Rational approximants to evaluate four-center electron repulsion integrals for 1s hydrogen Slater type functions

Abstract

Modelling a problem in quantum chemistry, within the framework of Hartree-Fock approach, requires the evaluation of four center two-electron integrals. The speed up of the integral evaluation is a key point in order to get a method suitable to deal with large molecules. The most expensive step of the process involves the evaluation of the two-electron integrals. Here we propose a method to compute those involving 1s hydrogen Slater type orbitals, which is based upon an expression propossed by Shavit and Karplus in 1965. The key point of the technique is the use of a rational approximation of the integrand which then, allows us to solve the integral analitically by the method of residues. Two different rational are proposed and some examples are presented showing evidence of a good numerical behavior.