Overlap, effective-potential, and projection-operator bicentric integrals over complex Slater-type orbitals

The algorithm of Silverstone and Moats [Phys. Rev. A 16, 1731 (1977)] for the expansion of a function about a displaced center is used to derive analytical expressions for some bicentric integrals appearing in molecular and solid-state calculations. The 〈a‖b〉 (overlap), 〈a‖${\mathit{V}}_{\mathrm{eff}}$(b)‖a’〉 (effective-potential), and 〈a‖P(b)‖a’〉 (projection-operator) bicentric integrals over complex Slater-type orbitals (STO’s) are explicitly considered. Simple and compact formulas for the spherically averaged integrals are obtained by straightforward summation over the angular-momentum subspecies of center A. f o r t r a n routines adapted to a vector computer have been implemented to compute the atom-lattice bicentric integrals of the abinitio perturbed ion method, a Hartree-Fock-Roothaan scheme recently developed by us for the study of ionic and van der Waals crystals. This algorithm is 4–40 times faster than one based on elliptic coordinates and the Mulliken orientation of the A-B diatomic molecule. Furthermore, its efficiency increases progressively with the principal and angular quantum numbers of the complex STO, showing the potentiality of this method in the study of closed-shell systems containing heavy atoms or ions.