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.


We discuss best N-term approximation spaces for one-electron wavefunctions $\phi_i$ and reduced density matrices ρemerging from Hartree-Fock and density functional theory. The approximation spaces $A^\alpha_q(H^1)$ for anisotropicwavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted $\ell_q$ spaces of wavelet coefficients toproof that both $\phi_i$ and ρ are in $A^\alpha_q(H^1)$ for all $\alpha > 0$ with $\alpha = \frac{1}{q} - \frac{1}{2}$ . Our proof is based on the assumption that the $\phi_i$ possess an asymptotic smoothness property at the electron-nuclear cusps.