Rep:Mod:SAITYM954

Organic Computational

Conformational analysis using Molecular Mechanics

Cyclopentadiene dimer 1 and 2 and the hydrogenation product of the cyclopentadiene 2, 3 and 4, were modeled on Avagadro and their geometries were optimized using the MMFF94(s) force field option. The energies of the optimized energies are given in Table 1.

TABLE 1

Type of molecule	Cyclopentadiene dimer 1	Cyclopentadiene dimer 2	Hydrogenation product 3	Hydrogenation product 4
molecular model	cyclopentadiene dimer 1	cyclopentadiene dimer 2	hydrogenation product 3	hydrogenation product 4
Total bond stretching energy(kcal/mol)	3.54317	3.46793	3.31151	2.82308
Total angle bending energy(kcal/mol)	30.77258	33.18901	31.93319	24.68545
Total stretch bending energy(kcal/mol)	-2.04144	-2.08220	-2.10211	-1.65717
Total torsional energy(kcal/mol)	-2.73092	-2.94964	-1.46866	-0.37823
Total out-of-plane bending energy(kcal/mol)	0.01476	0.02183	0.01309	0.00028
Total van der Waals energy(kcal/mol)	12.80160	12.35898	13.63920	10.63705
Total electrostatic energy(kcal/mol)	13.01367	14.18476	5.11950	5.14702
Total energy(kcal/mol)	55.37342	58.19067	50.44571	41.25749

Although it can be seen that the total energy of the cyclopentadiene dimer 1 is lower than 2, cyclopentadiene dimerises to produce specifically the cyclopentadiene dimer 2. From this information, it can be concluded that although the cyclopentadiene dimer 1 is the more stable product out of the two dimers and therefore the thermodynamic product, the dimerisation of pentadiene is kinetically controlled and therefore favours the kinetic product, cyclopentadiene dimer 2.

The cyclopentadiene dimer 2 can hydrogenate to initially form two products, 3 and 4. Product 3 and 4 have double bonds hydrogenated in the cyclopentene ring and the norbornene ring respectively. Product 4 is seen to be predominantly favored product due to it being the lower energy product as well as the double bond in the norbornene ring reacting with hydrogen approximately 5 times faster than the double bond in the cyclopentene ring. The relative ease of hydrogenation of the respective double bonds can be attributed to the difference in different energies listed in Table 1 between product 3 and 4 and somewhat can be explained by analyzing them. It can be seen that product 4 has substantially lower energy in total angle bending energy, and total van der Waals energy, with a slightly lower energy in total bond stretching energy, relative to product 3, whereas product 3 is only slightly lower in energy in total electrostatic energy and total torsional energy relative to product 4. This explains the big difference in total energy favoring product 4 and also shows that the difference in energy between the two products 3 and 4 is mostly contributed by the difference in total angle bending energy, and total van der Waals energy. The possible explanation why the total angle bending energy, and total van der Waals energy is lower in product 4 is that ,looking at the reactant (cyclopentadiene dimer 2), the hydrogen atom on the unsaturated carbon in the norbornene ring is almost in plane and in closer proximity with the hydrogen atom on the saturated carbon atom adjacent to it than the hydrogen atom on the unsaturated carbon in the cyclopentene ring. The closer proximity of the hydrogen atom in the norbornene ring means that, there is a greater release in strain and therefore lowering of energy especially in total angle bending energy, and total van der Waals energy when the double bond in the norbornene ring is hydrogenated opposed to the cyclopentene ring. This explains why hydrogenation of double bond in the norborene ring, and therefore synthesis of product 4, is favored relative to product 3.

Atropisomerism in an Intermediate related to the Synthesis of Taxol

Key intermediate for the synthesis of Taxol, 9 and 10, was modeled on Avagadro and its geometry was optimized using the MMFF94s force-field option. The respective energies of the intermediate are given in Table 2.

