Calculation of the average properties of atoms in molecules

Abstract

An algorithm for calculating atomic properties, based on the topological theory of molecular structure, is described and applied. For any given molecular system atoms are rigorously defined in terms of the topological properties of the system's charge distribution rho (x) in three-dimensional space. The essential feature of this distribution is that its only local maxima, the attractors of the associated gradient vector field grad rho (x), occur at the positions of the nuclei. The region of space occupied by an atom, the atomic basin, is the space traversed by all gradient paths of grad rho (x) which terminate at its nucleus. This property is used to construct a coordinate transformation which maps each atomic basin onto three-dimensional space. The Jacobian J, of this transformation depends solely on the second derivatives of rho (x). The determinant of J is obtained by solving a first-order differential equation governed by grad2 rho (x). Any atomic property may then be calculated by an integration of an associated single-particle density over the basin of the atom. Numerical integrations of some atomic properties of diatomic and polyatomic molecules are reported.