Numerical methods for Multicenter integrals for numerically defined basis functions applied in molecular calculations

An alternative approach to using functions defined analytically as basis functions for molecular orbital calculations is to use functions defined numerically on some mesh. It is then necessary to evaluate various integrals involving products of such functions that are centered at different points in space, usually the nuclei. This article discusses in detail the problem of evaluating overlap and kinetic energy integrals, nuclear attraction three-center integrals, and electron-electron repulsion four-center integrals for such functions. The problem of evaluating these functions in translated coordinate systems, which arises in density functional theory applications, and the associated convergence problems are also discussed. (C) 2003 Wiley Periodicals, Inc.