Table 2

Type of Molecule	Intermediate 9(chair)	Intermediate 10(chair)	Hydrogenated Intermediate 9	Hydrogenated Intermediate 10
Molecular Model	''	''	''	''
Total bond stretching energy(kcal/mol)	7.66637	7.60691	7.06510	6.41196
Total angle bending energy(kcal/mol)	28.29002	18.81375	28.68337	22.31678
Total stretch bending energy(kcal/mol)	-0.07465	-0.14531	0.28404	0.29516
Total torsional energy(kcal/mol)	0.27125	0.25598	10.40618	9.20328
Total out-of-plane bending energy(kcal/mol)	0.97178	0.84841	0.09869	0.03531
Total van der Waals energy(kcal/mol)	33.11267	33.22378	33.34614	31.27316
Total electrostatic energy(kcal/mol)	0.30537	-0.05004	0.00000	0.00000
Total energy(kcal/mol)	70.54281	60.55348	79.88353	69.53565

Table 2 (cont.)

Type of Molecule	Intermediate 9(boat)	Intermediate 10(boat)
Molecular Model	''	''
Total bond stretching energy(kcal/mol)	8.00455	7.76754
Total angle bending energy(kcal/mol)	30.20403	19.02758
Total stretch bending energy(kcal/mol)	-0.03535	-0.13479
Total torsional energy(kcal/mol)	2.70443	3.74744
Total out-of-plane bending energy(kcal/mol)	0.94585	0.95707
Total van der Waals energy(kcal/mol)	35.80197	34.99801
Total electrostatic energy(kcal/mol)	0.29435	-0.06080
Total energy(kcal/mol)	77.91981	66.30205

The intermediate 10 was calculated to be the more thermodynamically stable intermediate relative to intermediate 9. This is mostly due to the difference in total angle bending energy which can be attributed possibly to the position of the O atom which experience less steric repulsion in intermediate 10 than in intermediate 9. The intermediates had lower total energies when the configuration of the 6-membered ring was in a chair configuration rather than a boat configuration. This suggests that the chair configuration is favored over the boat configuration in the 6-membered rings for these intermediates.

The functionalisation of the alkene for these intermediate has been reported to be extremely slow. This can be explained by the the energies listed in Table 2. There is a tendency in polycyclic systems for bridge head atoms to favor sp2 configuration rather than sp3. This is due to the extra stability afforded by these 'cage structures' as well as it being due to the sp2 intermediates having less strain than its parent polycycloalkane configurations. This effect can be seen in the energy table above where the total torsional energy is significantly lower in energy in the intermediates than their respective hydrogenated product leading to lower total energy in the intermediate.

Spectroscopic Simulation using Quantum Mechanics

Molecules 17 and 18 which are derivatives of molecules 8 and 9 were processed in a HPC and its ¹H and ¹³C NMR were calculated . The DOI for the data of the calculations are given in the reference.

Table3

Type of Molecule	Molecule 17 Chair	Molecule 17 boat	Molecule 18 Chair	Molecule 18 boat
Molecular model	''	''	''	''
Sum of electronic and thermal Free Energies	-1651.440152	-1651.437358	-1651.464202	-1651.462786

The Sum of electronic and thermal Free Energies, is the free energy, ΔG , of the molecule and can be used to comapre relative energies of these molecules. It can be sen that molecule 18 is generally favoured. however contrary to molecules 9 and 10, the molecule with the 6-membered ring in the boat configuration has lower relative energies and is favored. The ¹H and ¹³C NMR for both molecule 17 and 18 are as follows

NMR of molecule 17(boat)

1H	13C	NMR atom labels	NMR atom labels 2
click to expand	click to expand	click to expand	click to expand

NMR of molecule 18(boat)

1H	13C	NMR atom labels	NMR atom labels 2
click to expand	click to expand	click to expand	click to expand

NMR assignments

1H 17	13C 17	1H 18	13C 18
click to expand	click to expand	click to expand	click to expand

Comaprison between literature and calculated NMR

1H 17	13C 17	1H 18	13C 18
click to expand	click to expand	click to expand	click to expand

The calculated NMRs were generally in agreement with literature. The ¹H NMRs did not show great agreement with literature but chemical shift values were generally in the right place. On the other hand ¹³C NMRs showed good agreement with literature values. The calculated NMRs shifts tended to be higher than the chemical shifts in literature but this is thought to be due to lack of precise correction. The NMRs of the chair conformations were also calculated and these NMR generally tended to have chemical shifts at lower magnetic field relative to NMRs of the molecules with boat conformations. The NMR chemical shift of the carbon atoms attached to the sulfur atom must be corrected due to spin-orbit coupling errors. This explains the large deviation of chemical shift of C-12 and a possible small deviation at C-17 and C-18. However the literature for spin-orbit coupling error for the C-S bond could not be found and therefore the chemical shift values were left uncorrected on the presented data but is expected to be around -6ppm correction for each C-S bond.

