Quadrature schemes for integrals of density functional theory

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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.