of peaks. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data at 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be different due to spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). On initially viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''. The larger proportion of '''S''' to '''R''' could be due to enhanced interactions (hydrogen bonding, Van der Waal's forces, etc) between the catalyst and the alkene, and furthermore, the arrangement of this transition state appears less sterically hindered that that forming the '''R''' product. These differences must be very slight, as the relative proportions is not greatly changed. The arrangement of these transition states can be found <jmolFile text="here">R styrene mol.mol</jmolFile> for '''R''' and <jmolFile text="here">S Styrene mol.mol</jmolFile> for '''S'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. This may be due to sterics or orbital overlaps in the transition state, however it is unclear from simply looking at these transition states why one is so strongly favoured over the other. The [R,S] diastereoisomer can be found <jmolFile text="here">R,S 1 mol.mol</jmolFile>, and the [S,R] diastereoisomer can be found <jmolFile text="here">S,R 1 mol.mol</jmolFile>. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T11:09:47Z

Jp1611: /* Spectroscopy of an Intermediate Related to the Synthesis of Taxol */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one peak, but computationally shown as a number of peaks. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data at 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be different due to spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''. The larger proportion of '''S''' to '''R''' could be due to enhanced interactions (hydrogen bonding, Van der Waal's forces, etc) between the catalyst and the alkene, and furthermore, the arrangement of this transition state appears less sterically hindered that that forming the '''R''' product. These differences must be very slight, as the relative proportions is not greatly changed. The arrangement of these transition states can be found <jmolFile text="here">R styrene mol.mol</jmolFile> for '''R''' and <jmolFile text="here">S Styrene mol.mol</jmolFile> for '''S'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. This may be due to sterics or orbital overlaps in the transition state, however it is unclear from simply looking at these transition states why one is so strongly favoured over the other. The [R,S] diastereoisomer can be found <jmolFile text="here">R,S 1 mol.mol</jmolFile>, and the [S,R] diastereoisomer can be found <jmolFile text="here">S,R 1 mol.mol</jmolFile>. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T11:07:35Z

Jp1611: /* Spectroscopy of an Intermediate Related to the Synthesis of Taxol */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one peak, but computationally shown as a number of peaks. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''. The larger proportion of '''S''' to '''R''' could be due to enhanced interactions (hydrogen bonding, Van der Waal's forces, etc) between the catalyst and the alkene, and furthermore, the arrangement of this transition state appears less sterically hindered that that forming the '''R''' product. These differences must be very slight, as the relative proportions is not greatly changed. The arrangement of these transition states can be found <jmolFile text="here">R styrene mol.mol</jmolFile> for '''R''' and <jmolFile text="here">S Styrene mol.mol</jmolFile> for '''S'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. This may be due to sterics or orbital overlaps in the transition state, however it is unclear from simply looking at these transition states why one is so strongly favoured over the other. The [R,S] diastereoisomer can be found <jmolFile text="here">R,S 1 mol.mol</jmolFile>, and the [S,R] diastereoisomer can be found <jmolFile text="here">S,R 1 mol.mol</jmolFile>. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T11:00:13Z

Jp1611: /* Jacobsen Catalyst */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''. The larger proportion of '''S''' to '''R''' could be due to enhanced interactions (hydrogen bonding, Van der Waal's forces, etc) between the catalyst and the alkene, and furthermore, the arrangement of this transition state appears less sterically hindered that that forming the '''R''' product. These differences must be very slight, as the relative proportions is not greatly changed. The arrangement of these transition states can be found <jmolFile text="here">R styrene mol.mol</jmolFile> for '''R''' and <jmolFile text="here">S Styrene mol.mol</jmolFile> for '''S'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. This may be due to sterics or orbital overlaps in the transition state, however it is unclear from simply looking at these transition states why one is so strongly favoured over the other. The [R,S] diastereoisomer can be found <jmolFile text="here">R,S 1 mol.mol</jmolFile>, and the [S,R] diastereoisomer can be found <jmolFile text="here">S,R 1 mol.mol</jmolFile>. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:56:09Z

Jp1611: /* Jacobsen Catalyst */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''. The larger proportion of '''S''' to '''R''' could be due to enhanced interactions (hydrogen bonding, Van der Waal's forces, etc) between the catalyst and the alkene, and furthermore, the arrangement of this transition state appears less sterically hindered that that forming the '''R''' product. These differences must be very slight, as the relative proportions is not greatly changed. The arrangement of these transition states can be found <jmolFile text="here">R styrene mol.mol</jmolFile> for '''R''' and <jmolFile text="here">S Styrene mol.mol</jmolFile> for '''S'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. This may be due to sterics in the transition state. For the <jmolFile text="[R,S]">R,S 1 mol.mol</jmolFile> diastereoisomer, the benzene ring is close to the ''tert''-butyl groups, however in the <jmolFile text="[S,R]">S,R 1 mol.mol</jmolFile> isomer, it is the alkyl chain - less rigid and so could adapt to any clashes - that is closest. This explains some of the shown stability of this transition state. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

File:S,R 1 mol.mol

2013-11-22T10:55:49Z

Jp1611:

Rep:Mod:JPSO

2013-11-22T10:54:10Z

Jp1611: /* Jacobsen Catalyst */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''. The larger proportion of '''S''' to '''R''' could be due to enhanced interactions (hydrogen bonding, Van der Waal's forces, etc) between the catalyst and the alkene, and furthermore, the arrangement of this transition state appears less sterically hindered that that forming the '''R''' product. These differences must be very slight, as the relative proportions is not greatly changed. The arrangement of these transition states can be found <jmolFile text="here">R styrene mol.mol</jmolFile> for '''R''' and <jmolFile text="here">S Styrene mol.mol</jmolFile> for '''S'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. This may be due to sterics in the transition state. For the [R,S] diastereoisomer, the benzene ring is close to the ''tert''-butyl groups, however in the [S,R] isomer, it is the alkyl chain - less rigid and so could adapt to any clashes - that is closest. This explains some of the shown stability of this transition state. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