Analysis of the properties of the synthesised alkene epoxides

The alkenes styrene and trans-Stilbene were chosen, and its epoxide derivatives were analysed.

Crystal structures of the two catalyst for epoxidation 21 and 23

The Shi asymmetric Fructose catalyst and the Jacobsen asymmetric catalyst which are labelled as catalyst 21 and 23 respectively are the stable precursors of the catalyst and are used in catalysing the epoxidation of alkenes. Its structures are shown below.

Catalysts 21 and 23

catalyst 21	catalyst 23	anomeric centre of catalyst 21	Stereoisomer A and B of catalyst 21
The Shi asymmetric Fructose catalyst	The Jacobsen asymmetric catalyst	alpha and beta anomers of catalyst 21 (click to expand)	Stereoisomer A and B of catalyst 21 (click to expand)

crystal structures of catalyst 21 and 23

catalyst 21	catalyst 23
''	''

Labels on Atoms

catalyst 21	catalyst 23
The Shi asymmetric Fructose catalyst	The Jacobsen asymmetric catalyst

Catalyst 21, forms a crystal structure stabilized by hydrogen bonding between the hydrogen atoms on carbon C8,C9 and C6 and oxygen atoms O1 and O2. Two stereoisomer, A and B, exist for catalyst 21 and in the crystal structure, the A isomer forms infinite zig-zag chain connected by hydrogen bonding with B isomer further stabilizing the crystal sturcture as side-chains. The C-O bond of the anomeric center, located on C2, has unusual properties. It can be seen that oxygen atoms bonded to C2, O6 and O2, have unusually short C-O bond lengths 1.403A. Looking at the average C-O bond length which is 1.43, there is a big difference in bond length. This shortened C-O bond length could be accounted for by the anomeric effect where there are stabilizing interaction between the bonding orbitals of oxygen and anti-bonding orbital of carbon. This effect also explains why the C2-C3 and C2-C1 are one of the longest C-C bonds in the molecule.

Catalyst 23 form crystal structures where the catalyst assume an asymmetric position shown above. The crystal structure consists only of Van der Waal's interactions. The tert-butyl group present in the molecule gives the bent shape that is present in the molecule due to steric repulsion and it has been found that when these tert-butyl groups present in positions C17 and C4 were substituted for triisopropylsiloxyl groups, the molecule took a flat shape instead of a bent shape as previously seen.

NMR analysis of the epoxide products

The DOI for the data of the calculations for these epoxides are given in the reference.

Calculated NMR of styrene oxide

1H styrene oxide	13C styrene oxide	labels on atoms	NMR atom assignment

Calculated NMR of trans-Stilbene oxide

1H trans-Stilbene oxide	13C trans-Stilbene	labels on atoms	NMR atom assignment

NMR chemical shift data and comparison with literature

1H styrene oxide	13C styrene oxide	1H trans-Stilbene oxide	13C trans-Stilbene

The calculated NMRs showed very good agreement with literature, and shows that these computated epoxide models can be used to predict properties of real molecules with a relatively good accuracy. As expected, the NMR values of enantiomers and diastereoisomers of the epoxides were the same.

Assigning the absolute configuration of the product

Calculated and reported literature for the epoxides, styrene oxide and trans-stilbene oxide

The reported and calculated optical rotations are shown in the table below.

optical rotations of epoxides at 598nm

	(R)-styrene oxide		(S)-styrene oxide		(R,R)-trans-stilbene oxide		(S,S)-trans-stilbene oxide
	calculated	literature	calculated	literature	calculated	literature	calculated	literature
optical rotation (598nm)/degrees	-30.43	-33.3	30.10	32.1	297.90	310	-297.67	no literature found

