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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.
