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

Heinz-Jürgen Flad; Wolfgang Hackbusch; Reinhold Schneider

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 2, page 261-279
- ISSN: 0764-583X

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topFlad, Heinz-Jürgen, Hackbusch, Wolfgang, and Schneider, Reinhold. "Best N-term approximation in electronic structure calculations. II. Jastrow factors." ESAIM: Mathematical Modelling and Numerical Analysis 41.2 (2007): 261-279. <http://eudml.org/doc/250137>.

@article{Flad2007,

abstract = {
We present a novel application of best N-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
$\mathcal\{F\}^\{(2)\}$ near electron-electron and electron-nuclear cusps. Based
on Nitsche's characterization of best N-term approximation spaces
$A_\{q\}^\{\alpha\}(H^\{1\})$, we prove that $\left. \mathcal\{F\}^\{(2)\}\in
A_\{q\}^\{\alpha\}(H^\{1\})\right. $ for q>1 and $\alpha=\frac\{1\}\{q\}-\frac\{1\}\{2\}$
with respect to a certain class of anisotropic wavelet tensor product bases.
Computational arguments are given in favour of this specific class compared to
other possible tensor product bases. Finally, we compare the approximation
properties of wavelet bases with standard Gaussian-type basis sets frequently
used in quantum chemistry.
},

author = {Flad, Heinz-Jürgen, Hackbusch, Wolfgang, Schneider, Reinhold},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Best N-term approximation; wavelets; electron
correlations; Jastrow factor.},

language = {eng},

month = {6},

number = {2},

pages = {261-279},

publisher = {EDP Sciences},

title = {Best N-term approximation in electronic structure calculations. II. Jastrow factors},

url = {http://eudml.org/doc/250137},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Flad, Heinz-Jürgen

AU - Hackbusch, Wolfgang

AU - Schneider, Reinhold

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/6//

PB - EDP Sciences

VL - 41

IS - 2

SP - 261

EP - 279

AB -
We present a novel application of best N-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
$\mathcal{F}^{(2)}$ near electron-electron and electron-nuclear cusps. Based
on Nitsche's characterization of best N-term approximation spaces
$A_{q}^{\alpha}(H^{1})$, we prove that $\left. \mathcal{F}^{(2)}\in
A_{q}^{\alpha}(H^{1})\right. $ for q>1 and $\alpha=\frac{1}{q}-\frac{1}{2}$
with respect to a certain class of anisotropic wavelet tensor product bases.
Computational arguments are given in favour of this specific class compared to
other possible tensor product bases. Finally, we compare the approximation
properties of wavelet bases with standard Gaussian-type basis sets frequently
used in quantum chemistry.

LA - eng

KW - Best N-term approximation; wavelets; electron
correlations; Jastrow factor.

UR - http://eudml.org/doc/250137

ER -

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