The optical rotations are in good agreement with the reported literature values. Although the literature value for the optical rotation for (S,S)-trans stilbene oxide could not be found, assuming that the value of the optical rotation for (R,R)-trans stilbene oxide, which has good agreement with reported literature value , is accurate, it can also be assumed that the computed value of (S,S)-trans stilbene is also correct as they are diasteroisomers of each other and the optical rotation of diastereoisomers should be equal but opposite which it very nearly is. Optical rotations of less than a 100 degrees, cannot usually be calculated accurately using this computational methods, but it seems as though the optical rotation of styrene has been calculated relatively accurately. This could be due to styrene being a relatively simple molecule. The sign of optical rotation cannot be used to predict the absolute configuration S or R, due to the direction of the optical rotation being completely random depending on the molecule for R and S. This can be seen in the computed values of optical rotation where R and S configurations have both direction of optical rotation assigned between the two molecules.

Using the calculated properties of transition state for the reaction

The calculated energies of transition state for the epoxidation of the chosen alkenes were used to assign the absolute configuration of epoxides, styrene oxide and trans-stilbene oxide. The energy calculation were provided by the Imperial College Chemistry department. The label R or S of the transition state refers to the face of the alkene that the catalsyt react to and therefore R and S of the same number are enantiomers of each other. Below the difference in free energy ΔG is calculated and the equilibrium constant, K, which refers to the ratio of R and S produced is calculated by the equation ΔG=-RTlnK. The calculated K is then used to work out the enantiomeric excess for either R or S. For example if K=0.6149, in this case it means that for every mole of S enantiomer produced, 0.6149 moles of R enatiomer is produced. ee=((R-S)/(R+S))x100%, where R+S =1, and therefore ee= ((1/1.6146)-(0.6149/1.6149)/(1))x100%= 23.84% ee for S.

Shi epoxidation of styrene

For the epoxidation of styrene using Shi's catalyst. 8 possible transition states can be envisaged

structures of transiton state (R)

R1	R2	R3	R4
''	''	''	''

structures of transiton state (S)

S1	S2	S3	S4
''	''	''	''

Summary of energies for styrene transition state (R and S)(Shi epoxidation) 2625.5

Type of transition	S1	S2	S3	S4
Sum of electronic and thermal Free Energies	-1303.733828	-1303.724178	-1303.727673	-1303.738503
Type of transition	R1	R2	R3	R4
Sum of electronic and thermal Free Energies	-1303.730703	-1303.730238	-1303.736813	-1303.738044
	R1-S1	S2-R2	S3-R3	R4-S4
Difference in Free energy(hartree)	0.003125	0.00606	0.00914	0.000459
Difference in Free energy(kJ/mol)	8.205	15.911	23.997	1.205
Equlibrium constant(K)	0.0365	0.001629	0.0000624	0.6149
Enantimeric excess of (R or S)	92.9%(S)	99.8%(R)	99.9%(R)	23.84%(S)

Literature for this reaction have reported to give the enatiomeric excess to the R enantiomer at 81%. It is therefore very likely that the approach and orientation of the catalyst will be either 2 or 3.

Jacobsen epoxidation of styrene

structures of transiton state

R5	R6	S5	S6
''	''	''	''

Summary of energies for styrene transition state (Jacobsen epoxidation)

Type of transition	S5	S6
Sum of electronic and thermal Free Energies	-3343.969197	-3343.963191
Type of transition	R5	R6
Sum of electronic and thermal Free Energies	-3343.960889	-3343.962162
	R1-S1	R2-S2
Difference in Free energy(hartree)	0.008308	0.001029
Difference in Free energy(kJ/mol)	21.812654	2.7016395
Equlibrium constant	0.000125	0.32866
Enantimeric excess(ee) of (R or S)	99.9%(S)	50.5%(S)

Literature for this epoxidation has reported ee of 46% favoring S enantiomer. This is in good agreement with the second transition state and therefore the catalyst is likely to be orientated as such.

