The Hylleraas‐CI method in molecular calculations: Two‐electron integrals

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Abstract
In the Hylleraas‐CI method, first proposed by Sims and Hagstrom, correlation factors of the type r are included into the configurations of a CI expansion. The computation of the matrix elements requires the evaluation of different two‐, three‐, and four‐electron integrals. In this article we present formulas for the two‐electron integrals over Cartesian Gaussian functions, the most used basis functions in molecular calculations. Most of the integrals have been calculated analytically in closed form (some of them in terms of the incomplete Gamma function), but in one case a numerical integration is required, although the interval for the integration is finite and the integrand well‐behaved. We have also reported on partial and preliminary computations for the H2 molecule using our four‐center general formulas; a basis set of s‐ and p‐type functions yielded at R = 1.4001 Å an energy of ‐ 1.174380 a.u. to be compared with Kolos and Wolniewicz value of ‐ 1.174475.