EXPANSION FORMULAE FOR ONE- AND TWO-CENTER CHARGE DENSITIES OVER COMPLETE ORTHONORMAL SETS OF EXPONENTIAL TYPE ORBITALS AND THEIR USE IN EVALUATION OF MULTICENTER-MULTIELECTRON INTEGRALS

摘要

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of Psi(alpha)-exponential type orbitals (Psi(alpha)-ETO alpha = 1, 0, -1, -2,...) introduced by the author. Three-center overlap integrals of Psi(alpha) appearing in these relations are expressed through the two-center overlap integrals between Psi(alpha)-orbitals. The general formulae obtained for the charge densities are utilized for the evaluation of arbitrary multicenter-multielectron integrals occurring when the complete orthonormal sets of Psi(alpha)-ETO are used as basis functions in the Hartree-Fock-Roothaan and explicitly correlated methods. The relationships for charge densities and multicenter-multielectron integrals obtained are valid for the arbitrary quantum numbers, screening constants, and location of Psi(alpha)-orbitals.