Molecular integrals over spherical Gaussian-type orbitals: II. Modified with plane-wave phase factors

Multi-centre molecular integrals over spherical Gaussian-type orbitals modified with plane-wave phase factors, which arise in the close-coupling treatment of ion–atom collisions as well as in some molecular structure calculations, are evaluated analytically in closed form by means of the Fourier transform and the addition theorem of harmonic polynomials. The resulting integral formulae for spherical Gaussian orbitals, consisting of vector-coupling coefficients and well known functions, are more compact than those for their counterparts, Cartesian Gaussian orbitals. Practical techniques are suggested for the efficient implementation of the present formulae.