File:R,S 1 mol.mol

2013-11-22T10:54:06Z

Jp1611:

Rep:Mod:JPSO

2013-11-22T10:47:25Z

Jp1611: /* Shi Catalyst */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''. The larger proportion of '''S''' to '''R''' could be due to enhanced interactions (hydrogen bonding, Van der Waal's forces, etc) between the catalyst and the alkene, and furthermore, the arrangement of this transition state appears less sterically hindered that that forming the '''R''' product. These differences must be very slight, as the relative proportions is not greatly changed. The arrangement of these transition states can be found <jmolFile text="here">R styrene mol.mol</jmolFile> for '''R''' and <jmolFile text="here">S Styrene mol.mol</jmolFile> for '''S'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:46:21Z

Jp1611: /* Shi Catalyst */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''. The larger proportion of '''S''' to '''R''' could be due to enhanced interactions (hydrogen bonding, Van der Waal's forces, etc) between the catalyst and the alkene, and furthermore, the arrangement of this transition state appears less sterically hindered that that forming the '''R''' product. These differences must be very slight, as the relative proportions is not greatly changed. The arrangement of these transition states can be found <jmolFile text="here">R styrene mol.mol</jmolFile> for '''R''' and <jmolFile text="here">S styrene mol.mol</jmolFile> for '''S'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

File:S Styrene mol.mol

2013-11-22T10:45:52Z

Jp1611:

Rep:Mod:JPSO

2013-11-22T10:43:33Z

Jp1611: /* Shi Catalyst */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''. The larger proportion of '''S''' to '''R''' could be due to enhanced interactions (hydrogen bonding, Van der Waal's forces, etc) between the catalyst and the alkene, and furthermore, the arrangement of this transition state appears less sterically hindered that that forming the '''R''' product. These differences must be very slight, as the relative proportions is not greatly changed.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

File:R styrene mol.mol

2013-11-22T10:43:21Z

Jp1611:

Rep:Mod:JPSO

2013-11-22T10:36:31Z

Jp1611: /* Assigning the Absolute Configurations of the Epoxide Products */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and [R,R] or [S,S] respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation. These values indicate, however, that the [R] stereoisomer of the styrene epoxide was made, along with the [R,R] stereoisomer of the ''trans''-stillbene epoxide.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:30:37Z

Jp1611: /* Hydrogenation of the Cyclopentadiene Dimer */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst, D. Skála and J. Hanika, ''Petroleum and Coal'', '''2003''', ''45'', pp. 105-108</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:29:12Z

Jp1611: /* Calculated NMR of the Product Epoxides */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.
 
All the NMR spectra, both computational and literature, were run using CDCl3 as a solvent.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:23:44Z

Jp1611: /* Jacobsen Catalyst */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and [R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 

====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:22:10Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:21:47Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield. 
[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:21:10Z

Jp1611: /* Assigning the Absolute Configurations of the Epoxide Products */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| style="text-align: center;" |-31 || style="text-align: center;" |-24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||style="text-align: center;" |294 ||style="text-align: center;" |319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.
[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:19:16Z

Jp1611: /* Spectroscopy of an Intermediate Related to the Synthesis of Taxol */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule and it is clear that molecule '''12''' is slightly lower in energy.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||294 ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.
[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:15:47Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||294 ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====

In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.
[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]][[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:15:15Z

Jp1611: /* Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||294 ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:14:54Z

Jp1611: /* Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||294 ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|center|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:13:53Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||294 ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:13:26Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||294 ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====

In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.
[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:13:04Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||294 ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|300px|thumb|Center|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|300px|thumb|Center|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-22T10:08:22Z

Jp1611: /* Assigning the Absolute Configurations of the Epoxide Products */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) ||294 ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°. Therefore these similarities should be taken very carefully. It can be assumed that the opposite enantiomer of each of the two epoxides would have an equal but opposite optical rotation.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|100px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|100px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:55:37Z

Jp1611: /* Assigning the Absolute Configurations of the Epoxide Products */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}
From the table, it can be seen that the literature and computational values for the two epoxides are similar, however a number of drastically different values were found in reaxys for this particular enantiomer of styrene, varying from -40° to +20°.

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|100px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|100px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:53:17Z

Jp1611: /* Assigning the Absolute Configurations of the Epoxide Products */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| -31 || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|100px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|100px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:50:54Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|100px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|100px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:50:41Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====

In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.
[[File:Crotonic Acid.jpg|100px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|100px|thumb|Right|Crotonic acid epoxide]]

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:50:11Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====

In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.
[[File:Crotonic Acid.jpg|100px|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|100px|RIGHT|Crotonic acid epoxide]]

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:49:48Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====

In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.[[File:Crotonic Acid.jpg|100px|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|100px|RIGHT|Crotonic acid epoxide]]

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:49:29Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|100px|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|100px|RIGHT|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:49:11Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|RIGHT|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:48:50Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|thumb|RIGHT|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:48:31Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|thumb|RIGHT|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:48:02Z

Jp1611: /* Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|300px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 

====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|thumb|Left|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:47:48Z

Jp1611: /* Investigating the non-covalent interactions (NCIs) in the active-site of the reaction transition state */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|200px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|thumb|Left|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:47:26Z

