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Year 3 Synthetic Modelling Lab: 1C

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

PART 1: Conformational analysis using Molecular Mechanics

Conformations and Hydrogenation of Cyclopentadiene

This part of the modelling exercise concentrates on establishing whether the cyclodimerisation of cyclopentadiene and its subsequent hydrogenation is under thermodynamic control due to the stability of the products, or under kinetic control due to the lower energy transition state. This is achieved interpreting the results obtained from the molecular mechanics technique.

ENDO and EXO Cyclodimerisation products

Upon dimerisation of cyclopentadiene via a Diels Alder [_π4_s+_π2_s] cycloaddition two possible products may form: an endo or an exo conformer, as shown in the picture on the right. The Diels-Alder are a type of pericyclic reactions which proceed in a concerted fashion. The normal electron demand of such a reaction involves an electron deficient dienophile (low energy LUMO) reacting with an electron rich diene (high energy HOMO) in its cis-conformation. Endo conformer is formed predominantly rather than exo. In order to assess why this is the case, both geometries were otpimized in Avogadro using the following settings:

• Force Field: MMFF94s
• Algorithm: Conjugate gradients
• Steps per update: 4

Cyclodimerisation of cyclopentadiene

Table 1. Optimized geometries of cyclopentadiene dimer.

	ENDO	EXO
Structure
Total Bond Stretching Energy(kcal/mol)	3.46480	3.54444
Total Angle Bending Energy (kcal/mol)	33.22508	30.78197
Total Torsional Energy (kcal/mol)	-2.95330	-2.73235
Total Van der Waals Energy (kcal/mol)	12.33274	12.79366
Electrostatic (kcal/mol)	14.18229	13.01273
C1-C2-C3 (°)	118.6	115.6
Total Energy (kcal/mol)	58.19044	55.37325

This dimerisation reaction involves 6π electrons, which fits the 4n+2 Huckel rule of aromaticity with n=1. Thus thermal reaction proceeds suprafacially via a Huckel transition state, according to Woodward-Hoffmann rules. The reason for two possible products lies in the orientation of the reactants relative to each other in the transition state. While the exo product is ~2.8 kcal/mol lower in energy and hence is the thermodynamic product of the reaction, the endo conformer is a major product of the reaction, which suggests that this Diels-Alder [_π4_s+_π2_s] cycloaddition is contolled by the kinetics. The kinetic product is formed faster than the thermodynamic one due to favourable secondary orbital overlap (SOO)to explain the observed endo-stereoselectivity of the Diels-Alder, as proposed by Woodward and Hoffmann. SOO is defined as a positive overlap and together with the steric effects lowers the transition state, which accounts for a a faster formation of the kinetic product over the thermodynamic.

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

Hydrogenation of ENDO dimer

We have looked at the reasons for a given stereoselectivity of the cyclodimerisation of cyclopentadiene above. This section now concentrates on the regioselectivity of the hydrogenation reaction of the endo dimer specifically. It has been observed that hydrogenation proceeds stepwise to give initially one of the dihydro derivatives 3 or 4 and only after a prolonged hydrogenation the tetrahydro derivative. The objective of this exercise is to determine, with the aid of molecular mechanics modelling, whether the hydrogenation of the cyclopentadiene dimer is under kinetic or thermodynamic control. If the reaction is under thermodynamic control, then the formation of the more thermodynamically stable derivative will be favoured over the other.

Hydrogenation scheme of the endo dimer

In order to determine which of the derivatives is the more thermodynamically stable one, once again the geometries of both molecules were optimized in Avogadro using the same settings for molecular mechanics approach as above.

Table 2. Optimized geometries of hydrogenation products.

	Hydro 3	Hydro 4
Structure
Total Bond Stretching Energy(kcal/mol)	3.30795	2.82308
Total Angle Bending Energy (kcal/mol)	30.86410	24.68542
Total Torsional Energy (kcal/mol)	0.05877	-0.37828
Total Van der Waals Energy (kcal/mol)	13.28245	10.63715
Electrostatic (kcal/mol)	5.12101	5.14702
Total Energy (kcal/mol)	50.72296	41.25749

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

A closer look into these two parameters is summarised in table 3.

Table 3. Conformational analysis of derivatives 3 and 4.

