Integration of atoms in molecules : A critical examination

The theory of atoms in molecules rigorously defines reliable, accurate, consistent and stable average atomic properties. Obtaining these properties poses a complicated integration which is revisited in this paper and critically examined ab ovo. An integration algorithm using an analytical representation of the interatomic surface is proposed. This new technique is implemented in the program MORPHY 2.0, allowing automatic integration of all atoms in one input deck without external topological information. The present algorithm is illustrated via a few selected molecules with emphasis on the accuracy of (high) atomic electrostatic moments. It is shown that the theory of 'atoms in molecules' yields sufficiently accurate moments to reproduce the exact ab initio electrostatic potential.