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 for and 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.
Mots-clés : best N-term approximation, wavelets, electron correlations, Jastrow factor
@article{M2AN_2007__41_2_261_0,
author = {Flad, Heinz-J\"urgen and Hackbusch, Wolfgang and Schneider, Reinhold},
title = {Best $N$-term approximation in electronic structure calculations. {II.} {Jastrow} factors},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {261--279},
publisher = {EDP-Sciences},
volume = {41},
number = {2},
year = {2007},
doi = {10.1051/m2an:2007016},
mrnumber = {2339628},
zbl = {1135.81029},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2007016/}
}
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: Modélisation mathématique et analyse numérique PY - 2007 SP - 261 EP - 279 VL - 41 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2007016/ DO - 10.1051/m2an:2007016 LA - en ID - M2AN_2007__41_2_261_0 ER -
%0 Journal Article %A Flad, Heinz-Jürgen %A Hackbusch, Wolfgang %A Schneider, Reinhold %T Best $N$-term approximation in electronic structure calculations. II. Jastrow factors %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 261-279 %V 41 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2007016/ %R 10.1051/m2an:2007016 %G en %F M2AN_2007__41_2_261_0
Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Schneider, Reinhold. Best $N$-term approximation in electronic structure calculations. II. Jastrow factors. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Molecular Modelling, Tome 41 (2007) no. 2, pp. 261-279. doi : 10.1051/m2an:2007016. http://archive.numdam.org/articles/10.1051/m2an:2007016/
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