# 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

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topFlad, 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

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

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