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2014-03-10T12:11:39Z

Pb1611: /* Jacobsen Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the Cambridge Crystallographic Database for a structure of the Shi catalyst has resulted in a NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and is represented by molecules '''A''' and '''B'''. A detailed study of the unit cell<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation.<ref name="shi1"/> However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction lies in a donation of electron density into the C-O antibonding MO, which results in a weakening and lengthening of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor was located by searching the Cambridge crystal database. This resulted in two crystal structures, untit cells TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in TOVNIB01, the methyl groups of the t-butyl are staggered whilst in TOVNIB02, the methyl groups are eclipsed. Staggering the methyl groups results in the shortening the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(22)-H(47) in TOVNIB02 is 2.32 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.
===Trans-stilbene===
[[Image:PB1611Stilbenescheme.png|center|500px]]
[[Image:PB1611Opti_transstilbene_pic.png|center|250px]]
{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|}
 

While the computed data is in good agreement overall with the experimental spectrum, a few apsects are worth pointing out. Firstly, the computed chemical shift values all appear slightly lower in ppm than the experimental ones. Furthermore, the fluxionality effects are not take into account in these calculations (a lack of time-averaging effects)and hence chemically equivalent protons appear as distinct in the simulated spectrum. The experimental values here were compared to the highest chemical shifts of those on the aromatic ring.

===Styrene===

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

Rep:Mod:buikiwiki

2014-03-10T12:02:09Z

Pb1611: /* Jacobsen Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the Cambridge Crystallographic Database for a structure of the Shi catalyst has resulted in a NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and is represented by molecules '''A''' and '''B'''. A detailed study of the unit cell<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation.<ref name="shi1"/> However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction lies in a donation of electron density into the C-O antibonding MO, which results in a weakening and lengthening of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor was located by searching the Cambridge crystal database. This resulted in two crystal structures, untit cells TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in TOVNIB01, the methyl groups of the t-butyl are staggered whilst in TOVNIB02, the methyl groups are eclipsed. Staggering the methyl groups results in the shortening the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(22)-H(47) in TOVNIB02 is 2.32 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.
===Trans-stilbene===
[[Image:PB1611Stilbenescheme.png|center|500px]]
[[Image:PB1611Opti_transstilbene_pic.png|center|250px]]
{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|}
 

While the computed data is in good agreement overall with the experimental spectrum, a few apsects are worth pointing out. Firstly, the computed chemical shift values all appear slightly lower in ppm than the experimental ones. Furthermore, the fluxionality effects are not take into account in these calculations (a lack of time-averaging effects)and hence chemically equivalent protons appear as distinct in the simulated spectrum. The experimental values here were compared to the highest chemical shifts of those on the aromatic ring.

===Styrene===

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

Rep:Mod:buikiwiki

2014-03-10T11:57:10Z

Pb1611: /* Anomeric Effect */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the Cambridge Crystallographic Database for a structure of the Shi catalyst has resulted in a NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and is represented by molecules '''A''' and '''B'''. A detailed study of the unit cell<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation.<ref name="shi1"/> However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction lies in a donation of electron density into the C-O antibonding MO, which results in a weakening and lengthening of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.
===Trans-stilbene===
[[Image:PB1611Stilbenescheme.png|center|500px]]
[[Image:PB1611Opti_transstilbene_pic.png|center|250px]]
{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|}
 

While the computed data is in good agreement overall with the experimental spectrum, a few apsects are worth pointing out. Firstly, the computed chemical shift values all appear slightly lower in ppm than the experimental ones. Furthermore, the fluxionality effects are not take into account in these calculations (a lack of time-averaging effects)and hence chemically equivalent protons appear as distinct in the simulated spectrum. The experimental values here were compared to the highest chemical shifts of those on the aromatic ring.

===Styrene===

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

Rep:Mod:buikiwiki

2014-03-10T11:56:35Z

Pb1611: /* Shi Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the Cambridge Crystallographic Database for a structure of the Shi catalyst has resulted in a NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and is represented by molecules '''A''' and '''B'''. A detailed study of the unit cell<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation.<ref name="shi1"/> However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction lies in a donation of electron density into the C-O antibonding MO, which results in a weakening and lengthening of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.
===Trans-stilbene===
[[Image:PB1611Stilbenescheme.png|center|500px]]
[[Image:PB1611Opti_transstilbene_pic.png|center|250px]]
{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|}
 

While the computed data is in good agreement overall with the experimental spectrum, a few apsects are worth pointing out. Firstly, the computed chemical shift values all appear slightly lower in ppm than the experimental ones. Furthermore, the fluxionality effects are not take into account in these calculations (a lack of time-averaging effects)and hence chemically equivalent protons appear as distinct in the simulated spectrum. The experimental values here were compared to the highest chemical shifts of those on the aromatic ring.

===Styrene===

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

File:PB1611Stilbenescheme.png

2014-03-10T11:47:12Z

Pb1611: uploaded a new version of "File:PB1611Stilbenescheme.png"

Rep:Mod:buikiwiki

2014-03-10T11:41:40Z

Pb1611: /* Trans-stilbene */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.
===Trans-stilbene===
[[Image:PB1611Stilbenescheme.png|center|500px]]
[[Image:PB1611Opti_transstilbene_pic.png|center|250px]]
{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|}
 

While the computed data is in good agreement overall with the experimental spectrum, a few apsects are worth pointing out. Firstly, the computed chemical shift values all appear slightly lower in ppm than the experimental ones. Furthermore, the fluxionality effects are not take into account in these calculations (a lack of time-averaging effects)and hence chemically equivalent protons appear as distinct in the simulated spectrum. The experimental values here were compared to the highest chemical shifts of those on the aromatic ring.

