Three-center nuclear attraction integrals for density functional theory and nonlinear transformations

Abstract

In the present work, we present the progress realized in the fast and accurate numerical evaluation of three-center nuclear attraction integrals. These integrals are required for density functional theory and also for any accurate ab initio molecular structure calculations. They occur in many millions of terms, even for small molecules and require rapid and accurate evaluation, best obtained over Slater type functions. The Fourier transform method allowed analytic expressions to be developed for these integrals. These analytic expressions turned out to be extremely difficult to evaluate precisely and rapidly because of the presence of spherical Bessel integrals. Different approaches were used to develop efficient algorithms for the numerical evaluation of these spherical Bessel integrals. These approaches are discussed and comparisons in accuracy and rapidity are presented to demonstrate that the approaches based on nonlinear transformations present a valuable contribution to the literature on molecular integrals over Slater type functions. © Springer-Verlag 2004.