Hartree-Fock energy partitioning in terms of Hirshfeld atoms

A Hirshfeld decomposition scheme of the Hartree-Fock total molecular energy into atomic energies is presented. The calculations are performed by direct numerical integration and the results are compared for a set of 28 molecules containing different kinds of atoms. The calculated atomic energies show a strong dependency on changes of atomic electron population and hybridization. Linear correlations are found between the energy and the population for H, these being related to the electronegativity of this atom and to the external potential created by the remaining atoms. The proposed energy partitioning scheme appears to be useful for studies such as proton acidity, the anomeric effect and group transferability, and allows atomic virial ratios to be obtained. Finally, the atomic potential energies are found to mimic trends based on exact expressions as well as trends displayed by molecular quantities, thus lending credibility to the partitioning scheme used.