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MiS Preprint

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

Heinz-Jürgen Flad, Wolfgang Hackbusch and Reinhold Schneider


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.

MSC Codes:
41A50, 41A63, 65Z05, 81V70
best n-term approximation, electron correlations, wavelets, jastrow factor

Related publications

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