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Rep:Mod:bigbang007

2014-03-09T18:25:57Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy / (kcal/mol)||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy / (kcal/mol)||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that for <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' (100.49578 kcal/mol) after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy / (kcal/mol)||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy / (kcal/mol)||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': Avogadro is not good for drawing large complicated molecules, it is always better to draw them in Chemdraw first before importing them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T18:23:58Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy / (kcal/mol)||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy / (kcal/mol)||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that for <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' (100.49578 kcal/mol) after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

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</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': Avogadro is not good for drawing large complicated molecules, it is always better to draw them in Chemdraw first before importing them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T18:22:07Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy / (kcal/mol)||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that for <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' (100.49578 kcal/mol) after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': Avogadro is not good for drawing large complicated molecules, it is always better to draw them in Chemdraw first before importing them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T18:14:12Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that for <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' (100.49578 kcal/mol) after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': Avogadro is not good for drawing large complicated molecules, it is always better to draw them in Chemdraw first before importing them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T18:09:51Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that for <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18'''(100.49578 kcal/mol) after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': Avogadro is not good for drawing large complicated molecules, it is always better to draw them in Chemdraw first before importing them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T18:00:39Z

Hd1311: /* Limitations of Software */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that for <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': Avogadro is not good for drawing large complicated molecules, it is always better to draw them in Chemdraw first before importing them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:55:19Z

Hd1311: /* New candidates for investigations */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that for <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:54:05Z

Hd1311: /* New candidates for investigations */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that for <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 21''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:45:14Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that for <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:41:21Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it may not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:37:21Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''9''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''9''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing down and the cyclohexane ring adopting chair||'''10''' with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||'''10''' with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:33:41Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of the cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and the cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:30:27Z

Hd1311: /* Atropisomerism in an Intermediate related to the Synthesis of Taxol */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule '''9''' and '''10''' ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:29:04Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, angle bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:24:58Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute the most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:22:45Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in the norbornene ring is five times faster than that in the cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relative stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:18:24Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer '''1''' is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:16:01Z

Hd1311: /* The Hydrogenation of Cyclopentadiene Dimer */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer '''2''' rather than exo dimer '''1''' via Diels Alder ['''4+2'''] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer '''2''' gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer '''2''' is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:12:12Z

Hd1311: /* Optical Rotatory Power (ORP) */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref> shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is only highly accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T17:09:06Z

Hd1311: /* Optical Rotatory Power (ORP) */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

The [α]<sub>d</sub> from literature shows -90.5 deg for '''E2 1S2R''', whereas computational result is 35.86 deg. This maybe due to the fact that the computational ORP analysis is more accurate when analyzing molecules with [α]<sub>d</sub> magnitude of greater than 100 deg.

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T16:52:15Z

Hd1311: /* Results and Discussions */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.(see below)

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T16:49:00Z

Hd1311: /* Assigning the absolute configuration of the epoxides */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

The use of ECD to assign the absolute configurations of the epoxides are insignificant in this case since no appropriate chromophore exists for the epoxides.

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

VCD is a much better option over ECD since as one can see from '''Table 16''', within each enantiomeric pair, the VCDs are mirror images of each other and this is due to opposite vibrations present in each enantiomeric pair. However, such instrument is not available in our department at the moment.

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T16:30:30Z

Hd1311: /* Using the (calculated) properties of transition state for the reaction */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

From Table '''17''' and '''18''', one can see that the choice of catalyst for epoxidation is crucial as differnt catalysts give different stereochemical outcomes. E.g. E1 R,R is favored with 99.2 % ee over E1 S,S when using Shi catalyst. Whereas when Jacobsen catalyst is used, opposite results obtained with E1 S,S being more favored.

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T16:16:51Z

Hd1311: /* Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remaining BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T16:15:44Z

Hd1311: /* Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

'''QTAIM''' analysis in this case is just supplementary to previous '''NCI''' analysis, some BCPs are involved in bond formations whereas the remained BCPs are mainly for maintaining the relative orientation of catalyst to the substrate.

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T16:03:29Z

Hd1311: /* Investigating the non-covalent interactions in the active site of the reaction transition state */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is going to alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T16:01:31Z

Hd1311: /* Investigating the non-covalent interactions in the active site of the reaction transition state */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs. In addition, the way of how active catalyst binds to the alkene is gonna alter the stereochemical outcome of the product, as one can see from '''Table 19'''.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T15:58:31Z

Hd1311: /* Investigating the non-covalent interactions in the active site of the reaction transition state */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
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</jmol>
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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green regions (green indicates mildly attractive interactions) are possibly indications of strong H bonding interactions between Hs on methyl groups and oxygen lone pairs.

