Fast and accurate evaluation of three‐center, two‐electron Coulomb, hybrid, and three‐center nuclear attraction integrals over Slater‐type orbitals using the SD transformation

In this work, Slater-type atomic orbitals (STOs) are expanded over B functions to exploit the compact Fourier transform of these functions. The analytic representations of three-center nuclear attraction integrals and multicenter bielectronic integrals over B functions involve semiinfinite highly oscillatory integrals, which can be transformed into infinite series. These integrals must be evaluated precisely and quickly. This work describes an efficient method for the evaluation of these integrals based on the nonlinear SD transformation, recently developed by Safouhi. The SD method was applied to multicenter integrals over B functions, and it is shown that this method is highly efficient compared with alternatives previously used. The SD approach should lead to a definitive suite of ab initio Slater software. The convergence properties were analyzed and they showed that the approximations obtained using the SD approach converge to the exact values of the semiinfinite integrals without any constraint. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004