Best N-term Approximation in Electronic Structure Calculations I. One-electron Reduced Density Matrix

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 Aq (H ) 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 q spaces of wavelet coefficients to proof that both φi and ρ are in A α q (H ) 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. Mathematics Subject Classification. 41A50, 41A63, 65Z05, 81V70. Received: May 11, 2005. Revised: August 11, 2005.