The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the , with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root equation for an infinite dimensional,...
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the
-for Galerkin discretizations of the Hartree-Fock equation 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...
The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the
-for Galerkin discretizations of the Hartree-Fock equation 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...
We present a novel application of best -term approximation theory
in the framework of electronic structure calculations. The paper focusses on the
description of electron correlations within a Jastrow-type ansatz for the
wavefunction. As a starting point we discuss certain natural assumptions on
the asymptotic behaviour of two-particle correlation functions
near electron-electron and electron-nuclear cusps. Based
on Nitsche's characterization of best -term approximation spaces
, we prove that...
We discuss best -term approximation spaces for one-electron wavefunctions and
reduced density matrices
emerging from Hartree-Fock and density functional theory. The approximation spaces for anisotropic
wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces.
We have used the norm equivalence of these spaces to weighted spaces of wavelet coefficients to
proof that both and are in for all with
. Our proof is based on the assumption...
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