===Styrene===

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

Rep:Mod:buikiwiki

2014-03-10T11:27:03Z

Pb1611: /* Calculated NMR Properties of the Products */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.
===Trans-stilbene===
[[Image:PB1611Stilbenescheme.png|center|500px]]
[[Image:PB1611Opti_transstilbene_pic.png|center|250px]]
{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|}
 
===Styrene===

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

Rep:Mod:buikiwiki

2014-03-10T11:25:37Z

Pb1611: /* Calculated NMR Properties of the Products */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.
[[Image:PB1611Stilbenescheme.png|center|500px]]
[[Image:PB1611Opti_transstilbene_pic.png|center|250px]]
{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|}
 

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

File:PB1611Stilbenescheme.png

2014-03-10T11:24:37Z

Pb1611:

Rep:Mod:buikiwiki

2014-03-10T11:18:25Z

Pb1611: /* Calculated NMR Properties of the Products */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.
[[Image:PB1611Opti_transstilbene_pic.png|center|250px]]
{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|}
 

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

File:PB1611Opti transstilbene pic.png

2014-03-10T11:17:30Z

Pb1611:

Rep:Mod:buikiwiki

2014-03-10T11:15:29Z

Pb1611: /* Calculated NMR Properties of the Products */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.

{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|}
 

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

Rep:Mod:buikiwiki

2014-03-10T11:14:52Z

Pb1611: /* Calculated NMR Properties of the Products */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.

{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

{| class="wikitable floatcenter"
|+ '''Table 11'''. 13C NMR of Trans-stilbene.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR13C.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated[http://dx.doi.org/10042/28005] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (100 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm) (degeneracy=2 in all)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 134.08
| style="text-align: center;" | 137.1
|-
| style="text-align: center;" | 124.22
| style="text-align: center;" | 128.5
|-
| style="text-align: center;" | 123.52
| style="text-align: center;" scope="row" rowspan="4"| 125.5
|-
| style="text-align: center;" | 123.21
|-
| style="text-align: center;" | 123.08
|-
| style="text-align: center;" | 118.27
|-
| style="text-align: center;" | 66,43
| style="text-align: center;" | 62.8
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

Rep:Mod:buikiwiki

2014-03-10T11:00:08Z

Pb1611: /* References */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.

{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | [http://dx.doi.org/10042/28005 Simulated] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>
<ref name="litvalues1">C. Wiles, M. J. Hammond and P. Watts, ''Beilstien Journal of Organic Chemistry'', 2009, '''113''', 63-7064</ref>

Rep:Mod:buikiwiki

2014-03-10T10:55:40Z

Pb1611: /* Calculated NMR Properties of the Products */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.

{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | [http://dx.doi.org/10042/28005 Simulated] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental<ref name="litvalues1"/> (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>

Rep:Mod:buikiwiki

2014-03-10T10:53:51Z

Pb1611: /* Calculated NMR Properties of the Products */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.

{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="5"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="5" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="5" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (400 MHz, CDCl3)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 7.57
| scope="col" width="115px"| s, 2H
| scope="row" rowspan="2"| 7.59-7.25
| scope="row" rowspan="2"| m, 10H
|-
| 7.48
| s, 8H
|-
| 3.54
| s, 2H
| 3.87
| s, 2H
|}
 

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>

File:PB1611TransstilbeneNMR13C.svg

2014-03-10T10:41:26Z

Pb1611:

Rep:Mod:buikiwiki

2014-03-10T10:38:32Z

Pb1611: /* Calculated NMR Properties of the Products */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==
The structures of epoxides of (R,R)-trans-stilbene and (R)-styrene were initially optimized in Avogadro using MMFF94s force field to then further optimize them with GaussView using DFT method at B3LYP/6-31G(d,p) level of therory. The results obained are presented below together with the spectroscopical simulations.

{| class="wikitable floatcenter"
|+ '''Table 10'''. 1H NMR of Trans-stilbene.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611TransstilbeneNMR1H.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Chloroform)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>

File:PB1611TransstilbeneNMR1H.svg

2014-03-10T10:37:34Z

Pb1611:

Rep:Mod:buikiwiki

2014-03-10T06:40:39Z

Pb1611: /* Jacobsen Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 10. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

==Calculated NMR Properties of the Products==

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>

Rep:Mod:buikiwiki

2014-03-10T06:40:06Z

Pb1611: /* Crystallographic Database Search */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.
==Calculated NMR Properties of the Products==

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>

Rep:Mod:buikiwiki

2014-03-10T06:38:50Z

Pb1611: /* Shi Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="shi1"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

The structure of the Shi catalyst is strongly influenced by the presence of stereoelectronic interactions. In particular, an important role is played by the anomeric interactions, which arise from the electron density donation from the high energy oxygen lone pair, ''nO'', into the low lying ''σ*'' antibonding MO on the adjacent C-O bond. These interactions are maximised when the donor orbital ''nO'' is aligned antiperiplanar (app) to the acceptor orbital ''σ*C-O'', since this provides them with an optimal overlap. In six-membered ring systems the substituent groups usually prefer to adopt an equatorial position, in order to avoid 1,3-diaxial repulsive interactions. However, when an anomeric centre is present in the ring, the stabilisation arising form anomeric interactions overcomes the destabilisation due to 1,3-diaxial repulsion, thus, favouring the alignment of the acceptor group in an axial position.<ref name="Clayden"/>
 
The presence of anomeric interactions in the structure of a molecule is determined by looking at the C-O bond length. In fact, the ''nO'' →''σ*C-O'' interaction consists in a donation of electron density into the C-O antibonding MO, which results in a weakening (i.e. lengthening) of the C-O acceptor bond. Considering that the typical C-O bond length is 1.43 Å, any deviation from this value would suggest the presencce of an anomeric interaction.
 
By inspection of molecules '''A''' and '''B''' and from analysis of the length of the C-O bonds present in the structure, as reported in '''Table 12''', three anomeric centres are present in the Shi catalyst crystal structure, which correspond to C22, C14 and C19 in molecule '''A''', and C10, C2 and C7 in molecule '''B'''.
 
