Rep:Mod:ms7109 module1

Modelling with Molecular Mechanics

The Hydrogenation of the Cyclopentadiene Dimer

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Endo/Exo selectivity in the dimerisation of cyclopentadiene

Figure 1: Exo (left) and Endo(right) isomers from dimerisation of cyclopentadiene

Figure 2: 1,4 strain in the endo isomer between two carbon atoms four bonds away

Cyclopentadiene can easily dimerise via a 4π_S + 2π_S cycloaddition of two cyclopentadienes. Two diastereoisomers (Fig. 1) are possible, Baldwin determined that the endo isomer is preferred, however at higher temperatures it can be converted to the exo form. In this experiment, the optimised geometry of the two isomers is determined using Allinger's MM2 force field by minimising their energies. The calculated energies are tabulated below in Table 1 with individual energy values for each of the force field parameters.

Table 1. Energies of the exo and endo isomers

	Energies/ kcal mol-1
	Stretch	Bend	Stretch-Bend	Torsion	Van der Waals	Dipole-Dipole	Total
Exo	1.286	20.581	-0.838	7.655	4.232	0.378	31.877
Endo	1.250	20.847	-0.835	9.511	4.320	0.448	33.998

Results show that the exo isomer is thermodynamically more favourable by about 2.121 Kcal mol^-1. The difference arises from the higher torsional strain present in the endo form, specifically the 1,4-strain illustrated in fig. 2. Nevertheless, the endo isomer is the major product due to kinetic factors controlling the reaction. By considering the Frontier molecular orbitals of the two approaching cyclopentadienes a favourable HOMO/LUMO orbital overlap in the rear of the endo isomer results in the stabilisation of the transition state energy. Since these interactions are not present in the transition state of the exo isomer the major product is indeed the endo as determined by Baldwin.

Hydrogenation of the cyclopentadiene dimer

Figure 3: Derivative products from the Hydrogenation of Cyclopentadiene, product 1 (left) and product 2 (right)

Figure 4: Bond angles for the two double bonds present in cyclopentadiene

Hydrogenation of the endo dimer may yield two dihydro derivatives while further hydrogenation will completely reduce all alkene bonds. To determine which of the two derivatives will predominate, the same method as above is used; minimisation of their energies (Table 2) will tell us the most thermodynamically stable form and indicate whether the kinetics of the reaction has an overriding influence.

Table 2. Energies of the dihydro derivatives

	Energies/ kcal mol-1
	Stretch	Bend	Stretch-Bend	Torsion	Van der Waals	Dipole-Dipole	Total
Product 1	1.277	19.866	-0.835	10.807	5.633	0.162	35.685
Product 2	1.097	14.525	-0.549	12.498	4.512	0.141	31.152

The table demonstrates the higher stability of product 2 (by about 4.533 Kcal mol^-1) and the greatest difference between the two originating from bending. The bridge on the norbornene ring puts a lot of strain on the double bond of dicyclopentadiene, such so that the ideal bond angle of 120° for an sp² carbon is forced to decrease to about 108°. On the other hand, the corresponding angle for the double bond on the 5 membered ring is only reduced to 113° (Fig. 4). This angular strain encourages selective hydrogenation of the former and a thermodynamic preference for product 2. This does not mean it will be the major product since the transition states have to be experimentally determined.

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Stereochemistry and Reactivity of an Intermediate in the synthesis of Taxol

Figure 5: Intermediates with carbonyl pointing up, cyclohexyl in chair (left) and twist-boat (right) conformation

Figure 6: Intermediates with carbonyl pointing down, cyclohexyl in chair (left) and twist-boat (right) conformation

In the synthesis of Taxol, Paquette isolated two atropisomeric ketone conformers, one has the carbonyl group pointing up and the other one down. Since they are atropisomers they cannot inter-convert between each other due to the high steric demand blocking the free rotation of the carbonyl group, however the cyclohexyl ring can undergo a structure change to reduce any torsional strain (Fig. 5 and 6). Using MM2 and MMFF94 minimisation we aim to determine the most stable conformation from their corresponding energies (Table 3.)

Table 3. Energies of all possible conformations of the intermediate

Conformation	Total Energy kcal mol-1		MM2 Parameter Energies kcal mol-1
	MM2	MMFF94	Stretch	Bend	Torsion	Van der Waals	Dipole-Dipole
Carbonyl up (Chair)	54.782	77.077	3.094	18.759	20.320	14.078	-1.814
Carbonyl up (Twist-boat)	53.304	76.292	2.949	17.210	21.285	14.504	-1.730
Carbonyl down (Chair)	42.683	60.566	2.619	11.339	19.665	12.874	-2.002
Carbonyl down (Twist-boat)	48.158	66.338	2.634	13.970	20.982	13.940	-1.584

Figure 7: Bond angle change between the bridge and the carbon-carbon bond undergoing hydrogenation

Molecular modelling enables the detection of the chair and twist-boat conformation for each of the two atropisomers. MM2 and MMFF94 generate different results, specifically the higher values from MMFF94 minimisation, nonetheless they roughly follow the same trend by being proportional to each other. Results above indicate a higher stability for the isomer with the carbonyl group pointing down, between the two cyclohexane structures the chair is 5.48 kcal mol^-1 lower in energy than the twist-boat, this is expected as ring-flipping energy diagrams for cyclohexane confirm the chair structures as the global minima and the twist-boat as local minima.

