Coulomb integrals for Gaussian, Slater, Bessel and polynomial-type functions

We present a unified study of two-center Coulomb integrals, involving Gaussian, Slater. Bessel and polynomial radial factors combined with Cartesian and spherical angular factors, performed with the shift operators technique. The master formula for these integrals appears as a linear combination of polynomials of the relative coordinates of the centers. These polynomials are independent of the type of radial factor, and only three families arise: two corresponding to angular factors of the same type and a mixed one. The coefficients depend on the types of both the angular and radial factors. We consider the 30 most important cases and give simple rules for obtaining them in terms of only six reference integrals. (C) 2001 Elsevier Science B.V. All rights reserved.