Quadrature schemes for integrals of density functional theory

Abstract

The evaluation of integrals which arise in density functional theory, as applied to molecules, as discussed. Becke's scheme for reducing them to a sum of integrals over atom based polyhedra is used. Within each of these regions, quadratures for the spherical polar coordinates are examined; in particular we compare a Euler-Maclaurin based scheme with Gauss schemes. Upon specific investigations we find that the Euler-Maclaurin scheme is favoured for radial quadrature and Gauss-Legendre quadrature is preferred for theta. We investigate the number of quadrature points required for a given accuracy, and we demonstrate our favoured approach by calculations on a variety of molecules.