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Best N-term approximation in electronic structure calculations. II. Jastrow factors
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- Journal:
- ESAIM: Mathematical Modelling and Numerical Analysis / Volume 41 / Issue 2 / March 2007
- Published online by Cambridge University Press:
- 16 June 2007, pp. 261-279
- Print publication:
- March 2007
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- Article
- Export citation
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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.