Jp1611: /* Investigating the non-covalent interactions (NCIs) in the active-site of the reaction transition state */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|thumb|Left|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:46:46Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|thumb|Right|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|thumb|Left|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:45:37Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|thumb|Left|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" ">Akita, Hiroyuki; Kawaguchi, Tomoko; Enoki, Yuko; Oishi, Takeshi
''Chemical and Pharmaceutical Bulletin'', '''1990''' , ''38'', # 2 pp. 323 - 328</ref> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:42:57Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|thumb|Left|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80°<ref name=" "> - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:42:04Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|200px|thumb|Left|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|200px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80° - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:41:37Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|300px|thumb|Left|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|300px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80° - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:41:17Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|300px|thumb|Left|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|300px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80° - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:40:50Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|300px|thumb|Left|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|300px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80° - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:40:27Z

Jp1611: /* New Candidates for Investigation */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|300px|thumb|Left|Crotonic Acid]]
[[File:Crotonic acid epoxide.jpg|300px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80° - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>

Rep:Mod:JPSO

2013-11-21T15:39:27Z

Jp1611: /* Analysis of the Properties of the Synthesised Alkene Epoxides */

==Synthesis and Computational Experiment - 1C==
This page details the steps undertaken to investigate the properties, reactions and energies of various organic molecules.
 
===Conformational analysis using Molecular Mechanics===
In this part of the experiment, different conformations of various molecules were modeled to examine their relative energies and stabilities
 
====Hydrogenation of the Cyclopentadiene Dimer====
In this section, the ''endo'' and ''exo'' forms of the cyclopentadiene dimer were modeled and their relative energies calculated using the '''MMFF94s''' calculation of the ''Avogadro'' program.
 

The ''endo'' and ''exo'' forms were drawn and the energy minimised to this level. The resulting values were: 55.37kcal/mol for the ''exo'' conformer, and 58.19kcal/mol for the ''endo'' form. Thermodynamically, this would predict that the ''exo'' state would be the major form, however this is contrary to the observed result, in which the ''endo'' product is the only form seen. This can only be due to the reaction proceeding kinetically, and is driven by some secondary orbital overlap effect.
The thermodynamic stability of the ''exo'' form compared to the ''endo'' form is most likely due to the through space inter-atomic distances between the closest carbon atoms, of which the ''exo'' form has a distance of 3.4Å, and the ''endo'' form 3.0Å. In the two structures shown, the higher of the two is the ''endo'' conformer, and the lower is the ''exo''.
<jmol><jmolApplet> <title>endo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Endo.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>exo</title> <color>white</color> <size>200</size> <uploadedFileContents>Cyclopentadiene Exo.mol</uploadedFileContents> </jmolApplet></jmol>
 
[[File:Hyd.Cyclopentadiene 3.bmp|100px|thumb|right|Conformer 3]]
[[File:Hyd.Cyclopentadiene 4.bmp|100px|thumb|right|Conformer 4]]
The hydrogenated ''endo'' forms of these compounds were then subjected to analysis by running an '''MMFF94s''' calculation in order to interpret the reaction with respect to kinetic or thermodynamic effects. The values given by this calculation can be seen below:
{| class="wikitable"
|-
! Value !! Conformer 3 !!Conformer 4
|-
| Stretching Energy/kcal.mol-1|| 3.30778 || 2.81592
|-
| Bending Energy/kcal.mol-1|| 28.95052 || 23.07703
|-
| Torsion Energy/kcal.mol-1|| 0.06492 || -0.35025
|-
| Van der Waals Energy/kcal.mol-1|| 13.27863 || 10.58073
|-
| Electrostatic Energy/kcal.mol-1|| 5.12098 || 5.14736
|-
| Total Energy/kcal.mol-1|| 50.72283 || 41.27080
|}
 
From the total energies it is clear that ''conformer 4'' is the more stable of the hydrogenated dimer. This would imply that this geometry is the most thermodynamically stable form. Literature suggests that this is also the kinetic product of the mono-hydrogenated product<ref>[''Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst'', D. Skála and J. Hanika, Petroleum and Coal, 2003, '''45''', pp. 105-108]</ref>. If left for a longer period of time, the tetra-hydrogenated product results, however conformation 4 forms first.
 
The calculated values in this section show that the dimerisation of cyclopentadiene is kinetically controlled as the thermodynamically most unstable product is favoured, however the hydrogenation of this ''endo'' form of dicyclopentadiene proceeds in a manner by which it seems as though the resulting product is both the thermodynamic and kinetic product. This is manifested in the above data, where it can be seen that ''conformer 4'' has lower energies throughout. This could be due to the lower ''bending energy'' in 4 than in 3, therefore producing a less sterically hindered, and therefore more stable, product. These lower energies could also lead to a lower kinetic barrier as the two molecules can combine more easily.
 

====Atropisomerism in an Intermediate Related to the Synthesis of Taxol====
[[File:Taxol Intermediates.jpg|300px|thumb|right|Intermediates in production of Taxol]]
In this section, a key intermediate in the synthesis of the drug [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Taxol..jpg taxol] (used to treat ovarian cancer) was investigated to find the most stable form and to understand why this molecule reacts so slowly. The two isomers investigated were molecules '''9''' and '''10'''. Again, an MMFF94s calculation was used in ''Avogadro'' to calculate the relative energies of these two intermediates. In carrying out these calculations, it was found that there were two different 'boat' conformations for the cyclohexane part of the intermediate. These conformers are labeled as '''a''' and '''b''' in the table below, where the energies for the two intermediates can be seen:

{| class="wikitable"
|-
! Value !! <jmolFile text="Intermediate 9a">Taxol 9a.mol</jmolFile>!!<jmolFile text="Intermediate 9b">Taxol 9b.cml</jmolFile>!!<jmolFile text="Intermediate 10a">Taxol 10a..cml</jmolFile>!!<jmolFile text="Intermediate 10b">Taxol 10b..cml</jmolFile>
|-
| Stretching Energy/kcal.mol-1|| 7.65783 || 7.81145 || 7.59479 || 8.08713
|-
| Bending Energy/kcal.mol-1|| 29.144 || 30.16978 ||19.50716 || 23.93167
|-
| Torsion Energy/kcal.mol-1|| 0.49692 || 4.37249 ||0.23180 || 5.58194
|-
| Van der Waals Energy/kcal.mol-1|| 33.12548 || 35.41179 ||33.27081 || 35.33326
|-
| Electrostatic Energy/kcal.mol-1|| 0.28220 || 0.28277 ||-0.05426 || 0.36636
|-
| Total Energy/kcal.mol-1|| 70.70642 || 78.04828 ||60.55030 || 73.30037
|}
For intermediate '''9''', one of the conformations appeared to be a ''twist-boat'', clearly giving the higher of the two energies. This data shows that the lowest overall energy is provided by intermediate '''10a''', and so this is therefore the form that the compound will isomerise to if left for a period of time. This stability of '''10a''' (≈10kcal/mol less than '''9a''') is likely to be due to there being unfavourable bond angle in '''9'''. In '''9a''', the C-C=O angle was measured to be 117.4°, whereas in '''10a''' it was 120.4°. As this carbon is sp2 hybridised, the most favourable bond angle will be the one that is closer to the optimal value of 120°, which is clearly intermediate '''10'''.
 
Studies have also shown that this alkene reacts unusually slowly due to a phenomenon known as ''hyperstability''<ref name="ja00398a003">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref>, in which alkenes are highly stabilised due to their position at a bridgehead. This positioning means that they are less strained than their parent hydrocarbon, and therefore show decreased reactivity at the double bond. This stability has been shown to be due to the "cage" structure of the molecule, and its ability to effectively guard the double bond and prevent it reacting. These hydrogenated molecules - <jmolFile text="Molecule 9">Hyd. Taxol 9.cml</jmolFile> and <jmolFile text="Molecule 10">Hyd. Taxol 10.cml</jmolFile> were modeled using 'ChemBio3D' and the bond angles where the C=C bond was previously were measured to be 119.8 °and 120° respectively - clearly unfavourable bond angles for an sp3 carbon atom. This torsional strain is another reason by which these types of alkenes are hyperstable.

===Spectroscopic Simulation using Quantum Mechanics===
[[File:Spectroscopic 1, 11 to12 taxol.gif|400px|thumb|right|Molecules 11 and 12]]
In this section, spectroscopic simulations of molecules were run, in order to correlate the computational data with that attained experimentally.
====Spectroscopy of an Intermediate Related to the Synthesis of Taxol====
Molecules '''11''' and '''12''' were drawn in ''Avogadro'' and optimised as before to the '''MMFF94s''' level. The geometry of the cyclohexane part of the molecules was adjusted to be in a ''chair'' conformation, so that the energy would go to a minimum. The energies of these molecules were calculated to be 110.44939kcal/mol and 102.40556kcal/mol respectively. The lowest energy of these two molecules ('''12''') was the used to calculate the NMR spectrum. The molecule used to carry out this calculation can be found <jmolFile text="here">Taxol 12 (18).mol</jmolFile>.
 
This was done by running a '''Geometry Optimisation''' from the ''Gaussian'' extension of ''Avogadro'', selecting a '''B3LYP/6-31G(d,p)''' level and adding the keywords: '''SCRF(CPCM, solvent=chloroform)''', '''FREQ''', '''NMR''' and '''EmpiricalDispersion=GD3'''. This generated a '''.com''' file which was then submitted to the HPC.
 
Once completed, this file was downloaded to ''GaussView'' and the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_C_NMR.jpg 13C NMR], [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_H_NMR.jpeg 1H NMR], and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Mol_12_IR.jpeg IR] spectra observed. The data attained from these computationally generated spectra along with the literature values can be seen below:
 