Trans-Stilbene transition state

Similar to the styrene transition state, the energies of the trans-stilbene transition states were analysed. There are 8 possible transition state that can be envisaged for this reaction

Shi epoxidation of trans-stilbene

structures of transiton state (R)

RR1	RR2	RR3	RR4
''	''	''	''

structures of transiton state (S)

SS1	SS2	SS3	SS4
''	''	''	''

Summary of energies for tans-stilbene transition state (R and S)(Shi epoxidation) 2625.5

Type of transition	SS1	SS2	SS3	SS4
Sum of electronic and thermal Free Energies	-1534.683440	-1534.685089	-1534.693818	-1534.691858
Type of transition	RR1	RR2	RR3	RR4
Sum of electronic and thermal Free Energies	-1534.687808	-1534.687252	-1534.700037	-1534.699901
	SS1-RR1	SS2-RR2	SS3-RR3	SS4-RR4
Difference in Free energy(hartree)	0.004368	0.002163	0.006219	0.008043
Difference in Free energy(kJ/mol)	11.4681	5.6789	16.3279	21.1169
Equlibrium constant(K)	0.009784	0.1011	0.001377	0.0001994
Enantimeric excess of (RR or SS)	98.1%(RR)	81.6%(RR)	99.7%(RR)	99.9%(RR)

Literature for this epoxidation has reported ee>95% favouring RR configuration which is in good agreement with transition states 1,3 and 4. This epoxidation is therefore likely to take any of the transition, 1,3 and 4, as the transiton state for this reaction.

Jacobson epoxidation of trans-stilbene

structures of transiton state

RR5	SS5
''	''

Summary of energies for trans-stilbene transition state (Jacobsen epoxidation)

Type of transition	SS5
Sum of electronic and thermal Free Energies	-3574.923087
Type of transition	RR5
Sum of electronic and thermal Free Energies	-3574.921174
	RR5-SS5
Difference in Free energy(hartree)	0.001913
Difference in Free energy(kJ/mol)	5.0225
Equlibrium constant	0.1318
Enantimeric excess(ee) of (RR or SS)	76.7%(SS)

Literature for this epoxidation reported ee of 25% favouring the SS configuration. Although computed energies predicted the SS configuration to be favored, there is a big difference in the value of ee. This could be due to error in experimental data, or lack of accuracy in the computational data and therefore further analysis maybe needed to clarify this.

Overall it can be concluded that the predictions for the absolute configuration of these epoxide reactions using different catalyst via computational methods are relatively accurate, as can be seen by the good agreement with literature values.

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

NCI ananlysis was done on both R2 and S2 transitions for comparison. These are transitons of the reaction between the Si catalyst and styrene.

Molecular model showing NCI

R2	S2

The second transition state heavily favours the R enantiomer with an ee=99.8%(R), The R2 transition has a large mildly attractive surface of interaction almost completely surrounding the double bond of the styrene, which is the reaction site. The S2 transition in comaprison has a smaller midly attractive NCI surface relative to R around the double bond and has a cone like NCI interaction above the phenyl group which could become mildly repulsive upon closer approach of the catalyst to styrene which could suggest slight steric hinderance in S2. This difference in the magnitude of NCI interaction around the double bond could explain why R2 is so favored relative to the S2.

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

The QTAIM of R2 only was analyzed this time. There are total of 6 weak non-covalent BCP between the catalyst and styrene of which 5 of the 6 weak non-covalent BCP are near the active site. There is a weak non-covalent BCP between the reactive oxygen atom of the catalyst and the sp2 carbon of the styrene. This confirms the interaction previously described in NCI analysis of the catalysis at the active site. There are also 2 weak non-covalent BCP between the oxygen of the catalyst and hydrogen of the styrene at the active site, which suggest hydrogen bonding. This hydrogen bonding will help keep the catalyst stable at the active site and may explain why this transition state is so favoured.

Suggesting new candidates for investigations

A suggestion for a small epoxide for computational analysis in the future is pulgenone epoxide. Is it synthesized from pulgenone at 94% yield via a reaction with 30% H₂O₂ in aqueous lithium hydroxide. Pulgeneone oxide has reported optical rotation of 562.3 and molecular mass of 168.236 and should be a good candidate for future computational research of epoxide reactions.

Conclusion

The computational methods used were generally successful in predicting accurate NMR simulations and optical rotation values, and had good agreement with literature. It was also successfully used to explain the reactivity of molecules and transition states using energy values calculated from these methods. For the transition states ee was calculated and explained using NCI and QTAIM analysis with generally good success.