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

Abstract

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\ensuremath{\Vert}b〉 (overlap), 〈a\ensuremath{\Vert}${\mathit{V}}_{\mathrm{eff}}$(b)\ensuremath{\Vert}a'〉 (effective-potential), and 〈a\ensuremath{\Vert}P(b)\ensuremath{\Vert}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. fortran 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.