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

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 on a expression proposed by Shavitt and Karplus in [J. Chem. Phys. 43 (1965) 398]. After a change of variables performed on a suitable semi-infinite integral given in [J. Chem. Phys. 43 (1965) 398], the integrand is replaced by a rational approximant which is able to be solved analytically using the method of residues. We suggest two alternatives: a pure interpolation and an Hermite interpolant strategy. In both cases, we present evidence of the good numerical behavior of our proposal on some class of examples. Besides, the method requires a computational effort comparable with a two-dimensional numerical integration.