Rep:Mod:cr1411

Introduction

This computational experiment is aimed at modelling compounds and use molecular mechanics to carry out predictions of different of their properties such as regioselectivity or enantioselectivity, but also spectroscopic data such as NMR spectrum calculations. In the first part of the module, the regioselectivity of the dimerisation of cyclopentadiene and of its product's subsequent hydrogenation are investigated. An example of atropisomerism is studied for a ketone intermediate in the synthesis of Taxol. ¹H NMR and ¹³C NMR spectra calculations are carried out for another Taxol intermediate and the data obtained used to check the literature assignments for this compound. The second part of the computational experiment involves the study of the enantioselectivity of the Shi and Jacobsen epoxidations of two alkenes, namely styrene and β-methylstyrene. Various properties such as optical rotation, ¹H NMR and ¹³C NMR spectra are reported.

The hydrogenation of cyclopentadiene dimer

The geometries of the dimers 1-4 were optimised using the MMFF94(s) force field option in Avogadro; the results are summarised in Table 1.

Table 1. Energies of the dimers.

Energy (kcal/mol)/Compound	1	2	3	4
Total bond stretching energy	3.54	3.46	3.31	2.81
Total angle bending energy	30.77	33.91	31.68	25.66
Total stretch bending energy	-2.04	-2.09	-2.09	-1.63
Total torsional energy	-2.73	-2.94	-1.18	-0.31
Total out-of-plane bending energy	0.01	0.02	0.01	0.01
Total Van der Waals energy	12.80	12.22	13.66	10.30
Total electrostatic energy	13.01	14.02	5.12	5.15
Total energy	55.39	58.60	50.51	41.97

Between the two cyclopentadiene dimers, compound 1 has the lowest total energy and is thus the thermodynamic product (the most stable). On the other hand, compound 2 is the kinetic product, that is the one the most rapidly formed. It can be noted that the angle bending energy is the energy contribution that determines the total energy difference between the two isomers: it is significantly higher in compound 2.

The isomer formed during the reaction is the endo product and this can be explained in terms of orbital interactions between the diene and dienophile: in the endo conformer, there are favourable bonding interactions between the frontier orbitals of the diene and dienophile at the back of the molecule. These stabilise the molecule and hence determine the stereochemistry of the end product. This interaction is not present in the case of the exo product.

Diagram arranged from

The dimerisation of cyclopentadiene is thus kinetically controlled: the reaction specifically gives the kinetic endo dimer 2.

Between the two hydrogenation products, compound 4 displays a lower total energy with respect to compound 3 and is thus the most stable: compound 4 is the thermodynamic product whilst compound 3 is the kinetic product. The stretching, bending, torsional and Van der Waals contributions to the energy are all smaller in the former case, with the exception of the electrostatic energy being slightly lower for dimer 3, as the unfavourable steric repulsions between the olefinic hydrogen atoms and the ones bridging the two cycles are minimised.
It has been reported that the product formed was isomer 4; the hydrogenation reaction thus proceeds under thermodynamic control.

Atropisomerism in an intermediate related to the synthesis of taxol

The atropisomers 9 and 10 of the Taxol intermediate, along with their corresponding parent hydrocarbons, were optimised using MMFF94(s) in Avogadro to determine their relative stabilities; the results are summarised in Table 2.

Table 2. Energies of the atropisomers and their corresponding parent hydrocarbons.

Energy (kcal/mol)/Compound
Total bond stretching energy	7.72	7.59	7.48	6.58
Total angle bending energy	28.32	18.79	27.58	24.41
Total stretch bending energy	-0.06	-0.14	0.32	0.32
Total torsional energy	0.08	0.19	13.66	11.02
Total out-of-plane bending energy	0.96	0.84	0.04	0.05
Total Van der Waals energy	33.22	33.34	35.38	31.58
Total electrostatic energy	0.30	-0.06	0.00	0.00
Total energy	70.55	60.56	84.47	73.96

