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

Heinz-Jürgen Flad; Wolfgang Hackbusch; Reinhold Schneider

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 1, page 49-61
  • ISSN: 0764-583X

Abstract

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We discuss best N-term approximation spaces for one-electron wavefunctions φ i and reduced density matrices ρ 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 ρ are in A q α ( H 1 ) for all α > 0 with α = 1 q - 1 2 . Our proof is based on the assumption that the φ i possess an asymptotic smoothness property at the electron-nuclear cusps.

How to cite

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Flad, Heinz-Jürgen, Hackbusch, Wolfgang, and Schneider, Reinhold. "Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix." ESAIM: Mathematical Modelling and Numerical Analysis 40.1 (2006): 49-61. <http://eudml.org/doc/249694>.

@article{Flad2006,
abstract = { We discuss best N-term approximation spaces for one-electron wavefunctions $\phi_i$ and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces $A^\alpha_q(H^1)$ 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 $\ell_q$ spaces of wavelet coefficients to proof that both $\phi_i$ and ρ are in $A^\alpha_q(H^1)$ for all $\alpha > 0$ with $\alpha = \frac\{1\}\{q\} - \frac\{1\}\{2\}$. Our proof is based on the assumption that the $\phi_i$ possess an asymptotic smoothness property at the electron-nuclear cusps. },
author = {Flad, Heinz-Jürgen, Hackbusch, Wolfgang, Schneider, Reinhold},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Best N-term approximation; wavelets; Hartree-Fock method; density functional theory.; electron wave function; best -term approximation},
language = {eng},
month = {2},
number = {1},
pages = {49-61},
publisher = {EDP Sciences},
title = {Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix},
url = {http://eudml.org/doc/249694},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Flad, Heinz-Jürgen
AU - Hackbusch, Wolfgang
AU - Schneider, Reinhold
TI - Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/2//
PB - EDP Sciences
VL - 40
IS - 1
SP - 49
EP - 61
AB - We discuss best N-term approximation spaces for one-electron wavefunctions $\phi_i$ and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces $A^\alpha_q(H^1)$ 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 $\ell_q$ spaces of wavelet coefficients to proof that both $\phi_i$ and ρ are in $A^\alpha_q(H^1)$ for all $\alpha > 0$ with $\alpha = \frac{1}{q} - \frac{1}{2}$. Our proof is based on the assumption that the $\phi_i$ possess an asymptotic smoothness property at the electron-nuclear cusps.
LA - eng
KW - Best N-term approximation; wavelets; Hartree-Fock method; density functional theory.; electron wave function; best -term approximation
UR - http://eudml.org/doc/249694
ER -

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Citations in EuDML Documents

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  1. Harry Yserentant, The mixed regularity of electronic wave functions multiplied by explicit correlation factors
  2. Heinz-Jürgen Flad, Reinhold Schneider, s∗-compressibility of the discrete Hartree-Fock equation
  3. Heinz-Jürgen Flad, Wolfgang Hackbusch, Reinhold Schneider, Best -term approximation in electronic structure calculations. II. Jastrow factors
  4. Heinz-Jürgen Flad, Reinhold Schneider, -compressibility of the discrete Hartree-Fock equation
  5. Harry Yserentant, The mixed regularity of electronic wave functions multiplied by explicit correlation factors

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