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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
80/2005

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

Heinz-Jürgen Flad, Wolfgang Hackbusch and Reinhold Schneider

Abstract

We present a novel application of best $N$-term approximation theory in the framework of electronic structure calculations. The paper focus 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 asymp\-totic 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 $\mathcal{F}^{(2)}\in A_{q}^{\alpha}(H^{1})$ 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.

Received:
Sep 8, 2005
Published:
Sep 8, 2005
MSC Codes:
41A50, 41A63, 65Z05, 81V70
Keywords:
best n-term approximation, electron correlations, wavelets, jastrow factor

Related publications

inJournal
2007 Repository Open Access
Heinz-Jürgen Flad, Wolfgang Hackbusch and Reinhold Schneider

Best N-term approximation in electronic structure calculations. Pt. 2 : Jastrow factors

In: ESAIM / Mathematical modelling and numerical analysis, 41 (2007) 2, pp. 261-279