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T15:53:00Z

Hd1311: /* Investigating the non-covalent interactions in the active site of the reaction transition state */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

The large green region (green indicates mildly attractive interactions) as one ca

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T15:49:02Z

Hd1311: /* New candidates for investigations */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

discusssionskaddlaksdhkashdsakjdaadsdafffagagfahggagr

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''') are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are shown in '''Table 21'''. In addition, these two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T15:44:58Z

Hd1311: /* New candidates for investigations */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

discusssionskaddlaksdhkashdsakjdaadsdafffagagfahggagr

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> optical rotation data for Pulegone oxides </div>

Cis R-(+)-pulegone oxide and Cis S-(-)-pulegone oxide ('''Figure 12''')are the suggested new candidates for investigation. Their optical properties from literature <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> are given in '''Table 21'''. These two molecules can be synthesized from R-(+)-pulegone which is commercially readily available from Sigma Aldrich with cost of £225 / 100 g.

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T15:37:25Z

Hd1311: /* Future improvement */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

discusssionskaddlaksdhkashdsakjdaadsdafffagagfahggagr

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Optical literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> data for Pulegone oxides </div>

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvements====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T15:36:23Z

Hd1311: /* Future improvement */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

discusssionskaddlaksdhkashdsakjdaadsdafffagagfahggagr

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Optical literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> data for Pulegone oxides </div>

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvement====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, if had time, one could compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T15:34:33Z

Hd1311: /* Future improvement */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

discusssionskaddlaksdhkashdsakjdaadsdafffagagfahggagr

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Optical literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> data for Pulegone oxides </div>

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvement====
If had time, the computational optical rotation analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, one can compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T15:32:38Z

Hd1311: /* Future improvement */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
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</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

discusssionskaddlaksdhkashdsakjdaadsdafffagagfahggagr

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Optical literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> data for Pulegone oxides </div>

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvement====
If had time, the computational optical analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM''' analysis, one can compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>

Rep:Mod:bigbang007

2014-03-09T15:27:51Z

Hd1311: /* Limitations of Software and Future improvements */

== Conformational analysis using Molecular Mechanics (Part 1) ==
===The Hydrogenation of Cyclopentadiene Dimer===

The dimerisation of cyclopentadiene preferentially forms endo dimer 2 rather than exo dimer 1 via Diels Alder [4+2] Cyclo-addition ('''Scheme 1'''). Hydrogenation of dimer 2 gives either dihydro derivative 3 or 4 ('''Figure 1''') before prolonged hydrogenation to form tetrahydro derivative. The aim of this exercise is to establish whether the dimerisation of cyclopentadiene and hydrogenation of dimer 2 is kinetically or thermodynamically controlled.

All four molecules were drawn in Chemdraw first before they were imported into Avogadro to make 3D structures followed by optimization using MMFF94(s) with steepest descent. ('''Table 1''')
[[File:DimerisationHD.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Scheme 1.''' ''Dimerisation of cyclopentadiene via cycloaddition''</div>

[[File:3and4jepg.jpg | center ]]
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 1.''' ''Structures of Dihydro derivative 3 and 4 of dimer 2''</div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer1</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer1_using_avogadromolfile.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer2</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer2molfilehaha.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer3</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer3mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>dimer4</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Dimer4mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Dimer '''1'''|| Dimer '''2'''|| Dihydro derivative '''3''' || Dihydro derivative '''4'''
|-
| Total bond stretching energy / (kcal/mol)||3.54283||3.46733||3.31126||2.82301
|-
| Total angle bending energy / (kcal/mol)||30.77281||33.19139||31.93650||24.68568
|-
| Total stretch bending energy / (kcal/mol) || -2.04133||-2.08213||-2.10212||-1.65715
|-
| Total torsional energy / (kcal/mol)||-2.73034||-2.94943||-1.47005||-0.37815
|-
| Total out-of-plane bending energy ||0.01486||0.02196||0.01319||0.00028
|-
| Total van der Waals energy / (kcal/mol)||12.80095||12.35735||13.63736||10.63680
|-
| Total electrostatic energy / (kcal/mol)||13.01366||14.18423||5.11953||5.14702
|-
| Total energy / (kcal/mol) ||55.37344 || 58.19070|| 50.44567||41.25749
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 1.''' ''Molecule '''1''', '''2''', '''3''' and '''4''' optimized using MMFF94(s) force field with steepest descent''</div>

The total energy of dimer '''1''' (55.37344 kcal/mol) is about 3 kcal/mol lower than that of dimer '''2''' (58.19070 kcal/mol), and this deviation is mainly due to difference in total angle bending energy. Thus, dimer 1 is favored thermodynamically. However, dimerization of cyclopentadiene specially produces dimer '''2''' rather than dimer '''1''' indicating the reaction is kinetically controlled.