''' Computational and Literature NMR Shifts '''
{| class="wikitable"
|-
! Computational 1H δ (ppm)!! Literature 1H δ (ppm)<ref name="ja00157">Paquette, Leo A.; Pegg, Neil A.; Toops, Dana; Maynard, George D.; Rogers, Robin D.
''Journal of the American Chemical Society'', '''1990''' , ''112'', # 1, 277 - 283. {{DOI|10.1021/ja00157a043}}</ref>!!Computational 13C δ (ppm)!!Literature 13C δ (ppm)<ref name="ja00157"/>
|-
| style="text-align: center;" |0.42 (1H)|| style="text-align: center;" |1.03 (s, 3H) || style="text-align: center;" |22.26 || style="text-align: center;" |19.83
|-
| style="text-align: center;" |0.83 (1H)|| style="text-align: center;" |1.07 (s, 3H) ||style="text-align: center;" |23.11 ||style="text-align: center;" |21.39
|-
| style="text-align: center;" |1.06 (2H)|| style="text-align: center;" |1.10 (s, 3H) ||style="text-align: center;" |25.26 ||style="text-align: center;" |22.21
|-
| style="text-align: center;" |1.26 (1H)|| style="text-align: center;" |1.20-1.50 (m, 3H) ||style="text-align: center;" |25.70 ||style="text-align: center;" |25.35
|-
| style="text-align: center;" |1.42 (1H)|| style="text-align: center;" |1.58 (t, 1H) ||style="text-align: center;" |27.69 ||style="text-align: center;" |25.56
|-
| style="text-align: center;" |1.50 (2H)|| style="text-align: center;" |1.70-2.20 (m, 6H) ||style="text-align: center;" |30.42 ||style="text-align: center;" |30.00
|-
| style="text-align: center;" |1.60 (3H)|| style="text-align: center;" |2.35-2.70 (m, 4H) ||style="text-align: center;" |32.66 ||style="text-align: center;" |30.84
|-
| style="text-align: center;" |1.69 (1H)|| style="text-align: center;" |2.70-3.00 (m, 6H) ||style="text-align: center;" |35.31 ||style="text-align: center;" |35.47
|-
| style="text-align: center;" |1.81 (2H)|| style="text-align: center;" |5.21 (m, 1H) ||style="text-align: center;" |39.15 || style="text-align: center;" |36.78
|-
|style="text-align: center;" |1.96 (4H)|| style="text-align: center;" |- ||style="text-align: center;" |39.95 || style="text-align: center;" |38.73
|-
| style="text-align: center;" |2.08 (1H) || style="text-align: center;" |- ||style="text-align: center;" |41.72 || style="text-align: center;" |40.82
|-
| style="text-align: center;" |2.28 (1H) || style="text-align: center;" |- ||style="text-align: center;" |46.30 || style="text-align: center;" |43.28
|-
|style="text-align: center;" |2.52 (2H) || style="text-align: center;" |- ||style="text-align: center;" |49.84 || style="text-align: center;" |45.53
|-
| style="text-align: center;" |2.84 (2H) || style="text-align: center;" |-||style="text-align: center;" |53.85|| style="text-align: center;" |50.94
|-
|style="text-align: center;" |2.97 (1H) || style="text-align: center;" |-||style="text-align: center;" |58.49|| style="text-align: center;" |51.30
|-
|style="text-align: center;" |3.03 (1H) || style="text-align: center;" |-||style="text-align: center;" |62.08|| style="text-align: center;" |60.53
|-
|style="text-align: center;" |3.15 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |91.54|| style="text-align: center;" |74.61
|-
|style="text-align: center;" |3.22 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |123.92|| style="text-align: center;" |120.90
|-
|style="text-align: center;" |3.30 (1H) || style="text-align: center;" |-||style="text-align: center;" |151.46|| style="text-align: center;" |148.72
|-
|style="text-align: center;" |5.33 (1H) ||style="text-align: center;" |- ||style="text-align: center;" |209.75|| style="text-align: center;" |211.49
|}
From this data, it is clear that the computationally generated values are very similar to that found in the literature, particularly for the 13C NMR data. There are also fewer peaks in the literature for the 1H NMR data than were generated computationally. This is most likely due to protons actually being in very similar environments, meaning that they would be seen experimentally as just one, but computationally shown as a number. The ranges of δ values in the literature (e.g 2.70-3.00) which correspond to a multiplet imply that there were multiple separate signals overlapping, that merged into one signal.
 
It is likely that different conformations (chair and boat) of molecule '''18''' would have produced slightly different chemical shifts, but it is unlikely that they would have been drastically different from the most stable chair conformation used in this calculation.
 
The (relatively slight) differences between chemical shifts for both sets of NMR data is potentially due to the difference in solvent used. In the computational calculation, CDCl3 was used, however in the literature, C6D6 was used. The largest variation is in the 13C NMR data, for 91.54ppm (computational), where the corresponding literature value is 74.61ppm. This peak is due to the quaternary carbon at the head of the cyclopentyl ring, that is bonded to two sulphur atoms, and is likely to be from spin-orbit coupling errors, that originate from this carbon being bonded to two much heavier atoms. This is corrected simply by taking off a number of ppm from that of the computationally generated shift.
 
A final reason for slight differences between the computational and experimental values could be again due to conformers. In the computational spectrum, it was limited to the cyclohexane part of the molecule being solely in one of the 4 possible conformations. The experimental moleule would not have been limited to this, and so the spectrum would have been made up of average shifts from the relative contributions of each conformation.
 
The energies of these two conformations ('''11''' and '''12''') were also viewed from the '''.log''' file generated. A table of these values can be seen below:
 
'''Thermochemical Data for Molecules 11 and 12'''
{| class="wikitable"
|-
!Quantity!!Molecule 11 !!Molecule 12
|-
| Sum of electronic and zero-point Energies/kcal.mol1 || -1036270|| -1036278
|-
|Sum of electronic and thermal Energies/kcal.mol1 || -1036256 || -1036265
|-
| Sum of electronic and thermal Enthalpies/kcal.mol1 || -1036255 || -1036264
|-
|Sum of electronic and thermal Free Energies/kcal.mol1 || -1036300 || -1036308
|-
|}
The final of these quantities corresponds to the ''Gibbs Free Energy'' of the molecule.

===Analysis of the Properties of the Synthesised Alkene Epoxides===
[[File:Trans-Stillbene pic.jpg|300px|thumb|right|''Trans''-Stillbene]]
[[File:Styrene pic.jpg|300px|thumb|left|Styrene]]
[[File:Styrene Epoxide pic.jpg|300px|thumb|left|Styrene Epoxide]]
[[File:Trans-Stillbene Epoxide pic.jpg|300px|thumb|right|''Trans''-Stillbene Epoxide]]
In this section, asymmetric epoxidation reactions involving <jmolFile text="Styrene">Styrene mol.mol</jmolFile> and <jmolFile text="trans-Stillbene">Trans-Stillbene mol.mol</jmolFile> to produce the epoxides shown were investigated using similar analytical techniques to those already used. This analysis involves the 'use' of two different asymmetric eopxidation catalysts - the ''Shi'' and ''Jacobsen'' - which produce two different chiral alkene epoxides of unknown absolute configurations. The ''Shi'' catalyst reacts with a ''trans-'' alkene to produce an epoxide of the same geometry, whereas the ''Jacobsen'' catalyst reacts with ''cis-'' alkenes. This section of the study involves modeling the catalysts and products, in order to compute NMR spectra, and find the absolute configurations of the epoxides formed.
 