	Hydro 3	Hydro 4
Structure
Relative Angle Bending Energy (kcal/mol)	6.17868	0
Relative Van der Waals Energy (kcal/mol)	2.64530	0
Relative Total Energy (kcal/mol)	9.46547	0

Starting with the angle bending term, which represents the non-ideality and hence a raise in energy as the angles deviate from their preferred values. Analysis of angles in both molecules showed that the angle at the bridging CH₂ unit in both norbornane and norbornene is ~93° which is quite far away from the preferred sp³ carbon angle of 109.5°. This raised the energy term in both systems. However further angle examinations have shown that the angle measured and demonstrated in jmol files is found to be 107.2° in 3 and 102.9° in 4. While in 4 this is a sp³ carbon center and 102.9 is only ~7° away from ideality, in structure 3 this angle is at the sp² hybridised carbon, which is now much further away from its preferred value of 120°. This results in a greater angle strain in the molecule, accounting for the big energy difference between the two hydro derivatives.
Examining the Van der Waals interactions between the non-bonded atoms in the molecule, it is observed that the distance between colour-labelled atoms is less that the sum of their Van der Waals radii, leading to repulsion. This effect raises the energy of the system according to how much smaller the distance is from the preferred value. For carbon atoms, this preferred distance, ie the sum of Van der Waals radii, is known to be ~0.340 nm. Although there are clear deviations from this preferred value in both molecules, both distances measure in 4 are longer than the analogous distances in 3. Furthermore, derivative 4 has one less repulsive interactions than 3 since the distance between blue and yellow atoms actually exceeds 0.340 nm. This factor accounts for 4 being lower in energy overall.

Now those two parameters have been examined closely, it can be concluded that hydro derivative 3 lies higher in energy than 4 due to effects of angle strain and repulsive Van der Waals interactions, which it has one more of than derivative 4.

Atropisomerism in an intermediate related to the synthesis of Taxol

oxy-Cope rearrangement of a carbinol

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

Table 4. Optimized geometries of conformers of 9.

	Chair 1	Chair 2	Twist Boat	Boat
Structure
TOTAL ENERGY (kcal/mol)	77.35875	70.54037	76.30219	85.31047
Total Bond Stretching Energy(kcal/mol)	8.09936	7.70190	7.95686	8.45651
Total Angle Bending Energy (kcal/mol)	31.48847	28.2951	29.77755	36.46909
Total Torsional Energy (kcal/mol)	1.3020	0.15583	2.55003	1.96577
Total Van der Waals Energy (kcal/mol)	36.05711	33.18713	34.65181	37.23578
Electrostatic (kcal/mol)	0.04448	0.30377	0.32294	0.23787
C1-C4 (Å)	3.899	3.087	3.086	3.889
Dihedral angle C1-C2-C3-C4 (°C)	162.7	8.9	8.3	162.7
C2-C3-C4 (°C)	128.0	124.4	124.5	129.2

Table 5. Optimized geometries of conformers of 10.

	Chair 1	Chair 2	Twist Boat 1	Twist Boat 2
Structure
TOTAL ENERGY (kcal/mol)	60.55464	74.97473	66.31086	68.87968
Total Bond Stretching Energy(kcal/mol)	7.58791	8.50447	7.74486	7.82959
Total Angle Bending Energy (kcal/mol)	18.79316	21.56068	19.07872	21.12109
Total Torsional Energy (kcal/mol)	0.19670	7.28263	3.65530	4.43732
Total Van der Waals Energy (kcal/mol)	33.32706	35.86507	35.07716	34.65108
Electrostatic (kcal/mol)	-0.05540	0.40028	-0.06953	-0.04570
C1-C4 (Å)	3.091	3.162	3.104	3.121
Dihedral angle C1-C2-C3-C4 (°C)	12.4	22.1	13.5	14.3
C2-C3-C4 (°C)	123.6	124.9	123.9	124.5

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

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

Chair 2 9		Chair 1 10

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

Since Chair 2 of 10 has been identified as the most energetically stable structure, this would be the sole product of an anionic oxy-Cope rearrangement that proceeds under thermodynamic control.

9 and 10 as Hyperstable Olefins

It has been reported that the alkene structures 9 and 10 described above reacted abnormally slowly for an alkene functionalisation. This unexpected inert behaviour of alkenes in this case is explained as a specific example of hyperstability due to the position of the C=C double bond next to the bridgehead. Olefinic strain is said to be the difference between the total strain energy of the most stable conformation of an alkene and the most stable conformation of its parent hydrocarbon, ie the saturated molecule. A negative olefinic strain is usually the case, when the alkene form is more reactive relative to its parent hydrocarbon. However, structures 9 and 10 exhibit the behaviour of a special case of hyperstable alkenes, that are known to react at an abnormally slow rate due to the fact that the molecule is less strained in its olefin form rather than saturated form.