Similarly, by comparing total energy of dihydro derivative '''3''' and '''4''', one can deduce that if the reaction is thermodynamically controlled, formation of molecule '''4''' is favored over molecule '''3''', and '''4''' is more stable than '''3'''. Indeed, literature study <ref name="study">D. Skala, J. Hanika, "Kinetics of dicyclopentadiene hydrogenation using Pd/C catalyst", ''Petroleum and Coal'', '''2003''', ''45 (3-4)'', 105–108.</ref> shows the hydrogenation of the double bond using Pd/C as catalyst in norbornene ring is five times faster than that in cyclopentene ring of the dimer '''2'''. Thus, molecule '''4''' is the preferred product and the reaction is thermodynamically controlled. Within stretching (str), bending (bnd),torsion (tor), van der Waals (vdw) and electrostatic energy terms, bending and van der Waals energy terms contribute most to the relatively stability of '''4''' over '''3'''.

===Atropisomerism in an Intermediate related to the Synthesis of Taxol===

Molecule 9 and 10 ('''Figure 2''') are key intermediates in the synthesis of Taxol (a drug used in the treatment of ovarian cancers). They are atropisomers with respect to each other and the high steric strain energy barrier to rotation within these two intermediates allowing them to be isolated separately. The main difference in terms of geometry between two atropisomers comes down to the orientation of C=O group as whether it is pointing up or down. The objective for this section is to explore which of the intermediates is more stable using Avogadro with MMFF94(s) force field.

[[File:Molecule9and10chem.jpg | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 2.''' ''Structures of atropisomers '''9''' and '''10'''''</div>

====Results and Discussions====
The total energies of molecules '''9''' and '''10''' can be altered by changing the position of the trans-alkene H (up or down with respect to structures shown in '''Figure 2''') as well as the conformation of cyclohexane ring (chair and boat). The lowest energy structures of molecules '''9''' and '''10''' lie with the alkene H pointing up and cyclohexane ring adopting chair conformation. ('''Table 2''')

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Properties'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule9mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule10mol.mol</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent9.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>parent10</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Parent10.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
|Molecule label || Molecule '''9'''|| Molecule '''10'''|| Parent Hydrocarbon of '''9''' || Parent Hydrocarbon of
'''10'''
|-
| Total bond stretching energy / (kcal/mol)||7.68872||7.59350||6.94420||6.42510
|-
| Total angle bending energy / (kcal/mol)||28.28780||18.79618||32.03408||22.28431
|-
| Total stretch bending energy / (kcal/mol) || -0.06988||-0.14163||0.30160||0.29425
|-
| Total torsional energy / (kcal/mol)||0.17522||0.20421||9.50507||9.19384
|-
| Total out-of-plane bending energy ||0.96979||0.84520||0.25574||0.03607
|-
| Total van der Waals energy / (kcal/mol)||33.18616||33.31300||32.71128||31.30102
|-
| Total electrostatic energy / (kcal/mol)||0.29968||-0.05585||0.00000||0.00000
|-
| Total energy / (kcal/mol) ||70.53750 || 60.55461|| 81.75198||69.53459
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 2.''' ''Molecule '''9''', '''10''' and their corresponding parent hydrocarbons optimized using MMFF94(s) force field with steepest descent''</div>

From '''Table 2''' one can see that intermediate '''10''' is more stable than molecule '''9''' since it is about 10 kcal/mol lower in energy. Therefore, on standing, it is more likely for atropisomer '''9''' to convert into atropisomer '''10'''.

In order to rationalize why the intermediates react slowly towards hydrogenation, the parent hydrocarbon molecules were drawn and optimized at the same level of theory (MMFF94(s)). As we can see that the total energies of the intermediates are lower than that of their corresponding parent hydrocarbons indicating the intermediates have lower strain and are much more stable. In addition, literature<ref name="hyper stable">W. F. Maier, P. Von Rague Schleyer, ''J. Am. Chem. Soc.'', '''1981''', ''103'', 1891. {{DOI|10.1021/ja00398a003}}</ref> suggests that the cage structure within bridgehead olefins also contributes to the overall stability of the intermediates.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"| Geometry
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHdownandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>9withHupandtwistedboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownchair.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHdownboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>molecule9</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>10withHupboat.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''9'''with the alkene H pointing down and the cyclohexane ring adopting chair||9 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||9 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing down and the cyclohexane ring adopting chair||10 with the alkene H pointing down and the cyclohexane ring adopting slightly twisted boat||10 with the alkene H pointing up and the cyclohexane ring adopting slightly twisted boat
|-
| Energy||77.63255||82.62521||77.90904||61.03452||77.83977||66.28665
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 3.''' ''Other structures of Molecules '''9''', '''10''' and their corresponding energies after optimization with MMFF94(s) force field''</div>

== Spectroscopic Simulation using Quantum Mechanics (Part 1)==
=== A practice molecule: Spectroscopy of an intermediate related to the synthesis of Taxol ===

The spectroscopic data have been reported in literature<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> for molecules '''17''' and '''18''' ('''Figure 3'''), which are the derivatives of '''9''' and '''10''' respectively. The objective here is to simulate <sup>1</sup>H and <sup>13</sup>C NMR spectra and compare them with the values given in literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> to see whether the simulated spectra are consistent with the literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> or not.

