'''Experiment 1C: Advanced molecular modelling and assigning the absolute configuration of an epoxide.'''

All calculations for optimising geometry have been carried out on Avogadro with a force field of MMFF94s and algorithm conjugate gradient unless stated otherwise.
==Part 1==
==='''The Hydrogenation of Cyclopentadiene Dimer'''===

[[File:Cyclopentadiene reaction JN.JPG|350px|thumb|'''scheme 1''']]

Cyclopentadiene dimerises to form a preference of the endo product '''2'''. Molecule '''1''' and '''2''' were optimised and the results are displayed on Table 1.
{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| Table 1
|-
| molecule || Molecule 1 ||molecule 2
|-
|JMOL || <jmolFile text=molecule 1>Molecule 1 optimised jn.cml</jmolFile> || <jmolFile text=molecule2>Molecule 2 optimised jn.cml</jmolFile>
|-
| Total Bond Stretching Energy/ Kcalmol1 || 3.54300 || 3.46799
|-
| Total Angle Bending Energy/ Kcalmol1 || 30.77259 || 33.18857
|-
| Total Stretch Bending Energy/ Kcalmol1 || -2.04138 || -2.08221
|-
| Total out of Plane Bending Energy/ Kcalmol1 || 0.01477 || 0.02184
|-
| Total Torsional Energy/ Kcalmol1 || -2.73046|| -2.94987
|-
| Total Van der Waals Energy/ Kcalmol1 ||12.80124|| 12.35926
|-
| Total Electrostatic Energy/Kcalmol1 ||13.01367 || 14.18510
|-
| Total Energy/Kcalmol1 || 55.37342 || 58.19067
|-
| file ||[[File:Molecule 1 optimised jn.cml]] || [[File:Molecule 2 optimised jn.cml]]
|}

[[File:Exo endo mechanism JN.jpg|350px|right|thumb|Image of Mechanism (fig.1)]]

From Table 1, the most stable conformation is '''1''' (exo, thermodynamic), this suggests that the cycloaddition is under kinetic control, due to '''2''' (kinetic product) being formed. To understand the preference of '''2''' the mechanism of both products needs to be looked at. The cycloaddition proceeds via a [4+2] cycloaddition with a diene and dienophile.

Comparing the two TS#, '''2''' is lower in energy this is due to secondary orbital interactions figure 1.<ref name="clayden"></ref> as the “diene” has been angled at 60 degrees to have optimal bond overlap <ref name="orbital symmetry"></ref>. The interaction as seen in the image is between the HOMO of the diene and LUMO of dieneophile, whereas 1 has no extra stabilising features. As the endo conformer has a lower energy barrier it is formed first (kinetic). This reaction can be altered by heat and pressure to alter the preference for thermodynamic control.
 '''2''' can be hydrogenated to form '''3''' and '''4''' (fig.2) and after prolonged exposure to hydrogen can form the hydrogenated species.

[[File:Hydrogenation of 2 JN.JPG|350px|thumb| hydrogenation of 2 (fig.2)]]
[[File:Reaction scheme of hydrogenation of 2 JN.JPG|350px|thumb| scheme 2 (fig.3)]]

{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| Table 2
|-
| Molecule || Molecule 3 ||molecule 4
|-
|JMOL || <jmolFile text= molecule 3>Molecule 3 optimised jn.cml</jmolFile> || <jmolFile text= molecule 4> Molecule 4 optimised jn.cml</jmolFile>
|-
| Total Bond Stretching Energy/ Kcalmol1 ||3.30843 || 2.82312
|-
| Total Angle Bending Energy/ Kcalmol1 ||30.86217 || 24.68536
|-
| Total Stretch Bending Energy/ Kcalmol1 || -1.92666 || -1.65720
|-
| Total out of Plane Bending Energy/ Kcalmol1 ||0.01524 || 0.00028
|-
| Total Torsional Energy/ Kcalmol1 || 0.05968 || -0.37840
|-
| Total Van der Waals Energy/ Kcalmol1 || 13.28307 || 10.63732
|-
| Total Electrostatic Energy/Kcalmol1 || 5.12096 || 5.14702
|-
| Total Energy/Kcalmol1 || 50.72289 || 41.25749
|-
| File || [[File:Molecule 3 optimised jn.cml]] || [[File:Molecule 4 optimised jn.cml]]
|}

Table 2 shows that '''4''' is more stable than '''3''' indicating to hydrogenation occurring at the Norborene unit first (fig.3) as it is the thermodynamic product. This is due to the Norborene double bond being more reactive than cyclopentadiene as the double bond for Norborene= 1.34162 Å and cyclopentadiene= 1.33793 Å, furthermore population analysis conducted by Zou has shown that there is more charge density on the Nornborene centre <ref name="zou"></ref> therefore it is more susceptible to attack. The largest difference in energies between the two compounds is the bending ~10 kcal/mol as the norborene is more strained.

==='''Antropisomerism in an intermediate related to the synthesis of Taxol'''===
[[File:Reaction scheme for 9 and 10JN.JPG|350px|thumb|Scheme 3]]
Scheme 3 proceeds via an “atropselective anionic oxy-cope rearrangement” <ref name="Paq"></ref>which allows a ketone to have a double bond adjacent to a bridgehead <ref name="paq2"></ref> which have previously thought to be unstable.
{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| table 3
|-
| Molecule || Molecule '''9''' ||molecule'''10'''
|-
|JMOL|| <jmolFile text=molecule9>Molecule 9 optimised jn.cml</jmolFile> || <jmolFile text=molecule10>Molecule 10 optimised jn.cml</jmolFile>
|-
| Total Bond Stretching Energy || 7.62279 kcal/mol || 7.59461 kcal/mol
|-
| Total Angle Bending Energy || 28.30292 kcal/mol || 18.80546 kcal/mol
|-
| Total Stretch Bending Energy || -0.08556 kcal/mol || -0.14231 kcal/mol
|-
| Total out of Plane Bending Energy || 0.97378 kcal/mol ||0.84545 kcal/mol
|-
| Total Torsional Energy || 0.37699 kcal/mol || 0.23497 kcal/mol
|-
| Total Van der Waals Energy || 33.06715 kcal/mol || 33.26621 kcal/mol
|-
| Total Electrostatic Energy || 0.30731 kcal/mol || -0.05403 kcal/mol
|-
| Total Energy || 70.56538 kcal/mol || 60.55035 kcal/mol
|-
| File ||[[File:Molecule 9 optimised jn.cml]] || [[File:Molecule 10 optimised jn.cml]]
|}

The lowest energy structure is a chair conformation (cyclohexane) with hydrogen’s pointed away from the ring. The most stable conformation is '''10''' as there is no steric clashes with the carbonyl and cyclopropane group however this reaction is under kinetic control. As the reaction proceeds via an endo chair TS# forming '''9''' (fig.4) where the structure forms a intermediate like benzene structure and also allows for good orbital alignment and reduced double bonds<ref name="paq3"></ref>
[[File:TS molecule9 JN.jpg|350px|thumb| TS# 9 (fig .4)]]
 The twist boat for both <jmolFile text= 9>Molecule 9twistboat optimised jn.cml</jmolFile> and <jmolFile text=10>Molecule 10 twist boat optimised jn.cml</jmolFile> was also found the energy is 77.90285 Kcal/mol and 66.29687 Kcal/mol respectively.Due a significant increase in the torsional energy, this was as expected due to twist boat being unstable compared to chair. There should also be a twist chair and boat however these could not be optimised on Avogadro as they are energy maximum.[[File:Molecule 9twistboat optimised jn.cml]] [[File:Molecule 10twist boat optimised jn.cml]]

 
As previously mentioned bridgehead olefins have thought to be unstable due to steric strain. Olefinic Strain<ref name= "hyper"></ref> (OS) has been used to establish the stability of the double bond by comparing with the parent hydrocarbon.
 OS= olefin strain Energy (most stable conformer) – Parent hydrocarbon Strain Energy ( most stable conformer)
 <jmolFile text= parent_hydrocarbon_of_9 >Compound 9 hydrocarbon optimised.cml</jmolFile>
 <jmolFile text= parent_hydrocarbon_of_9>Molecule 10 hydrocarbon optimisedJN.cml</jmolFile>
{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| Table 4
|-
|[[File:Molecule 9 jn chemdraw.JPG|250px| thumb| Molecule 9]]|| [[File:Molecule 9 hydrocarbon JN.JPG|250px| thumb| Parent hydrocarbon of 9]]||[[File:Molecule 10 JN chemdraw.JPG|250px|thumb| Molecule 10]] || [[File:Molecule 10 hydrocarbon JN.JPG|250px| thumb| Parent hydrocarbon of 10]]
|-
|70.56538 kcal/mol || 79.88027 kcal/mol || 60.55035 kcal/mol|| 69.54682 kcal/mol
|-
|}
 The OS values are '''10'''=-8.99647 kcal/mol and '''9'''= -9.31489 Kcal/mol these results show that the alkene is more stable than the parent hydrocarbon group. These type of olefins have been named hyperstable olefin <ref name= "physical"></ref> as the OS vale is negative. This is due to the smaller bridging group (cyclopropane) being cis to the hydrogen to form a cage structure
<ref name="paq2"></ref> and greater strain from the parent hydrocarbon.

