REPRESENTATION, COMPARISON, AND ANALYSIS OF MOLECULAR DEFORMATIONS

In terms of the Born-Oppenheimer approach to chemistry, molecules may be represented as three-dimensional objects, and their structures may be compared: this comparison is of crucial importance to successful mo lecular modelling. Furthermore, molecular modelling techniques presupp ose that a suitable molecular representation is available. This paper outlines various methods for representing molecular structure, such as positional coordinates - an example of which are crystallographic coo rdinates - and internal parameters such as bond distances and angles. The similarity between two molecules may be established by maximally s uperimposing them, and then determining the extent to which they canno t be brought to coincide. This is the approach used in many molecular modelling programs. Alternatively, instead of viewing the molecules as objects embedded in three-dimensional space, they can also be thought of as representative points within a hyperdimensional space spanned b y a set of 3N-6 independent geometric coordinates that define the stru cture of the molecule (N is the number of atoms). In this case, the si milarity between two molecules can be expressed in terms of the distan ce between their representative points. Preferred conformations may be identified by examining the distributions of representative points fo r closely related molecules within these hyperdimensional spaces. Howe ver, in order to compare ensembles of molecules, multidimensional stat istical techniques have had to be employed. The methods of principal c omponent and cluster analysis are described and are illustrated by mea ns of simple two-dimensional examples. Finally, two examples are taken from the chemical literature to demonstrate how the multivariate stat istical methods can be applied in practice, and what type of results t hey yield.