In particular by considering the anomeric interactions for molecule '''A''':
* the C22-O10 bond is 0.022 Å longer than C22-O11, due to the O11 LP donation into the C22-O10 σ* orbital;
* the C14-O12 bond is 0.018 Å longer than C14-O8, due to the O8 LP donation into the C14-O12 σ* orbital;
* the C19-O8 bond is 0.063 Å longer than C19-O7, due to the O7 LP donation into the C19-O8 σ* orbital.
 
By considering the anomeric interactions for molecule '''B''':
* the C10-O4 bond is 0.030 Å longer than C10-O5, due to the O5 LP donation into the C10-O4 σ* orbital;
* the C2-O6 bond is identical to C2-O2 bond length, due to two anomeric interactions cancelling each other;
* the C7-O2 bond is 0.028 Å longer than C7-O1, due to the O1 LP donation into the C7-O2 σ* orbital.
 
A final remark concerns the bond length of C16-O10 in molecule '''A''' and C4-O4 in molecule '''B''' being shorter than typical C-O bond length, despite them not being subject to anomeric interactions. This observation could be explained by considering that the presence of the carbonyl group adjacent to C16 and C4 makes them slightly δ+ and the O10 and O14 slightly δ-. Thus, the partial charges attractive interactions result in stronger (i.e. shorter) C16-O10 and C4-O4 bonds.

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>

Rep:Mod:buikiwiki

2014-03-10T06:35:48Z

Pb1611: /* References */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="crystal shi"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>
<ref name="shi1">M.Durik, V.Langer, D.Gyepesova, J.Micova, B.Steiner, M.Koos, Acta Crystallogr., 2001, 57, o672. {{DOI|10.1107/S160053680101073X}}</ref>

Rep:Mod:buikiwiki

2014-03-10T06:35:23Z

Pb1611: /* Shi Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
The search of the crystallographic structure of the Shi catalyst in the CCD has reported the NELQEA unit cell.
<ref name="shi1"/> NELQEA unit cell is asymmetric and contains two molecules '''A''' and '''B'''. A detailed study of the unit cell performed by Durik ''et al''.<ref name="crystal shi"/> has reported that in both molecules the pyranose ring assumes a 3S0 conformation and the ''cis''-fused 1,3-dioxolane ring assumes a E4 conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E2 in molecule '''A''' and E4 in molecule '''B'''.
 
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>

Rep:Mod:buikiwiki

2014-03-10T06:28:23Z

Pb1611: /* References */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====
===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>
<ref name="jac1">E. McGarrigle, D. Gilheany, "Chromium− and Manganese−salen Promoted Epoxidation of Alkenes", ''Chem. Rev'', 2005, '''105''' (5), 1563–1602 {{DOI|10.1021/cr0306945}}</ref>

Rep:Mod:buikiwiki

2014-03-10T06:25:51Z

Pb1611: /* Jacobsen Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====
===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="Jacobsen"></ref><ref name="jac1"/>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

Rep:Mod:buikiwiki

2014-03-10T06:15:27Z

Pb1611: /* Jacobsen Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====
===Jacobsen Catalyst===
Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor (23) was located by searching the Cambridge crystal database. This yielded two crystal structures for (23), TOVNIB01 and TOVNIB02.
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}
For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge - this supports previous work by Jacobsen and Katsuki.<ref name="j14"></ref><ref name="j15"></ref>
 
The main difference between TOVNIB01 and TOVNIB02 is that in the former, the methyl groups of the t-butyl are staggered whilst in the latter, the methyl groups are eclipsed. Staggering the methyl groups appears to shorten the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(20)-H(49) in TOVNIB02 is 2.36 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02. This can be seen below:
 
Though the angle indicated for TOVNIB01 is slightly smaller than for TOVNIB02, both angles are approximately 154°, indicating that both complexes are not planar. Instead, the complex appears to be concaved and so, one face of the molecule is more sterically hindered than the other. This makes attack from the top face of the molecule [where the Mn=O is pointing upwards] more favourable than if it was completely planar.

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

Rep:Mod:buikiwiki

2014-03-10T06:09:30Z

Pb1611: /* Jacobsen Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====
===Jacobsen Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|550px|x424px|center]] || colspan="2"| [[Image:PB1611TOVNIB02.png|550px|x424px|center]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

File:PB1611TOVNIB01.png

2014-03-10T06:08:24Z

Pb1611: uploaded a new version of "File:PB1611TOVNIB01.png"

File:PB1611TOVNIB02.png

2014-03-10T06:07:35Z

Pb1611:

Rep:Mod:buikiwiki

2014-03-10T05:57:56Z

Pb1611: /* Jacobsen Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====
===Jacobsen Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|center|550px|x424px]] || colspan="2"| [[Image:PB1611TOVNIB02.png|center|550px|x424px]]
|-
| '''Bond''' || '''Length(Å)''' || '''Bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.323
|-
|Mn1-O1 || 1.869 || Mn1-O1 || 1.872
|-
|C20-O2 || 1.317 || C20-O2 || 1.318
|-
|Mn2-O2 || 1.858 || Mn2-O2 || 1.861
|-
|H17-H51 || 4.977 || H17-H52 || 2.577
|-
|H19-H52 || 2.975 || H19-H50 || 5.045
|-
|H18-H50 || 2.694 || H18-H51 || 2.924
|-
|H20-H49 || 2.963 || H20-H49 || 4.756
|-
|H21-H48 || 4.706 || H21-H48 || 2.866
|-
|H22-H47 || 2.421 || H22-H47 || 2.328
|}

