An extremely efficient approach for accurate and rapid evaluation of three-centre two-electron Coulomb and hybrid integrals overBfunctions

Abstract

Analytic expressions of three-centre two-electron Coulomb and hybrid integrals over B functions are obtained using the Fourier transform method thoroughly explored by Steinborn's group. These analytic expressions involve semi-infinite integrals which are slowly convergent due to the presence of hypergeometric and spherical Bessel functions in the integrands. We have proven that these hypergeometric functions can be expressed as finite expansions and the integrands involving these series satisfy all the conditions required to apply the H approach which greatly simplifies the application of the nonlinear -transformation. This work presents a rapid and accurate evaluation of these integrals, obtained by using a new approach, which we called S. This new method is based on the H and methods and some practical properties of spherical Bessel, reduced Bessel and sine functions. The S method has greatly simplified the calculations, avoiding the long and difficult implementation of the successive zeros of the spherical Bessel function and a method for solving linear systems, which are required by H and .