The lowest value of the total energy was obtained when the cyclohexane ring of both atropisomers had a chair conformation, which lies the lowest energy (it is actually an energy minimum). The boat conformation is indeed higher in energy (it is an energy maximum for cyclohexane) due to unfavourable steric repulsion between the flagpole hydrogen atoms. Between both conformers 9 and 10, compound 10 has a lower total energy and is thus the most stable. The "Olefin Strain" (OS) energy, that is the difference in strain energy between the alkene and its parent hydrocarbon, was then calculated for both atropisomers in order to determine the relative reactivity of both bridgehead alkenes:
Compound 9: OS= 84.47-70.55= 13.92 kcal/mol
Compound 10: OS= 73.96-60.56= 13.40 kcal/mol

Both values are lower than 17 kcal/mol; both isomers are thus very stable: they represent a case of "hyperstable" olefins They have a total energy lower than their corresponding parent hydrocarbon and hence display a very low reactivity. Between the two compounds, atropisomer 10 has the lower OS value and is hence expected to react more slowly than atropisomer 9.

Spectroscopy of an intermediate related to the synthesis of Taxol

The two isomers of the Taxol intermediate were first optimised using MMFF94(s) in Avogadro. Their ¹H and ¹³C NMR spectra were then simulated; the results are summarised in Table 3. The ¹H and ¹³C NMR chemical shifts computed were then used to check whether the values reported in literature were correctly assigned. The difference between the calculated and reported values was thus determined and plotted against the corresponding atom studied.^,

Table 3. Isomers of the Taxol intermediate.

Energy (kcal/mol)/Compound
Total bond stretching energy	16.23	14.39
Total angle bending energy	34.97	27.81
Total stretch bending energy	0.46	0.44
Total torsional energy	18.38	14.38
Total out-of-plane bending energy	2.39	1.04
Total Van der Waals energy	54.82	50.64
Total electrostatic energy	-7.22	-6.45
Total energy	120.03	102.25
1H NMR spectrum
1H NMR summary
13C NMR spectrum
13C NMR summary

As expected from the results in the previous section, compound 18 has the lowest strain energy and is therefore the most stable.

A comparison of selected chemical shifts from the ¹H NMR spectrum of both isomers, along with a complete revision of their ¹³C NMR spectra were then carried out; the results are summarised in Tables 4, 5, 6 and 7.

The NMR prediction for isomer 17 can be accessed here: DOI:10042/26559

Table 4. Calculated and experimental ¹H NMR chemical shifts for isomer 17.

H atom	δ (ppm)	literature value (ppm)	Δδ (ppm)
H(a)	5.53	4.84	0.69
H(b)	2.68	2.99	-0.31
H(c)	2.35	1.00-0.80	1.35-1.55

While the deviations observed for H(a) and H(b) are minor, the one for H(c) is important. The value reported in the literature is thus likely to be incorrect for this proton.

Table 5. Table 7. Calculated and experimental ¹³C NMR chemical shifts for isomer 17.

C atom	δ (ppm)	literature value (ppm)	Δδ (ppm)
1	33.18	32.66	0.52
2	60.33	52.52	7.81
3	64.55	56.19	8.36
4	91.27	72.88	18.39
5	40.07	35.85	4.22
6	22.05	20.96	1.09
9	44.19	38.81	5.38
10	47.63	45.76	1.87
11	32.87	28.79	4.08
12	116.91	125.33	-8.42
13	149.37	144.63	4.74
14	27.36	25.66	1.70
15	31.46	28.29	3.17
16	52.85	46.80	6.05
17	46.64	39.80	6.84
18	214.46	218.79	-4.33
19	54.01	48.50	5.51
20	26.87	23.86	3.01
21	21.56	18.71	2.85
24	30.68	26.88	3.80

The deviation from the calculated ¹³C NMR chemical shifts are significant for isomer 17. In particular, the difference in chemical shifts for the carbon atoms 2, 3, 4, 9, 12, 16, 17 and 19 is higher than 5 ppm, which suggests an inaccurate conformation of the molecule in these regions, unless the values reported in the literature are wrong. The average |Δδ| is 5.11 ppm, the maximum 18.39 ppm.

