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

We present a unified study of two-center Coulomb integrals, involving Gauss ian, Slater. Bessel and polynomial radial factors combined with Cartesian a nd 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 a re 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. W e 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.