These alkene-containing compounds are known to be very stable and unlikely to hydrogenate . Double bonds attached to the bridge are stabilised by the nearly ideal bond angle of 119°, although following hydrogenation (Fig. 7), the new bond between the bridge and the sp³ hybridised carbon remains at 118° differing greatly from the ideal sp³ bond of 109.5°. Furthermore the additional hydrogen atoms on the molecule increase Van-der Waals repulsions. All these negative effects upon hydrogenation make the alkene intermediate highly stable.

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Modelling Using Semi-empirical Molecular Orbital Theory

Regioselective Addition of Dichlorocarbene

Figure 8: electrophilic addition of dichlorocarbene to endo double bond

9-Chloro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene reacts with electrophilic reagents such as dichlorocarbene via a regioselective addition of the double bond endo to the chlorine susbtituent. To explain why the endo double bond is more nucleophilic one has to determine the molecular orbitals involved in the reaction. The first step is MM2 minimisation to optimize the geometry of the compound, then the MOPAC/PM6 method is used to calculate the energies of the orbitals and to display them graphically.

HOMO-1	HOMO	LUMO	LUMO+1	LUMO+2

Out of the orbitals above the HOMO is responsible for nucleophilic attack on the carbene, it is clear that most of the electron density is localized on the endo double bond thus supporting the regioslectivity described. The reason for why the exo double bond is less nucleophilic is due to an antiplanar overlap of the filled π-orbital into a low lying Cl-C σ* (LUMO+1)

To determine the influence of the C-Cl bond on the vibrational frequencies of the molecule a gaussian method will be applied to calculate the characteristic vibrational modes of the starting 9-Chloro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene and its mono hydrogenated form where the exo double bond is replaced by a single C-C bond.

Dialkene			Monoalkene
722.61 Cl-C	1740.87 C=C exo	1760.99 C=C endo	779.93 Cl-C	1753.76 C=C endo	No exo C=C bond

The spectra above show numerous additional peaks between 1000 to 1750 cm^-1 for the monoalekene compared with the dialkene, these arise from the extra two hydrogen atoms which lead to more vibrational modes throughout the molecule. In the dialkene one can see a difference in energy between the two double bonds, the exo being lower due to overlap with the C-Cl σ* orbital which diffuses electron density and weakens the bond. Another way to prove this is to consider the bond lengths of both pi bonds: 1.336 for exo and 1.334 for endo. In the mono hydrogenated molecule the C-Cl bond is a lot stronger since the loss of exo double bond removes this orbital overlap thus placing less electron density into its antibonding σ*.

Monosaccharide Chemistry: glycosidation

Glycosidation of D-glucose involves the substitution of a leaving group at the anomeric centre by a nucleophile (e.g. ROH, RNH₂,RSH), this goes via a planar oxonium ion forming a mixture of α and β anomers (Fig. 8). By adding an ester (E.g. an acetyl group) on the 2-OH a high degree of stereocontrol can be achieved known as neighbouring group effect. The carbonyl on the acetyl can stabilise the oxonium ion thus sterically blocking one face. As a result the nucleophile attacks the opposite face, anti-periplanar to the C-OAc bond, in a S_N2 like reaction (Fig. 9).

Figure 8. Anomeric mixture from glycosidation.

Figure 9. Neighbouring group effect and stereocontrol.

Minimising the energies of compounds A to D can help us predict which is the most stable, both MM2 and MOPAC/PM6 interfaces can be used, however PM6 will be the most accurate since it takes into consideration electronic effects. For the calculations, R will be substituted with a methyl group because, unlike the usually used acyl group, its computational demand is minimal (only 30 seconds to run PM6). All four compounds have two possible conformers; one with the acyl group pointing above the plane of the oxonium cation and the other below, the energies of both will be determined with MM2 and PM6.

