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Computational Labs - (Module 1) Organic Chemistry

Author: Thomas McDevitt

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Abstract

Molecular modelling is a computational method used to calculate common properties of molecules. These can extend to spectroscopic properties, but it mainly concerns itself with the computing of geometric properties of a molecule by calculating a simple sum of the individual bond properties, namely:

• Compressive/tensile strain
• Bayer strain (bending energy)
• Pitzer strain (torsional energy)
• Van der Waals forces (as a function of the internuclear separation; the Lennard Jones potential)

No wavefunctions are taken into account; this is a purely classical method to calculating properties and in doing so, the ideal method can be found by iterating until a conformational minima is found.

This module aims to explore the capabilities of molecular modelling, to expose the weaknesses and overcome them by adding alternative mechanics which will provide reasonable approximations to the true answers that don't involve fully-fledged quantum calculations as these would not be completed in a reasonable amount of time.

Throughout this module, the Allinger MM2 method is used. It assigns an energy to its calculated conformational minima which can be used to effectively compare isomers but it should be noted that it is not as an absolute value in any way since this energy has no thermodynamic relevance.

The Hydrogenation of Cyclopentadiene Dimers

Cyclopentadiene

The cyclopentadiene molecule. Total energy: 6.48 kcal/mol

Cyclopentadiene is an unsaturated organic molecule that can act as both the diene and the dienophyl in an intermolecular Diels-Alder reaction, which it undergoes as it dimerizes to form dicyclopentadiene. In theory, there are two possible outcomes of this - one is that it forms the endo-Diels-Alder product and the other is that the exo-Diels-Alder product is formed.

Exo- dicyclopentadiene. (Molecule 1)

Endo- dicyclopentadiene. (Molecule 2)

However, in practice, the endo- product is formed preferentially. This can be rationalised by exploring both potential products and their properties using molecular modelling.

	Cyclopentadiene	Cyclopentadiene
	Exo- product	Endo- product
Stretch:	1.29	1.25
Bend:	20.59	20.87
Stretch-Bend:	-0.84	-0.84
Torsion:	7.67	9.51
Non-1,4 VDW:	-1.43	-1.56
1,4 VDW:	4.23	4.32
Dipole/Dipole:	0.38	0.45
Total:	31.88	34.00

Note: energy values given in kcal/mol.

The endo- overlap.

The exo- overlap.

From these results, it can be seen that the majority of the increased energy of the endo- product arises from torsional strain, which arises as a result of the dihedral angle between atoms which are three bonds apart being locked closer to the high energy eclipsed conformation instead of the preferred staggered conformation. This can be seen in the molecules in the eclipsing conformation of the two groups with double bonds (which are more sterically hindering than the protruding CH₂ group) in the endo- dimer which is avoided in the exo- case.

The lower energy of the exo- product renders it the thermodynamic product - however, the endo- product is formed instead since the path to the endo- product passes through a sterically unfavourable overlap between both cyclopentadiene monomers. The final exo- product is lower, but since the formation of the endo- product has a much lower kinetic barrier (lower activation energy), under non-equilibrating conditions it will be formed over the other.

Hydrogenation of the endo- dimer gives two products (without extended hydrogenation, which leads to complete saturation of the molecule).

Product 3

Product 4

	Molecule 3	Molecule 4
	Molecule 3	Molecule 4
Stretch:	1.24	1.10
Bend:	18.91	14.52
Stretch-Bend:	-0.76	-0.55
Torsion:	12.18	12.49
Non-1,4 VDW:	-1.53	-1.06
1,4 VDW:	5.74	4.51
Dipole/Dipole:	0.16	0.14
Total:	35.94	31.16

This time, the torsion energies are far closer together, but the bending interaction raises the energy of molecule 3 to the point at which its energy is much higher. As a result, it can be concluded that upon hydrogenation of a cyclopentadiene dimer, product 4 will be produced.