The NMR prediction for isomer 18 can be accessed here: DOI:10042/26560

Table 6. Calculated and experimental ¹H NMR chemical shifts for isomer 18.

H atom	δ (ppm)	literature value (ppm)	Δδ (ppm)
H(a)	5.38	5.21	0.17
H(b)	2.11	1.58	0.53

The deviations observed for H(a) and H(b) are small; the values from literature match the ones calculated. The assignments in the literature have thus been correctly reported for the ¹H NMR spectrum of isomer 18.

Table 7. Calculated and experimental ¹³C NMR chemical shifts for isomer 18.

C atom	δ (ppm)	literature value (ppm)	Δδ (ppm)
1	36.18	35.47	0.71
2	56.21	51.30	4.91
3	67.47	60.53	6.94
4	88.95	74.61	14.34
5	41.19	38.73	2.46
6	21.64	19.83	1.81
9	44.37	40.82	3.55
10	46.72	43.28	3.44
11	31.98	30.84	1.14
12	118.45	120.90	-2.45
13	148.79	148.72	0.07
14	28.59	25.56	3.03
15	25.11	22.21	2.90
16	55.43	50.94	4.49
17	37.57	36.78	0.79
18	213.14	211.49	1.65
19	49.99	45.53	4.46
20	25.76	25.35	0.41
21	23.18	21.39	1.79
24	28.96	30.00	-1.04

The deviations from the calculated chemical shifts are also important in the case of isomer 18 but are less marked than for isomer 17; the average |Δδ| is 3.12 ppm, the maximum 14.34 ppm. For both isomers 17 and 18, the maximum deviation observed is for carbon 4, that is for the spiroatom. As its value is above 5 ppm, it is likely the computed conformation of the molecule is wrong in this region.

The thermodynamic properties of both isomers were further explored; the results are summed up in Table 8. They corroborate the ones found above: isomer 18 has the lowest energies and is thus the most stable.

Table 8. Thermodynamic quantities of the isomers.

Energy (Hartree/particle)/Compound	17	18
Zero-point correction	0.467223	0.467690
Thermal correction to Energy	0.489128	0.489220
Thermal correction to Enthalpy	0.490072	0.490164
Thermal correction to Gibbs Free Energy	0.418832	0.420446
Sum of electronic and zero-point Energies	-1651.389634	-1651.415536
Sum of electronic and thermal Energies	-1651.367729	-1651.394007
Sum of electronic and thermal Enthalpies	-1651.366785	-1651.393062
Sum of electronic and thermal Free Energies	-1651.438025	-1651.462780

Analysis of the properties of the synthesised alkene epoxides

The crystal structure of the Shi and Jacobsen catalysts

The Cambridge crystal database (CCDC) was searched using the Conquest program for the Shi and Jacobsen catalysts, their structure analysis with the Mercury program is reported below.

Shi catalyst

Table 9. C-O bond lengths for the Shi catalyst.

C-O	bond length (Å)
C1-O1	1.429
C9-O1	1.423
C2-O2	1.423
C2-O6	1.408
C9-O2	1.454
C4-O4	1.415
C10-O4	1.456
C5-O5	1.437
C10-O5	1.428

It can be noted that the C-O bonds formed from the pyranose ring increase in the order C₄-O₄<C₂-O₂<C₅-O₅; the smaller value obtained for C₄-O₄ suggests a higher degree of strain for this bond. It can further be noted that the C₉-O₁ bond length is very close to the one measured for C₁₀-O₅, whilst C₉-O₂ is similar to C₁₀-O₄. At the anomeric centre, the C-O bond length in the pyranose ring is 1.408 Å, which is smaller than the value of 1.426 Å recorded for the simple pyranose unit. The adjacent C-O bond length on the 1,3-dioxolane ring is much shorter: 1.408 Å.

