CHEMICAL VALENCE FROM THE 2-PARTICLE DENSITY-MATRIX

The two-particle approach to the covalent and ionic valence indices is presented within the restricted and unrestricted Hartree- Fock theori es (RHF and UHF). It is based on the analysis of contributions from th e two-particle density matrix GAMMA in the orthogonal atomic orbital ( OAO) representation. The atomic and diatomic valence indices are ident ified with respect to the reference states of separated atoms or ions and their physical interpretation is given. It is found that ionic ind ices originate from the Coulomb part of GAMMA, while the covalent indi ces are related to its exchange part. They are shown to be related to the differences, with respect to the reference state values, of the co ndensed GAMMA-matrix elements, measuring a total probability of simult aneously finding two electrons on atoms A and B. An interpretation of a second-order Taylor expansion around the reference states of the pro posed electron pair valence indices is given. Illustrative valence dia grams for the two atomic orbital model are presented for both the A B and A + B+ reference limits, and their implications for the bond des cription are briefly discussed. The valence indices for simple diatomi cs and polyatomics are generated within the RHF and UHF schemes. The p roblem of the residual valence in the RHF approach is examined and the RHF predictions for alternative reference states are compared.