Stereochemistry of Nucleophilic additions to a pyridinium ring (NAD⁺ analogue)

Molecule 5

Molecule 5 has been discovered to react with Grignard reagent MeMgI in a stereospecific reaction creating the enantiomeric product molecule 6 with a selectivity of about 95% . Molecule 5 and its conformation can be seen to the left. It was drawn into BioChem3D and the energy minimized using a MMFF94 method due to a bug in the MM2 method with analysing the effect of a positivily charged nitrogen. A total energy of 57.44 kcal/mol was obtained. It can be seen that the carbonyl oxygen is slightly out of the plane of the benzyl group (dihedral angle = 15o). When considering the mechanism of the reaction, it is easy to see that the carbonyl has a steering effect on the attack of the nucleophilic methyl species offered by Grignard reagents, being the cause of the stereospecificity of this reaction. Should the molecular modelling method (MM2) be used to minimize the molecule, a much lower energy is obtained (38.00 kcal/mol) and the dihedral angle between the carbonyl oxygen and the phenyl ring is nearly 0o. Another thing worth noting is that the molecule can only be minimized as only the starting product or final product - including the Grignard reagent yields an error message relating to the Mg atom, suggesting that the molecular mechanics for magnesium have not been programmed into the engine and cannot be handled by the program as it is.

Molecule 5

The mechanism of the formation of molecule 6 from 5. The starting reagent (excluding MeMgI) is molecule 5, and the final product is molecule 6.

Molecule 7 was then drawn and optimized using the MMFF94 method as was done with molecule 5. A total energy of 98.28 kcal/mol was obtained (differing to the less accurate 62.76 kcal/mol obtained using the MM2 method). Again, the carbonyl oxygen falls out of the plane of the nearby phenyl group but in the opposite direction this time, with a dihedral angle of -37o. The higher energy corresponds to the much higher torsional strain caused by linking a less flexible phenyl group to the seven-membered ring (as opposed to the cyclopentane group at the corresponding position in molecule 5) and the steric clash of the secondary butyl group attached to the amine adjacent to the carbonyl carbon, the latter of which effects a the higher dihedral angle of the carbonyl oxygen as can be seen in the diagram on the right. The carbonyl oxygen once again directs the stereospecific attack of the aniline on the position para- to the nitrogen group in the pyridine component, but this time instead of directing it into place as it did for the Grignard reagent, forces the aniline away from it through a coulombic repulsion between its lone pairs and the lone pairs on nitrogen in aniline. This effectively forces attack of the aniline from the opposite face to the carbonyl, causing the stereochemistry shown.

Molecule 5 Molecule 7

The mechanism of the formation of molecule 8 from 7. The starting reagent (excluding aniline) is molecule 7, and the final product is molecule 8.

In both of these cases, the seven-membered ring is essentially locked into its conformation. It has the potential to be able to undergo ring-flipping under extreme conditions but at room temperature it is hindered from switching conformations by a large kinetic barrier induced by steric repulsions, rendering it an atropisomer. The isomerism that results from this drives both reactions in the above examples to their shown stereospecificity and as such the reactions are said to be atropenantioselective.

Stereochemistry and Reactivity of an Intermediate in the Synthesis of Taxol

Taxol intermediate up

Molecule 9 Carbonyl faces upwards.

Taxol intermediate up

Molecule 10 Carbonyl faces downwards.

One of the key intermediates in the synthesis of taxol comes in two isomers - one of which involves the carbonyl group facing upwards (molecule 9, left) and the other involves the same carbonyl group facing downwards (molecule 10, right). Molecular modelling (MM2) will be used to determine which of these is the lower energy form. The resulting energy calculations are as follows.

	Molecule 9	Molecule 10
Stretch:	2.54	2.56
Bend:	11.71	10.66
Stretch-Bend:	0.39	0.32
Torsion:	19.02	19.67
Non-1,4 VDW:	-0.85	-1.30
1,4 VDW:	12.42	12.54
Dipole/Dipole:	0.14	-0.18
Total:	45.38	44.27

Taxol intermediate up

An interesting thing to note is that molecule 9 can also be minimized with the cyclohexane ring in a twist-boat conformation. Total energy: 50.05 kcal/mol

It can be seen that molecule 10 has lower energy, hence it can be deduced that this is the isomer that predominantly exists and that molecule 9 will preferentially isomerise to form molecule 10 under the right conditions. However, these are atropisomers, meaning that (particularly at low temperatures) they can be isolated from each other as they are prevented from isomerising to their alternate forms by kinetic barriers which they can't overcome without enough energy.

The primary difference in the two energies of these molecules is the bend energy; the instability induced when bonds are formed at angles away from their optimum value (e.g. an sp³ hybridised carbon favours all of its bond angles to be 109^o28' (in a tetrahedral geometry) whereas any bonds bent as such that they deviate from this optimum value will raise the energy. This is difficult to observe by eye in a system with so many molecules.