Short distance interactions (lower than the sum of their Van der Waals radii, of range 2.391-3.206 Å) are further observed. All intermolecular, these are essentially H bonds, but dipole-dipole interactions are also observed. For example, the oxygen of the carbonyl atom establishes 2 H bonds (2.646 and 2.669 Å) with hydrogen atoms from adjacent molecules and one dipole-dipole interaction with a carbon atom (3.094 Å) from one of these molecules. In each 1,3-dioxolane ring, one oxygen atom is involved in 1 H-bond, the other in 2 H bonds, which stabilise the compound's crystal structure.

Jacobsen catalyst

On each aromatic ring, the two t-Butyl groups adopt a staggered conformation with respect to each other; this corresponds to a minimum in energy and is thus the most stable conformation. H atoms from the t-Butyl groups also establish short contacts of 2.364 Å with H atoms of a t-Butyl group from a neighbouring molecule.

Distances between Hydrogen atoms of two adjacent t-Butyl groups on the aromatic rings were also measured; they ranged between 2.421 and 8.968 Å. Attractive non-covalent interactions (Van der Waals forces) are then expected to be formed between H atoms separated by a distance lying approximately in the lower part of this range (2.421-5.695 Å).

As for the Shi catalyst, intermolecular H bonds are observed, this time between N and H atoms from adjacent molecules. Their length is 2.650 Å. More general dipole-dipole interactions are also present, between C and H atoms (2.842 Å), and Cl and H atoms, where the the Chlorine atom establishes dipole-dipole interactions with two H atoms of two adjacent molecules. Their length is 2.759 Å and 2.775 Å, respectively.

Calculated NMR properties of the epoxide products

The two epoxide products, styrene oxide and β-methylstyrene oxide, were first optimised using MMFF94(s) in Avogadro. Their ¹H and ¹³C NMR spectra were then simulated and used to check assigned values in literature^, as per the Taxol intermediates above (cf. Tables 11, 12, 14 and 15).

Styrene oxide

Table 10. Optimisation of styrene oxide.

	Energy (kcal/mol)
Total bond stretching energy	1.84
Total angle bending energy	1.42
Total stretch bending energy	-0.75
Total torsional energy	2.35
Total out-of-plane bending energy	0.00
Total Van der Waals energy	13.67
Total electrostatic energy	3.08
Total energy	21.62

The NMR prediction for styrene oxide can be accessed here: DOI:10042/2661

Table 11. Calculated and experimental ¹H NMR chemical shifts for styrene oxide.

H atom	δ (ppm)	literature value (ppm)	Δδ (ppm)
H(a)	7.49	7.26-7.36	0.13-0.23
H(b)	7.30	7.26-7.36	0.06-0.16
H(c)	3.66	3.87	0.21
H(d)	3.11	3.15	0.04
H(e)	2.53	2.81	0.28

From the graph above, the deviations between the calculated and reported ¹H NMR chemical shift are very small, which indicates a correct assignment in the literature.

Table 12. Calculated and experimental ¹³C NMR chemical shifts for styrene oxide.

C atom	δ (ppm)	literature value (ppm)	Δδ (ppm)
1	123.42	128.4	-4.98
2	122.96	125.5	-2.54
3	124.13	137.6	-13.47
4	118.27	125.5	-7.23
5	123.13	125.5	-2.37
6	122.96	125.5	-2.54
7	54.05	52.4	1.65
8	53.45	51.2	2.25

In the case of the ¹³C NMR chemical shifts, important deviations are observed for the Carbon atoms 1, 3 and 4, that is for carbon atoms in the aromatic ring.

β-methyl styrene oxide

Table 13. Optimisation of β-methylstyrene oxide.

	Energy (kcal/mol)
Total bond stretching energy	1.89
Total angle bending energy	1.74
Total stretch bending energy	-0.76
Total torsional energy	2.90
Total out-of-plane bending energy	0.00
Total Van der Waals energy	14.32
Total electrostatic energy	3.04
Total energy	23.12

The NMR prediction for β-methylstyrene oxide can be accessed here: DOI:10042/26613

Table 14. Calculated and experimental ¹H NMR chemical shifts for β-methylstyrene oxide.

