Evaluation of multielectron molecular integrals over Slater-type orbitals using binomial coefficients

Abstract

The analytical expressions are derived for the expansion of one- and two-centre electron charge density over Slater-type orbitals (STOs) in terms of STOs about a new centre. The expansion coefficients in these formulae are expressed through the overlap integrals. Using the expansion formulae obtained for the electron charge density, the general formulae are established for the multicentre molecular integrals with an arbitrary multielectron operator. The final results are expressed in terms of both the expansion coefficients of the electron charge density and the one-centre multielectron basic integrals with the same operator. In the formulae for the multicentre molecular integrals, all the expansion coefficients of the electron charge density and the one-centre basic integrals appearing in the Hartree-Fock-Roothaan equations for molecules are expressed through the binomial coefficients. The final results are especially useful for the calculation of these quantities for large quantum numbers. Using the derived expressions in terms of binomial coefficients, multielectron molecular integrals over STOs can be evaluated efficiently and accurately from the series expansion formulae. The relationships obtained are valid for the arbitrary location, quantum numbers and screening constants of atomic orbitals.