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

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations are expressed through the two-center overlap integrals between -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 exponential type orbitals 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 orbitals.