Currently displaying 1 – 5 of 5

Showing per page

Order by Relevance | Title | Year of publication

Error estimates for the Coupled Cluster method

Thorsten RohwedderReinhold Schneider — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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,...

s∗-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen FladReinhold Schneider — 2012

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen FladReinhold Schneider — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Best -term approximation in electronic structure calculations. II. Jastrow factors

Heinz-Jürgen FladWolfgang HackbuschReinhold Schneider — 2007

ESAIM: Mathematical Modelling and Numerical Analysis

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 ( 2 ) near electron-electron and electron-nuclear cusps. Based on Nitsche's characterization of best -term approximation spaces A q α ( H 1 ) , we prove that...

Best -term approximation in electronic structure calculations I. One-electron reduced density matrix

Heinz-Jürgen FladWolfgang HackbuschReinhold Schneider — 2006

ESAIM: Mathematical Modelling and Numerical Analysis

We discuss best -term approximation spaces for one-electron wavefunctions φ i and reduced density matrices emerging from Hartree-Fock and density functional theory. The approximation spaces A q α ( H 1 ) 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 q spaces of wavelet coefficients to proof that both φ i and are in A q α ( H 1 ) for all α > 0 with α = 1 q - 1 2 . Our proof is based on the assumption...

Page 1

Download Results (CSV)