====Crystal Structure of Shi and Jacobsen Catalysts====
The Cambridge crystal structure database was searched to find the various bond lengths for the [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Shi_Catalyst_Pic.jpg Shi catalyst] and [https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Jacobsen_Catalyst_pic.jpg Jacobsen catalyst.]
 
In the <jmolFile text="Shi catalyst">Shi Lone Pairs.mol</jmolFile>, there are a number of stabilising interactions due to the 2 (O-C-O) sections (anomeric centres). From first viewing the molecule, it may appear that there are 3 of these interactions, 2 on each of the cyclopentyl rings, and one on the cyclohexyl ring. However, due to the steric arrangement of the molecule, it is impossible for the centre on the cyclohexyl ring to be stabilised by interaction between the oxygen lone pair and the C-O antibonding orbital (σ*). These interactions do occur in the cyclopentyl rings as there is sufficient overlap between the two orbitals. For a good overlap to occur, the oxygen lone pair and the C-O σ* orbitals must be ''syn-periplanar''. In the A summary of these bonds can be found below: 
'''Summary of bond Lengths in Shi Catalyst''' [[File:Shi Catalyst Bonds pic.jpg|300px|thumb|left|Shi Catalyst Bond Numbering]]
{| class="wikitable"
|-
!Bond!!Length(Å)
|-
| 1 || 1.409
|-
|2 || 1.439
|-
| 3 || 1.403
|-
|4 || 1.403
|-
| 5 ||1.441
|-
| 6 || 1.413
|-
|}
The bond lengths show that there are two bonds ('''2''' and '''5''') that are clearly affected by this donation into the (low energy) C-O σ* orbital, however their adjacent bonds ('''1''' and '''6''') do not appear to have been affected (given that the normal C-O bond length is 1.43Å). However, these bonds lengths are still longer than those unaffected by this anomeric effect. This may be due to the cyclopentyl rings not being exactly planar, and these interactions being slightly weaker than those for bonds '''2''' and '''5'''. It is clear that there is no such antibonding effect in the cyclohexyl ring ('''3''' and '''4''') as the bonds are of equal length and are shorter than normal C-O bonds.
 [[File:Jacobsen Catalyst bond lengths.jpg|300px|thumb|right|Jacobsen Catalyst Inter-Fragment Distances]]

The distance between the closest two tert-butyl groups in the <jmolFile text="Jacobsen catalyst">Jacobsen bond lengths mol.mol</jmolFile> was then measured. As can be seen from the diagram, the closest approach of the two primary carbons is 3.696Å - only slightly longer than double the Van der Waal's radius of carbon (3.4Å). This means that this side of the catalyst is very sterically hindered, especially as other parts of the molecule prohibit rotation, leading to the preference of the incoming alkene to approach from over the cyclohexane ring. Finally, the distance between two of the hydrogens of the tert-butyl group was measured to be 2.421Å - potentially Van der Waal's attractive - and therefore contributes to the preference of these groups to hinder the attach of the alkene. The maximum attraction distance of these two hydrogens is 2.4Å, meaning that rotation of the two methyl groups could lead these atoms to become closer, and therefore more attractive.
 

====Calculated NMR of the Product Epoxides====
The epoxides that were investigated were (R)-phenylethylene oxide (from styrene) and (R,R)-''trans''-stillbene oxide (from ''trans''-stillbene). Clearly, two isomers of these epoxides can be formed (''S'' and ''trans'' respectively), however each were found to have identical NMR spectra The NMR spectra were calculated using a similar method to before, and the data can be found below: 
'''Summary of NMR Data for (R)-phenylethylene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="00397911.2012.699578">Chen, Xin-Zhi; Ji, Li; Qian, Chao; Wang, Ya-Na; Qian, Chao
''Synthetic Communications'', '''2013''' , ''43'', # 16 pp. 2256 - 2264. {{DOI|10.1080/00397911.2012.699578}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="00397911.2012.699578"/>
|-
| style="text-align: center;" |2.53 (1H) || style="text-align: center;" |2.81 (1H) || style="text-align: center;" |53.48 || style="text-align: center;" |51.2
|-
|style="text-align: center;" |3.12 (1H)|| style="text-align: center;" |3.13 (1H) || style="text-align: center;" |54.06 || style="text-align: center;" |52.4
|-
| style="text-align: center;" |3.66 (1H) || style="text-align: center;" |3.84 (1H) || style="text-align: center;" |118.27 || style="text-align: center;" |125.5
|-
|style="text-align: center;" |7.29 (1H) || style="text-align: center;" |7.27-7.34 (5H) || style="text-align: center;" |122.25 || style="text-align: center;" |128.1
|-
| style="text-align: center;" |7.49 (4H) || style="text-align: center;" |- || style="text-align: center;" |123.41 || style="text-align: center;" |128.5
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |124.13 || style="text-align: center;" |137.6
|-
| style="text-align: center;" |- || style="text-align: center;" |- || style="text-align: center;" |135.14 || style="text-align: center;" |-
|-
|}
From the data it is clear that the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/6/63/Styrene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/98/Styrene_Epox_C_NMR.jpeg 13C] NMR spectra for (R)-phenylethylene oxide are very similar to that in the literature, except in the fact that for the carbon NMR, the computationally generated spectrum shows 7 environments, whereas the experimental only shows 6. This could be due to the computationally generated spectrum putting two of the benzene ring carbons into different chemical environments, when in actual fact they are chemically equivalent. This correlation clearly leads to the assumption that this epoxide has been modeled correctly.
 