==='''Spectroscopic Simulation using Quantum Mechanics'''===

 As molecule 17 & 18 are derived from 9 & 10 their optimum geometry was easier to find through Avogadro.
[[File:Molecule 17-18 reaction JN.JPG|350px|thumb| Isomerisation of 17 (fig.5)]]

{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| add text
|-
| Molecule || Molecule 17 ||molecule 18
|-
|JMOL|| <jmolFile text=molecule17>Molecule 17 optimised jn.cml</jmolFile> || <jmolFile text=molecule18>Molecule_18_optimsed_jn.cml‎l</jmolFile>
|-
| Total Bond Stretching Energy || 15.55629 kcal/mol || 15.06218 kcal/mol
|-
| Total Angle Bending Energy || 32.46034 kcal/mol || 30.81050 kcal/mol
|-
| Total Stretch Bending Energy || 0.01692 kcal/mol || 0.61136 kcal/mol
|-
| Total out of Plane Bending Energy || 1.21094 kcal/mol || 0.90163 kcal/mol
|-
| Total Torsional Energy || 11.47903 kcal/mol || 9.74196 kcal/mol
|-
| Total Van der Waals Energy || 51.22577 kcal/mol || 49.43692 kcal/mol
|-
| Total Electrostatic Energy || -7.56054 Nkcal/mol || -6.11184 kcal/mol
|-
| Total Energy || 104.38876 kcal/mol || 100.45270 kcal/mol
|-
| File ||[[File:Molecule 17 optimised jn.cml]] || [[File:Molecule_18_optimsed_jn.cml]]
|}

From the table it is clear to molecule '''18''' is the lowest energy, as '''17''''s C=O is having unfavorable interactions with two methyl groups. This is similar to the observation of '''9''' and '''10''', using the MM2 mechanics on chem bio 3D molecule '''18'''= 64.3689 kcal/mol and molecule '''17'''= 75.3929 kcal/mol which matches to the value from literature <ref name="paq2"></ref>. As this reaction is under kinetic control (previously mentioned for '''10'''/'''9''') THF and heat are required to drive the equilibrium to '''18''', due to the restriction of the sigma bond due to an activation barrier (discussed later) therefore they are stable as separate isomers and can be analysed by NMR to differentiate.
 
The NMR of '''18''' was calculated {{DOI|10042/28212}}

'''HNMR'''
{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''literature'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''calculated'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''atom number'''
|-
| 5.21||1||m||5.97|||| 29
|-
| 3-2.7||5||m||3.15||||47
|-
| ||||||3.1||||44
|-
| ||||||2.96||||46
|-
| ||||||2.95||||32
|-
| ||||||2.89||||45
|-
| ||||||2.82||||33
|-
| ||||||2.76||||31
|-
| 2.7-2.35||4||m||2.67||||26
|-
| ||||||2.55||||25
|-
| ||||||2.53||||34
|-
| ||||||2.43||||38
|-
| 2.2-1.7||6||m||||||
|-
| ||||||2.3||||40
|-
| ||||||2||||27
|-
| ||||||1.96||||28
|-
| ||||||1.85||||39
|-
| ||||||1.81||||24
|-
| ||||||||
|-
| ||||||||
|-
| 1.58||1||t||1.57||||30
|-
| 1.5-1.2||3||m||||
|-
| ||||||1.5||||35
|-
| ||||||1.34||||37
|-
| ||||||1.4||average methyl
|-
| 1.1||3||s||1.21||||36
|-
| 1.07||3||s||1.266666667||average methyl ||
|-
| 1.03||3||s||1.133333333||average methyl ||
|}

[[File:Molecule 18 hnmr JN.jpg|350px| thumb| 1HNMR of Molecule 18 (fig.6) ]]

[[File:Molecule 18 Cnmr JN.jpg|350px| thumb| 13CNMR of Molecule 18 (fig.7) ]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''carbon NMR'''
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|
|-
| literature||||calculated||atom
|-
| 211.49||||211.92||8
|-
| 148.72||||147.87||3
|-
| 120.9||||120.13||6
|-
| 74.61||||92.84||15
|-
| 60.53||||65.93||10
|-
| 51.3||||54.93||5
|-
| 50.964||||54.76||11
|-
| 45.53||||49.53||4
|-
| 43.28||||48.04||14
|-
| 40.82||||45.65||20
|-
| 38.73||||44||19
|-
| 36.78||||41.47||12
|-
| 35.47||||38.51||7
|-
| 30.84||||33.7||16
|-
| 30||||32.47||9
|-
| 25.56||||28.6||2
|-
| 25.35||||26.5||23
|-
| 22.21||||24.45||1
|-
| 21.39||||24||13
|-
| 19.83||||22.58||22
|-
|
|}
[[File:Molecule 18 benzene atoms jn.jpg|350px|thumb| Molecule 18 labeled (fig. 8)]]

This calculation was carried out in Benzene to have comparable numbers with literature. At first glance the NMR has the hydrogen’s in similar environments (fig.6), though the shift have shifted to the right slightly as this is a static NMR and does not take into account movement of hydrogen’s. This is evident with the methyl groups especially as their motion is faster than the NMR timescale. The NMR is a good fit, and that the optimisation of the conformation is correct.

 
The C NMR should be more accurate as C rotation is restricted more, carbons involved in C=X bond fit extremely well. At first glance carbon single bond seems to be shifted especially with the Sulphur group attached (fig.7) <s>(explanation from literature)</s>.

Mean Average Error (MAE)<ref name= "MAE"></ref> was calculated MAE=(1/N)(Sum of |Scalc-SExp| )= 76.816/20= 3.840ppm

The calculated error is less than 5ppm again showing that the conformation was correctly optimised.

Comparing the free energies of '''17''' {{DOI|10042/28213}} and '''18''' the energy difference is -796.645023680292 KJ/mol this shows that there is a high activation barrier for the isomerisation. Agreeing that the two isomers are stable in the separate conformations.

== part 2 ==

===The crystal structures of the two catalysts===

'''Shi Catalyst''' <ref name= "shi"> </ref>
 Anomeric centres are found within the substructure of an O-C-O subunit (fig.9), where the alcohol group prefers the axial position due to the anomeric effect.
 [[File:Anomeric_effect_JN.jpg‎|350px| thumb| anomeric effect (fig.9)]]
[[File:Shi catalst image with labels JN.JPG|350px| left| thumb| Shi Catalyst Crystal Structure (fig.10)]]

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''ATOM'''
| align="center" style="background:#f0f0f0;"|'''BOND LENGTH/ Å'''
|-
| C2-O2||1.403
|-
| C2-O6||1.403
|-
| C7-O2||1.441
|-
| C7-01||1.413
|-
| C10-O5||1.409
|-
| C10-04||1.4393
|-
|C2-C1||1.510
|}
 The crystal structure (fig.10) shows that cyclohexane is in a chair conformation . The values of anomercic centres is presented in the table above, the two acetal groups have the anomeric and effect. This is evident as the average ether bond is 1.420 Å <ref name= "ester"></ref> and the adjacent C-O are longer and shorter this figure. Whereas for O6-C2-O2 the adjacent C-O bonds are exactly the same indicting to equal contribution also suggesting that the C2-O2 is equatorial to the ring also the C2-C1 is 1.51 Å the second longest C-C bond after C2-C1, indicating to a lengthening of the bond due to the anomeric effect.

 '''Jacobsen Catalyst'''<ref name= "jac"></ref>

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Jacobsen spacefill jn.mol</uploadedFileContents>
</jmolApplet></jmol>

[[File:Jacobsen spacefill JN.JPG|350px| right|thumb|Jacobsen Spacefill image (fig.11)]]

 The bulky tBu group protects the metal center in the planar region and helps to direct attack by small molecules Trans to the cl group (fig.11). The tBu groups also interact with adjacent unit cells that are close to enforce this protection.
 Cl forms a short interaction with 2 hydrogen's in another Mn complex which helps to stablise the structure to donate more electron density into the Mn centre.

