Besselian: calculation of multicenter matrix elements

Abstract

The article is an author's review and includes also some new developments in calculation of multicenter matrix elements for investigating molecular structures using exponentially decreasing atomic orbitals. The Bessel atomic orbitals ( B-functions) as basis functions having the simplest representation in momentum space among the spherical exponential type atomic orbitals (ETO) are considered. The important integral representation for the B-functions product allows one to reduce four-center molecular electron repulsion matrix elements to integrals over the unit three-dimensional cube. The operator representation of multicenter integrals results in calculation of the latters with scalar B-functions, so the computing of the matrix elements of the spherical AOs with high angular momentum quantum numbers reduces to differentiation of the integrals of the simplest ETOs. For this purpose a method is suggested to replace the differentiation procedure by Fourier transforms in polyspherical coordinates in R n ( n=6,9). The results of numerical calculations confirm the efficiency of the Besselian algorithms suggested allowing them to compete with the Gaussian ideology.