Below is the same data, but for 1,2-diphenylethylene epoxide:
 
'''Summary of NMR data for (R,R)-''trans''-stillbene oxide'''
{| class="wikitable"
|-
!Comptuational 1H (ppm)!!Literature 1H (ppm)<ref name="jo7016923">Berardi, Serena; Bonchio, Marcella; Carraro, Mauro; Conte, Valeria; Sartorel, Andrea; Scorrano, Gianfranco
''Journal of Organic Chemistry'', '''2007''' , ''72'', # 23 pp. 8954 - 8957. {{DOI|10.1021/jo7016923}}</ref>!!Comptuational 13C (ppm)!!Literature 13C (ppm)<ref name="chem.200601307">Mai, Enzo; Schneider, Christoph
''Chemistry--A European Journal'', '''2007''' , ''13'', # 9 pp. 2729 - 2741. {{DOI|10.1002/chem.200601307}}</ref>
|-
| style="text-align: center;" |4.30 (2H) || style="text-align: center;" |4.36 (2H) || style="text-align: center;" |62.02 || style="text-align: center;" |59.88
|-
|style="text-align: center;" |7.25 (2H)|| style="text-align: center;" |7.18 (10H) || style="text-align: center;" |122.11 || style="text-align: center;" |127.0
|-
| style="text-align: center;" |7.33 (4H) || style="text-align: center;" |- || style="text-align: center;" |122.32 || style="text-align: center;" |127.6
|-
|style="text-align: center;" |7.40 (2H) || style="text-align: center;" |- || style="text-align: center;" |122.62 || style="text-align: center;" |127.9
|-
| style="text-align: center;" |7.50 (2H) || style="text-align: center;" |- || style="text-align: center;" |131.28 || style="text-align: center;" |134.5
|-
|}
Once again, there is good correlation between the computationally generated [https://wiki.ch.ic.ac.uk/wiki/images/4/45/Stillbene_Epox_H_NMR.jpeg 1H] and [https://wiki.ch.ic.ac.uk/wiki/images/9/94/Stillbene_Epox_C_NMR.jpeg 13C] spectra and the experimental data. In the 13C NMR, the values are all slightly different, however the magnitude of the differences between the more deshielded carbons is similar in both computational and literature spectra. Again, this shows that the computationally generated molecule is similar to the actual molecule. 
IR data for the [https://wiki.ch.ic.ac.uk/wiki/images/f/f3/Styrene_Epox_IR.jpeg styrene epoxide] and [https://wiki.ch.ic.ac.uk/wiki/images/8/81/Stillbene_Epox_IR.jpeg stillbene epoxide] were also generated.

====Assigning the Absolute Configurations of the Epoxide Products====
In this section, the configurations of the epoxides synthesised from styrene and ''trans''-stillbene were analysed. Due to the nature of the two catalysts, two isomers of each product can be made(R or S and (R,R) or (S,S) respectively), each with a different value for the optical rotation. The two values will, however, simply be of the opposite sign, i.e if the rotation for one was +20°, the opposite isomer would be -20°. Therefore, only one of the two isomers was calculated for each product epoxide.
 
This calculation was carried out by submitting the calculation (based on the '''.log''' file from the NMR) to the HPC. The values calculated using this method could then be compared to literature values:
 
'''Comparison of Computational and Literature Optical Rotations'''
{| class="wikitable"
|-
!colspan="2"|Styrene Epoxide!!colspan="2"|Stillbene Epoxide
|-
| '''Computational Value (°)''' || '''Literature Value (°)''' || '''Computational Value (°)''' || '''Literature Value (°)'''
|-
| || -24<ref name="j.tet.2008.10.019">David C. Forbes, Sampada V. Bettigeri, Samit A. Patrawala, Susanna C. Pischek, Michael C. Standen, S-Methylidene agents: preparation of chiral non-racemic heterocycles, ''Tetrahedron'', ''65'', # 1, '''2009''', pp. 70-76, ISSN 0040-4020, {{DOI|10.1016/j.tet.2008.10.019}}</ref> (R-stereoisomer) || ||319.8<ref name="jo900330n">Wang, Bin; Wu, Xin-Yan; Wong, O. Andrea; Nettles, Brian; Zhao, Mei-Xin; Chen, Dajun; Shi, Yian
''Journal of Organic Chemistry'', '''2009''', ''74'', # 10 pp. 3986 - 3989 {{DOI|10.1021/jo900330n}}</ref> ([R,R]-Diastereoisomer)
|-
|}

====Using the Calculated Transition States to determine the Favoured Enantiomer====
In this section, a number of different transition state arrangements of the reaction were analysed for Styrene (Shi catalyst) and ''cis''-β-methyl styrene (Jacobsen catalyst).
=====Shi Catalyst=====
The thermochemical data for the Shi catalysed transition state was viewed to determine which of the transition state arrangements - and therefore which isomer (R or S) - would predominate. Tables of this data can be found below, in which the numbers '''1''' to '''4''' are simply the 4 transition states. 