Spectroscopic Simulation Using Quantum Mechanics

Spectroscopy of an Intermediate Related to the Synthesis of Taxol

This section used copmutational methods to simulate NMR spectra of a molecule. This time, molecules 17 and 18 are under examination. These are the derivatives of previously discussed atropisomers 9 and 10. By analogy to the situation above, where 10 was found to be energetically more stable than 9, this time 18 is expected to be more thermodynamically stable due to the relative orientation of the carbonyl and the bridging isopropyl groups. 18 is a derivative of 10 with the carbonyl group pointing away from the bridgehead. This theory was tested using molecular mechanics technique as before.

Table 6. Optimized geometries of 17 and 18.

	17	18
Structure	17	18
Total Bond Stretching Energy(kcal/mol)	13.82478	14.58589
Total Angle Bending Energy (kcal/mol)	30.91985	28.76319
Total Torsional Energy (kcal/mol)	9.10099	7.74527
Total Van der Waals Energy (kcal/mol)	48.35898	49.16084
Electrostatic (kcal/mol)	-1.08921	-2.21691
Total Energy (kJ/mol)	429.218	416.391
Total Energy (kcal/mol)	102.51694	99.45322

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

¹H NMR Spectrum of 18

Table 7 presents the comparison of the computed and experimental proton NMR values recorded in deuterated benzene.

Table 7. ¹H NMR of 18.

		Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)			Experimental (300 MHz, C6D6)
		δ (ppm)	Peak analysis		δ (ppm)	Peak analysis
		5.90	s, 1H		5.21	m, 1H
		5.20	s, 1H
		3.13	s, 1H		3.00-2.70	m, 6H
		3.07	s, 1H
		2.89	s, 1H
		2.79	s, 1H
		2.57	s, 1H		2.70-2.35	m, 4H
		2.41	s, 1H
		2.26	s, 2H		2.20-1.70	m, 6H
		2.18	s, 1H
		1.99	s, 2H
		1.84	s, 3H
		1.66	s, 1H
		1.56	s, 2H		1.58	t, 1H, J=5.4 Hz
		1.48	s, 2H		1.50-1,20	m, 3H
		1.30	s, 2H
		1.21	s, 3H
		0.97	s, 2H		1.10	s, 3H
		0.91	s, 1H		1.07	s, 3H
		0.65	s, 1H		1.03	s, 3H

The following chart was produced to illustrate the correlations of experimental and computed ppm values.

Now, it is easier to see the good agreement, in general, between the spectra. However, there is one obvious deviation from the experimental chemical shift, almost by 0.7ppm, and it is observed for the proton that is found next to the double bond. This could be the result of a few aspects of this computer simulation:

• does not account for any fluxionality effects, like the rotation around the bonds, thus differentiating between the protons that in the experimental spectrum are observed as equivalent
• needs corrections for protons in close proximity to the heavier elements like sulphur, that arises in spin-orbit coupling effects, changing the chemical shifts
• makes approximations for the given level of theory in order to solve Schrodinger's equation for the system.

¹³C NMR of 18

Table 8 presents the comparison of the computed and experimental proton NMR values recorded in deuterated benzene.

Table 8. ¹³C NMR of 18.

		Simulated (Ref: TMS B3LYP/6-31G(d,p) Benzene)		Experimental (75 MHz, C6D6)
		δ (ppm)		δ (ppm)
		211.82		211.49
		147.28		148.72
		119.59		120.90
		69.07		74.61
		56.82		60.53
		55.20		51.30
		54.28
		53.56		50.94
		49.74		45.53
		45.27		43.28
		44.10		40.82
		41.27		38.73
		38.55		36.78
		33.71		35.47
		33.23		30.84
		28.50		30.00
		26.40		25.56
		26.07		25.35
		25.23		22.21
		22.47		21.39
		22.15		19.83

Analogous chart was produced to illustrate the correlations of experimental and computed ppm values for the carbon NMR.

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

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

In the synthetic part of this experiment, both the Shi and the Jacobsen catalysts are synthesised in order to carry out four assymmetric epoxidations of the two alkenes of choice. The alkenes studied are: styrene and trans-stilbene. The objective of this part of the exercise is to apply the experience of computational modelling gained in Part 1 to study key aspects of alkene epoxidation reactions, and use them to assign the absolute configuration of the obtained epoxides, rationalising the enantioselectivity. Overall, asymmetric epoxidations study is broken down into following studies:

• Catalysts' structure
  • Product NMR spectra
    • Absolute configuration
      • Interactions it the active site of a catalyst

We will start by examining the nature of epoxidation catalysts Shi and Jacobsen. The diagrams below represent activation processes for both the Shi and the Jacobsen's catalysts.

