Rep:Mod:jyn111cnjg

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

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.

Avogadro Calculation Summary

Table 1
molecule	Molecule 1	molecule 2
JMOL	molecule	molecule2
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

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 as the “diene” has been angled at 60 degrees to have optimal bond overlap . 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 e.g increasing temperature favours the thermodynamic.
2 can be hydrogenated to form 3 and 4 (fig.2) and after prolonged exposure to hydrogen can form the hydrogenated species.

hydrogenation of 2 (fig.2)

scheme 2 (fig.3)

Avogadro Calculation Summary

Table 2
Molecule	Molecule 3	molecule 4
JMOL	molecule	molecule
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 therefore the reaction is thermodynamically controlled. This is due to the Norborene double bond being more reactive than cyclopentadiene as the double bond, as the bond length 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 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. And 3 and 4 can be altered again by varying reaction conditions.

Antropisomerism in an intermediate related to the synthesis of Taxol

Scheme 3

Scheme 3 proceeds via an “atropselective anionic oxy-cope rearrangement” which allows a ketone to have a double bond adjacent to a bridgehead which have previously thought to be unstable.

Avogadro Calculation Summary

table 3
Molecule	Molecule 9	molecule10
JMOL	molecule9	molecule10
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.

TS^# 9 (fig .4)

The twist boat for both 9 and 10 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 (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)
parent_hydrocarbon_of_9
parent_hydrocarbon_of_9

Avogadro Calculation Summary

Table 4
Molecule 9	Parent hydrocarbon of 9	Molecule 10	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 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 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.

Isomerisation of 17 (fig.5)

Avogadro Calculation Summary

add text
Molecule	Molecule 17	molecule 18
JMOL	molecule17	molecule18
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 of 65.7 and 70.0 kcal/mol . 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

literature	'	'	calculated	'	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

¹HNMR of Molecule 18 (fig.6)

¹³CNMR of Molecule 18 (fig.7)

carbon NMR
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

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, therfore an average had to be taken. 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). Adding a heteroatom atom on the carbon effets the static NMR as it withdraws electron density explaing the large variance for sulphur. Mean Average Error (MAE) was calculated MAE=(1/N)(Sum of |S_calc-S_Exp| )= 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, which is atropisomerism.

part 2

The crystal structures of the two catalysts

Shi Catalyst
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.

anomeric effect (fig.9)

Shi Catalyst Crystal Structure (fig.10)

ATOM	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 and the adjacent C-O are longer and shorter this value. 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

Pentahelicene

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 R Styrene Oxide , S Styrene Oxide , (1R,2R)-(+)-1-Phenylpropylene oxide and (1S,2S)-(-)-1-Phenylpropylene oxide.

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

R (HNMR)	'	'	'	S (HNMR)	'
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)

R Styrene oxide HNMR

R Styrene Oxide CNMR

S Styrene oxide HNMR

S Styrene oxide CNMR

literature CNMR styrene oxide	calculated	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.

HNMR of (R,R)Methyl Strene Oxide

CNMR of (R,R)Methyl Strene Oxide

HNMR of (S,S)Methyl Strene Oxide

CNMR of (S,S)Methyl Strene Oxide

(1R,2R)-(+)(methyl styrene)

HNMR	R Conformer	'
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

CNMR	R conformer	'
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

Conformation	Literature optical Rotation	Calculated Optical Rotation
R Styrene Oxide	-24	-30.12 DOI:10042/28262
S Styrene Oxide	+34.3	+30.11 DOI:10042/28263
R,R Methyl Styrene Oxide	+46	+46 DOI:10042/28264
s,s Methyl Styrene Oxide	-46.9	-46.9DOI:10042/28261

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 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 ${\mathrm{\Delta }}_r{G}^{\circ }=-RT\ln K$ ensuring delta G is negative.
were R= Gas Constant, T= Temperature (298.15k) K= Equilibrium Constant
$K=\frac{[product]}{[reactant]}$, instead of concentration mole fractions has been used where x= mole fraction of reactant and y= mole fraction of product. Therefore$$\begin{gathered} Enatiomeric \\ Excess=100(y-x) \end{gathered}$$ for the most stable transition state.

Epoxide	Catalyst	stable conformer	delta G/ JmolK	K	ee	Literature
Styrene Oxide	Shi	S	-1205	1.626	23.84%
Styrene Oxide	Jacobsen	S	-18470	1721	99.88%	48
Trans B Methyl Styrene Oxide	Shi	RR	-20219	3485	99.99%	98
Trans B Methyl Styrene Oxide	Jacobsen	SS	-21364	5530	99.96%	92

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 RR conformer as the cyclohexane unit is in a chair and has more positive interactions ( discussed in NCI and QTAIM ) Compared to the most stable SS conformer ,SS 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 SS 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 RR 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 S, 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. Also as R and S are similar in energy there is a smaller barrier therfore smaller ee.

Jacobsen Catalyst: Again the the S 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 R seriers (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)

Shi Catalys	Styrene Oxide	'
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

Jacobsen Catalyst	Styrene Oxide	'
TS	R Conformer/ kJ/mol	S Conformer KJ/mol
1	-8779569.983	-8779591.796
2	-8779573.325	-8779576.027

Shi Catalyst	Trans Bmethyl Styrene Oxide	'
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

Jacobsen Catalyst	Trans Bmethyl Styrene Oxide	'
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.

NCI

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 atoms. 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 stablising the formation of a double bond.

QTAIM of Transition states for Shi epoxidation of trans-β-methyl styrene (R,R Series)

Suggesting new candidates for investigations

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 two 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. Therefore there should be a higher ee for Jacobsen compared to Shi. 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, before money was invested.