Extrapolation methods for improving convergence of spherical Bessel integrals for the two‐center Coulomb integrals

Abstract

AbstractMulti‐center two‐electron Coulomb integrals over Slater‐type functions are required for any accurate molecular electronic structure calculations. These integrals, which are numerous, are to be evaluated rapidly and accurately. Slater‐type functions are expressed in terms of the so‐called B functions, which are best suited to apply the Fourier transform method. The Fourier transform method allowed analytic expressions for these integrals to be developed. Unfortunately, the analytic expressions obtained turned out to be extremely difficult to evaluate accurately due to the presence of highly oscillatory spherical Bessel integrals. In this work, we used techniques based on nonlinear transformation and extrapolation methods for improving convergence of these oscillatory spherical Bessel integrals. These techniques, which led to highly efficient and rapid algorithms for the numerical evaluation of three‐ and four‐center two‐electron Coulomb and exchange integrals, are now shown to be applicable to the two‐center two‐electron Coulomb integrals. The numerical results obtained for the molecular integrals under consideration illustrate the efficiency of the algorithm described in the present work compared with algorithms using the epsilon (ε) algorithm of Wynn and Levin's u transform. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006