This article presents a variation of the integral transform method to evaluate multicenter bielectronic integrals (12͉34), with 1s Slater-type orbitals. It is proved that it is possible to define, out of the expression of (12͉34) given by the integral transform method, a function F(q) that has the property of having a unique Q, such that F(Q) ϭ (12͉34). Therefore, F(q) may be used to calculate (12͉34). It is shown that the evaluation of F(Q) turns out to be simpler than the three-dimensional integral involved in the calculation of (12͉34), and an algorithm is presented to calculate Q. The results show that relative errors on the order of 10 Ϫ3 or lower are obtained very efficiently. In addition, it is shown that the proposed algorithm is very stable.
ABSTRACT:A new approach for evaluating the four-center bielectronic integrals (12͉34), involving 1s Slater-type orbitals, is presented. The method uses the multiplication theorem for Bessel functions. The bielectronic integral is expressed in terms of a finite sum of functions, and a scaling parameter is introduced. In the present work, the scaling parameter used is an average. The results show that the first term in the sum is always the principal contribution, and the remainder has a corrective character. The whole scheme and its numerical trend are understood on the basis of a theorem recently proved.
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