Spin-independent three-body effective valence-shell operators: Application to molecular oxygen

A mathematical construction is presented that uniquely defines a set of spin-independent effective valence-shell Hamiltonian (H^v) three-body matrix elements. These spin-independent H^v matrix elements separate direct and exchange portions of the three-body H^v matrix elements and therefore provide the most natural form for comparisons with parameterization schemes of semiempirical electronic structure methods in which the three-body matrix elements are incorporated into semiempirical one- and two-body Hamiltonian matrix elements in an averaged manner. Ab initio H^v three-body matrix elements of O₂ are computed through third order of quasidegenerate perturbation theory and are analyzed as a function of internuclear distance and atomic orbital overlap to aid in understanding how these three-body matrix elements may be averaged into semiempirical one- and two-body matrix elements. © 1992 John Wiley & Sons, Inc.