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

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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.

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