The structures of molecular topological spaces

Abstract

The concepts of general topology are employed to derive a mathematical description of the structures of molecules. It is shown that a topological space on a finite set of points induces a unique graph and that as a consequence there is a uniquely determined topological space associated with every alternant molecule. This space is shown to be identical to the quotient space which results from partitioning the region of real space occupied by a molecule into atomic subregions. The molecular topological space is connected if and only if the molecule is connected and the only molecules having equivalent topological spaces are stereoisomers. Nonalternants are topologically distinguished from alternants by the fact that their graphs are not derivable from a topological space as are those of alternants. A set of graph-theoretical techniques for analyzing the combinatorial structure of finite topologies is developed. The cardinality of the molecular topology is found to be a measure of molecular complexity and the cardinalities of the subspace topologies associated with the bonds of the molecule are accurate measures of relative bond strength. Several empirical correlations between physical properties of molecules and topological measures are found.