In this exercise, molecule '''17''' was chosen as an example for the spectra simulation and it was optimized using Avogadro with MMFF94(s) force field first. A .com file was then generated for the lowest energy structure with key word line containing "# B3LYP/6-31G(d,p) Opt SCRF=(CPCM,Solvent=chloroform) Freq NMR EmpiricalDispersion=GD3" before it was sent to HPC for spectra simulation.

[[File:HDmolecule17and18.jpg |center | px200]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 3.''' ''Structures of molecules '''17''' and '''18'''''</div>

====Results and Discussions====

Just like its parent molecule '''9''', The total energy of '''17''' can also be altered with respect to the geometry of the cyclohexane ring. The lowest energy structure after optimization with MMFF94(s) force field is shown in '''Table 4''' (the left one )with cyclohexane ring adopts chair conformation. Other structures of the same molecule after optimization at the same level of theory with higher energies are also shown as well (the mid and right one, not all possible structures are drawn).

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Possible structures of molecule 17'''
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule17avolowest.cml‎</uploadedFileContents>
</jmolApplet></jmol>
| align="center" style="background:#f0f0f0;"|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avohehe.cml</uploadedFileContents>
</jmolApplet></jmol>
|<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Molecule17avoanot.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
| Energy||104.31700||118.02981||120.10595
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 4.''' ''Structures of molecule '''17''' after optimization using Avogadro with MMFF94(s) force field''</div>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule17</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎HDlowest17HPC.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 4.''' ''Geometry of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''[[File:LowestHNMR17.svg]]'''
| align="center" style="background:#f0f0f0;"|'''[[File:LowestCNMR17.svg]]'''
|-
|align="center" style="background:#f0f0f0;" | <sup>1</sup>H NMR Spectrum ||align="center" style="background:#f0f0f0;" | <sup>13</sup>C NMR Spectrum
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 5.''' ''Simulated NMR spectra of molecule '''17''' after re-optimization at B3LYP/6-31G(d,p) level of theory using HPC {{DOI|10042/27701}}</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>1</sup>H NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>1</sup>H NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:HNMRSUMMARYLOWEST.PNG]]|| <sup>1</sup>H NMR (300 MHz, CDCI<sub>3</sub>) δ 4.84(dd, '''''J''''' =7.2,4.7Hz, 1H),3.40-3.10(m,4H),2.99(dd,'''''J'''''=6.8, 5.2 Hz, 1H), 2.80-1.35 (series of m, 14H), 1.38 (s, 3H), 1.25 (s, 3H), 1.10 (s, 3H), 1.00-0.80 (m, 1H)
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 6.''' ''Table of <sup>1</sup>H NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Hnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 5.''' ''Comparison between computational <sup>1</sup>H NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

Excel was used to draw comparisons between computational NMR data and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>. From '''Figure 5''', one can see that significant deviation starts from atom 12 and onwards. This is due to the assumption made when plotting the literature date: e.g. it is assumed that the 14Hs are equally distributed over chemical shift range of 2.80-1.35. However, in reality, it maybe not be the case.

From '''Figure 6''' one can see that computational <sup>13</sup>C NMR data matches with literature much better than that of <sup>1</sup>H NMR. This is due to each C environment is defined explicitly and unlike <sup>1</sup>H NMR, where an assumption was drawn in plotting the data.

