Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix

Abstract

We discuss best N-term approximation spaces for one-electron wavefunctions φi and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces Aqα(H1) 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 ℓq spaces of wavelet coefficients to proof that both φi and ρ are in Aqα (H 1) for all α > 0 with α = 1/q - 1/2. Our proof is based on the assumption that the φi possess an asymptotic smoothness property at the electron-nuclear cusps. © EDP Sciences, SMAI 2006.