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

Rep:Mod:buikiwiki

2014-03-10T05:47:06Z

Pb1611: /* Shi Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====
===Jacobsen Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| TOVNIB01 !!colspan="2"| TOVNIB02
|-
| colspan="2"| [[Image:PB1611TOVNIB01.png|center|550px|x424px]] || colspan="2"| [[Image:PB1611TOVNIB02.png|center|550px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.317 || C1-O1 || 1.345
|-
|Mn1-O1 || 1.869 || C7-O1 || 1.380
|-
|C20-O2 || 1.317 || C2-O2 || 1.390
|-
|Mn2-O2 || 1.858 || C7-O2 || 1.443
|-
|H17-H51 || 4.977 || C2-O6 || 1.408
|-
|H19-H52 || 2.975 || C6-O6 || 1.414
|-
|H18-H50 || 2.694 || C4-O4 || 1.406
|-
|H20-H49 || 2.963 || ||
|-
|H21-H48 || 4.706 || ||
|-
|H22-H47 || 2.421 || ||
|}

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

File:PB1611TOVNIB01.png

2014-03-10T05:36:42Z

Pb1611:

Rep:Mod:buikiwiki

2014-03-10T05:16:36Z

Pb1611: /* Shi Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å)'''
|-
|C1-O1 || 1.400 || C1-O1 || 1.345
|-
|C7-O1 || 1.413 || C7-O1 || 1.380
|-
|C2-O2 || 1.403 || C2-O2 || 1.390
|-
|C7-O2 || 1.441 || C7-O2 || 1.443
|-
|C2-O6 || 1.403 || C2-O6 || 1.408
|-
|C6-O6 || 1.420 || C6-O6 || 1.414
|-
|C4-O4 || 1.395 || C4-O4 || 1.406
|-
|C10-O4 || 1.439 || C10-O4 || 1.438
|-
|C5-O5 || 1.416 || C5-O5 || 1.418
|-
|C10-O5 || 1.409 || C10-O5 || 1.416
|}
====Anomeric Effect====

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

Rep:Mod:buikiwiki

2014-03-10T05:08:18Z

Pb1611: /* Shi Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! !! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| colspan="4"| [[Image:PB1611NELQEA.png|center|1000px|x424px]]
|-
| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å''')
|-
|C1-O1 || 1.400 || C1-O1 || 1.439
|-
|C7-O1 || 1.413 || C10-O5 || 1.409
|-
|C2-O2 || 1.403 || C2-O6 || 1.403
|-
|C7-O2 || 1.441 || C2-O2 || 1.403
|-
|C2-O6 || 1.403 || C7-O2 || 1.441
|-
|C6-O6 || 1.420 || C7-O1 || 1.413
|-
|C4-O4 || 1.395 || C7-O1 || 1.413
|-
|C10-O4 || 1.439 || C4-O4 || 1.395
|-
|C5-O5 || 1.416 || C7-O1 || 1.413
|-
|C10-O5 || 1.409 || C7-O1 || 1.413
|}
====Anomeric Effect====

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

Rep:Mod:buikiwiki

2014-03-10T04:52:55Z

Pb1611: /* Shi Catalyst */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
{| class="wikitable center" border="1"
|+ Table 9. Crystal Structure of the Shi catalyst
! !! colspan="2"| Molecule '''A-left''' !!colspan="2"| Molecule '''B-right'''
|-
| '''Structure'''|| colspan="4"| [[Image:PB1611NELQEA.png|center|1147px|x424px]]
|-
| rowspan="11"|'''Bond Distances'''|| '''C-O bond''' || '''Length(Å)''' || '''C-O bond''' || '''Length(Å''')
|-
|C22-O10 || 1.438 || C10-O4 || 1.439

|-
|C22-O11 || 1.416 || C10-O5 || 1.409

|-

|C14-O12 || 1.408 || C2-O6 || 1.403
|-
|C14-O8 || 1.390 || C2-O2 || 1.403
|-
|C19-O8 || 1.443 || C7-O2 || 1.441
|-
|C19-O7 || 1.380 || C7-O1 || 1.413
|-

|C16-O10 || 1.406 || C4-O4 || 1.395
|-
|}
====Anomeric Effect====

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

File:PB1611NELQEA.png

2014-03-10T04:43:51Z

Pb1611: uploaded a new version of "File:PB1611NELQEA.png"

File:PB1611NELQEA.png

2014-03-10T04:35:17Z

Pb1611:

Rep:Mod:buikiwiki

2014-03-10T04:18:23Z

Pb1611: /* PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]
 
==Crystallographic Database Search==
===Shi Catalyst===
====Anomeric Effect====

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

Rep:Mod:buikiwiki

2014-03-10T04:15:07Z

Pb1611: /* PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|600px|right]]

 

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

Rep:Mod:buikiwiki

2014-03-10T04:14:21Z

Pb1611: /* PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|400px|left]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|500px|right]]

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

Rep:Mod:buikiwiki

2014-03-10T04:12:08Z

Pb1611: /* PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.
[[Image:PB1611Shi_scheme.png|thumb|Shi activation process|300px|center]]
[[Image:PB1611Jacobsen_scheme.png|thumb|Jacobsen activation process|500px|center]]

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

File:PB1611Jacobsen scheme.png

2014-03-10T04:11:40Z

Pb1611:

File:PB1611Shi scheme.png

2014-03-10T03:42:14Z

Pb1611:

Rep:Mod:buikiwiki

2014-03-10T03:27:25Z

Pb1611: /* PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: '''styrene''' and '''trans-stilbene'''.
The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:
*Catalysts' structure
**Product NMR spectra
***Absolute configuration
****Interactions it the active site of a catalyst
We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi<ref name="Hanks"/><ref name="Shi"/> and the Jacobsen's<ref name="Hanson"/><ref name="Jacobsen"/> catalysts.

