MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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

Heinz-Jürgen Flad, Wolfgang Hackbusch and Reinhold Schneider


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.

MSC Codes:
41A50, 41A63, 65Z05, 81V70
best n-term approximation, wavelets, Hartree-Fock method, Density functional theory

Related publications

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