Evaluation of two- and three-center overlap integrals over complete orthonormal sets of ??-ETOs using their addition theorems

With the help of addition theorems for complete orthonormal sets of Psi(alpha)-ETOs in momentum space (alpha = 1,0,-1,-2,...) introduced by the author, the general expansion formulas are established for the two- and three-center overlap integrals occurring when Hartree-Fock-Roothaan and explicitly correlated methods, respectively, are employed. The relationships obtained are valid for the arbitrary quantum numbers, screening constants and location of Psi(alpha)supercript stop-ETOs.