Another interesting thing to consider is how the olefin group in these molecules is placed. Bredt's rule states:

“In polycyclic systems having atomic bridges, the existence of a compound having a carbon-carbon or carbon-nitrogen double bond at a bridgehead position is not possible, except when the rings are large, because of the strain which would be introduced in its formation by the distortion of bond angles and/or distances. As a corollary, reactions which should lead to such compounds will be hindered or will give products having other structures.”

One may argue that molecules 9 and 10 are large enough to accommodate Bredt's rule, though numerous other examples of bridgehead olefins in medium-sized ring systems have since been isolated since the discovery of hyperstable olefins - alkene groups which have negative strain energies rendering them even more stable than their parent saturated hydrocarbons. In this case, the hydrogenated versions of molecules 9 and 10 (labelled 9b and 10b respectively) will be drawn out and optimized using the MM2 method in BioChem3D and the energies examined.

	Unsaturated Energy / kcal mol-1	Saturated Energy / kcal mol-1	OS / kcal mol-1
Molecule 9	45.41	54.41	-9.00
Molecule 10	54.95	60.97	-6.02

Here, 'OS' refers to the olefin strain energy, in these cases the stabilisation effected onto the molecule by the unsaturation with respect to the parent hydrocarbon. This extra stability is not caused by steric hindrance or extra π-stability, but due to the stability of the cage-like structure and, in these cases, hydrogenation of the olefin group would change the hybridisation of the relevent bridgehead carbons and put more strain onto the rings, raising the energy of the molecule. As such, they are resilient to hydrogenation and in general would be very unreactive.

Modelling Using Semi-empirical Molecular Orbital Theory

Molecule 12

Molecule 12 as minimized by MM2.

We move away now from the classical approach to molecular modelling. This section exposes and overcomes the weaknesses in the MM2 method used by introducing basic quantum mechanics into what has been a purely classical solution up to this point.

Diagram of molecule 12.

9-Chloro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene was drawn out and optimized using the MM2 method. The molecular orbitals were then calculated using the MOPAC/PM6 method. The HOMO -1, HOMO, LUMO, LUMO +1 and LUMO +2 were then examined in more detail.

HOMO -1

HOMO

LUMO

LUMO +1

LUMO +2

Molecule 13
The olefin anti- to the chlorine
has been hydrogenated.

From the calculated HOMO, it can be seen that there is a lot of electron density on the olefin group syn- to the chloride group whereas there is much less on the olefin group anti- to it. Therefore, the olefin group that is syn- with respect to the chloride will be a lot more electron dense and will be preferentially targetted by electrophiles such as dichlorocarbene or a peracid.

The computer-generated infrared spectrum of molecule 12.

The frequencies of vibrations of molecules 12 and 13 were then calculated using the Imperial College SCAN and vibration/absorption frequencies recorded.

	C-Cl stretch	C=C olefin stretch
Molecule 12	770.9 cm-1	1737.1 cm-1 (anti), 1757.4 cm-1(syn)
Molecule 13	775.0 cm-1	1758.1 cm-1 (syn)

The computer-generated infrared spectrum of molecule 13.

The syn- olefin stretching frequency shows very little change between spectra - what little change there is will simply be due to the minor changes in structure of the molecule. The anti- olefin stretching frequency disappears from molecule 12 to 13 since this is the functional group which is being changed, meaning the equivalent molecular stretch in 13 will correspond to that of a different functional group. The C-Cl stretch, however, has changed by a small yet considerable amount. The stretch occurs at a higher wavenumber (and as such, higher energy) potentially due to an interaction between the occupied anti-C=C_π-orbital (HOMO -1) and the unoccupied C-Cl p_σ*-orbital (LUMO +1) which can occur in molecule 12 as a donation of electrons from the C=C_π-orbital into the C-Cl_σ*-orbital, lowering its bond order, making it more labile and hence lowering the wavenumber of the vibration. Upon hydrogenation of the olefin group in question, the symmetry of the C=C bond changes from π to σ, reducing if not eradicating this interaction, allowing the rigidity and hence wavenumber to rise again.

This interaction would also effect the strength of the olefin group anti- to the chloride. The lower wavenumber suggests that the bond has risen in stability due to the interaction.