To conclude, both <sup>1</sup>H and <sup>13</sup>C NMR data have been successfully interpreted using computational method with <sup>1</sup>H NMR deviates more from literature than <sup>13</sup>C NMR does. Other factors, which may contribute to the deviations, are spin-orbit coupling errors within the computational calculation;<ref name="Spinorbit">R. Jain, T. Bally, P.R. Rablen,''J. Org. Chem.'', '''2009''', ''74'', 4017–4023 {{DOI|10.1021/jo900482q}}</ref><ref name="NMR2">{{DOI|10.1021/jo900408d}},[http://www-jmg.ch.cam.ac.uk/tools/nmr/ Applet],{{DOI|10.1021/ja105035r}}</ref> the heavy atom effect caused by the two sulfur atoms; the fluxionality of the Hs on methyl groups; the temperature and pressure at which the measurements were taken.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''' <sup>13</sup>C NMR data from computational method '''
| align="center" style="background:#f0f0f0;"|'''<sup>13</sup>C NMR data from literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> '''
|-
| [[File:CNMRSUMMARYLOWEST.PNG]]|| <sup>13</sup>C NMR (75 MHz, CDCI<sub>3</sub>) ppm 218.79, 144.63, 125.33, 72.88, 56.19, 52.52, 48.50, 46.80, 45.76, 39.80, 38.81, 35.85, 32.66, 28.79, 28.29, 26.88, 25.66, 23.86, 20.96, 18.71
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 7.''' ''Table of <sup>13</sup>C NMR data from computational method {{DOI|10042/27701}} and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

[[File:Cnmrcomparison.PNG | center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 6.''' ''Comparison between computational <sup>13</sup>C NMR results and literature <ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref> </div>

In order to compare the relative energies of molecule '''17''' and '''18''', molecule '''18''' was optimized using exactly the same approach as that for molecule '''17'''. Free energy ΔG is labelled as sum of electronic and thermal Free Energies. From '''Table 8''', one can see that the free energies of '''17''' (-1651.459445 Hartrees) and '''18''' (-1651.463260 Hartrees) are very similar with '''18''' being slightly lower in the energy. This indicates that '''18''' is more stable and should be favored thermodynamically, which indeed is confirmed by literature.<ref name="spectra">Spectroscopic data: L. Paquette, N. A. Pegg, D. Toops, G. D. Maynard, R. D. Rogers, ''J. Am. Chem. Soc.,'', '''1990''', ''112'', 277-283. {{DOI|10.1021/ja00157a043}}</ref>

{| align=center
|-
|
<jmol><jmolApplet><title>molecule18</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>‎Molecule18avolowest.cml</uploadedFileContents>
</jmolApplet></jmol>
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 7.''' ''Geometry of molecule '''18''' after optimization at MMFF94(s) level of theory using Avogadro</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Types of Energies'''
| align="center" style="background:#f0f0f0;"|'''Molecule 17'''
| align="center" style="background:#f0f0f0;"|'''Molecule 18'''
|-
| Zero-point correction / (Hartree / Particle)||0.467967||0.467823
|-
| Thermal correction to Energy||0.489479||0.489248
|-
| Thermal correction to Enthalpy||0.490424||0.490192
|-
| Thermal correction to Gibbs Free Energy||0.420585||0.421083
|-
| Sum of electronic and zero-point Energies (E= E<sub>elec</sub> + ZPE)||-1651.412064||-1651.416520
|-
| Sum of electronic and thermal Energies (E= E<sub>0</sub> + E<sub>vib</sub> + E<sub>rot</sub> + E<sub>trans</sub>)||-1651.390551||-1651.395096
|-
| Sum of electronic and thermal Enthalpies (H= E + RT)||-1651.389607||-1651.394151
|-
| Sum of electronic and thermal Free Energies (G= H - TS)||-1651.459445||-1651.463260
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 8.''' ''Vibrational analysis of molecules '''17''' and '''18''' (energy unit is Hartree)</div>

== Analysis of the properties of the synthesized alkene epoxides (part 2)==

===The crystal structures of Shi and Jacobsen Catalysts===

'''21''' and '''23''' ('''Figure 8''') are the precursors of Shi and Jacobsen Catalysts respectively. The crystal structures of these two precursors, which were obtained from Cambridge crystal database (CCDC) using the '''Conquest''' program, were exploited utilizing the '''Mercury''' program.

[[File:Twoprecursors.jpg| center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 8.''' '' The stable precursors of the Shi and the Jacobsen catalysts</div>

====Results and Discussions====

{| align=center
|-
|
<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>350</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 5 28;measure 4 28;measure 5 14;measure 4 12;measure 6 16;measure 6 10;measure 2 10;measure 2 19;measure 1 19;measure 1 7;
</script><uploadedFileContents>NELQEAshi-precursor.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 9.''' ''Crystal structure of precursor '''21''' obtained from Cambridge Crystal database using the Conquest program''</div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
|align="center"style="background:#f0f0f0;"|'''[[File:Bondlength21chemd.jpg]]
|align="center"style="background:#f0f0f0;"|'''[[File:Inductiveeffect21.jpg]]
| align="center" style="background:#f0f0f0;"|'''
{| class="wikitable" style="margin: 1em auto 1em auto;"
|-
! Atom
! C-O bond length/nm
|-
| O5-C10
| 0.1409
|-
| O4-C10
| 0.1439
|-
| O6-C2
| 0.1403
|-
| O3-C2
| 0.1403
|-
| O3-C7
| 0.1441
|-
| O1-C7
| 0.1413
|}
|-
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 9.''' ''C-O bond lengths of all anomeric centers within precursor '''21'''''</div>

