A New Method for Approximating the Coulomb Potentials Generated by the Product of Two 1s Slater Orbitals

Abstract

The present chapter is a study in the evaluation of the Coulomb Potential (CP)generated by the product of two Slater Type Orbitals (STO). This study is motivatedby the recent developements carried out in our research group, see refs. [1,2,3]. Themethos presented in these references open several possibilities. Here, the effortsare directed to obtain approximated values of a parameter called Q, similar to thatdefined in [1], and also, to improve the evaluations in the intermediate auxiliaryintegrals which are analogous to those defined in [2]. The CP is represented as a serieswhose terms involve integrals which are functions of the approximated value for Q.This parameter is deermined in two differents ways: as an appropriated average andconsidering a model of the error of truncation of the series expansion. In both casesthe value of CP corresponds to the truncated series evaluated at these particular valuesof the parameter. The interest in this approach resides in the fact that it is possibleto perform all the necessary integrals in the complex plane, similarly as it is donein ref. [3]. This step is performed by using rational functions to approximate thenonoscilating parts of the integrands. The error observed in the obtained CP valuescan be explained from the errors involved in the rational functions used. The testcalculations are performed for the ethylene molecule.