The following chapter outlines the theoretical framework underlying the calculations on which the work in this thesis is based. A number of approximations must be made in order to solve the quantum mechanical equations governing all but the smallest of systems. These approximations are described and justified.
In order to analyse the results of ab initio calculations, it is useful to have a measure of local atomic properties such as ionic charges and bond populations. Unfortunately, the methods used for the electronic structure calculations, based on the use of a plane wave basis set to represent the electronic eigenstates, do not provide natural definitions of these quantities. Chapter details a method by which these local properties may be calculated by projection of the quantum mechanical eigenstates, resulting from an ab initio calculation, onto a localised atomic basis set. The implementation of this technique is described in Appendix . Applications of this population analysis to molecular and bulk systems are discussed. These include the use of ionic charges and bond populations as measures of ionicity and covalency of bonding, and bond population as a measure of bond modulus.
Chapter describes the use of the techniques detailed in the previous chapters in a study of the acetylcholine molecule. This molecule has been widely studied using semi-empirical calculations and conventional experimental techniques due to its central rôle in neurotransmission. Thus, it is a good subject for the validation of an ab initio approach.
The cytochromes P450, an important superfamily of enzymes which are of current interest in pharmacology and toxicology, are investigated in Chapter . These enzymes are responsible for the metabolism of many endogenous and xenobiotic compounds, including drugs. The interactions between ligand molecules and the active site of these enzymes are modelled and the results compared with experiment. The use of `computational experiments' is demonstrated in an exploration of the rôle of a water molecule at the active site of the enzyme in the inhibition of the catalytic reaction.
Finally, Chapter summarises the contents of this thesis and suggests some possible directions for future research.