The expected C-O bond length is 0.142 nm, which is the sum of the covalent radii of C and O. However, as one can see from '''Table 9''' most C-O bonds are shorter than the expected bond length and this is due to anomeric effect: e.g. the lones pairs on O5 is donated into the C10-O4 σ• anti-bonding orbital and this results in shortening of C10-O5 and lengthening of C10-O4. The direction of lone donation is determined by the inductive effect which is caused by the electron withdrawing carbonyl group. (The dotted arrow indicates the direction of inductive effect within molecule '''21''')

{| align=center
|-
|<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>frame 8;vectors 4;vectors scale 5.0;color vectors red;vibration 10;measure 46 93;measure 89 50;measure 51 88;measure 45 94;measure 77 86;measure 79 84;measure 53 63;measure 59 55;
</script><uploadedFileContents>HDjacobpre.mol2</uploadedFileContents>
</jmolApplet>
</jmol>
|}

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 10.''' ''Crystal structure of precursor '''23''' obtained from Cambridge Crystal database using the Conquest program''</div>

The metal center Mn in the Jacobsen catalyst precursor '''23''' has coordination number of five and it adopts square based pyramidal structure ('''Figure 10''') with cl ligand occupying the axial position rather than trigonal bipyramid. This can be rationalized as the tetradentate ligand has aromatic rings within its structure and it prefers to adopt a planar like structure while binding to the metal center to avoid any torsional strain generated when trying to fit itself into a trigonal bi-pyramid.(The trigonal bi-pyramidal structure is higher in energy than the square based pyramidal geometry). In addition, the attractive interactions between the Hs on adjacent t-butyl groups (0.23-0.29 nm) lower the overall energy of the complex further, thus making the square based pyramidal structure even more favorable.

===Calculated NMR properties of the Epoxide===

The NMR spectra of epoxides (E'''1''', E'''2''') formed from tran-Stilbene and 1,2-dihydronaphthalene were simulated using the same approach as that for molecule '''17'''. (Figure '''11''')

[[File:Epoxideanalysis.jpg| center ]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 11.''' '' Epoxides of trans-Stilbene and 1,2-dihydronaphthalene </div>

====Results and Discussions====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1RR</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideRRavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>E1SS</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>TransstillbeneepoxideSSavobeforeHPC.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E1''' '''RR'''||'''E1 SS'''
|-
| Energy||39.45682||39.45704
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 10.''' '' Structures of '''E1''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''Geometry'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1r2r</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1R2RbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
| align="center" style="background:#f0f0f0;"|'''<jmol><jmolApplet><title>1s2s</title><color>white</color>
<size>150</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>4epoxide1S2SbeforeHPCAVO.cml</uploadedFileContents>
</jmolApplet></jmol>'''
|-
| Description||'''E2 1S2R'''||'''E2 1R2S'''||'''E2 1R2R'''||'''E2 1S2S'''
|-
| Energy||30.22440||30.68345||68.09538||68.09535
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 11.''' '' Structures of '''E2''' after optimization using Avogadro at MMFF94(s) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>13</sup>C NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>13</sup>C NMR {{DOI|10042/27802}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR <sup>1</sup>H NMR {{DOI|10042/27801}}'''
| align="center" style="background:#f0f0f0;"|'''E1 SS <sup>1</sup>H NMR {{DOI|10042/27802}}'''
|-
|[[File:StilbeneRRCNMR.PNG|250px]]||[[File:StilbeneSSCNMR.PNG|250px]]||[[File:HNMRofstillbeneRR.PNG|250px]]||[[File:StillSSHnmr.PNG|250px]]
|-
| [[File:CNMRofRRstillbene.svg|250px]]||[[File:CNMRofSSstilbene.svg|250px]]||[[File:HNMRofRRStillbene.svg|250px]]||[[File:HNMRofSSstillbene.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 12.''' '' Simulated NMR spectra of '''E1''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>13</sup>C NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>13</sup>C NMR {{DOI|10042/27814}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2R <sup>1</sup>H NMR {{DOI|10042/27812}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S <sup>1</sup>H NMR {{DOI|10042/27814}}'''
|-
|[[File:1s2rCNMRE2.PNG|250px]]||[[File:Cnmr1r2sE2.PNG|250px]]||[[File:HNMRE21s2r.PNG|250px]]||[[File:HNMR1r2sE2.PNG|250px]]
|-
| [[File:CNMRofE21S2R.svg|250px]]||[[File:CNMR1R2SE2.svg|250px]]||[[File:1s2rHnmrE2.svg|250px]]||[[File:HNMR1R2SE2.svg|250px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>13</sup>C NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>13</sup>C NMR {{DOI|10042/27833}}'''
| align="center" style="background:#f0f0f0;"|'''E2 RR <sup>1</sup>H NMR {{DOI|10042/27832}}'''
| align="center" style="background:#f0f0f0;"|'''E2 SS <sup>1</sup>H NMR {{DOI|10042/27833}}'''
|-
|[[File:CNMRE2RR.PNG|250px]]||[[File:CNMRE2SS.PNG|250px]]||[[File:HNMRE2RR.PNG|250px]]||[[File:HNMRE2SS.PNG|250px]]
|-
| [[File:CNMRofE2RR.svg|250px]]||[[File:CNMRE2SS.svg|250px]]||[[File:HNMRE2RR.svg|250px]]||[[File:HNMRE2SS.svg|250px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 13.''' '' Simulated NMR spectra of '''E2''' after re-optimization using HPC at B3LYP/6-31G(d,p) level of theory </div>