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
<ref name="dimers">M. A. Fox, R. Cardona, N.J. Kiwiet, "Steric Effects vs. Secondary Orbital Overlap in Diels-Alder Reactions. MNDO and AM1 Studies", ''J. Org. Chem.'', '''1987''', ''52'', 1469-1474. {{DOI|10.1021/jo00384a016}}</ref>
<ref name="hydro">[http://www.vurup.sk/sites/vurup.sk/archivedsite/www.vurup.sk/pc/vol45_2003/issue3-4/pdf/05.pdf D. Skala and J. Hanika, "Kinetics of Dicyclopentadiene Hydrogenation using Pd/C Catalyst", ''Petroleum and Coal'', '''2003''', ''45'', 105-108]</ref>
<ref name="Paquette">S. W. Elmore, L. A. Paquette, "The First Thermally-induced Retro-oxy-Cope Rearrangement", Tetrahedron Letters, 1991, '''32''', 319-322 {{DOI|10.1016/s0040-4039(00)92617-0}}</ref>
<ref name="atropisomerism">P. Lloyd-Williams and E. Giralt, "Atropisomerism, biphenyls and the Suzuki coupling: peptide antibiotics", ''Chem. Soc. Rev.'', 2001, '''30''', 147-157 {{DOI|10.1039/B001971M}}</ref>
<ref name="olefins">W. F. Maier, P. von Rague Schleyer, "Evaluation and Prediction of the Stability of Bridgehead Olefins", ''J. Am. Chem. Soc.'', 1981, '''103''' (8), 1891-1900 {{DOI|10.1021/ja00398a003}}</ref>
<ref name="Hanks">A. Burke, P. Dillon, K. Martin and T. W. Hanks, "Catalytic Asymmetric Epoxidation Using a Fructose-Derived Catalyst", ''J. Chem. Educ.'', 2000, '''77''', 217 {{DOI|10.1021/ed077p271}}</ref>
<ref name="Shi">O. A. Wong, B. Wang, M-X Zhao and Y. Shi, "Asymmetric Epoxidation of trans-β-methylstyrene and 1-phenylcyclohexene using a D-fructose Derived Ketone", ''J. Org. Chem.'', 2009, '''74''', 335-6338 {{DOI|10.1021/jo900739}}</ref>
<ref name="Hanson">J. Hanson, "Synthesis and Use of Jacobsen's Catalyst: Enantioselective Epoxidation in the Introductory Organic Laboratory", ''J. Chem. Educ.'', 2001, '''78''', 1266 {{DOI|10.1021/ed078p1266}}</ref>
<ref name="Jacobsen">E. N. Jacobsen, W. Zhang, A. R. Muci, J. R. Ecker, L. Deng, "Highly Enantioselective Epoxidation Catalysts Derived from 1,2-diaminocyclohexane", ''J. Am. Chem. Soc.'', 1991, '''113''', 7063-7064 {{DOI|10.1021/ja00018a068}}</ref>

Rep:Mod:buikiwiki

2014-03-10T03:19:23Z

Pb1611: /* References */

=Year 3 Synthetic Modelling Lab: 1C<ref name="script"/>=
Computational modelling has been proved to accurately predict and rationalise the outcomes of reactions as well as new types of reactions and general properties of molecules. This computational exercise is "twinned" with the synthesis experiment 1S in the third year lab. The following computational study and analysis involves the asymmetric epoxidations of an alkenes and its characterisation by NMR spectroscopy and chiroptical measurements. The operational techniques from Part 1 will be used in Part 2 to assign the absolute stereochemistry of the synthesised epoxides in the undergraduate lab.
 

=PART 1: Conformational analysis using Molecular Mechanics=
==Conformations and Hydrogenation of Cyclopentadiene==
This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

===ENDO and EXO Cyclodimerisation products===

Upon dimerisation of cyclopentadiene via a Diels Alder [π4s+π2s] cycloaddition two possible products may form: an ''endo'' or an ''exo'' conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its ''cis''-conformation. ''Endo'' conformer is formed predominantly rather than ''exo''. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:
*Force Field: '''MMFF94s'''
*Algorithm: '''Conjugate gradients'''
*Steps per update: '''4'''
 
[[Image:PB1611_Endoexo_pic.png|thumb|Cyclodimerisation of cyclopentadiene|250px|right]]
{| class="wikitable floatleft" style="text-align:center;" border="1"
|+ '''Table 1'''. Optimized geometries of cyclopentadiene dimer.
! !! style="background: #0D4F8B; color: white;"| ENDO!! style="background: #0D4F8B; color: white;"| EXO
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611endodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endo_dimer1.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611exodimer.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_exo_dimer1.cml</uploadedFileContents><text>Click to view</text>
</jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.46480 || 3.54444
|-
! Total Angle Bending Energy (kcal/mol)
| 33.22508 || 30.78197
|-
! Total Torsional Energy (kcal/mol)
| -2.95330 || -2.73235
|-
! Total Van der Waals Energy (kcal/mol)
| 12.33274 || 12.79366
|-
! Electrostatic (kcal/mol)
| 14.18229 || 13.01273
|-
! C1-C2-C3 (°)
| 118.6 || 115.6
|-
! '''Total Energy''' (kcal/mol)
| '''58.19044''' || '''55.37325'''
|}
 
 
This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules.<ref name="Clayden"/> The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the ''exo'' product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the ''endo'' conformer is a major product of the reaction, which suggests that this Diels-Alder [π4s+π2s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann<ref name="dimers"/>. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.<ref name="dimers"/>

Using molecular mechanics approach allows us to look at different terms' contributions to the overall energy value. The table above summarises these important parameters that represent the deviations from ideality. Comparing the two dimer conformations, we observe that the difference in the total energy of dimers is mainly due to the angle bending energy, which is higher in the endo conformation by ~2.4 kcal/mol. Since the C1-C2-C3 angle for endo is further away from the ideal 109.5° for sp3 hydridisation, but both are not ideal, the reason for relative stability of ''exo'' over ''endo'' is mainly due to the effects of angle strain.

===Hydrogenation of ENDO dimer===
We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the ''endo'' dimer specifically. It has been observed<ref name="hydro"/> that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives '''3''' or '''4''' and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.
 
