Similarity of molecular shape.

The similarity of one molecule to another has usually been defined in terms of electron densities or electrostatic potentials or fields. Here it is expressed as a function of the molecular shape. Formulations of similarity (S) reduce to very simple forms, thus rendering the computerised calculation straightforward and fast. 'Elements of similarity' are identified, in the same spirit as 'elements of chirality', except that the former are understood to be variable rather than present-or-absent. Methods are presented which bypass the time-consuming mathematical optimisation of the relative orientation of the molecules. Numerical results are presented and examined, with emphasis on the similarity of isomers. At the extreme, enantiomeric pairs are considered, where it is the dissimilarity (D = 1 - S) that is of consequence. We argue that chiral molecules can be graded by dissimilarity, and show that D is the shape-analog of the 'chirality coefficient', with the simple form of the former opening up numerical access to the latter.