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

Published online by Cambridge University Press:  16 June 2007

Heinz-Jürgen Flad,
Wolfgang Hackbusch and
Reinhold Schneider
Heinz-Jürgen Flad
Affiliation:
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22-26, 04103 Leipzig, Germany. wh@mis.mpg.de
Wolfgang Hackbusch
Affiliation:
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22-26, 04103 Leipzig, Germany. wh@mis.mpg.de
Reinhold Schneider
Affiliation:
Institut für Informatik Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany.
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Abstract

We present a novel application of best N-term approximation theoryin the framework of electronic structure calculations. The paper focusses on thedescription of electron correlations within a Jastrow-type ansatz for thewavefunction. As a starting point we discuss certain natural assumptions onthe asymptotic behaviour of two-particle correlation functions $\mathcal{F}^{(2)}$ near electron-electron and electron-nuclear cusps. Basedon Nitsche's characterization of best N-term approximation spaces $A_{q}^{\alpha}(H^{1})$ , we prove that $\left.\mathcal{F}^{(2)}\inA_{q}^{\alpha}(H^{1})\right.$ 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 toother possible tensor product bases. Finally, we compare the approximationproperties of wavelet bases with standard Gaussian-type basis sets frequentlyused in quantum chemistry.


Keywords

Best N-term approximationwaveletselectroncorrelationsJastrow factor.

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 2: Special issue on Molecular Modelling , March 2007, pp. 261 - 279
Copyright
© EDP Sciences, SMAI, 2007

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