MiS Preprint Repository

We discuss best $N$-term approximation spaces for one-electron wavefunctions ${\varphi }_i$ and reduced density matrices $\rho$ emerging from Hartree-Fock and density functional theory. The approximation spaces $A_q^{\alpha }(H^1)$ for anisotropic wavelet 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 to proof that both ${\varphi }_i$ and $\rho$ are in $A_q^{\alpha }(H^1)$ for all $\alpha >0$ with $\alpha =\frac{1}{q}-\frac{1}{2}$. Our proof is based on the assumption that the ${\varphi }_i$ possess an asymptotic smoothness property at the electron-nuclear cusps.