H atom	δ (ppm)	literature value (ppm)	Δδ (ppm)
H(a)	7.49	7.24-7.39	0.10-0.25
H(b)	7.42	7.24-7.39	0.03-0.18
H(c)	7.49	7.24-7.39	0.10-0.25
H(d)	7.31	7.24-7.39	-0.08-0.07
H(e)	7.49	7.24-7.39	0.10-0.25
H(f)	3.41	3.57	0.16
H(g)	2.79	3.32-3.40	0.53-0.61
H(h)	0.72	1.45	0.73
H(i)	1.59	1.45	0.14
H(j)	1.68	1.45	0.23

As for styrene oxide, the differences in ¹H NMR chemical shifts observed for methylstyrene oxide are not significant; the values reported in literature are thus correct.

Table 15. Calculated and experimental ¹³C NMR chemical shifts for β-methylstyrene oxide.

C atom	δ (ppm)	literature value (ppm)	Δδ (ppm)
1	123.33	127.70	-4.37
2	122.73	125.70	-2.97
3	124.07	128.30	-4.23
4	118.49	125.70	-7.21
5	134.98	135.84	-0.86
6	122.80	125.70	-2.90
7	60.58	59.70	0.88
8	62.32	59.70	2.62
9	18.84	18.10	0.74

As per styrene oxide above, the most significant deviations in ¹³C NMR chemical shifts are seen for the carbon atoms 1, 3 and 4. This suggests an inaccurate conformation of the molecule in this region.

Determination of the absolute configuration of the epoxide products

Calculated chiroptical properties

Table 16. Optical rotation data for the epoxide products.

parameter/epoxide	styrene oxide	methylstyrene oxide
literature value for optical rotation (in chloroform)	-33.3° (589 nm) (R)	-43.6° (589 nm) (S,S)
calculated optical rotation (in chloroform)	-30.12 (589 nm) -94.05 (365 nm) DOI:10042/26761	46.8° (589 nm) 137.69 (365 nm) DOI:10042/26762
computed Vibrational Circular Dichroism spectrum	DOI:10042/26763	DOI:10042/26764

The values obtained for the optical rotation of both products are of the same range than the ones found in literature, however with an opposite sign in the case of β-methylstyrene oxide. Hence the computed enantiomers have the following absolute configurations: (R)-(-)-styrene oxide and (R,R)-(+)-methylstyrene oxide.

Calculated transition states for the epoxidation

In order to check the absolute configuration of the epoxide products that was assigned in the section above, the relative free energy (determined computationnally) of the transition states of styrene and methylstyrene was identified. This then allowed to find the ratio of concentrations between the two enantiomers for each epoxidation, and hence the enantiomeric excess (ee) of one enantiomer over the other. This latter parameter was determined with the formula ee=[(% more abundant enantiomer-50)*100]/50).

Using the Shi catalyst

The thermodynamic quantities of the eight possible transition states for the epoxidation of β-methylstyrene using the Shi catalyst are summarised in Tables 17-20. The ratio of concentrations K between enantiomers was then calculated for each case, along with the enantiomeric excess; the results are summed up in Table 21.

β-methylstyrene

Table 17. Thermodynamic quantities of the transition state 1.

Energy /Transition State	(R,R)	(S,S)
Zero-point correction (Hartree/particle)	0.4681	0.4681
Thermal correction to Energy	0.4943	0.4938
Thermal correction to Enthalpy	0.4952	0.4953
Thermal correction to Gibbs Free Energy	0.4134	0.4102
Sum of electronic and zero-point Energies	-1342.9683	-1342.9625
Sum of electronic and thermal Energies	-1342.9421	-1342.9363
Sum of electronic and thermal Enthalpies	-1342.9412	-1342.9353
Sum of electronic and thermal Free Energies	-1343.0230	-1343.0179

Table 18. Thermodynamic quantities of the transition state 2.