 
[[Image:PB_ENDO_Hydrogenation.png|thumb|Hydrogenation scheme of the ''endo'' dimer|600px|center]]
 
In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 2'''. Optimized geometries of hydrogenation products.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="250px" | [[Image:PB1611hydro3.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
! scope="col" width="250px" | [[Image:PB1611hydro4.png|250px]] <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents><text>Click to view</text></jmolAppletButton></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 3.30795 || 2.82308
|-
! Total Angle Bending Energy (kcal/mol)
| 30.86410 || 24.68542
|-
! Total Torsional Energy (kcal/mol)
| 0.05877 || -0.37828
|-
! Total Van der Waals Energy (kcal/mol)
| 13.28245 || 10.63715
|-
! Electrostatic (kcal/mol)
| 5.12101 || 5.14702
|-
! '''Total Energy''' (kcal/mol)
| '''50.72296''' || '''41.25749'''
|}
 

The results obtained show that derivative '''4''' is thermodynamically more stable than '''3''', since it lies ~9.5 kcal/mol lower in energy. The largest deviations for ideality are seen to be mainly due to the angle bending parameter, which is observed to be ~6.2 kcal/mol higher in '''3''', and also due to the total Van der Waals contributions, which raised '''3''' in energy by ~2.6 kcal/mol.

A closer look into these two parameters is summarised in table 3.
 
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 3'''. Conformational analysis of derivatives 3 and 4.
! !! style="background: #0D4F8B; color: white;"| Hydro 3!! style="background: #0D4F8B; color: white;"| Hydro 4
|-
! '''Structure'''
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro3.cml</uploadedFileContents></jmolApplet></jmol>
! scope="col" width="350px" | <jmol><jmolApplet><title></title><color>white</color><size>350</size><script>select atomno="3"; color blue; select atomno="7"; color green; select atomno="8"; color yellow; measure 3 7; measure 3 8; measure 2 3 4</script><uploadedFileContents>PB1611Opti_endohydro4.cml</uploadedFileContents></jmolApplet></jmol>
|-
! Relative Angle Bending Energy (kcal/mol)
| 6.17868 || 0
|-
! Relative Van der Waals Energy (kcal/mol)
| 2.64530 || 0
|-
! '''Relative Total Energy''' (kcal/mol)
| '''9.46547''' || '''0'''
|}
 
Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH2 unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp3 carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in '''3''' and 102.9° in '''4'''. While in '''4''' this is a sp3 carbon center and 102.9 is only ~7° away from ideality, in structure '''3''' this angle is at the sp2 hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
 
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in '''4''' are longer than the analogous distances in '''3'''. Furthermore, derivative '''4''' has one less repulsive interactions than '''3''' since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for '''4''' being lower in energy overall.
 
Now those two parameters have been examined closely, it can be concluded that hydro derivative '''3''' lies higher in energy than '''4''' due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative '''4'''.
 

==Atropisomerism in an intermediate related to the synthesis of Taxol==
[[Image:PB1611OxyCope_scheme.png|thumb|oxy-Cope rearrangement of a carbinol|300px|right]]
This section looks into the analysis of the key intermediate in the synthesis of Taxol, as proposed by Paquette et al.<ref name="Paquette"/> The reaction is a reversible atropselective anionic oxy-Cope rearrangement from a carbiol that results in either product '''9''' or '''10''', which are examples of atropisomers.<ref name="atropisomerism"/> These isomers cannot readily interconvert due to the restricted bond rotation around C-C that results in the carbonyl group pointing either up or down in the product. Given the fact the reaction is reversible, the more thermodynamically stable product will be the sole product of the reaction. To assess which of the '''9''' or '''10''' is the major product of this reaction, both geometries were optimized in Avogadro using molecular mechanics method with the settings as previously stated. Based on the possible geometries of the hexane ring as either a chair or a boat conformation, along with the two possible orientations of the carbonyl group, the following structures were located and optimized to their energy-minima.

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 4'''. Optimized geometries of conformers of 9.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat!! style="background: #0D4F8B; color: white;"| Boat
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_tboat1.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str9_boat2.cml</uploadedFileContents><text>View here</text>
</jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''77.35875''' || '''70.54037''' || '''76.30219''' || '''85.31047'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 8.09936 || 7.70190 || 7.95686 || 8.45651
|-
! Total Angle Bending Energy (kcal/mol)
| 31.48847 || 28.2951 || 29.77755 || 36.46909
|-
! Total Torsional Energy (kcal/mol)
| 1.3020 || 0.15583 || 2.55003 || 1.96577
|-
! Total Van der Waals Energy (kcal/mol)
| 36.05711 || 33.18713 || 34.65181 || 37.23578
|-
! Electrostatic (kcal/mol)
| 0.04448 || 0.30377 || 0.32294 || 0.23787
|-
! C1-C4 (Å)
| 3.899 || 3.087 || 3.086 || 3.889
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 162.7 || 8.9 || 8.3 || 162.7
|-
! C2-C3-C4 (°C)
| 128.0 || 124.4 || 124.5 || 129.2
|}
 