=== The calculated NMR properties of your products and assigning the absolute configuration of the product ===
 The selected epoxides were optimised <jmolFile text=" R Styrene Oxide">(R)-(+)-Styrene oxide optimised.cml</jmolFile> , <jmolFile text=" S Styrene Oxide ">(S)Styrene oxide JNoptimised.cml</jmolFile> , <jmolFile text="(1R,2R)-(+)-1-Phenylpropylene oxide ">(1R,2R)-(+)-1-Phenylpropylene oxide JNoptimised.cml </jmolFile> and <jmolFile text="(1S,2S)-(-)-1-Phenylpropylene oxide ">(1S,2S)-(-)-1-Phenylpropylene oxide methyl styrene.cml </jmolFile>.
 
 Styrene Oxide
 The calculated 1HNMR and 13CNMR spectrum for the R ( {{DOI|10042/28236}} an S ( {{DOI|10042/27190}} conformation are identical (seen in the table below) as they have the same environments. There is no way to distinguish between the the two therefore optical rotation calculation is required to identify the two compounds.
 Fig. 12 shows the labelled atoms

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''R (HNMR)'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''S (HNMR)'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| literature <ref name= "HNMRstyrene"></ref>||calculated||atom||||calculated||atom
|-
| 7.4-7.3||7.515||14||||7.514||11
|-
| ||7.513||12||||7.513||14
|-
| ||7.483||10||||7.483||12
|-
| ||7.446||11||||7.446||13
|-
| ||7.3||13||||7.3||10
|-
| 3.83||3.66||15||||3.66||15
|-
| 3.12||3.11||16||||3.11||17
|-
| 2.77||2.53||17||||2.53||16
|-
|
|}
[[File:Styrene Oxide Labelled JN.jpg|350px|thumb| Styrene Oxide Atoms Labelled (fig. 12)
{|
|[[File:R styrene oxide HNMR JN.jpg|250px| thumb | R Styrene oxide HNMR]]
|[[File:R styrene oxide CNMR JN.jpg|250px| thumb| R Styrene Oxide CNMR]]
|[[File:S styrene oxide HNMR JN.jpg|250px| thumb| S Styrene oxide HNMR]]
|[[File:S styrene oxide CNMR JN.jpg|250px| thumb| S Styrene oxide CNMR]]
|}

{| class="wikitable" style="float:left; "
| align="center" style="background:#f0f0f0;"|'''literature CNMR styrene oxide''' <ref name= "nmrmethyl"></ref>
| align="center" style="background:#f0f0f0;"|'''calculated'''
| align="center" style="background:#f0f0f0;"|'''atom (R conformer)'''
|-
| 126||120.62||average of 4&6
|-
| 129||123.775||average of 3&5
|-
| 138.5||135.13||5
|-
| 128.7||122.95||2
|-
| 52.4||54.05||7
|-
| 51||53.45||8
|}

The HNMR matches closely with literature values and 1s experiment and the CNMR has a MAE= 3.97ppm showing that the structure has been optimised properly.

Trans β Methyl- Styrene Oxide
 Again the calculated NMR for the RR {{DOI|10042/28246}} and the SS {{DOI|10042/28247}} was identical.

{|
|[[File:Rmethyl styrene H nmr JN.jpg|250px|thumb| HNMR of (R,R)Methyl Strene Oxide]]
|[[File:Rmethyl styrene c nmr JN.jpg|250px|thumb| CNMR of (R,R)Methyl Strene Oxide]]
|[[File:Smethyl styrene H nmr JN.jpg|250px| thumb| HNMR of (S,S)Methyl Strene Oxide]]
|[[File:Smethyl styrene Cnmr JN.jpg| 250px|thumb| CNMR of (S,S)Methyl Strene Oxide]]
|}
[[File:Methyl styrene image JN.jpg| 250px| thumb| (1R,2R)-(+)(methyl styrene)]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''HNMR'''
| align="center" style="background:#f0f0f0;"|'''R Conformer'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| LITERATURE <ref name= "nmrmethyl"></ref>||CALCULATED||METHYL STYRENE OXIDE ATOM
|-
| 7.27||7.5||12
|-
| ||7.5||15
|-
| ||7.48||13
|-
| ||7.42||14
|-
| ||7.31||11
|-
| 3.55||3.41||16
|-
| 3.12||2.79||17
|-
| ||1.68||20
|-
| ||1.59||19
|-
| ||0.72||18
|-
| 1.43||1.33||19/18/20 average
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''CNMR'''
| align="center" style="background:#f0f0f0;"|'''R conformer'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| LITERATURE <ref name= "nmrmethyl"></ref>||CALCULATED||METHYL STYRENE OXIDE ATOM
|-
| 137.7||134.975||2
|-
| 128.3||124.072||6
|-
| 59.4||62.3201||8
|-
| 58.9||60.5757||7
|-
| 17.8||18.8375||10
|-
| 125.4||120.6415||average of 1/3
|-
| 127.9||123.0275||average of 5/ 4
|-
|
|}

Again an average for the Methyl group had to be taken (discussed earlier) and the NMR matches up well as it is a small molecule. Furthermore for the C NMR an average of the phenyl ring had to be taken as literature 13CNMR could not distinguish between 1/3 and 5/4 because of the rotation of C2-C7. The MAE= 3.17ppm which is smaller than molecule '''18''' possibly due to the being less heteroatoms n the centre and it is smaller therefore less chance error for optimising the structure.

---
Optical Rotation

The table below shows the optical rotation of the the epoxides
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Conformation'''
| align="center" style="background:#f0f0f0;"|'''Literature optical Rotation'''
| align="center" style="background:#f0f0f0;"|'''Calculated Optical Rotation'''
|-
| R Styrene Oxide||-24 <ref name= "d"></ref>||-30.12
|-
| S Styrene Oxide||+34.3 <ref name= "e"></ref>||+30.11
|-
| R,R Methyl Styrene Oxide ||+46 <ref name= "g"></ref> ||+46
|-
| s,s Methyl Styrene Oxide ||-46.9 <ref name= "f"></ref>||-46.9
|-
|
|}

The calculations were carried out in the solvent chloroform, as expected the optical rotations for the conformers are the opposite signs indicating to a correct calculation. For Methyl Styrene Oxide the values match to the literature whereas for Styrene Oxide there is deviations. However comparing literature values on Reaxys there is a wide rang of optical rotation reported due to varying concentrations and Gaussian does not give information on the concentration and I have presumed that the temperature is 298.15k. There is a wide range for Styrene Oxide again possibly due to gaussian having a 100% of the enatiomer whereas literature reaction may not have a 100% of ee.
---

===Transition States===

Using the calculated transition states provided by Rzepa (and any images of TS or JMOL were provided by [[Mod:organic#Using the (calculated) properties of transition state for the reaction (β-methyl styrene only)|Rzepa]]) the enatiomeric excess of the epoxides can be calculated. This is done by finding delta G betwwen the most stable R and S conformer. As <math>\Delta_r G^\circ = -R T \ln K \,</math>
 were R= Gas Constant, T= Temperature (298.15k) K= Equilibrium Constant
 <math>K=\frac{[product]} {[reactant]}</math>, instead of concentration mole fractions has been used where x= mole fraction of reactant and y= mole fraction of product. Therefore<math>\ Enatiomeric\ Excess= 100(y-x)</math> for the most stable transition state.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Epoxide'''
| align="center" style="background:#f0f0f0;"|'''Catalyst'''
| align="center" style="background:#f0f0f0;"|'''stable conformer'''
| align="center" style="background:#f0f0f0;"|'''delta G/ JmolK'''
| align="center" style="background:#f0f0f0;"|'''K'''
| align="center" style="background:#f0f0f0;"|'''ee'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| Styrene Oxide||Shi||S||-1205||1.626||23.84%||
|-
| Styrene Oxide||Jacobsen||S||-18470||1721||99.88%|| 48 <ref name= "a"></ref>
|-
| Trans B Methyl Styrene Oxide||Shi||RR||-20219||3485||99.99%|| 98 <ref name= "b"></ref>
|-
| Trans B Methyl Styrene Oxide||Jacobsen||SS||-21364||5530||99.96%|| 92 <ref name= "c"></ref>
|-
|
|}
 

All the catalysts attack the the alkene on the less substituted carbon.
 Trans β methyl Styrene Oxide
 '''Shi catalyst:''' The most stable conformer is the <jmolFile text="RR">R,R series TS methyl stryrene SHI JN.mol</jmolFile> conformer as the cyclohexane unit is in a chair and has more positive interactions ( discussed in [[Mod:jyn111cnjg#NCI|NCI]] and [[Mod:jyn111cnjg#QTAIM|QTAIM]] ) Compared to the most stable SS conformer ,<jmolFile text="SS">S,S series methyl styrene TS JN.mol</jmolFile> TS# has a methyl directly over a benzene group and a acetal group eclipsed over the ‘alkene ‘ unit which is unfavourable interactions. The RR series has the shi catalyst attacking on the Re face.
 '''Jacobsen catalyst:''' The stable conformer is the <jmolFile text="SS">S,S series Jacobsen Methyl styrene Jn.mol</jmolFile> where the metallic double bond is attacking the Si face. This is a favorable for SS as the two benzene rings can interact with each other, whereas the <jmolFile text="RR">S,S series Jacobsen Methyl styrene Jn.mol</jmolFile> has the two benzenes 'ring' slipped therefore the forming bond cannot be stablised by the ring current.

