Overlap Integrals With Respect to Quantum Numbers Over Slater-Type Orbitals Via the Fourier-Transform Method

Abstract

A unified analytical treatment of overlap integrals over Slater-type orbitals, using the Fourier transform method, is presented. Our approach leads to considerable simplification of the derivation of analytical representations for the overlap integrals over Slater type orbitals. In this approach, the representations of overlap integrals with both the same and different screening parameters have been obtained with the help of the Rayleigh expansion of a plane wave in terms of spherical Bessel functions and spherical harmonics. Analytical expressions obtained by this method have been expressed in terms of Gaunt coefficients, which are the product of spherical harmonics, Gegenbauer, and binomial coefficients. These overlap integrals have also been calculated with respect to the differences in n<inf>1</inf> - l<inf>1</inf> and n<inf>2</inf> - l<inf>2</inf> numbers that are even or odd. © 2004 Wiley Periodicals, Inc.