Calculation of the one-electron two-center integrals over Slater-type orbitals by means of the ellipsoidal coordinates method

A method for the calculation of one-electron two-center integrals is described. Using an ellipsoidal coordinate system, both the overlap, kinetic energy, and nuclear attraction integrals are expressed in terms of the so-called sigma function introduced by Baba-Ahmed et al. [A. Baba-Ahmed and J. Gayoso, Int. J. Quant. Chem. 23, 71 (1983), Eq. (51)] and which is easily programmed for a computer. The present investigation offers an advantage in that general formulas are derived which facilitate computation of the overlap and related two-center integrals over all Slater-type orbitals (STOs) with eventual nonintegral values of the principal quantum number. The proposed algorithm permits to avoid the procedure of interpolation [A. Baba-Ahmed and J. Gayoso, Theor. Chim. Acta, 62, 507 (1983), Eqs. 11-14] used to overcome the difficulty introduced by the presence of nonintegral quantum numbers. Finally, numerical aspects of the proposed algorithm are analyzed and comparisons with other approaches are given. (C) 1997 John Wiley & Sons, Inc.