Energy/Transition State	(R,R)	(S,S)
Zero-point correction (Hartree/particle)	0.4672	0.4676
Thermal correction to Energy	0.4938	0.4940
Thermal correction to Enthalpy	0.4947	0.4949
Thermal correction to Gibbs Free Energy	0.4102	0.4130
Sum of electronic and zero-point Energies	-1342.9622	-1342.9610
Sum of electronic and thermal Energies	-1342.9356	-1342.9347
Sum of electronic and thermal Enthalpies	-1342.9347	-1342.9337
Sum of electronic and thermal Free Energies	-1343.0192	-1343.0156

Table 19. Thermodynamic quantities of the transition state 3.

Energy/Transition State	(R,R)	(S,S)
Zero-point correction (Hartree/particle)	0.4680	0.4671
Thermal correction to Energy	0.4942	0.4935
Thermal correction to Enthalpy	0.4951	0.4944
Thermal correction to Gibbs Free Energy	0.4135	0.4116
Sum of electronic and zero-point Energies	-1342.9747	-1342.9683
Sum of electronic and thermal Energies	-1342.9486	-1342.9419
Sum of electronic and thermal Enthalpies	-1342.9476	-1342.9410
Sum of electronic and thermal Free Energies	-1343.0293	-1343.0238

Table 20. Thermodynamic quantities of the transition state 4.

Energy/Transition State	(R,R)	(S,S)
Zero-point correction (Hartree/particle)	0.4677	0.4672
Thermal correction to Energy	0.4939	0.4937
Thermal correction to Enthalpy	0.4949	0.4947
Thermal correction to Gibbs Free Energy	0.4133	0.4113
Sum of electronic and zero-point Energies	-1342.9780	-1342.9688
Sum of electronic and thermal Energies	-1342.9518	-1342.9423
Sum of electronic and thermal Enthalpies	-1342.9508	-1342.9414
Sum of electronic and thermal Free Energies	-1343.0324	-1343.0247

Table 21. Enantiomeric excesses determination.

Parameter/Transition State	TS1	TS2	TS3	TS4
Free energy difference ΔG[(S,S)-(R,R)](kcal/mol)	5.1*10-3	3.6*10-3	5.5*10-3	7.7*10-3
Free energy difference ΔG[(S,S)-(R,R)](J/mol)	21.04	15.19	23.04	32.22
Ratio of concentrations K; K=exp[-ΔG/(RT)]	0.992	0.994	0.991	0.987
ee of (S,S) (%)	98.4	98.8	98.2	97.4

From Tables 17-20, the transition state lying the lowest in energy and hence the most stable corresponds to the one leading to the (R,R) epoxide (Table 20), and where the phenyl group of the alkene is oriented exo with respect to the fructose. Hence the (R,R) enantiomer would be expected to be the major product. However, the results from Table 21 indicate the (S,S) epoxide is formed instead, with an ee of 97.4%, lit 91%(corresponding to the transition state the lowest in energy). These results are thus in opposition to the ones obtained in the section above, where it was found that the computed enantiomer had the (R,R) configuration.

Styrene

Table 22. Thermodynamic quantities of the transition state 1.

Energy /Transition State	(R) TS1	(S) TS1
Zero-point correction (Hartree/particle)	0.4399	0.4396
Thermal correction to Energy	0.4646	0.4646
Thermal correction to Enthalpy	0.4655	0.4655
Thermal correction to Gibbs Free Energy	0.3869	0.3849
Sum of electronic and zero-point Energies	-1303.6777	-1303.6791
Sum of electronic and thermal Energies	-1303.6530	-1303.6542
Sum of electronic and thermal Enthalpies	-1303.6521	-1303.6532
Sum of electronic and thermal Free Energies	-1303.7307	-1303.7338

Table 23. Thermodynamic quantities of the transition state 2.

Energy/Transition State	(R) TS2	(S) TS2
Zero-point correction (Hartree/particle)	0.4396	0.4393
Thermal correction to Energy	0.4644	0.4642
Thermal correction to Enthalpy	0.4653	0.4651
Thermal correction to Gibbs Free Energy	0.3856	0.3860
Sum of electronic and zero-point Energies	-1303.6762	-1303.6709
Sum of electronic and thermal Energies	-1303.6515	-1303.6460
Sum of electronic and thermal Enthalpies	-1303.6505	-1303.6451
Sum of electronic and thermal Free Energies	-1303.7302	-1303.7242

Table 24. Thermodynamic quantities of the transition state 3.