{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 5'''. Optimized geometries of conformers of 10.
! !! style="background: #0D4F8B; color: white;"| Chair 1!! style="background: #0D4F8B; color: white;"| Chair 2!! style="background: #0D4F8B; color: white;"| Twist Boat 1!! style="background: #0D4F8B; color: white;"| Twist Boat 2
|-
! '''Structure'''
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10chair2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat1.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
! scope="col" width="200"| <jmol><jmolAppletButton><uploadedFileContents>PB1611Opti_str10tboat2.cml</uploadedFileContents><text>View here</text></jmolAppletButton></jmol>
|-
! '''TOTAL ENERGY''' (kcal/mol)
| '''60.55464''' || '''74.97473''' || '''66.31086''' || '''68.87968'''
|-
! Total Bond Stretching Energy(kcal/mol)
| 7.58791 || 8.50447 || 7.74486 || 7.82959
|-
! Total Angle Bending Energy (kcal/mol)
| 18.79316 || 21.56068 || 19.07872 || 21.12109
|-
! Total Torsional Energy (kcal/mol)
| 0.19670 || 7.28263 || 3.65530 || 4.43732
|-
! Total Van der Waals Energy (kcal/mol)
| 33.32706 || 35.86507 || 35.07716 || 34.65108
|-
! Electrostatic (kcal/mol)
| -0.05540 || 0.40028 || -0.06953 || -0.04570
|-
! C1-C4 (Å)
| 3.091 || 3.162 || 3.104 || 3.121
|-
! Dihedral angle C1-C2-C3-C4 (°C)
| 12.4 || 22.1 || 13.5 || 14.3
|-
! C2-C3-C4 (°C)
| 123.6 || 124.9 || 123.9 || 124.5
|}
 

The tabulated results show that atropisomer '''10''' is in general more stable than '''9''', since almost all of its conformers lie lower in energy than those of '''9'''. The energy range across the conformers of '''10''' is 60.55 - 74.97 kcal/mol, while for '''9''' it is 70.54 - 85.31 kcal/mol. This observation can presumably be due to the stereoelectronic factors that do not favour the proximity of the carbonyl and the bridging isopropyl groups, which is the case in '''9'''. The most stable conformer of '''9''' is ''chair 2'', and ''chair 1'' for '''10'''. Both of these lowest energy conformers have cyclohexane in the chair conformation, which is expected due to the minimised torsional strain in the ring. However, lowest energy conformer of '''9''' is still margianlly higher in energy than that of '''10'''. ''Chair 1'' of '''10''' lies 9.99 kcal/mol lower in energy than ''Chair 2'' of '''9'''.

Molecular mechanics approach in computational modelling, again, allows us to have a closer look at the energy contributions from different parameters in order to examine the nature of the energy difference between the structures. Inspection of tables 4 and 5 shows that the major contribution to the observed energy difference of ~9.99 kcal/mol is due to the angle bending term, while the other parameters' contributions are fairly equal. The angle bending term in '''9''' raises its energy relative to '''10''' by ~9.5 kcal/mol. This accounts for 95% of the energy difference between the structures and will be examined further to see why this is the case.

{| class="wikitable floatcenter" style="text-align:center; margin-left: 265px" border="1"
!scope="col" width="250px"| ''Chair 2'' '''9'''
| scope="row" rowspan="2"|
!scope="col" width="250px"| ''Chair 1'' '''10'''
|-
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str9_chair2.cml</uploadedFileContents></jmolApplet></jmol>
|scope="col" width="250px"|<jmol><jmolApplet><title></title><color>white</color><size>250</size><script>select atomno="4"; color blue; measure 6 4 13</script><uploadedFileContents>PB1611Opti_str10chair1.cml</uploadedFileContents></jmolApplet></jmol>
|}
 

The angles in both structures were measure in Avogadro and the relevant angles are labelled in the structures above. In both structures, the angles labelled deviate from ideality (109.5°), however 123° in '''9''' is further away from the desired value than 118.2° in '''10'''. This effect accounts for the raised angle bending term relative to '''10'''.

Since ''Chair 2'' of '''10''' has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.
====9 and 10 as Hyperstable Olefins====
It has been reported<ref name="olefins"/> that the alkene structures '''9''' and '''10''' described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures '''9''' and '''10'''
exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.<ref name="olefins"/>

==Spectroscopic Simulation Using Quantum Mechanics==
===Spectroscopy of an Intermediate Related to the Synthesis of Taxol===
[[Image:PB16111718.png|300px|thumb|right]]
This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules '''17''' and '''18''' are under examination. These are the derivatives of previously discussed atropisomers '''9''' and '''10'''. By analogy to the situation above, where '''10''' was found to be energetically more stable than '''9''', this time '''18''' is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. '''18''' is a derivative of '''10''' with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.
{| class="wikitable floatcenter" style="text-align:center;" border="1"
|+ '''Table 6'''. Optimized geometries of 17 and 18.
! !! style="background: #0D4F8B; color: white;"| 17!! style="background: #0D4F8B; color: white;"| 18
|-
! '''Structure'''
!<jmol><jmolApplet><title>17</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
! <jmol><jmolApplet><title>18</title><color>white</color>
<size>250</size>1<uploadedFileContents>PB1611.cml</uploadedFileContents>
</jmolApplet></jmol>
|-
! Total Bond Stretching Energy(kcal/mol)
| 13.82478 || 14.58589
|-
! Total Angle Bending Energy (kcal/mol)
| 30.91985 || 28.76319
|-
! Total Torsional Energy (kcal/mol)
| 9.10099 || 7.74527
|-
! Total Van der Waals Energy (kcal/mol)
| 48.35898 || 49.16084
|-
! Electrostatic (kcal/mol)
| -1.08921 || -2.21691
|-
! '''Total Energy''' (kJ/mol)
| 429.218 || 416.391
|-
! '''Total Energy''' (kcal/mol)
| '''102.51694''' || '''99.45322'''
|}
 

As expected, structure '''18''' was found to be lower in energy, namely by ~3.06 kcal/mol. After the initial optimizations in Avogadro, the molecules were saved as GaussView input files to perform ab initio calculations on HPC. This calculation optimizes the structure with higher accuracy (B3LYP/6-31G(d,p) level of theory used) and produces the simulated proton and carbon NMR spectra.