Structure based Mini project using DFT-based Molecular orbital methods

Overview

This miniproject will discuss the stereospecific photochemical dimerisation of 2-butene DOI:10.1021/ja01030a066 . Other than fragmentation products, two primary products were obtained.

The primary reaction scheme, excluding isomerization of but-2-ene and fragmentation.

Isomer A Isomer A as minimized by MM2.

Isomer A Isomer A as minimized by SCAN.

Isomer B Isomer B as minimized by MM2.

Isomer B Isomer B as minimized by SCAN.

NMR will be the primary method to detect these compounds and tell them apart from each other. The lack of heteroatoms (and hence, very limited selection of identifiable functional groups) makes infrared spectroscopy less useful.

The Dominant Product

The two products were then drawn into BioChem3D and optimized using the MM2 and MMFF94 methods.

	Isomer A	Isomer B
MM2 energy / kcal mol-1	34.86	32.80
MMFF94 energy / kcal mol-1	22.93	20.11

Both methods calculate isomer B to have the lower energy, suggesting that it would be the predominantly formed product in this reaction. This is also the choice of product selected by chemical intuition when examining the transition states.

But-2-ene dimerises photochemically by a pericyclic reaction via a Möbius transition state. The two possibilities for the overlap are:

The dimerisation of but-2-ene, showing the possible overlaps and generated transition states.

The Lennard-Jones potential .

It can be seen that isomer B is more kinetically accessible due to an unfavourable steric clash between the methyl groups which can be avoided to an extent by formation of the exo- isomer. However, the empirical data shows that endo- form is formed at the ratio of 1.3:1.0 (0.022:0.017), contradicting what would be expected from computational stability calculations and chemical intuition upon considering the reaction mechanism.

This may be due to the fact that molecular modelling methods endeavor to find one single optimum geometry without taking into account conformational flexibility that occurs at room temperature (and almost all other experimental conditions).

The internuclear distance between some of the hydrogen nuclei in isomer A, as optimized by SCAN.

The image to the left shows the Lennard-Jones potential. It shows that at very close radii, molecules repel each other very strongly but at slightly higher radii, they do in fact exert an attractive force over each other (though at much higher radii this effect becomes negligible) and this effect can be significant in appropriately sized molecules. The van-der-Waals radius of Hydrogen (when interacting with other hydrogens) is 1.2Å, meaning that they attract each other most strongly (the minimum in the Lennard-Jones potential curve occurs) at about 2.4Å. The internuclear separation between the hydrogens on the methyl groups that are cis- with respect to each other in isomers A and B is to the order of about 2.2-2.5Å. When taking into account free rotation of the methyl groups, it is difficult to quantify exactly how much the molecule is stabilised by the attractive van der Waals force - but however much this is, it will apply more to isomer A than B since there are more cis-cis methyl group relations. This source of error cannot be overcome by molecular modelling and, as such, by using purely computational mechanics, the dominant isomer could be predicted wrongly (and has been in this case, according to experimental data).

Prediction of Spectroscopic Data

NMR Spectra - Isomer A

Isomer A.

The molecules were optimized with SCAN and then sent back again to SCAN for chemical shift calculations. The spin-decoupled spectra were returned and then analysed. The method used to calculate the chemical shifts has certain errors owing to heteroatoms, but since isomers A and B have only carbon and hydrogen, this doesn't apply. The method is, however, highly sensitive to the conformation, meaning that a chemical shift will arise for every individual entity within the molecule without account for conformational switching which will occur at room temperature (or most other experimental conditions). In the cases of isomers A and B, the SCAN optimized conformations show some staggering of the cyclobutane rings which, in reality, will be able to flip (for instance, in the labelled diagram of isomer A to the left, if carbon atoms 4 and 1 are slightly closer to the average 'height' of the methyl groups and 2 and 3 are slightly further down, these would be able to swap so that 4 and 1 ended up further away and 2 and 3 rose up slightly). Another thing not accounted for is free rotation of the methyl groups. In practise, when this occurs, the NMR spectra show an 'average' chemical shift (unless performed at exceedingly low temperatures). These two conformational flexibilities will ultimately render the methyl protons to be one environment and the ring-cyclobutane vicinal protons to form another. More relevent to ¹³carbon NMR, the methyl carbons will be one environment (which has an 'average' chemical shift of what they would have been at either extreme) and the ring cyclobutane carbons will be another.