Energy/Transition State	(R) TS3	(S) TS3
Zero-point correction (Hartree/particle)	0.4398	0.4399
Thermal correction to Energy	0.4645	0.4645
Thermal correction to Enthalpy	0.4654	0.4654
Thermal correction to Gibbs Free Energy	0.3861	0.3875
Sum of electronic and zero-point Energies	-1303.6831	-1303.6752
Sum of electronic and thermal Energies	-1303.6584	-1303.6506
Sum of electronic and thermal Enthalpies	-1303.6575	-1303.6497
Sum of electronic and thermal Free Energies	-1303.7368	-1303.7277

Table 25. Thermodynamic quantities of the transition state 4.

Energy/Transition State	(R) TS4	(S) TS4
Zero-point correction (Hartree/particle)	0.4395	0.4396
Thermal correction to Energy	0.4642	0.4644
Thermal correction to Enthalpy	0.4652	0.4653
Thermal correction to Gibbs Free Energy	0.3863	0.3848
Sum of electronic and zero-point Energies	-1303.6849	-1303.6837
Sum of electronic and thermal Energies	-1303.6601	-1303.6589
Sum of electronic and thermal Enthalpies	-1303.6592	-1303.6579
Sum of electronic and thermal Free Energies	-1303.7380	-1303.7385

Table 26. Enantiomeric excesses determination.

Parameter/Transition State	TS1	TS2	TS3	TS4
Free energy difference ΔG[(R)-(S)](kcal/mol)	3.1*10-3	-6.0*10-3	-9.1*10-3	5.0*10-4
Free energy difference ΔG[(R)-(S)](J/mol)	13.08	-25.36	-38.24	1.92
Ratio of concentrations K; K=exp[-ΔG/(RT)]	0.995	0.990	0.985	0.999
ee (%)	99.0 (R)	98.0 (S)	96.9 (S)	99.8 (R)

In the case of styrene oxide, the transition state the lowest in energy is the one leading to the formation of the (S) enatiomer (Table 25), and where the phenyl ring of the alkene is oriented exo with respect to the fructose (as per methylstyrene oxide above). However, the results from Table 26 above indicate that the (R) epoxide is formed instead, with an ee of 99.8%, lit.95%. This corroborates the results obtained in the previous section, where it was found that the computed enantiomer has the (R) configuration.

Using the Jacobsen catalyst

The thermodynamic quantities of the four possible transition states for the epoxidation of styrene using the Jacobsen catalyst are summarised in Tables 27 and 28. The ratio of concentrations K between enantiomers and enantiomeric excess was then calculated for each case; the results are summed up in Table 29.

Styrene

Table 27. Thermodynamic quantities of the transition state 1.

Energy /Transition State	(R) TS1	(S) TS1
Zero-point correction (Hartree/particle)	0.7356	0.7356
Thermal correction to Energy	0.7765	0.7765
Thermal correction to Enthalpy	0.7775	0.7775
Thermal correction to Gibbs Free Energy	0.6638	0.6632
Sum of electronic and zero-point Energies	-3343.8891	-3343.8968
Sum of electronic and thermal Energies	-3343.8482	-3343.8558
Sum of electronic and thermal Enthalpies	-3343.8473	-3343.8549
Sum of electronic and thermal Free Energies	-3343.9609	-3343.9692

Table 28. Thermodynamic quantities of the transition state 2.

Energy/Transition State	(R) TS2	(S) TS2
Zero-point correction (Hartree/particle)	0.7362	0.7365
Thermal correction to Energy	0.7767	0.7772
Thermal correction to Enthalpy	0.7776	0.7781
Thermal correction to Gibbs Free Energy	0.6642	0.6645
Sum of electronic and zero-point Energies	-3343.8902	-3343.8911
Sum of electronic and thermal Energies	-3343.8497	-3343.8505
Sum of electronic and thermal Enthalpies	-3343.8487	-3343.8495
Sum of electronic and thermal Free Energies	-3343.9622	-3343.9632

Table 29. Enantiomeric excesses determination.

