Molecular integrals over spherical Gaussian-type orbitals: I

Abstract

A novel derivation, involving the Fourier transform and the addition theorem of harmonic polynomials, is presented for multi-centre molecular integrals over spherical Gaussian-type orbitals. Compact closed-form formulae, consisting of vector-coupling coefficients and well known functions only, are obtained for all multi-centre molecular integrals. The resulting formulae manifest the angular and geometric dependence in vector-coupling coefficients and spherical harmonic functions, respectively, and require half as many summations as those for their counterparts, Cartesian Gaussian orbitals. An efficient computational method for molecular integrals over contracted Gaussian orbitals is suggested based on the present formulae for multi-centre molecular integrals.