A Kohn-Sham method involving the direct determination of the Coulomb potential on a numerical grid

Abstract For large molecules, the dominant cost in Hartree-Fock and density functional theory calculations is the evaluation of the Coulomb contribution to the Fock (or Kohn-Sham) matrix. We examine two approaches for the direct evaluation of the electronic Coulomb potential, either through the numerical solution of Poisson's equation or through an analytical integration. It is found that the second approach is less costly. A knowledge of the Coulomb potential greatly facilitates the evaluation of energy gradients. It is suggested that the analytic evaluation of the Coulomb potential followed by the numerical calculation of the relevant matrix elements may be the most cost effective way to proceed.

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