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.

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Wed Sep 24 12:24:18 BST 1997