HARTREE-FOCK DIFFERENCE APPROACH TO CHEMICAL VALENCE - 3-ELECTRON INDEXES IN UHF APPROXIMATION

The recently introduced set of quadratic ionic and covalent valence in dices from changes in the pair-diagonal part of the molecular (Hartree -Fock) two-electron density matrix, Delta Gamma((2))(a, b) (orthogonal atomic orbital [OAO] basis set), relative to separated atoms limit (S AL) is extended to cubic valence numbers; they are calculated from the corresponding changes in the three-electron density matrix, Delta Gam ma((3))(a, b, c). The two- and three-electron indices are given by the corresponding contributions to Delta Gamma((2)) and Delta Gamma((3)), which are quadratic and cubic in terms of relevant changes in the one -electron density matrix. The new valence measures are partitioned int o one-, two-, and three-center contributions comprising purely ionic ( covalent) and mixed ionic-covalent terms. For integral OAO occupations in the SAL, the sum of all three-electron contributions vanishes exac tly in the UHF approximation; for fractional occupations, they give ri se to a rather small correction to the overall two-electron valence in dex. The properties of cubic valence numbers are tested on a model thr ee-orbital description of a symmetric (ABA), collinear transition stat e and on the O-2(Q) (Q = 1,0, -1) and O-2-H+ systems. Preliminary resu lts for B2H6 are also given. (C) 1996 John Wiley & Sons, Inc.