The computed NMR spectrum is below.

Computer-generated decoupled NMR spectrum of Isomer A.

Carbon atom(s)	Computed δ / ppm	Predicted δ in practice / ppm
1, 4	160.56	162.03
2, 3	163.49	162.03
7, 8	181.78	183.46
5, 6	185.13	183.46

These chemical shifts make sense since carbon is a (marginally) more electronegative element than hydrogen (Pauling electronegativity of carbon = 2.55; hydrogen = 2.2) ultimately giving rise to the 'methyl inductive effect' which will cause the methyl substituents to increase the shielding of the cyclobutane ring carbons slightly, lowering their chemical shift as seen by the computed spectra.

The computed spectrum has chemical shifts for the hydrogen entities within the molecule, but these won't be analysed in much detail since the peaks appear at about (30±2)ppm whereas the ¹H peaks in literature appear at 0.87 (for the methyl protons) and 2.4 (for the vicinal ring protons). This exposes the errors involved in the method used for calculating ¹H chemical shifts and that they aren't accurate enough to be useful.

NMR Spectra - Isomer B

The computer-generated NMR spectra of isomer B.

Isomer B.

The analysis of the computed spectra for isomer B is much the same as it was for A. Carbon number Computed δ / ppm Predicted δ in practice / ppm 1, 4 159.28 159.65 2, 3 160.01 159.65 6, 7 179.94 180.69 5, 8 181.44 180.69

One thing worth noting is that the chemical shifts of the ring-carbons and the methyl carbons seem to have systematically shifted downwards by about 2.7ppm. This is almost certain to be due to the change in symmetry of the molecule - whether it physically changes the chemical shift of the carbon entities, or whether it induces a systematic error in the calculations performed on the molecule in the first place.

IR Spectra - Isomer A

The computer-generated infrared spectrum of isomer A.

As mentioned before, infrared spectroscopy isn't the most useful technique to analyse the products of this reaction since it is essentially a method of detecting functional groups, of which the potential molecules of this reaction have very little. Nonetheless, when forming a computer-generated spectra, it can still be useful to compare to literature to explore the accuracy of the calculations.

A table of key absorption frequencies is below.

Vibration	Wavenumber / cm-1 (computed)	Wavenumber / cm-1 (reference)
Vicinal Hydrogen Wag	1018	1000
Ring Shaking	1034	1016
Vicinal Hydrogen Swing	1374	1141
Methyl press (unison)	1436	1173
Methyl press (opposite)	1501	1316
Methyl bend	1520	1335
Methyl clap	1525	1376
		1392
		1455
		1470
Vicinal hydrogen stretch	3036	2880
Methyl double stretch	3040	2925
Methyl quadruple stretch	3043	2978

There is a lot of error involved in calculating the infrared absorption frequencies. This could be because they are calculated in the gas phase where as empirical infrared data is taken with the substance in its standard state at room temperature. This renders it difficult to assign computer generated peaks to those obtained experimentally - however, having said that, to an error of about 50-100 cm^-1, peaks occur for the most part in the same regions and to the same intensity.

IR Spectra - Isomer B

The computer-generated infrared spectrum of isomer B.

Vibration	Wavenumber / cm-1 (computed)	Wavenumber / cm-1 (reference)
Cross-methyl sway	1006	916
Vicinal hydrogen stretch	1387	1382
Methyl press (opposite)	1426	1457
Methyl wag	1516	1465
Methyl stretch (opposite)	3035	2875
Vicinal hydrogen saw	3042	2920
Methyl hydrogen saw	3105	2965

Alternative Techniques for Investigating the Products

Spectroscopy isn't the only way to tell the compounds apart. They could be deciphered quite easily from X-Ray crystallography. There is also the possibility that the melting points or boiling points could be recorded - though for this to be a good judge of which isomer has been obtained, the products will have to be separated and purified (which can be cumbersome) and then the melting (or boiling) points recorded at very high accuracy to be able to distinguish between them (and possibly done with repeats to improve accuracy) since similar structures will naturally lead to similar melting points. Comparing obtained melting points to literature will then suggest which product has been obtained.

Melting points:

• Isomer A: 122-122.5^oC
• Isomer B: Not given.

Boiling points:

• Isomer A: 128^oC
• Isomer B: 109^oC