Table 4. Minimisation energies of all possible compounds by MM2 and PM6

Energies kcal mol-1				Structure from PM6 with bond angle and bond length between oxonium ion and acyl group carbonyl oxygen
Compound		MM2 (Total Energy)	PM6 (heat of formation)
A	a) Acyl above	20.667	-85.818	A' A
	b) Acyl below	9.677	-87.818
B	a) Acyl above	9.805	-88.541	B B'
	b) Acyl below	24.528	-77.311
C	a) Acyl above	43.397	-67.496	C' C
	b) Acyl below	34.810	-91.662
D	a) Acyl above	28.097	-87.990	D D'
	b) Acyl below	38.281	-65.289

Figure 10. Anomeric effect: Favourable Orbital overlap for axial substituent vs. no orbital overlap for equatorial

A comparison of both methods suggest that MOPAC/PM6 is the most ideal in these measurements since the difference in energy between two conformers is not as high as MM2. Results also point out that the most stable conformer is the one where the acyl carbonyl points towards or is closest to the oxonium ion. For example, for compound A, the energy when the acyl is above the plane of the oxoxnium ion is -85.818kcal mol^-1 and the length between the carbonyl oxygen and oxonium ion is 0.393nm, whereas the other has a lower energy of -87.818kcal mol^-1 and an expected shorter length of 0.159nm. This trend also applies to compounds B. Upon formation of the dioxolenium bond, the energies destabilize for the more unstable conformers of A and B. For example A(a) -85.818kcal mol^-1 to C(a)-67.496kcal mol^-1 because the acyl is forced to rotate (144.4° to 112.2°) and bond to the oxonium ion thus increasing strain and steric repulsion. On the other hand, the more stable conformers A(b) and B(a) will remain at the same energy since they are already positioned at the most stable electronic conformation shown by a very small change in bond angle. For example A(b): -87.818kcal mol^-1 and 104.5° to C(b):-91.662kcal mol^-1 and 104.8°. The difference in energy between C(a)/C(b) and D(a)/D(b) comes from the anomeric effect (Fig. 10) which stabilises the conformers with an axial acyl-carbonyl substituent due to C-O σ* overlap with an oxygen lone pair. The ratio C(a)/C(b) and D(a)/D(b) can be determined by Boltzmann distribution = exp(-(-ΔE/kT)). ΔE is calculated by converting energies from kcal to KJ and dividing by Avogadro's number, K_B is the boltzmann constant and T is 298K. From this equation C(b)/C(a) = exp(40.9)=5.54 x 10¹⁷ and D(a)/D(b) with a lower ΔE = exp(38.4)=4.64 x 10¹⁶, confirming the absence of C(a) and D(b) in the product. The nucleophile attacks at the Burgi-Dunitz trajectory of 105°, this occurs only trans to the acyl group thus only the two conformers C(b) and D(a) are able to do this. Since they are also stabilised by the anomeric effect, diastereospecificity of glycosidation via neighbouring group effect works very well.

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Mini Project

(-)-Cubebol, a sesquiterpene, is a major constituent of cubeb oil and apart from its well known medical uses it has recently been exploited as a cooling flavouring agent. The paper published by Hodgson, Salik and Fox updates us on a new stereocontrolled synthesis of (-)-cubebol involving unsaturated terminal epoxides to carry out the crucial intramolecular cyclopropanation reaction (7). Unlike previous syntheses, this one proceeds via fewer steps and begins with cheap and commercially available (-)-menthol. Two key steps are the formylation of menthone (2) which may induce unwanted epimerisation of the i-Pr group and the cyclopropanation (7) stated above in which facial selectivity is controlled solely by the epoxide stereochemistry.

Figure 11. Total synthesis of Cubebol

Figure 12 alkoxide-inducing epimerization

Starting from the formylation, it is reported that under alkoxide/ formate ester conditions the hydroxymethyleneisomenthone predominates in a mixture with its trans isomer of 93:7 suggesting that an almost complete i-Pr epimerisation occurs. This is unwanted since cubebol specifically needs hydroxymethylenementhone as an intermediate in its synthesis, so why is the cis isomer the significant product? It is known that epimerization is alkoxide-induced and it occurs before the actual formylation (Fig. 12). MM2 minimisation can be used to determine and compare the lowest conformational energies of menthone and isomenthone.

Table 5. MM2 Minimisation energies (kcal mol^-1)

Isomer	Torsion	Non 1,4-Van der Waals	Total energy	Structure
Trans	5.078	-1.917	11.828
Cis	6.996	-2.700	12.833

Calculations above show that menthone is more stable by 1.00 kcal mol^-1 and is therefore the thermodynamic product of epimerization at equilibrium prior to formylation. The slight difference in energies between the two is due to a significant increase in torsional strain when the substituents become cis to each other and counteracting 1,4- Van der Waals attractions (2.4A Hydrogen contacts) which help stabilise the cis isomer. These results are contrary to experimental results since hydroxymethylenementhone is proven to be the minor product. Thus, one has to consider the kinetic effects too; a measurement of the transition state energies may help us to rationalise why the thermodynamically more stable isomer is not formed.

