A topological analysis of molecular shape and structure

Abstract

In a novel approach to molecular shape representation, molecular electronic density functions are treated as 3D hypersurfaces in a 4D Euclidean space, spanned by the three spatial coordinates and an electronic density threshold variable. The general objects resulting from this approach are topological spheres with handles, modeling the electron density. Based on this model, a new, simple representation of molecular topology of electron density is proposed, using a tree describing the evolution of topological spheres with handles as function of a varying density threshold. The vertices of the tree are characterized by nonnegative integers (the genea of the topological objects). This representation is compared to earlier, detailed 3D topological descriptions of molecular shape as well as to the more conventional molecular network (bond skeleton) representation. A variety of relevant topological equivalence relations of molecules are discussed and a new, global, molecular similarity measure is proposed. © 1996 John Wiley & Sons, Inc.