∗-compressibility of discrete Hartree-Fock equations

Abstract The Hartree-Fock equations are widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle methods. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equations in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown that the s∗-compressibility is in accordance with convergence rates obtained from best N -term approximation for solutions of the Hartree-Fock equations. This is a necessary requirement in order to achieve numerical solutions for these equations with optimal complexity using the recently developed adaptive wavelet algorithms of Cohen, Dahmen and DeVore.