Best N-term approximation in electronic structure calculations. II. Jastrow factors
ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 2, pp. 261-279.

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

DOI : 10.1051/m2an:2007016
Classification : 41A50, 41A63, 65Z05, 81V70
Mots clés : best N-term approximation, wavelets, electron correlations, Jastrow factor
Flad, Heinz-Jürgen  ; Hackbusch, Wolfgang  ; Schneider, Reinhold 1

1 Institut für Informatik Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany. ; Christian-Albrechts-Universität Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany.
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     title = {Best $N$-term approximation in electronic structure calculations. {II.} {Jastrow} factors},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Schneider, Reinhold. Best $N$-term approximation in electronic structure calculations. II. Jastrow factors. ESAIM: Modélisation mathématique et analyse numérique, 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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