Styrene Oxide '''Shi Catalyst:''' The stable conformer is the <jmolFile text="S">S (styrene oxide TS SHI Jn.mol</jmolFile>, however as the reacting carbon has no chiral centre it is difficult to establish which face of the alkene is being attacked. Also as there is no interactions to 'lock' the phenyl ring, this helps to explain why the ee is low. The <jmolFile text="R">R Shi styren oxide TS JN.mol</jmolFile> c<s>onformer is less stable as</s> .
 '''Jacobsen Catalyst:''' Again the the <jmolFile text="S">Sstyrene jacobsen ts JN.mol</jmolFile> conformer is the most stable conformation and has a greater enatiomeric excess compared to the Shi catalstyst this is due to the Ph groups having a stablising interaction compared to the <jmolFile text="R seriers">R styrene oxide jacoobsen ts JN.mol</jmolFile> (again because of ring slipage). This positive interactions between the rings helps to lock the Ph on the alkene in place allowing for a higher ee compared to Shi.

----
Calculated Transition States, (Appendix)
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Shi Catalys'''
| align="center" style="background:#f0f0f0;"|'''Styrene Oxide'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| TS ||R Conformer/ kJ/mol||S Conformer KJ/mol
|-
| 1||-818103.5424||-818105.5034
|-
| 2||-818103.2506||-818099.4479
|-
| 3||-818107.3765||-818101.6411
|-
| 4||-818108.149||-818108.437
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Jacobsen Catalyst'''
| align="center" style="background:#f0f0f0;"|'''Styrene Oxide'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| TS ||R Conformer/ kJ/mol||S Conformer KJ/mol
|-
| 1||-8779569.983||-8779591.796
|-
| 2||-8779573.325||-8779576.027
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Shi Catalyst'''
| align="center" style="background:#f0f0f0;"|'''Trans Bmethyl Styrene Oxide'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| TS||RR Conformer / KJ/mol||SS Conformer/Kjmol
|-
| 1||-3526107.076||-3526093.875
|-
| 2||-3526097.265||-3526087.734
|-
| 3||-3526123.622||-3526109.166
|-
| 4||-3526131.948||-3526111.729
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Jacobsen Catalyst'''
| align="center" style="background:#f0f0f0;"|'''Trans Bmethyl Styrene Oxide'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| TS||RR Conformer / KJ/mol||SS Conformer/Kjmol
|-
| 1||-8882733.571||-8882756.321
|-
| 2||-8882734.957||-8882744.154
|-
|
|}
----

===NCI===

NCI

The NCI was calculated for the most stable TS# for the Shi epoxidation for Trans methyl styrene. The jmol below shows the interactions between the two molecules; from the image all the interactions between the two are interactive which is expected as it is the most stable. It suggests that there is a hydrogen bond interaction with the acetal group and CH bond in the alkene. Furthermore there is an electrostatic attraction between a hydrogen and benzene. The only repulsive interactions are within the individual molecules themselves.

<jmol>
<jmolApplet>
<title>NCI</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0b/R%2CR_methyl_styrene_fineJmol.jvxl" translucent;</script>
<uploadedFileContents>R,R TRANS B methyl styrene fine.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>

===QTAIM===

The TS# of the Shi epoxidation for Trans methyl styrene was investigated further by QTAIM on Avogadro 2 to visualise which atoms are involved in the interactions established by NCI. The QTAIM (seen in the image below) show a hydrogen bond interaction between the acetal (the longer c-o bond) and two hydrogen’s which helps maintain the “trans” structure of the forming alkane. Furthermore these hydrogen’s also have a van der waals interaction with a methyl group. There is no interaction within the benzene group which makes this TS# favourable as there is no disruption to the aromatic structure. This calculation also shows the formation of the epoxide bond, where it attacks the less hindered face, as the only electron density for the C and O bond is located in the middle of the two. Whilst the electron density in the C=C is being withdrawn by the phenyl group indicating to a lengthening of the bond. Also the other dioxoarane oxygen is interacting with a methyl group away from the reaction centre.

[[File:QTAIM of TS JN.PNG|350px|thumb| QTAIM of Transition states for Shi epoxidation of trans-β-methyl styrene (R,R Series)]]

===Suggesting new candidates for investigations ===

[[File:Suggested alkene JN.jpg|350px|thumb| Suggested alkene]]
 The epoxide found through Reaxys is 2-((2R,3R)-3-phenyloxiran-2-yl)pyridine this is an interesting epoxide to study as there is only two optical rotation data and they are varied due to the solvent used. Also it has a bulkier substituent compared to Trans β Methyl Styrene Oxide therefore there should be more of an effect of using the catalysts.
 Furthermore the alkene 2-Stilbazole has an extra aromatic group this would be interesting to see how the TS# of the alkene interacts with the Jacobsen's 2 aromatic rings. Hopefully there should be more positive interactions as the N group should be able to donate electrons to stablise the TS# and lock the conformer in place. The alkene can be bought from Sigma Aldrich for £44.30 for 50MG as this is expensive for labs to have enough product to anaylse therefore computational analysis is useful for researches or industry to ascertain if a reaction will be successful.

=='''References'''==
<references>
<ref name="clayden">J.Clayden; N.Greeves; S.Warren; P.Wothers,Organic Chemistry, Oxford University Press, 2001.(1st ed.) </ref>

<ref name="orbital symmetry"> T. L. Gilchrist; R. C. Storr, Organic Reactions and Orbital Symmetry, Cambridge University Press, 1979, (2nd ed.) </ref>

<ref name="zou">J.Zou; X.Zhang, J.Kong; L.Wang, Fuel, 2008, '''87''', 3655-3659 {{DOI|10.1016/j.fuel.2008.07.006}} </ref>

<ref name= " Paq"> S. W. Elmore and L. Paquette, Tetrahedron Lett, 1991, 319,'''3''', 319–322 </ref>

<ref name="paq2"> L. Paquette, Angew Chem Int Ed engl,1990 '''29''', 609-620 </ref>

<ref name="paq3"> L.Paquette, N.Pegg, D.Toops, G.Maynard, and R.Rogers J.Am.Chem.Soc., 1990, 112, '''1''', 277-283 </ref>
<ref name= "hyper"> W. F. Maier, P. Von Rague Schleyer, J. Am. Chem. Soc., 1981, 103, 1891 </ref>
<ref name= "physical"> E.Anslyn and D.Dougherty,modern physical organic chemistry, University Science Books, 2006, 139 </ref>
<ref name= "MAE"> S.Smith and J.Goodman, J.org.chem. 2009,'''74''' 12, 4597-4607</ref>
<ref name= "jac"> J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin, Acta Cryst, 1999, '''C55''', 1766-1769 </ref>
<ref name= "shi"> M. Durík, V. Langer, D. Gyepesová, J. Micová, B. Steiner and M. Koós, Acta Cryst. 2001. '''E57''', o672-o674 </ref>
<ref name= "ester"> G.Glockler J. Phys.Chem 1958, 62, '''9''', 1049-1052 </ref>
<ref name= "nmrmethyl"> H.Hachiyaa, Y.Kon*a, Y.Onoa, K.Takumib, N.Sasagawab, Y.Ezakib, K.Sato* a Synthesis 2012, 44 '''11''', 1672-1678 </ref>
<ref name= "HNMRstyrene"> C.Siang; L.Aitao; L.Zhi; W.Shuke; L.Zhi; W.Shuke ACS Catalysis, 2013 , vol. 3, '''4''' ,752 - 759 </ref>
<ref name= "a"> J. Hanson; J. Chem. Educ., 2001, 78, '''9''', 1266 </ref>
<ref name= "b"> Y.Shi; US Patent: US6348608 B1, 2002 </ref>
<ref name= "c">F. Minutolo, D.Pini, P.Salvadori; Tetrahedron Lett., 1996, 37, 3376 </ref>
<ref name= "d"> Bettigeri, Sampada V.; Forbes, David C.; Patrawala, Samit A.; Pischek, Susanna C.; Standen, Michael C.
Tetrahedron, 2009 , 65, '''1''' 70 - 76</ref>
<ref name= "e"> McKinstry, Lydia; Myers, Andrew G. JOC, 1996 , vol. 61, '''7 ''' 2428 - 2440 </ref>
<ref name= "f"> Shi, Yian Patent: US6348608 B1, 2002 </ref>
<ref name= "g"> Besse; Renard; Veschambre Tetrahedron Asymmetry, 1994 , vol. 5, '''7''' 1249 - 1268</ref>
</references>

INITIALS. Author’s surname, Title, Publisher, Place of publication, Edition (if not the first), Year, Pages.

journal

INITIALS. Author’s surname, Title of journal (abbreviated), Year, Volume number, Pages.
books
INITIALS. Author’s surname, Title, Publisher, Place of publication, Edition (if not the first), Year, Pages.

journal

INITIALS. Author’s surname, Title of journal (abbreviated), Year, Volume number, Pages.

