ON THE EVALUATION OF CERTAIN TWO- AND THREE-CENTER MOLECULAR INTEGRALS OCCURRING IN ELECTROSTATIC CALCULATIONS

Abstract

A general method is developed for the evaluation of the three-center integrals which occur in the application of the Hellmann–Feynman theorem to the study of molecular binding. The method employs Gegenbauer polynomials for the series expansion of the radial dependence of the electric field. It is also shown that the same expansion greatly simplifies the evaluation of the two-center electrostatic penetration integrals. General formulae are presented for these latter integrals for all nonvanishing combinations of s, p, and d atomic orbitals for all principal quantum numbers.