Rep:Mod:se506-module1

Third Year Computational Chemistry Lab

Module 1 - Structure and Spectroscopy (molecular mechanics and the molecular orbital)

Introduction

Since the dawn of the Quantum Mechanics revolution in the early part of the 20th century answers have been sought to many simple and complex problems in chemistry and physics. In chemistry, the quantum mechanical approach proved highly successful as a means to understanding simple molecules, in terms of their bonding, their structure and therefore reactivity. However quantum mechanics falls down with more complex systems, not because it doesn't work, but because the sheer complexity of the mathematics involved and hence the computing constraints become significant. Chemists therefore needed other methods to understand the chemical systems they were working with. Such methods need not be exact but estimates (using known and well understood systems as a basis) to provide good theoretical backing to the known experimental data.

Enter Molecular Mechanics (MM), an extremely useful method for understanding an array of molecular properties without need to solve wave equations. At its core, the MM approach uses five easily computed terms, each one itself modelled from classical mathematics. Each term or group of terms accounts for a component of the system's (molecule's) total energy. The strain in the system is estimated from three terms, the sum of diatomic bond stretches (modelled from Hooke's law), the sum of tri-atomic bond deformation angles (also modelled from Hooke's law) and the sum of the tetra-atomic bond torsions (modelled on a cosine wave). The steric repulsion of a system may be estimated from the sum of non-bonded Van-der-Waals repulsions (modelled on a Lennard Jones 12,6 potential) Finally the extent of Hydrogen bonding in the system is extrapolated from the sum of all electrostatic attractions of bond dipoles. The model (or rather the computer programme carrying out the modelling) aims to find the total energy minimum of the system through optimising its molecular geometry. In essence, the bonds lengths and angles are varied, within the 3N-6 framework of 'molecular movement' to achieve the lowest energy conformation. The individual components of this total energy can then be analysed.

One must however, be careful when using the MM approach and be aware of its limitations. Essentially the estimations made using MM are based upon that of known systems. Therefore data for inputted systems will be obtained through interpolation of known data. As such, data given for new molecules may well be inaccurate and unreliable as no basis exists from which a model can be produced. Conversely, systems consisting of bonds primarily based upon simple diatomic bonding, for instance hydrocarbons, can be modelled very accurately. Additionally, problems may arise in systems where an intimate knowledge of the position of electron density is required. As such, systems containing aromaticity, hyperconjugation or interactions arising from secondary overlap, may be difficult or even impossible to model. In some cases, one must resort to quantum mechanics once more with a view to solving the wave equations associated with such systems.

Throughout this computational journey of discovery, several MM programmes will be used. Most prevalent amongst them is ChemBio 3D using the Allinger MM2 force field. In addition Ghemical and Avagadro will be used. It is worth noting that comparisons of energies of different molecules are only valid when the same force field has been employed.

A number of chemical reactions were analysed in this experiment using the MM approach.

NB - The numbers used to refer to the various compounds studied here come from the course guide.

The Hydrogenation of the cyclopentadiene dimer

Cyclopentadiene may dimerise spontaneously at room temperature over the course of several hours via a pericyclic cycloaddition. It is known that dimerisation results in the exclusive formation of the endo form dimer rather than the exo form. Hydrogenation of the dimer will give a dihydro derivative, of which there are two possible regioisomers. Further hydrogenation will give the tetrahydro form. Here, molecular modelling has been implemented to rationalise some of the observed reactivity of the dimerisation and hydrogenation of cyclopentadiene. Why is only the endo product formed on dimerisation and which of the two regioisomers of hydrogenation is most likely to form. The mm2 force field of ChemBio 3D has been used to optimise the geometries of the various forms involved and study their relative thermodynamic stabilities.

For the dimerisation, both endo and exo forms were inputted into ChemBio 3D and the following energy value were obtained: Exo = 31.88 kcal/mol, Endo = 34.02 kcal/mol

Clearly, the relative energies do not differ significantly and it would therefore be unwise to attach too great a weight to these figures. Yet the figures show that in the thermodynamic sense the exo form is slighly more stable than the endo form. Comparing the individual energy components it can be seen that the small energy difference comes from the torsional strain element (endo = 9.5, exo = 7.6). However, we know the endo form to be the observed product and therefore a kinetic argument should be applied to the dimerisation.

The two dihydro derivatives were also analysed in a mm2 force field in chemBio 3D and their energy values are as follows: 3 = 35.93 kcal/mol, 4 = 31.15 kcal/mol

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

The nucleophilic additions to two pyridinium ring derivatives were investigated here. In the first, the ring (5) is alkylated in the 4-position using a methyl magnesium iodide reagent. In the second the pyridinium derivative (7) is reacted with aniline, which acts to transfer a NHphenyl group to the 4-position of the ring. Both reagents have been investigated as models in the mm2 force field of ChemBio 3D. In both cases the geometry of the carbonyl has been varied to see what effect this has on the energy.

5 = 26.33 kcal/mol (C=O up), 26.32 kcal/mol (C=O down)

7 = 15.41 kcl/mol (C=O up), 15.20 kcal/mol (C=O down)

It can be seen from the data that the relative position of the carbonyl has very little impact on the thermodynamic stability of the two reagents.

Stereochemistry and Reactivity of an Intermediate in the Synthesis of Taxol

In the Paquette synthesis of the anti cancer drug Taxol, a key intermediate was found to have two isomers, which interconvert. Such isomers arise because of atropisomerism, a type of isomerism, which leads to isomers through restricted rotation about a single bond. Specifically this involves the position of the carbonyl group; it may be 'up' or 'down'. Using ChemBio 3D the more thermodynamically stable atropisomer was determined.

With Carbonyl group up = 50.01 kcal/mol

With Carbonyl group down = 68.99 kcal/mol

Therefore, on the basis of thermodynamic stability only, we may conclude that the more stable atropisomer, by quite a margin, is the one in which the carbonyl group is orientated 'up'

Scheyler et al first introduced the concept of alkene hyperstability in 1981. The term is used to describe cycloalkenes that shown a negative strain energy. It is believed that this phenomenom is due to an increase in the interaction between the vicinal and transanular hydrogens of the ring, as in the case of the Taxol intermediate under study here. These compounds are typically difficult to hydrogenate and functionalise.

How one might induce room temperature hydrolysis of a peptide

At RTP and a neutral pH the hydrolysis of a peptide may take in the order of 500 years. Obviously many of the processes fundamental to life involve the hydrolysis of peptides and therefore enzymes do exist in nature, which can achieve the hydrolysis in a very much shorter period that it would occur unaided, often this will be in under a second. In the lab, the hydrolysis can be accelerated too, by using an esterification method, which can be achieved in the order of minutes.

Two molecules (13 and 14) were designed to allow an intramolecular nucleophilic substitution to occur, involving nucleophilic attack by the hydroxyl group on the carbonyl carbon and the associated loss of a leaving group, gaseous ammonia. By considering entropic arguments it is the loss of ammonia that is undoubtedly the thermodynamic driving force behind the reaction.

Amazingly the compounds 13 and 14 differ only in the relative stereochemistry of the hydroxyl group yet there is a significant difference in the half-life of the reaction, 21 minutes for 13 cf. 840 minutes for 14.

The stabilities of 13 and 14 have been analysed in ChemBio 3D, the chair-chair conformation as in decalin has been used. Additionally, values for both axial and equatorial conformations of the N-substituent have been obtained.

Energy Values (kcal/mol)

Compound	Axial	Equatorial
13	17.93	21.13
14	10.04	11.00