Molecular integrals with Slater basis. IV. Ellipsoidal coordinate methods for three-center nuclear attraction integrals

We develop and check an updated version of the ellipsoidal coordinate methods for the calculation of three-center nuclear attraction integrals with Slater-type orbitals (STOs). A first set of recurrence relations allows us to express these integrals in terms of some basic potentials. The basic potentials are classified in short- and long-range types, and then calculated in specific ways from auxiliary functions obtained by using a new set of both stable and fast recurrence relations. Numerical tests show that the procedure enables to reach very high accuracy in the integrals with a low computational cost.