===1H NMR Spectrum of 18===
Table 7 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
 
{| class="wikitable floatcenter"
|+ '''Table 7'''. 1H NMR of 18.
| scope="col" width="500px" scope="row" rowspan="25"| [[Image:PB1611H18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="230px" colspan="2" style="background: #0D4F8B; color: white;" | Experimental (300 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px"| Peak analysis
|-
| scope="col" width="115px"| 5.90
| scope="col" width="115px"| s, 1H
| scope="row" rowspan="2"| 5.21
| scope="row" rowspan="2"| m, 1H
|-
| 5.20
| s, 1H
|-
| 3.13
| s, 1H
| scope="row" rowspan="4" | 3.00-2.70
| scope="row" rowspan="4" | m, 6H
|-
| 3.07
| s, 1H
|-
| 2.89
| s, 1H
|-
| 2.79
| s, 1H
|-
| 2.57
| s, 1H
| scope="row" rowspan="2"| 2.70-2.35
| scope="row" rowspan="2"| m, 4H
|-
| 2.41
| s, 1H
|-
| 2.26
| s, 2H
| scope="row" rowspan="5"| 2.20-1.70
| scope="row" rowspan="5"| m, 6H
|-
| 2.18
| s, 1H
|-
| 1.99
| s, 2H
|-
| 1.84
| s, 3H
|-
| 1.66
| s, 1H
|-
| 1.56
| s, 2H
| 1.58
| t, 1H, ''J''=5.4 Hz
|-
| 1.48
| s, 2H
| scope="row" rowspan="3"| 1.50-1,20
| scope="row" rowspan="3"| m, 3H
|-
| 1.30
| s, 2H
|-
| 1.21
| s, 3H
|-
| 0.97
| s, 2H
| 1.10
| s, 3H
|-
| 0.91
| s, 1H
| 1.07
| s, 3H
|-
| 0.65
| s, 1H
| 1.03
| s, 3H
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| The following chart was produced to illustrate the correlations of experimental and computed ppm values.
|}

[[Image:PB1611Nmrchart1.jpg|700px|center]]

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:
*does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
*needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
*makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

===13C NMR of 18===
Table 8 presents the comparison of the [http://dx.doi.org/10042/28003 computed] and experimental<ref name="Paquette"/> proton NMR values recorded in deuterated benzene.
{| class="wikitable floatcenter"
|+ '''Table 8'''. 13C NMR of 18.
| scope="col" width="600px" scope="row" rowspan="25"| [[Image:PB1611C18nmr.svg|500px]]
| scope="row" rowspan="25" scope="col" width="40px" style="background: white; border:0px" |
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)
| scope="row" rowspan="25" scope="col" width="10px" style="background: white; border:0px"|
! scope="col" width="100px" style="background: #0D4F8B; color: white;" | Experimental (75 MHz, C6D6)
|-
! scope="col" width="115px" | δ (ppm)
! scope="col" width="115px" | δ (ppm)
|-
| style="text-align: center;" | 211.82
| style="text-align: center;" | 211.49
|-
| style="text-align: center;" | 147.28
| style="text-align: center;" | 148.72
|-
| style="text-align: center;" | 119.59
| style="text-align: center;" | 120.90
|-
| style="text-align: center;" | 69.07
| style="text-align: center;" | 74.61
|-
| style="text-align: center;" | 56.82
| style="text-align: center;" | 60.53
|-
| style="text-align: center;" | 55.20
| style="text-align: center;" scope="row" rowspan="2" | 51.30
|-
| style="text-align: center;" | 54.28
|-
| style="text-align: center;" | 53.56
| style="text-align: center;" | 50.94
|-
| style="text-align: center;" | 49.74
| style="text-align: center;" | 45.53
|-
| style="text-align: center;" | 45.27
| style="text-align: center;" | 43.28
|-
| style="text-align: center;" | 44.10
| style="text-align: center;" | 40.82
|-
| style="text-align: center;" | 41.27
| style="text-align: center;" | 38.73
|-
| style="text-align: center;" | 38.55
| style="text-align: center;" | 36.78
|-
| style="text-align: center;" | 33.71
| style="text-align: center;" | 35.47
|-
| style="text-align: center;" | 33.23
| style="text-align: center;" | 30.84
|-
| style="text-align: center;" | 28.50
| style="text-align: center;" | 30.00
|-
| style="text-align: center;" | 26.40
| style="text-align: center;" | 25.56
|-
| style="text-align: center;" | 26.07
| style="text-align: center;" | 25.35
|-
| style="text-align: center;" | 25.23
| style="text-align: center;" | 22.21
|-
| style="text-align: center;" | 22.47
| style="text-align: center;" | 21.39
|-
| style="text-align: center;" | 22.15
| style="text-align: center;" | 19.83
|}
 
{|
|- style="background:white; border: 0px white style="text-align:center;"
|scope="col" width="1050px"| Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.
|}

[[Image:PB1611Nmrchart2.jpg|700px|center]]

Analogous considerations go into understanding the reasons behind the deviations in chemical shift values. The greatest deviation from experiment is by 5.53 ppm, which represents the most deshielded carbon adjacent to sulphur atoms. Again, this error arises due to the required correction for the heavier element like sulphur, and raises the chemical shift value.

=PART 2: Analysis of the Properties of the Synthesised Alkene Epoxides=

=References=
<references>
<ref name="script"> H. Rzepa, 'Structure Modelling, NMR Simulation and Chirotropical Properties', ''3rd Year Synthesis Lab'', Department of Chemistry, Imperial College London, 2013.</ref>
<ref name="Clayden">J. Clayden, N. Greeves, S. Warren and P. Wothers, ''Organic Chemistry'', Oxford University Press, Oxford, 8th ed., 2009</ref>
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Rep:Mod:buikiwiki

2014-03-10T02:38:38Z

Pb1611: /* Comparisson of the Simulated and Experimental Spectroscopic Data */

Rep:Mod:buikiwiki

2014-03-10T02:34:51Z

Pb1611: /* 13C NMR of 18 */

Rep:Mod:buikiwiki

2014-03-10T02:25:25Z

Pb1611: /* 1H NMR Spectrum of 18 */

Rep:Mod:buikiwiki

2014-03-10T02:09:02Z

Pb1611: /* 13C NMR of 18 */