Chemical valence from the two-particle density matrix

Abstract

The two-particle approach to the covalent and ionic valence indices is presented within the restricted and unrestricted Hartree-Fock theories (RHF and UHF). It is based on the analysis of contributions from the two-particle density matrix Γ in the orthogonal atomic orbital (OAO) representation. The atomic and diatomic valence indices are identified with respect to the reference states of separated atoms or ions and their physical interpretation is given. It is found that ionic indices originate from the Coulomb part of Γ, while the covalent indices are related to its exchange part. They are shown to be related to the differences, with respect to the reference state values, of the condensed Γ-matrix elements, measuring a total probability of simultaneously finding two electrons on atoms A and B. An interpretation of a second-order Taylor expansion around the reference states of the proposed electron pair valence indices is given. Illustrative valence diagrams for the two atomic orbital model are presented for both the A+B and A−+B+ reference limits, and their implications for the bond description are briefly discussed. The valence indices for simple diatomics and polyatomics are generated within the RHF and UHF schemes. The problem of the residual valence in the RHF approach is examined and the RHF predictions for alternative reference states are compared.