Shi activation process

Jacobsen activation process

Crystallographic Database Search

Shi Catalyst

The search of the Cambridge Crystallographic Database for a structure of the Shi catalyst has resulted in a NELQEA unit cell. NELQEA unit cell is asymmetric and is represented by molecules A and B. A detailed study of the unit cell has reported that in both molecules the pyranose ring assumes a ³S₀ conformation and the cis-fused 1,3-dioxolane ring assumes a E₄ conformation. However, the two molecules differ in the conformation of the second five-membered 1,3-dioxolane ring, which is E₂ in molecule A and E₄ in molecule B.

Table 9. Crystal Structure of the Shi catalyst

Molecule A-left		Molecule B-right
C-O bond	Length(Å)	C-O bond	Length(Å)
C1-O1	1.400	C1-O1	1.345
C7-O1	1.413	C7-O1	1.380
C2-O2	1.403	C2-O2	1.390
C7-O2	1.441	C7-O2	1.443
C2-O6	1.403	C2-O6	1.408
C6-O6	1.420	C6-O6	1.414
C4-O4	1.395	C4-O4	1.406
C10-O4	1.439	C10-O4	1.438
C5-O5	1.416	C5-O5	1.418
C10-O5	1.409	C10-O5	1.416

Anomeric Effect

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

Jacobsen Catalyst

Jacobsen's catalyst is a manganese-containing complex that is an effective catalyst for the asymmetric epoxidation of cis-olefins. In order to investigate the structure of Jacobsen's catalyst in more detail, the crystal structure of its precursor was located by searching the Cambridge crystal database. This resulted in two crystal structures, untit cells TOVNIB01 and TOVNIB02.

Table 10. Crystal Structure of the Shi catalyst

TOVNIB01		TOVNIB02
Bond	Length(Å)	Bond	Length(Å)
C1-O1	1.317	C1-O1	1.323
Mn1-O1	1.869	Mn1-O1	1.872
C20-O2	1.317	C20-O2	1.318
Mn2-O2	1.858	Mn2-O2	1.861
H17-H51	4.977	H17-H52	2.577
H19-H52	2.975	H19-H50	5.045
H18-H50	2.694	H18-H51	2.924
H20-H49	2.963	H20-H49	4.756
H21-H48	4.706	H21-H48	2.866
H22-H47	2.421	H22-H47	2.328

For two hydrogen atoms, the sum of the Van der Waals radii is 2.40 Å. As the hydrogens of the t-butyl groups indicated above for both crystal structures are separated by a distance greater than 2.40 Å, there must be attractive Van der Waals forces here. This leads to the t-butyl groups being pulled closer together, forcing the structure to be non-planar. In addition to this, the large steric bulk of the t-butyl groups means that it is sterically unfavourable for the alkene to approach from this end of the complex and instead, the alkene is more likely to approach over the diimine bridge.
The main difference between TOVNIB01 and TOVNIB02 is that in TOVNIB01, the methyl groups of the t-butyl are staggered whilst in TOVNIB02, the methyl groups are eclipsed. Staggering the methyl groups results in the shortening the H--H through-space distances, leading to greater attractive Van der Waals forces between the t-butyl groups. In addition to this, whilst all the H--H through-space distances in TOVNIB01 are greater than 2.40 Å, the through-space distance between H(22)-H(47) in TOVNIB02 is 2.32 Å, meaning that there is a degree of repulsion here; however, as the distance is only slightly shorter than 2.40 Å, this repulsion is expected to be weak. As the t-butyl groups in TOVNIB01 are closer together than in TOVNIB02, the structure of the complex is expected to be less planar than TOVNIB02.

Calculated NMR Properties of the Products

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

Trans-stilbene

Table 10. ¹H NMR of Trans-stilbene.

		Simulated[1] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)			Experimental (400 MHz, CDCl3)
		δ (ppm)	Peak analysis		δ (ppm)	Peak analysis
		7.57	s, 2H		7.59-7.25	m, 10H
		7.48	s, 8H
		3.54	s, 2H		3.87	s, 2H

Table 11. ¹³C NMR of Trans-stilbene.

		Simulated[2] (Ref: TMS B3LYP/6-31G(d,p) Chloroform)		Experimental (100 MHz, CDCl3)
		δ (ppm) (degeneracy=2 in all)		δ (ppm)
		134.08		137.1
		124.22		128.5
		123.52		125.5
		123.21
		123.08
		118.27
		66,43		62.8

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

References

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