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MiS Preprint
60/2005

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

Heinz-Jürgen Flad, Wolfgang Hackbusch and Reinhold Schneider

Abstract

We discuss best $N$-term approximation spaces for one-electron wavefunctions $\phi_i$ and reduced density matrices $\rho$ emerging from Hartree-Fock and density functional theory. The approximation spaces $A^\alpha_q(H^1)$ 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 $\phi_i$ and $\rho$ 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.

Received:
Jun 16, 2005
Published:
Jun 16, 2005
MSC Codes:
41A50, 41A63, 65Z05, 81V70
Keywords:
best n-term approximation, wavelets, Hartree-Fock method, Density functional theory

Related publications

inJournal
2006 Repository Open Access
Heinz-Jürgen Flad, Wolfgang Hackbusch and Reinhold Schneider

Best N-term approximation in electronic structure calculations. Pt. 1 : One-electron reduced density matrix

In: ESAIM / Mathematical modelling and numerical analysis, 40 (2006) 1, pp. 49-61