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Best \(N\)-term approximation in electronic structure calculations. II: Jastrow factors. (English) Zbl 1135.81029
Summary: 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 \({\mathcal F}^{(2)}\) 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 \(\alpha=\frac1q-\frac12\) 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:
81V70 Many-body theory; quantum Hall effect
41A50 Best approximation, Chebyshev systems
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
65Z05 Applications to the sciences
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