File:Suggested alkene JN.jpg

2014-03-21T21:03:39Z

Jyn111:

Rep:Mod:jyn111cnjg

2014-03-21T20:02:59Z

Jyn111: /* The crystal structures of the two catalysts */

'''Experiment 1C: Advanced molecular modelling and assigning the absolute configuration of an epoxide.'''

All calculations for optimising geometry have been carried out on Avogadro with a force field of MMFF94s and algorithm conjugate gradient unless stated otherwise.
==Part 1==
==='''The Hydrogenation of Cyclopentadiene Dimer'''===

[[File:Cyclopentadiene reaction JN.JPG|350px|thumb|'''scheme 1''']]

Cyclopentadiene dimerises to form a preference of the endo product '''2'''. Molecule '''1''' and '''2''' were optimised and the results are displayed on Table 1.
{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| Table 1
|-
| molecule || Molecule 1 ||molecule 2
|-
|JMOL || <jmolFile text=molecule 1>Molecule 1 optimised jn.cml</jmolFile> || <jmolFile text=molecule2>Molecule 2 optimised jn.cml</jmolFile>
|-
| Total Bond Stretching Energy/ Kcalmol1 || 3.54300 || 3.46799
|-
| Total Angle Bending Energy/ Kcalmol1 || 30.77259 || 33.18857
|-
| Total Stretch Bending Energy/ Kcalmol1 || -2.04138 || -2.08221
|-
| Total out of Plane Bending Energy/ Kcalmol1 || 0.01477 || 0.02184
|-
| Total Torsional Energy/ Kcalmol1 || -2.73046|| -2.94987
|-
| Total Van der Waals Energy/ Kcalmol1 ||12.80124|| 12.35926
|-
| Total Electrostatic Energy/Kcalmol1 ||13.01367 || 14.18510
|-
| Total Energy/Kcalmol1 || 55.37342 || 58.19067
|-
| file ||[[File:Molecule 1 optimised jn.cml]] || [[File:Molecule 2 optimised jn.cml]]
|}

[[File:Exo endo mechanism JN.jpg|350px|right|thumb|Image of Mechanism (fig.1)]]

From Table 1, the most stable conformation is '''1''' (exo, thermodynamic), this suggests that the cycloaddition is under kinetic control, due to '''2''' (kinetic product) being formed. To understand the preference of '''2''' the mechanism of both products needs to be looked at. The cycloaddition proceeds via a [4+2] cycloaddition with a diene and dienophile.

Comparing the two TS#, '''2''' is lower in energy this is due to secondary orbital interactions figure 1.<ref name="clayden"></ref> as the “diene” has been angled at 60 degrees to have optimal bond overlap <ref name="orbital symmetry"></ref>. The interaction as seen in the image is between the HOMO of the diene and LUMO of dieneophile, whereas 1 has no extra stabilising features. As the endo conformer has a lower energy barrier it is formed first (kinetic). This reaction can be altered by heat and pressure to alter the preference for thermodynamic control.
 '''2''' can be hydrogenated to form '''3''' and '''4''' (fig.2) and after prolonged exposure to hydrogen can form the hydrogenated species.

[[File:Hydrogenation of 2 JN.JPG|350px|thumb| hydrogenation of 2 (fig.2)]]
[[File:Reaction scheme of hydrogenation of 2 JN.JPG|350px|thumb| scheme 2 (fig.3)]]

{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| Table 2
|-
| Molecule || Molecule 3 ||molecule 4
|-
|JMOL || <jmolFile text= molecule 3>Molecule 3 optimised jn.cml</jmolFile> || <jmolFile text= molecule 4> Molecule 4 optimised jn.cml</jmolFile>
|-
| Total Bond Stretching Energy/ Kcalmol1 ||3.30843 || 2.82312
|-
| Total Angle Bending Energy/ Kcalmol1 ||30.86217 || 24.68536
|-
| Total Stretch Bending Energy/ Kcalmol1 || -1.92666 || -1.65720
|-
| Total out of Plane Bending Energy/ Kcalmol1 ||0.01524 || 0.00028
|-
| Total Torsional Energy/ Kcalmol1 || 0.05968 || -0.37840
|-
| Total Van der Waals Energy/ Kcalmol1 || 13.28307 || 10.63732
|-
| Total Electrostatic Energy/Kcalmol1 || 5.12096 || 5.14702
|-
| Total Energy/Kcalmol1 || 50.72289 || 41.25749
|-
| File || [[File:Molecule 3 optimised jn.cml]] || [[File:Molecule 4 optimised jn.cml]]
|}

Table 2 shows that '''4''' is more stable than '''3''' indicating to hydrogenation occurring at the Norborene unit first (fig.3) as it is the thermodynamic product. This is due to the Norborene double bond being more reactive than cyclopentadiene as the double bond for Norborene= 1.34162 Å and cyclopentadiene= 1.33793 Å, furthermore population analysis conducted by Zou has shown that there is more charge density on the Nornborene centre <ref name="zou"></ref> therefore it is more susceptible to attack. The largest difference in energies between the two compounds is the bending ~10 kcal/mol as the norborene is more strained.

==='''Antropisomerism in an intermediate related to the synthesis of Taxol'''===
[[File:Reaction scheme for 9 and 10JN.JPG|350px|thumb|Scheme 3]]
Scheme 3 proceeds via an “atropselective anionic oxy-cope rearrangement” <ref name="Paq"></ref>which allows a ketone to have a double bond adjacent to a bridgehead <ref name="paq2"></ref> which have previously thought to be unstable.
{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| table 3
|-
| Molecule || Molecule '''9''' ||molecule'''10'''
|-
|JMOL|| <jmolFile text=molecule9>Molecule 9 optimised jn.cml</jmolFile> || <jmolFile text=molecule10>Molecule 10 optimised jn.cml</jmolFile>
|-
| Total Bond Stretching Energy || 7.62279 kcal/mol || 7.59461 kcal/mol
|-
| Total Angle Bending Energy || 28.30292 kcal/mol || 18.80546 kcal/mol
|-
| Total Stretch Bending Energy || -0.08556 kcal/mol || -0.14231 kcal/mol
|-
| Total out of Plane Bending Energy || 0.97378 kcal/mol ||0.84545 kcal/mol
|-
| Total Torsional Energy || 0.37699 kcal/mol || 0.23497 kcal/mol
|-
| Total Van der Waals Energy || 33.06715 kcal/mol || 33.26621 kcal/mol
|-
| Total Electrostatic Energy || 0.30731 kcal/mol || -0.05403 kcal/mol
|-
| Total Energy || 70.56538 kcal/mol || 60.55035 kcal/mol
|-
| File ||[[File:Molecule 9 optimised jn.cml]] || [[File:Molecule 10 optimised jn.cml]]
|}

The lowest energy structure is a chair conformation (cyclohexane) with hydrogen’s pointed away from the ring. The most stable conformation is '''10''' as there is no steric clashes with the carbonyl and cyclopropane group however this reaction is under kinetic control. As the reaction proceeds via an endo chair TS# forming '''9''' (fig.4) where the structure forms a intermediate like benzene structure and also allows for good orbital alignment and reduced double bonds<ref name="paq3"></ref>
[[File:TS molecule9 JN.jpg|350px|thumb| TS# 9 (fig .4)]]
 The twist boat for both <jmolFile text= 9>Molecule 9twistboat optimised jn.cml</jmolFile> and <jmolFile text=10>Molecule 10 twist boat optimised jn.cml</jmolFile> was also found the energy is 77.90285 Kcal/mol and 66.29687 Kcal/mol respectively.Due a significant increase in the torsional energy, this was as expected due to twist boat being unstable compared to chair. There should also be a twist chair and boat however these could not be optimised on Avogadro as they are energy maximum.[[File:Molecule 9twistboat optimised jn.cml]] [[File:Molecule 10twist boat optimised jn.cml]]

