SPHERICALLY SYMMETRICAL PROPERTIES OF 2-CENTER OVERLAP INTEGRALS OVERARBITRARY 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 (ST Os). Using these formulas, a very interesting theorem regarding the an gular dependence is established. If we add the products of all the ove rlap integrals or all the translation coefficients with the same n and l values, but different m values, the result is independent of orient ation. The final results are of a simple structure and are, therefore, especially useful for machine computations of multielectron multicent er molecular integrals by expanding one- and two-center electron charg e density over STOs in terms of STOs about a new center.