Spherically symmetrical properties of two-center overlap integrals over arbitrary atomic orbitals and translation coefficients for Slater-type orbitals

The orthogonality relations are derived for the rotation coefficients of two-center overlap integrals over arbitrary atomic orbitals (AAOs) and expansion coefficients for translation of Slater-type orbitals (STOs). Using these formulas, a very interesting theorem regarding the angular dependence is established. If we add the products of all the overlap integrals or all the translation coefficients with the same n and l values, but different m values, the result is independent of orientation. The final results are of a simple structure and are, therefore, especially useful for machine computations of multielectron multicenter molecular integrals by expanding one- and two-center electron charge density over STOs in terms of STOs about a new center.