 
As previously mentioned bridgehead olefins have thought to be unstable due to steric strain. Olefinic Strain<ref name= "hyper"></ref> (OS) has been used to establish the stability of the double bond by comparing with the parent hydrocarbon.
 OS= olefin strain Energy (most stable conformer) – Parent hydrocarbon Strain Energy ( most stable conformer)
 <jmolFile text= parent_hydrocarbon_of_9 >Compound 9 hydrocarbon optimised.cml</jmolFile>
 <jmolFile text= parent_hydrocarbon_of_9>Molecule 10 hydrocarbon optimisedJN.cml</jmolFile>
{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| Table 4
|-
|[[File:Molecule 9 jn chemdraw.JPG|250px| thumb| Molecule 9]]|| [[File:Molecule 9 hydrocarbon JN.JPG|250px| thumb| Parent hydrocarbon of 9]]||[[File:Molecule 10 JN chemdraw.JPG|250px|thumb| Molecule 10]] || [[File:Molecule 10 hydrocarbon JN.JPG|250px| thumb| Parent hydrocarbon of 10]]
|-
|70.56538 kcal/mol || 79.88027 kcal/mol || 60.55035 kcal/mol|| 69.54682 kcal/mol
|-
|}
 The OS values are '''10'''=-8.99647 kcal/mol and '''9'''= -9.31489 Kcal/mol these results show that the alkene is more stable than the parent hydrocarbon group. These type of olefins have been named hyperstable olefin <ref name= "physical"></ref> as the OS vale is negative. This is due to the smaller bridging group (cyclopropane) being cis to the hydrogen to form a cage structure
<ref name="paq2"></ref> and greater strain from the parent hydrocarbon.

==='''Spectroscopic Simulation using Quantum Mechanics'''===

 As molecule 17 & 18 are derived from 9 & 10 their optimum geometry was easier to find through Avogadro.
[[File:Molecule 17-18 reaction JN.JPG|350px|thumb| Isomerisation of 17 (fig.5)]]

{| class="wikitable" border="1"
|+ Avogadro Calculation Summary
! scope="col" colspan="10"| add text
|-
| Molecule || Molecule 17 ||molecule 18
|-
|JMOL|| <jmolFile text=molecule17>Molecule 17 optimised jn.cml</jmolFile> || <jmolFile text=molecule18>Molecule_18_optimsed_jn.cml‎l</jmolFile>
|-
| Total Bond Stretching Energy || 15.55629 kcal/mol || 15.06218 kcal/mol
|-
| Total Angle Bending Energy || 32.46034 kcal/mol || 30.81050 kcal/mol
|-
| Total Stretch Bending Energy || 0.01692 kcal/mol || 0.61136 kcal/mol
|-
| Total out of Plane Bending Energy || 1.21094 kcal/mol || 0.90163 kcal/mol
|-
| Total Torsional Energy || 11.47903 kcal/mol || 9.74196 kcal/mol
|-
| Total Van der Waals Energy || 51.22577 kcal/mol || 49.43692 kcal/mol
|-
| Total Electrostatic Energy || -7.56054 Nkcal/mol || -6.11184 kcal/mol
|-
| Total Energy || 104.38876 kcal/mol || 100.45270 kcal/mol
|-
| File ||[[File:Molecule 17 optimised jn.cml]] || [[File:Molecule_18_optimsed_jn.cml]]
|}

From the table it is clear to molecule '''18''' is the lowest energy, as '''17''''s C=O is having unfavorable interactions with two methyl groups. This is similar to the observation of '''9''' and '''10''', using the MM2 mechanics on chem bio 3D molecule '''18'''= 64.3689 kcal/mol and molecule '''17'''= 75.3929 kcal/mol which matches to the value from literature [ref: J.Am.Chem.Soc.Vol.112 No 1 1990]. As this reaction is under kinetic control (previously mentioned for '''10'''/'''9''') THF and heat are required to drive the equilibrium to '''18''', due to the restriction of the sigma bond due to an activation barrier (discussed later) therefore they are stable as separate isomers and can be analysed by NMR to differentiate.
 
The NMR of '''18''' was calculated {{DOI|10042/28212}}

'''HNMR'''
{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''literature'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''calculated'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''atom number'''
|-
| 5.21||1||m||5.97|||| 29
|-
| 3-2.7||5||m||3.15||||47
|-
| ||||||3.1||||44
|-
| ||||||2.96||||46
|-
| ||||||2.95||||32
|-
| ||||||2.89||||45
|-
| ||||||2.82||||33
|-
| ||||||2.76||||31
|-
| 2.7-2.35||4||m||2.67||||26
|-
| ||||||2.55||||25
|-
| ||||||2.53||||34
|-
| ||||||2.43||||38
|-
| 2.2-1.7||6||m||||||
|-
| ||||||2.3||||40
|-
| ||||||2||||27
|-
| ||||||1.96||||28
|-
| ||||||1.85||||39
|-
| ||||||1.81||||24
|-
| ||||||||
|-
| ||||||||
|-
| 1.58||1||t||1.57||||30
|-
| 1.5-1.2||3||m||||
|-
| ||||||1.5||||35
|-
| ||||||1.34||||37
|-
| ||||||1.4||average methyl
|-
| 1.1||3||s||1.21||||36
|-
| 1.07||3||s||1.266666667||average methyl ||
|-
| 1.03||3||s||1.133333333||average methyl ||
|}

[[File:Molecule 18 hnmr JN.jpg|350px| thumb| 1HNMR of Molecule 18 (fig.6) ]]

[[File:Molecule 18 Cnmr JN.jpg|350px| thumb| 13CNMR of Molecule 18 (fig.7) ]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''carbon NMR'''
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|
|-
| literature||||calculated||atom
|-
| 211.49||||211.92||8
|-
| 148.72||||147.87||3
|-
| 120.9||||120.13||6
|-
| 74.61||||92.84||15
|-
| 60.53||||65.93||10
|-
| 51.3||||54.93||5
|-
| 50.964||||54.76||11
|-
| 45.53||||49.53||4
|-
| 43.28||||48.04||14
|-
| 40.82||||45.65||20
|-
| 38.73||||44||19
|-
| 36.78||||41.47||12
|-
| 35.47||||38.51||7
|-
| 30.84||||33.7||16
|-
| 30||||32.47||9
|-
| 25.56||||28.6||2
|-
| 25.35||||26.5||23
|-
| 22.21||||24.45||1
|-
| 21.39||||24||13
|-
| 19.83||||22.58||22
|-
|
|}
[[File:Molecule 18 benzene atoms jn.jpg|350px|thumb| Molecule 18 labeled (fig. 8)]]

This calculation was carried out in Benzene to have comparable numbers with literature. At first glance the NMR has the hydrogen’s in similar environments (fig.6), though the shift have shifted to the right slightly as this is a static NMR and does not take into account movement of hydrogen’s. This is evident with the methyl groups especially as their motion is faster than the NMR timescale. The NMR is a good fit, and that the optimisation of the conformation is correct.

 
The C NMR should be more accurate as C rotation is restricted more, carbons involved in C=X bond fit extremely well. At first glance carbon single bond seems to be shifted especially with the Sulphur group attached (fig.7) <s>(explanation from literature)</s>.

Mean Average Error (MAE)<ref name= "MAE"></ref> was calculated MAE=(1/N)(Sum of |Scalc-SExp| )= 76.816/20= 3.840ppm

The calculated error is less than 5ppm again showing that the conformation was correctly optimised.

Comparing the free energies of '''17''' {{DOI|10042/28213}} and '''18''' the energy difference is -796.645023680292 KJ/mol this shows that there is a high activation barrier for the isomerisation. Agreeing that the two isomers are stable in the separate conformations.

