Molecular integrals over slater-type orbitals. From pioneers to recent developments

Abstract

It can readily be demonstrated that atomic and molecular orbitalsmust decay exponentially at long-range. They should also possess cusps when two particles approach each other. Therefore, Slater orbitals are the natural basis functions in quantum molecular calculations. Their use was hindered over the last four decades by integration problems. Consequently, Slater orbitals were replaced by Gaussian expansions in molecular calculations (in spite of their more rapid decay and absent cusps). From the 90s until today considerable effort has been made by several groups to develop efficient algorithms which have fructified in new computer programs for polyatomic molecules. The key ideas of the different methods of integration: one-center expansion, Gauss transform, Fourier transform, use of Sturmians and elliptical co-ordinate methods are reviewed here, together with their advantages and disadvantages, and the latest developments within the field. A recent approximation separating the variables of the Coulomb operator will be described, as well as its usefulness in molecular calculations. Recently, due to the developments of the computer technology and the accuracy of the experiments, there is a renewed interest in the use of Slater orbitals as basis functions for Configuration Interaction (CI) and Hylleraas-CI atomic and molecular calculations, and in density functional and density matrix theories. © 2011 by Nova Science Publishers, Inc. All rights reserved.