'''Summary of Free Energies for Styrene - Shi Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of '''R''' Transition State/kJ.mol-1!!Free Energy of '''S''' Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-3422945.221 || style="text-align: center;" |-3422953.426
|-
|style="text-align: center;" |2|| style="text-align: center;" |-3422944.001 || style="text-align: center;" |-3422928.090
|-
| style="text-align: center;" |3 || style="text-align: center;" |-3422961.263 || style="text-align: center;" |-3422937.266
|-
|style="text-align: center;" |4 || style="text-align: center;" |-3422964.495 || style="text-align: center;" |-3422965.700
|-
|}
From this data, it is clear that both transition state '''4''' are the most stable, with the ''S'' form being slightly more stable (by 0.17 kJ/mol). The difference in free energy between the ''R'' and ''S'' forms (denoted ΔG here) allowed the rate constant for the rate constant, K, to be calculated using the equation: ''G = -RTlnK'', taking T to be 298.15K. This data is found in the table below: 
'''Calculated Free Energy and Rate Constant for ''R'' to ''S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''S''':'''R'''/kJ.mol-1!!Equilibrium Constant for '''S''':'''R'''
|-
| style="text-align: center;" |-1.205 || style="text-align: center;" |1.626
|-
|}
This value of the equilibrium constant suggests that for each molecule of configuration '''R''' formed, 1.63 molecules of configuration '''S''' form. Put more simply, 63% of the mixture will be '''S''', and 37% will be '''R'''.

=====Jacobsen Catalyst=====
The same procedure was carried out, but using the data for the use of the Jacobsen catalyst to epoxidise ''cis''-β-methyl styrene. For this alkene, it is possible for a different two enantiomers to form - [S,R] and [R,S]. The energies of these can be found below: 
'''Summary of Free Energies for ''cis''-β-methyl styrene - Jacobsen Transition State'''
{| class="wikitable"
|-
!Transition State!!Free Energy of [S,R] Transition State/kJ.mol-1!!Free Energy of [R,S] Transition State/kJ.mol-1
|-
| style="text-align: center;" |1 || style="text-align: center;" |-8882748.649 || style="text-align: center;" |-8882726.335
|-
|style="text-align: center;" |2|| style="text-align: center;" |-8882732.589 || style="text-align: center;" |-8882724.261
|-
|}
From the table, it can be seen that '''1''' for both the [S,R] and '[R,S] isomers is the most stable. These were therefore used as before to give the results shown below: 
'''Calculated Free Energy and Rate Constant for ''S,R'' to ''R,S'' ratio'''
{| class="wikitable"
|-
!ΔG of '''[S,R]''':'''[R,S]'''/kJ.mol-1!!Equilibrium Constant for '''[S,R]''':'''[R,S]'''
|-
| style="text-align: center;" |-22.314 || style="text-align: center;" |8118.6
|-
|}
This shows that the [S,R] enantiomer is highly favoured over the [R,S], with an enantiomeric excess of >99%. 
====Investigating the non-covalent interactions (NCIs) in the ''active-site'' of the reaction transition state====
In this section, the interactions within the transition states were analysed by examining the electrostatic attractions in these states, also known as non-covalent interactions. The transition state examined was that created by the reaction of [S,R]-dihydronaphthalene with the Shi catalyst. 4 of these transition states were viewed in order to find which had the lowest free energy value, and so was the transition state by which the reaction proceeded.
 

[[File:Shi-Napthalene NCI.jpg|300px|thumb|Right|Shi-Dihydronapthalene Transition State NCI]]
From the picture, it can be seen that there are areas that are very attractive - shown by blue/green, areas that are less attractive - shown by yellow, and areas that are repulsive - shown by red. In between the two molecules, there are regions of green, showing attractive interactions (likely to be hydrogen bonds between the H's (on dihydronapthalene) and O's (on Shi catalyst)) There is also a very unusual region at the point at which the epoxide is forming, where it appears that there are both attractive and repulsive forces operating. This could be due to both electons repelling each other, but the two regions also being attracted to one another due to interatomic forces attempting to form the bond.

 

====Investigating the Electronic topology (QTAIM) in the ''active-site'' of the reaction transition state====
In this section, the objective was to analyse the electron density in the covalent regions of the same transition state as used above, along with the weaker interactions found in the NCI investigation. The picture of these interactions can be seen below:
[[File:QTAIM JPS.jpg|400px|thumb|left|Dihydronapthalene QTAIM Analysis Picture]]
From this picture, a number of different interesting points can be seen, denoted by yellow dots. At these points, the derivative of the electron density is zero, and therefore the actual electron density is at a maximum. For the oxygen atoms in the catalyst, this dot is closer to the oxygen, clearly closer to this atom due to the larger electronegativity of the oxygen atom. This can also be seen for the hydrogen atoms on the napthalene ring. Also, the dotted lines in the picture denote weaker interations, in this case hydrogen bonds between oxygen and hydrogen, and it can be seen that the maximum electron density of this interaction is approximately in the middle of these two atoms.
 
====New Candidates for Investigation====
[[File:Crotonic Acid.jpg|300px|thumb|Left|Crotonic Acid]]
[[Crotonic acid epoxide.jpg|300px|thumb|Right|Crotonic acid epoxide]]
In this final section, ''Reaxys'' was searched using the criteria that the optical rotation of the materials searched for (epoxides) has that which was '''<+500°''' or '''>-500°'''. A potential candidate found was ''Crotonic acid'' and its corresponding eopoxide, 2,3-epoxybutyric acid. This was chosen as the alkene could be asymmetrically epoxidised, therefore producing diastereoisomers. These isomers were found to have relatively large optical rotations - ≈±80° - and therefore the results obtained experimentally and computationally could be analysed well. Furthermore, there is only one double bond, so it would be expected that this would be produced in a relatively high yield.

 

==References==
<references/>