Fast and Stable Algorithm for Analytical Evaluation of Two-Center Overlap Integrals over Slater-Type Orbitals with Integer and Noninteger Principal Quantum Numbers

Abstract

A unified algorithm is presented for analytical evaluation of two-center overlap integrals over Slater-type orbitals with integer and noninteger principal quantum numbers. Two-center overlap integrals are expressed as finite sum of Gaunt coefficients and auxiliary functions S<inf>n,n</inf> L,(p, t). Special attention is paid to the efficient calculation of this auxiliary function by introducing analytic and recurrence relations. In order to test the accuracy of the formula for two-center overlap integrals, we performed an extensive study in which quantum numbers, orbital exponents, and internuclear distances were varied over wide ranges. We found that the method presented here for two-center overlap integrals is fully reliable for very high quantum numbers and the computation times are very low. © 2004 Wiley Periodicals, Inc.