Theory of multicenter partitioning of molecular energies

The theory of analyzing molecular energies, as found from ab initio computations, in terms of the contributions from specific sets of atoms or centers is discussed. It is shown that the basis-function expansion of molecular wave functions in general leads to energetic interactions involving only one- through four-center terms. For the special case of self-consistent-field energies the formulas for the energy terms are given explicitly and several numerical properties are presented, including basis-set dependence, the differences between terms that arise in chemical reactions, and the first and second derivatives of individual terms with respect to molecular deformations. Expressions are also given for the multicenter resolution of correlation energies employing second-order many-body perturbation theory. Some numerical examples of the latter are also presented.