== part 2 ==

===The crystal structures of the two catalysts===

'''Shi Catalyst''' <ref name= "shi"> </ref>
 Anomeric centres are found within the substructure of an O-C-O subunit (fig.9), where the alcohol group prefers the axial position due to the anomeric effect.
 [[File:Anomeric_effect_JN.jpg‎|350px| thumb| anomeric effect (fig.9)]]
[[File:Shi catalst image with labels JN.JPG|350px| left| thumb| Shi Catalyst Crystal Structure (fig.10)]]

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''ATOM'''
| align="center" style="background:#f0f0f0;"|'''BOND LENGTH/ Å'''
|-
| C2-O2||1.403
|-
| C2-O6||1.403
|-
| C7-O2||1.441
|-
| C7-01||1.413
|-
| C10-O5||1.409
|-
| C10-04||1.4393
|-
|C2-C1||1.510
|}
 The crystal structure (fig.10) shows that cyclohexane is in a chair conformation . The values of anomercic centres is presented in the table above, the two acetal groups have the anomeric and effect. This is evident as the average ether bond is 1.420 Å [ ref: J. Phys.Chem 1958, 62 (9) pp 1049 -1052] and the adjacent C-O are longer and shorter this figure. Whereas for O6-C2-O2 the adjacent C-O bonds are exactly the same indicting to equal contribution also suggesting that the C2-O2 is equatorial to the ring also the C2-C1 is 1.51 Å the second longest C-C bond after C2-C1, indicating to a lengthening of the bond due to the anomeric effect.

 '''Jacobsen Catalyst'''<ref name= "jac"></ref>

<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>250</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Jacobsen spacefill jn.mol</uploadedFileContents>
</jmolApplet></jmol>

[[File:Jacobsen spacefill JN.JPG|350px| right|thumb|Jacobsen Spacefill image (fig.11)]]

 The bulky tBu group protects the metal center in the planar region and helps to direct attack by small molecules Trans to the cl group (fig.11). The tBu groups also interact with adjacent unit cells that are close to enforce this protection.
 Cl forms a short interaction with 2 hydrogen's in another Mn complex which helps to stablise the structure to donate more electron density into the Mn centre.

CRYSTAL STRUCTUREof shi catalyst [ doi:10.1|07/S160053680101073X ]

CRYSTAL STRUCTURE jacbobsen [ doi:10.1107/S0108270199009397 ]

=== The calculated NMR properties of your products and assigning the absolute configuration of the product ===
 The selected epoxides were optimised <jmolFile text=" R Styrene Oxide">(R)-(+)-Styrene oxide optimised.cml</jmolFile> , <jmolFile text=" S Styrene Oxide ">(S)Styrene oxide JNoptimised.cml</jmolFile> , <jmolFile text="(1R,2R)-(+)-1-Phenylpropylene oxide ">(1R,2R)-(+)-1-Phenylpropylene oxide JNoptimised.cml </jmolFile> and <jmolFile text="(1S,2S)-(-)-1-Phenylpropylene oxide ">(1S,2S)-(-)-1-Phenylpropylene oxide methyl styrene.cml </jmolFile>.
 
 Styrene Oxide
 The calculated 1HNMR and 13CNMR spectrum for the R ( {{DOI|10042/28236}} an S ( {{DOI|10042/27190}} conformation are identical (seen in the table below) as they have the same environments. There is no way to distinguish between the the two therefore optical rotation calculation is required to identify the two compounds.
cnmr of styrene oxide http://pubs.acs.org/doi/pdf/10.1021/ja00819a035
 Fig. 12 shows the labelled atoms

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''R (HNMR)'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''S (HNMR)'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| literature||calculated||atom||||calculated||atom
|-
| 7.4-7.3||7.515||14||||7.514||11
|-
| ||7.513||12||||7.513||14
|-
| ||7.483||10||||7.483||12
|-
| ||7.446||11||||7.446||13
|-
| ||7.3||13||||7.3||10
|-
| 3.83||3.66||15||||3.66||15
|-
| 3.12||3.11||16||||3.11||17
|-
| 2.77||2.53||17||||2.53||16
|-
|
|}
[[File:Styrene Oxide Labelled JN.jpg|350px|thumb| Styrene Oxide Atoms Labelled (fig. 12)
{|
|[[File:R styrene oxide HNMR JN.jpg|250px| thumb | R Styrene oxide HNMR]]
|[[File:R styrene oxide CNMR JN.jpg|250px| thumb| R Styrene Oxide CNMR]]
|[[File:S styrene oxide HNMR JN.jpg|250px| thumb| S Styrene oxide HNMR]]
|[[File:S styrene oxide CNMR JN.jpg|250px| thumb| S Styrene oxide CNMR]]
|}

{| class="wikitable" style="float:left; "
| align="center" style="background:#f0f0f0;"|'''literature CNMR styrene oxide'''
| align="center" style="background:#f0f0f0;"|'''calculated'''
| align="center" style="background:#f0f0f0;"|'''atom (R conformer)'''
|-
| 126||120.62||average of 4&6
|-
| 129||123.775||average of 3&5
|-
| 138.5||135.13||5
|-
| 128.7||122.95||2
|-
| 52.4||54.05||7
|-
| 51||53.45||8
|}

The HNMR matches closely with literature values and 1s experiment and the CNMR has a MAE= 3.97ppm showing that the structure has been optimised properly.

Trans β Methyl- Styrene Oxide
Again the calculated NMR for the RR {{DOI|10042/28246}} and the SS {{DOI|10042/28247}} was identical.

{|
|[[File:Rmethyl styrene H nmr JN.jpg|250px|thumb| HNMR of (R,R)Methyl Strene Oxide]]
|[[File:Rmethyl styrene c nmr JN.jpg|250px|thumb| CNMR of (R,R)Methyl Strene Oxide]]
|[[File:Smethyl styrene H nmr JN.jpg|250px| thumb| HNMR of (S,S)Methyl Strene Oxide]]
|[[File:Smethyl styrene Cnmr JN.jpg| 250px|thumb| CNMR of (S,S)Methyl Strene Oxide]]
|}
[[File:Methyl styrene image JN.jpg| 250px| thumb| (1R,2R)-(+)(methyl styrene)]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''HNMR'''
| align="center" style="background:#f0f0f0;"|'''R Conformer'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| LITERATURE||CALCULATED||METHYL STYRENE OXIDE ATOM
|-
| 7.27||7.5||12
|-
| ||7.5||15
|-
| ||7.48||13
|-
| ||7.42||14
|-
| ||7.31||11
|-
| 3.55||3.41||16
|-
| 3.12||2.79||17
|-
| ||1.68||20
|-
| ||1.59||19
|-
| ||0.72||18
|-
| 1.43||1.33||19/18/20 average
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''CNMR'''
| align="center" style="background:#f0f0f0;"|'''R conformer'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| LITERATURE||CALCULATED||METHYL STYRENE OXIDE ATOM
|-
| 137.7||134.975||2
|-
| 128.3||124.072||6
|-
| 59.4||62.3201||8
|-
| 58.9||60.5757||7
|-
| 17.8||18.8375||10
|-
| 125.4||120.6415||average of 1/3
|-
| 127.9||123.0275||average of 5/ 4
|-
|
|}

Again an average for the Methyl group had to be taken (discussed earlier) and the NMR matches up well as it is a small molecule. Furthermore for the C NMR an average of the phenyl ring had to be taken as literature 13CNMR could not distinguish between 1/3 and 5/4 because of the rotation of C2-C7. The MAE= 3.17ppm which is smaller than molecule '''18''' possibly due to the being less heteroatoms n the centre and it is smaller therefore less chance error for optimising the structure.

---
Optical Rotation

The table below shows the optical rotation of the the epoxides
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Conformation'''
| align="center" style="background:#f0f0f0;"|'''Literature optical Rotation'''
| align="center" style="background:#f0f0f0;"|'''Calculated Optical Rotation'''
|-
| R Styrene Oxide||-24||-30.12
|-
| S Styrene Oxide||+32.11||+30.11
|-
| R,R Methyl Styrene Oxide ||+46.78||+46
|-
| s,s Styrene Oxide ||-46.77||-46.9
|-
|
|}

The calculations were carried out in the solvent chloroform, as expected the optical rotations for the conformers are the opposite signs indicating to a correct calculation. For Methyl Styrene Oxide the values match to the literature whereas for Styrene Oxide there is deviations. However comparing literature values on Reaxys there is a wide rang of optical rotation reported due to varying concentrations and Gaussian does not give information on the concentration and I have presumed that the temperature is 298.15k.
---

===Transition States===

Using the calculated transition states provided by Rzepa (and any images of TS or JMOL were provided by [[Mod:organic#Using the (calculated) properties of transition state for the reaction (β-methyl styrene only)|Rzepa]]) the enatiomeric excess of the epoxides can be calculated. This is done by finding delta G betwwen the most stable R and S conformer. As <math>\Delta_r G^\circ = -R T \ln K \,</math>
 were R= Gas Constant, T= Temperature (298.15k) K= Equilibrium Constant
 <math>K=\frac{[product]} {[reactant]}</math>, instead of concentration mole fractions has been used where x= mole fraction of reactant and y= mole fraction of product. Therefore<math>\ Enatiomeric\ Excess= 100(y-x)</math> for the most stable transition state.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Epoxide'''
| align="center" style="background:#f0f0f0;"|'''Catalyst'''
| align="center" style="background:#f0f0f0;"|'''stable conformer'''
| align="center" style="background:#f0f0f0;"|'''delta G/ JmolK'''
| align="center" style="background:#f0f0f0;"|'''K'''
| align="center" style="background:#f0f0f0;"|'''ee'''
| align="center" style="background:#f0f0f0;"|'''Literature'''
|-
| Styrene Oxide||Shi||S||-1205||1.626||23.84%||
|-
| Styrene Oxide||Jacobsen||S||-18470||1721||99.88%||
|-
| Trans B Methyl Styrene Oxide||Shi||RR||-20219||3485||99.99%||
|-
| Trans B Methyl Styrene Oxide||Jacobsen||SS||-21364||5530||99.96%||
|-
|
|}
 

