title: Automatic Selection of Integral Thresholds by Extrapolation in Coulomb and Exchange Matrix Constructions.
abstract: We present a method to compute Coulomb and exchange matrices with predetermined accuracy as measured by a matrix norm. The computation of these matrices is fundamental in Hartree-Fock and Kohn-Sham electronic structure calculations. We show numerically that, when modern algorithms for Coulomb and exchange matrix evaluation are applied, the Euclidean norm of the error matrix ε is related to the threshold value τ as ε = cτ(α). The presented extrapolation method automatically selects the integral thresholds so that the Euclidean norm of the error matrix is at the requested accuracy. This approach is demonstrated for a variety of systems, including protein-like systems, water clusters, and graphene sheets. The proposed method represents an important step toward complete error control throughout the self-consistent field calculation as described in [J. Math. Phys. 2008, 49, 032103].
authors.affiliation: Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden.
authors.forename: Elias
authors.initials: E
authors.lastname: Rudberg
authors.affiliation: Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden.
authors.forename: Emanuel H
authors.initials: EH
authors.lastname: Rubensson
authors.affiliation: Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden.
authors.forename: Paweł
authors.initials: P
authors.lastname: Sałek