From '''Table 12''' and '''13''', one can deduce that the NMR data on its own can not identify the absolute configurations of the epoxides since within each enantiomeric pair, the corresponding NMR spectra are very similar to each other. Thus, further investigations such as optical rotation need to be conducted in order to assign the absolute configurations of the epoxides.

===Assigning the absolute configuration of the epoxides===

The epoxidation of alkene is stereospecific,
====The calculated chiroptical properties of the product====
====Optical Rotatory Power (ORP)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27838}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L1">Denmark, Scott E.; Matsuhashi, Hayao ''J. Org. Chem.'', '''2002''', ''67(10)'', 3479–3486.{{DOI|10.1021/jo020050h}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27839}}'''
| align="center" style="background:#f0f0f0;"|'''Literature<ref name="L2">Nakada, Masahisa; Niwa, Takashi ''J. Am. Chem. Soc.'', '''2012''', ''134(33)'', 13538–13541.{{DOI|10.1021/ja304219s}}</ref>'''
|-
| [α]<sub>d</sub>||297.93 deg (589nm)||239.2 deg (589nm, 25 <sup>o</sup>C, Chloroform)||-297.84 deg (589nm)||-205.2 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27840}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L3">Hu, Xiaoxue; Miao, Cheng-Xia; Sun, Wei; Wang, Shoufeng; Xia, Chungu; Xiong, Donglu; Xiong, Donglu ''European Journal of Organic Chemistry'', '''2011''', ''23'', 4289 -4292.{{DOI|10.1002/ejoc.201100512}}</ref>'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27841}}'''
| align="center" style="background:#f0f0f0;"|'''Literature <ref name="L4">Archelas; Furstoss; Pedragosa-Moreau ''Tetrahedron'', '''1996''', ''52(13)'', 4593 - 4606.{{DOI|10.1016/0040-4020(96)00135-4}}</ref>'''
|-
| [α]<sub>d</sub>||35.86 deg (589nm)|| -90.5 deg (589nm, 25 <sup>o</sup>C, Chloroform) ||155.82 deg (589 nm)||129 deg (589nm, 20 <sup>o</sup>C, Chloroform)
|-
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27843}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27844}}'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| [α]<sub>d</sub>||-246.60 deg (589nm)||N/A||246.61 deg (589 nm)||N/A
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 14.''' ''Comparison of ORPs between calculated values and literature </div>

====Electronic Circular Dichroism (ECD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27985}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27986}}'''
|-
| [[File:E1SS.PNG | 400px]]||[[File:E1RR_ECD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27987}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27988}}'''
|-
| [[File:E2_1S2SECD.PNG | 400px]]||[[File:E2_1R2R_ECD.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27989}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27990}}'''
|-
| [[File:E2_1S2R_ECD.PNG | 400px]]||[[File:1R2S_E2_ECD.PNG | 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 15.''' ''ECD analysis of E1 and E2 </div>

====Vibrational Circular Dichroism (VCD)====

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''E1 SS {{DOI|10042/27992}}'''
| align="center" style="background:#f0f0f0;"|'''E1 RR {{DOI|10042/27994}}'''
|-
| [[File:E1SS_VCD.PNG| 400px]]||[[File:E1RRVCD.PNG| 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2S {{DOI|10042/27995}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2R {{DOI|10042/27996}}'''
|-
| [[File:E2_1S2S_VCD.PNG | 400px]]||[[File:E2_1R2R.PNG | 400px]]
|-
| align="center" style="background:#f0f0f0;"|'''E2 1S2R {{DOI|10042/27997}}'''
| align="center" style="background:#f0f0f0;"|'''E2 1R2S {{DOI|10042/27998}}'''
|-
| [[File:E2_1S2R_VCD.PNG | 400px]]||[[File:E21R2SVCD.PNG| 400px]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 16.''' ''VCD analysis of E1 and E2 </div>

