Topology and Chemistry

Abstract

The determinants of chemical bonding are the chemical properties of the atoms and the constraints of three-dimensional (3-D) space into which the atoms must fit, but topology provides a convenient way of describing the resultant structure. This paper explores the topologies of various scalar fields associated with atoms in molecules and crystals and what they can tell us about chemical bonding. The scalar fields examined are the electron density, the electrostatic potential, and two simplified electrostatic potentials in which the contributions of the electron cores have been removed, namely the Madelung and the covalent field. Not all of the information contained in these fields is present in the topology but, since the topology is insensitive to the details of the field, it can often be determined using simplified calculations. Although the same topological model is used to explore all four fields, each field has its own distinctive topology and each provides different information about the nature of chemical bonding and structure. The analysis of these topologies, when combined with simple electrostatic theory and a few empirical observations, leads to a quantitative model of localized chemical bonding. In the process, the analysis provides insights into the nature of chemical bonding.