Numerical integration of the electron density

Abstract

Abstract In quantum chemistry three-dimensional integrals of the type [special characters omitted], are common. In general, the integrand F(r) extends over all the molecular space. Sometimes, as occurs in density functional theory, the integrals can not be solved analytically and numerical approximations must be used. In molecules, the integrand F(t) is dominated by cusps at atomic nuclei. A popular solution to this multicenter integration problem is the nuclear weight function scheme proposed by A. D. Becke. Two algorithms based on Becke's approach were developed by P. M. W. Gill et al. and by Becke. The latter was slightly modified by O. Treutler and R. Ahlrichs. These two different algorithms were written in Fortran 90 and incorporated in MUNgauss.This work investigates in detail Becke's scheme and the application of the previous two algorithms to integrate the charge density of a set of test molecules.