===Using the (calculated) properties of transition state for the reaction===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-1534.687808||-1534.683440||-1381.120782||-1381.131343
|-
| Free energy of Transition State 2 / Hartrees||-1534.687252||-1534.685089||-1381.125886||-1381.116109
|-
| Free energy of Transition State 3 / Hartrees||-1534.700037||-1534.693818||-1381.134059||-1381.126039
|-
| Free energy of Transition State 4 / Hartrees||-1534.699901||-1534.691858||-1381.126722||-1381.136239
|-
| Average of free energies of 4 transition states / Hartrees||-1534.69375||-1534.688551||-1381.126862||-1381.127433
|-
| Difference in free energies / Hartress||-0.005198||||0.00057025||
|-
| Ratio of K||246||||0.55||
|-
| Enantiomeric excess ||99.2% ee for RR||||28.6% ee for S, R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 17.''' ''Transition states analysis for Shi epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''E1 R,R'''
| align="center" style="background:#f0f0f0;"|'''E1 S,S'''
| align="center" style="background:#f0f0f0;"|'''E2 R,S'''
| align="center" style="background:#f0f0f0;"|'''E2 S,R'''
|-
| Free energy of Transition State 1 / Hartrees||-3574.921174||-3574.923087||-3421.359354||-3421.369033
|-
| Free energy of Transition State 2 / Hartrees||N/A||N/A||-3421.359499||-3421.361580
|-
| Average of free energies of 4 transition states / Hartrees||-3574.921174||-3574.923087||-3421.359427||-3421.365307
|-
| Difference in free energies / Hartrees||0.001913||||0.00588||
|-
| Ratio of K||0.13||||0.002||
|-
| Enantiomeric excess ||77.0% ee for S,S||||99.6% for S,R||
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 18.''' ''Transition states analysis for Jacobsen epoxidation of trans-Stilbene and 1,2-dihydronaphthalene </div>

===Investigating the non-covalent interactions in the active site of the reaction transition state===

Non-covalent interactions such as hydrogen bonds, electrostatic interactions can be defined by the properties of electron density as well as its curvatures. For this section, the transition states for Shi epoxidation of 1,2-dihydronaphthalene was chosen to do the NCI analysis.

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| <jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/e/ed/Output-1_denRSleft.cub.jvxl" translucent;</script>
<uploadedFileContents>Output-1_denRSleft.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>||<jmol>
<jmolApplet>
<title>Orbital</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0d/S%2CRright.cub.jvxl" translucent;</script>
<uploadedFileContents>S,Rright.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 19.''' ''NCI analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

discusssionskaddlaksdhkashdsakjdaadsdafffagagfahggagr

===Investigating the Electronic topology (QTAIM) in the active-site of the reaction transition state===

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|'''R,S'''
| align="center" style="background:#f0f0f0;"|'''S,R'''
|-
| [[File:LeftSR.PNG]]|| [[File:SRright.PNG]]
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 20.''' ''QTAIM analysis for transition states of Shi epoxidation of 1,2-dihydronaphthalene </div>

===New candidates for investigations===

[[File:Xixixhaha.jpg | center]]

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Figure 12.''' '' Epoxides of R-(+)-pulegone </div>

{| class="wikitable" style="margin: 1em auto 1em auto;"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Cis-R-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
| align="center" style="background:#f0f0f0;"|'''Cis-S-pulegone oxide <ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref>'''
|-
| [α]<sub>d</sub>|| 26 deg (589nm, CHCl<sub>3</sub>)||-17.3 deg (589nm, CHCl<sub>3</sub>)
|-
|}
<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">'''Table 21.''' ''Optical literature<ref name="oxide"> Brown, Geoffrey D.; Cheung, Kung-Kai; Ngo, Koon-Sin '' Journal of Chemical Research - Part S '', '''1998''', ''# 2 '', 80-81</ref> data for Pulegone oxides </div>

==Limitations of Software and Future improvements==
====Limitations of Software====
'''Avogadro''': it is always better to draw large molecules in Chemdraw first then import them to Avogadro to make 3D structures.

'''Optical Rotation Analysis''': only molecules with optical rotations of magnitude greater than 100 can be successfully picked to predict absolute configurations with near total confidence.

====Future improvement====
If had time, the computational optical analysis of pulegone oxides could be investigated. In addition, for the '''QTAIM'''analysis, one can compute '''Extensions/QTAIM/Molecular graph with lone pairs''' in order to locate the positions of lone pairs within molecules.

== References ==

<references/>