The recently introduced set of quadratic ionic and covalent valence indices from changes in the pair-diagonal part of the molecular (Hartree-Fock) two-electron density matrix, A r(')(a, b) (orthogonal atomic orbital [OAO] basis set), relative to separated atoms limit (SAL), is extended to cubic valence numbers; they are calculated from the corresponding changes in the three-electron density matrix, Ar(3)(a, b, c). The two-and three-electron indices are given by the corresponding contributions to Ar(2) and AI'(3), which are quadratic and cubic in terms of relevant changes in the one-electron density matrix. The new valence measures are partitioned into 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 exactly in the UHF approximation; for fractional occupations, they give rise to a rather small correction to the overall two-electron valence index. The properties of cubic valence numbers are tested on a model three-orbital description of a symmetric (ABA), collinear transition state and on the OF ( Q = 1,0, -1) and 02-H+ systems. Preliminary results for B2H, are also given. 0 1996 John Wiley & Sons, Inc.
sity matrix [3], relative to the separated atoms (ions) limit (SAL). The Hartree-Fock (UHF) approximation in the symmetrically orthogonalized atomic orbitals (OAO) has been adopted. While the original he recently proposed set of valence indices [ 1, set [ 11 has preserved some first-order contributions T 21, ionic and covalent, uses a finite-difference in terms of the corresponding changes in the oneapproach which extracts valence information electron density (charge-and-bond-order [CBO]) (atomic and diatomic) from the relevant contribu-matrix, the modified set of the so-called quadratic tions to changes in the molecular two-particle den-valence indices (QVIS) [2] formulates valence meas--0.