All the catalysts attack the the alkene on the less substituted carbon.
 Trans β methyl Styrene Oxide
 '''Shi catalyst:''' The most stable conformer is the <jmolFile text="RR">R,R series TS methyl stryrene SHI JN.mol</jmolFile> conformer as the cyclohexane unit is in a chair and has more positive interactions ( discussed in [[Mod:jyn111cnjg#NCI|NCI]] and [[Mod:jyn111cnjg#QTAIM|QTAIM]] ) Compared to the most stable SS conformer ,<jmolFile text="SS">S,S series methyl styrene TS JN.mol</jmolFile> TS# has a methyl directly over a benzene group and a acetal group eclipsed over the ‘alkene ‘ unit which is unfavourable interactions. The RR series has the shi catalyst attacking on the Re face.
 '''Jacobsen catalyst:''' The stable conformer is the <jmolFile text="SS">S,S series Jacobsen Methyl styrene Jn.mol</jmolFile> where the metallic double bond is attacking the Si face. This is a favorable for SS as the two benzene rings can interact with each other, whereas the <jmolFile text="RR">S,S series Jacobsen Methyl styrene Jn.mol</jmolFile> has the two benzenes 'ring' slipped therefore the forming bond cannot be stablised by the ring current.

Styrene Oxide '''Shi Catalyst:''' The stable conformer is the <jmolFile text="S">S (styrene oxide TS SHI Jn.mol</jmolFile>, however as the reacting carbon has no chiral centre it is difficult to establish which face of the alkene is being attacked. Also as there is no interactions to 'lock' the phenyl ring, this helps to explain why the ee is low. The <jmolFile text="R">R Shi styren oxide TS JN.mol</jmolFile> c<s>onformer is less stable as</s> .
 '''Jacobsen Catalyst:''' Again the the <jmolFile text="S">Sstyrene jacobsen ts JN.mol</jmolFile> conformer is the most stable conformation and has a greater enatiomeric excess compared to the Shi catalstyst this is due to the Ph groups having a stablising interaction compared to the <jmolFile text="R seriers">R styrene oxide jacoobsen ts JN.mol</jmolFile> (again because of ring slipage). This positive interactions between the rings helps to lock the Ph on the alkene in place allowing for a higher ee compared to Shi.

----
Calculated Transition States, (Appendix)
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Shi Catalys'''
| align="center" style="background:#f0f0f0;"|'''Styrene Oxide'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| TS ||R Conformer/ kJ/mol||S Conformer KJ/mol
|-
| 1||-818103.5424||-818105.5034
|-
| 2||-818103.2506||-818099.4479
|-
| 3||-818107.3765||-818101.6411
|-
| 4||-818108.149||-818108.437
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Jacobsen Catalyst'''
| align="center" style="background:#f0f0f0;"|'''Styrene Oxide'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| TS ||R Conformer/ kJ/mol||S Conformer KJ/mol
|-
| 1||-8779569.983||-8779591.796
|-
| 2||-8779573.325||-8779576.027
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Shi Catalyst'''
| align="center" style="background:#f0f0f0;"|'''Trans Bmethyl Styrene Oxide'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| TS||RR Conformer / KJ/mol||SS Conformer/Kjmol
|-
| 1||-3526107.076||-3526093.875
|-
| 2||-3526097.265||-3526087.734
|-
| 3||-3526123.622||-3526109.166
|-
| 4||-3526131.948||-3526111.729
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Jacobsen Catalyst'''
| align="center" style="background:#f0f0f0;"|'''Trans Bmethyl Styrene Oxide'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| TS||RR Conformer / KJ/mol||SS Conformer/Kjmol
|-
| 1||-8882733.571||-8882756.321
|-
| 2||-8882734.957||-8882744.154
|-
|
|}
----

===NCI===

NCI

The NCI was calculated for the most stable TS# for the Shi epoxidation for Trans methyl styrene. The jmol below shows the interactions between the two molecules; from the image all the interactions between the two are interactive which is expected as it is the most stable. It suggests that there is a hydrogen bond interaction with the acetal group and CH bond in the alkene. Furthermore there is an electrostatic attraction between a hydrogen and benzene. The only repulsive interactions are within the individual molecules themselves.

<jmol>
<jmolApplet>
<title>NCI</title><color>white</color><size>300</size>
<script>isosurface color orange purple "images/0/0b/R%2CR_methyl_styrene_fineJmol.jvxl" translucent;</script>
<uploadedFileContents>R,R TRANS B methyl styrene fine.cub.xyz</uploadedFileContents>
</jmolApplet>
</jmol>

===QTAIM===

The TS# of the Shi epoxidation for Trans methyl styrene was investigated further by QTAIM on Avogadro 2 to visualise which atoms are involved in the interactions established by NCI. The QTAIM (seen in the image below) show a hydrogen bond interaction between the acetal (the longer c-o bond) and two hydrogen’s which helps maintain the “trans” structure of the forming alkane. Furthermore these hydrogen’s also have a van der waals interaction with a methyl group. There is no interaction within the benzene group which makes this TS# favourable as there is no disruption to the aromatic structure. This calculation also shows the formation of the epoxide bond, where it attacks the less hindered face, as the only electron density for the C and O bond is located in the middle of the two. Whilst the electron density in the C=C is being withdrawn by the phenyl group indicating to a lengthening of the bond. Also the other dioxoarane oxygen is interacting with a methyl group away from the reaction centre.

[[File:QTAIM of TS JN.PNG|350px|thumb| QTAIM of Transition states for Shi epoxidation of trans-β-methyl styrene (R,R Series)]]

===Suggesting new candidates for investigations ===

=='''References'''==
<references>
<ref name="clayden">J.Clayden; N.Greeves; S.Warren; P.Wothers,Organic Chemistry, Oxford University Press, 2001.(1st ed.) </ref>

<ref name="orbital symmetry"> T. L. Gilchrist; R. C. Storr, Organic Reactions and Orbital Symmetry, Cambridge University Press, 1979, (2nd ed.) </ref>

<ref name="zou">J.Zou; X.Zhang, J.Kong; L.Wang, Fuel, 2008, '''87''', 3655-3659 {{DOI|10.1016/j.fuel.2008.07.006}} </ref>

<ref name= " Paq"> S. W. Elmore and L. Paquette, Tetrahedron Lett, 1991, 319,'''3''', 319–322 </ref>

<ref name="paq2"> L. Paquette, Angew Chem Int Ed engl,1990 '''29''', 609-620 </ref>

<ref name="paq3"> L.Paquette, N.Pegg, D.Toops, G.Maynard, and R.Rogers J.Am.Chem.Soc., 1990, 112, '''1''', 277-283 </ref>
<ref name= "hyper"> W. F. Maier, P. Von Rague Schleyer, J. Am. Chem. Soc., 1981, 103, 1891 </ref>
<ref name= "physical"> E.Anslyn and D.Dougherty,modern physical organic chemistry, University Science Books, 2006, 139 </ref>
<ref name= "MAE"> S.Smith and J.Goodman, J.org.chem. 2009,'''74''' 12, 4597-4607</ref>
<ref name= "jac"> J. W. Yoon, T.-S. Yoon, S. W. Lee and W. Shin, Acta Cryst, 1999, '''C55''', 1766-1769 </ref>
<ref name= "shi"> M. Durík, V. Langer, D. Gyepesová, J. Micová, B. Steiner and M. Koós, Acta Cryst. 2001. '''E57''', o672-o674 </ref>
</references>

books
INITIALS. Author’s surname, Title, Publisher, Place of publication, Edition (if not the first), Year, Pages.

journal

INITIALS. Author’s surname, Title of journal (abbreviated), Year, Volume number, Pages.
books
INITIALS. Author’s surname, Title, Publisher, Place of publication, Edition (if not the first), Year, Pages.

journal

INITIALS. Author’s surname, Title of journal (abbreviated), Year, Volume number, Pages.