Parameter/Transition State	TS1	TS2
Free energy difference ΔG[(R)-(S)](kcal/mol)	8.3*10-3	1.0*10-3
Free energy difference ΔG[(R)-(S)](J/mol)	34.76	4.31
Ratio of concentrations K; K=exp[-ΔG/(RT)]	0.986	0.998
Enantiomeric excess of R (%)	97.2	99.6

As for the epoxidation using the Shi catalyst, the transition state the lowest in energy is the one leading to the formation of the (S) product. However the (R) enantiomer is found to be formed from the enatiomeric excess calculation, with an ee of 97.2%. As per above with the Shi catalyst, this is in accordance with the result obtained for the epoxide computed.

Non-covalent interactions (NCI) analysis in the active site of the reaction transition state of β-methylstyrene oxide

The electron density of the transition state of the epoxidation of β-methylstyrene leading to the (S,S) epoxide was computed and an NCI analysis was carried out; the results are given in the diagram below:

Arrow 1 indicates the formation of the C-O bond of the epoxide in the transition state; it is half-covalent and is thus not an NCI per se. Arrow 2 shows the important mildly attractive interaction that spreads across the whole region located in between the Shi catalyst and its substrate, that is where the alkene interacts with the catalyst to form the epoxide product. Arrow 3 indicates the mildly repulsive interaction in the center of the alkene's aromatic ring. Arrow 4 shows the strongly repulsive interaction existing in the center of the 1,3-dioxolane ring of the catalyst.

Electronic topology (QTAIM) analysis in the active-site of the reaction transition state of β-methylstyrene

A QTAIM analysis complementary to the NCI analysis above was carried out for the transition state of β-methylstyrene; the results are given in the diagram below:

Numerous non-covalent critical points (BCPs) are observed between the Shi catalyst and the alkene. In particular, each dioxirane oxygen of the catalyst establishes one BCP with one end of the alkene double bond (arrows 2 and 3). These BCPs are located approximately mid-way between the two atoms they connect. There are further non-covalent BCPs which help stabilise the transition state, like for example the one between an oxygen atom of the 1,3-dioxolane ring and the tertiary carbon atom of the alkene (arrow 1).

Suggestion of a new candidate for investigation

Reaxys was searched for a compound with ORP.ORP<'-500'; trans-(2R,3R)-2-(4-methylphenyl)-3-phenyl oxirane (OR=-580° at 436 nm) was found:

However the corresponding alkene could not be found in the Sigma-Aldrich catalogue.

Conclusion

In this computational experiment, molecular mechanics was successfully applied to study the regioselectivity, atropisomerism and enantioselectivity of different compounds. Their NMR spectra could be further predicted and used to check the corresponding data reported in literature, which was shown to be wrong in some cases. However, limitations of computational predictions were also observed: in some cases, deviations between the calculated and experimental values were very high (well above 5 ppm), suggesting a wrong conformation in the region considered. Molecular mechanics was further used to determine the absolute configuration of the two epoxides styrene oxide and methylstyrene oxide by comparing the calculated value obtained for the optical rotation with the one found in literature. It was found by this method that the epoxides had the following absolute configurations: (R)-styrene oxide and (R,R)-methylstyrene oxide. The enantiomeric excesses determined from the calculated transition states were then used to check the absolute configuration of the products. The results corroborated for (R)-styrene oxide, however it was found that (S,S)-methylstyrene oxide was formed in excess. This last result is surprising, as the transition state the lowest in energy is observed for the one leading to the (R,R) product, this being due to phenyl group of the alkene being oriented exo with respect to the fructose, as in the case of the (R)-styrene transition state. The calculation of the enantiomeric excess for methyl styrene oxide might thus be wrong.