EVALUATION OF INTEGRALS OVER STOS ON DIFFERENT CENTERS AND THE COMPLEMENTARY CONVERGENCE CHARACTERISTICS OF ELLIPSOIDAL-COORDINATE AND ZETA-FUNCTION EXPANSIONS

One-electron integrals over three centers and two-electron integrals o ver two centers, involving Slater-type orbitals (STOs), can be evaluat ed using either an infinite expansion for 1/r(12) within an ellipsoida l-coordinate system or by employing a one-center expansion in spherica l-harmonic and zeta-function products. It is shown that the convergenc e characteristics of both methods are complimentary and that they must both be used if STOs are to be used as basis functions in ab initio c alculations. To date, reports dealing with STO integration strategies have dealt exclusively with one method or the other. While the ellipso idal method is faster, it does not always converge to a satisfactory d egree of precision. The zeta-function method, however, offers reliabil ity at the expense of speed. Both procedures are described and the res ults of some sample calculation presented. Possible applications for t he procedures are also discussed. (C) 1999 John Wiley & Sons, Inc.