Analytical evaluation of three- and four-center electron-repulsion integrals for Slater-type orbitals

Abstract

A particular method has been introduced for obtaining a spherical harmonic expansion of a Slater-type orbital about a point displaced from the orbital center. Utilizing this method, a general analytical formula has been established for the radial coefficients of the expansion which contains terms only of the product of the overlap integrals and the radial parts of Slater-type orbitals. By the use of the derived expression for a spherical harmonic expansion, three- and four-center electron-repulsion integrals with the arbitrary location of Slater-type orbitals are expressed in terms of overlap integrals and one of the one-center Coulomb, and two-center Coulomb, hybrid and exchange integrals over Slater-type orbitals for the evaluation of which, recently, the analytical formulas have been established by the author. The convergence for the expansion has been tested by calculating concrete cases.