Table 6. MM2 Minimisation energies for enolate transition states (kcal mol^-1)

Isomer	Total energy	Structure
Trans	29.612	Cubebol1
Cis	27.706	Cubebol2

Figure 13 Menthone and Isomenthone enolate transition states

The calculated energies of the transitions states confirm that the cis transition state is more stable, consequently it will have the lower activation energy barrier and will be the kinetically favoured product as experiments agree. An explanation for these energy differences originates from the stereo-electronically preferred axial formylation described below. Electrophilic attack of formate on the double bond occurs on the top face for menthone and on the bottom, sterically less hindered face, for isomenthone. However, figure (13.) shows that the methyl susbtituent can block the incoming formate on the top face destabilising this transition state and pushing the reaction towards hydroxymethyleneisomenthone. Like many other reactions in organic synthesis, here the kinetic factors override thermodynamic predictions. By using LDA, followed by HCO₂CHO₂CFO₃ at -78 degrees Celsius, hydroxymethylenementhone can be effectively isolated in high yields.

The second key step in the synthesis of (-)-cubebol is cyclopropanation, depending on the stereo-conformation of the epoxide one of two cyclopropyl alcohols can be formed. Literature reports that the iso-propyl group does not influence the efficiency of cyclopropanation if it lies on the same face as the alkene, but if the i-Pr changes its stereocentre a mixture of byproducts may form.

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Lastly, a computational spectroscopic evaluation of the absolute configuration of (-)-cubebol can be used to determine whether they agree with literature. ¹³C NMR can be predicted via the GIAO method which utilizes quantum mechanical density functional theory, unfortunately it produces small errors in the chemical shift of peaks due to excessive sensitivity to the conformation of the structure. Optimization of the molecule helps to correct any of these deviations, this is also done using the DFT model DOI:10042/to-10430 . Below are the results of ¹³C NMR prediction with TMS mPW1PW91/6-31G(d,p) GIAO as reference.

Carbon number or type	Chemical shift (ppm)
	DFT model	Literature
CHMe	19.8	18.7
C2	20.5	22.6
CHMeMe	21.3	19.6
CHMeMe	23.0	20.1
C1	24.8	26.4
C4	25.1	27.9
C6	30.0	29.5
C13	30.3	30.8
CMeMe2	31.6	31.7
C7	33.9	33.4
C5	34.0	33.6
C10	34.4	36.3
C9	37.4	39.0
C3	39.3	44.1
C-O	78.3	80.3

The table above shows how close the DFT NMR calculation DOI:10042/to-10399 matches the experimental NMR from the literature, however, there is a clear deviation as expected, the largest being by 4.8 ppm which is still within the 5 ppm maximum deviation range. This may arise from imprecise assignment of peaks by literature, for example Carbon-2 is predicted to have a peak at 20.5 ppm between those of methyl and i-Pr methyl whereas literature has assigned it lower downfield at 22.6 ppm. Nevertheless one expects the literature to have the correct NMR characterization thus making DFT calculations not as reliable, possibly because it doesn't consider equivalence of carbon atoms.

Vibrational normal modes of (-)-cubebol can also be predicted computationally, this time using B3LYP density functional method instead of mPW1PW91. The spectra shows very strong peaks between 3000-3200 cm^-1 and two at around 300 cm^-1. In the middle between 900-1700cm^-1 there are a number of medium/weak peaks but only two are significant enough to be analyzed.

Table 7. IR Vibrational modes for (-)-Cubebol (cm^-1)

B3LYP	Correction of stretches by 8%	Literature	Bond	Type of Vibration	peak size	Animation
3795	3491	3350	O-H	Stretch	Broad
ca. 3165	2928	2951	C-H	Stretch	Strong
ca. 3040	2827	2860	C-H	Stretch	Medium
1502	n/a	1490	C-H	CH3 bend	Weak
1143	n/a	1142	C-H	CH2 bend	Weak
964	897	910	CH3 and CH2	stretch	Weak

Table 7 summarizes the most significant IR frequencies in the spectrum obtained by DFT calculation DOI:10042/to-10429 . Bending modes are very similar to literature with only one peak differing by about 10 cm^-1. On the other hand, stretches deviate from literature by being systematically too high by 8%. The corrections are written in the table and a quick view at them demonstrates the closer resemblance to the literature values.

Further investigation of the properties of (-)-cubebol may be undertaken by computational means, such as the optical rotation of both the molecule and its isomer 7-epicubebol (cis substituents on the the cyclohexane ring). It may even be used prior to cyclopropanation to determine the epoxide stereochemistry. All in all, computational chemistry is a powerful tool not only to assess experimentally obtained data as done for ¹³C NMR and IR of (-)-cubebol but also to provide solutions to synthetic problems and to validate the reasoning behind a reaction's ismomeric preference as in the case of the formylation above.

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