Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix
Flad, Heinz-Jürgen ; Hackbusch, Wolfgang ; Schneider, Reinhold1
1 Institut für Informatik Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany. ; Christian-Albrechts-Universität Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany.
ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 1, pp. 49-61.

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(H1) for all α>0 with α=1q-12. Our proof is based on the assumption that the φi possess an asymptotic smoothness property at the electron-nuclear cusps.

DOI : 10.1051/m2an:2006007
Classification : 41A50, 41A63, 65Z05, 81V70
Mots-clés : best N-term approximation, wavelets, Hartree-Fock method, density functional theory
Flad, Heinz-Jürgen  ; Hackbusch, Wolfgang  ; Schneider, Reinhold 1

1 Institut für Informatik Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany. ; Christian-Albrechts-Universität Kiel, Christian-Albrechts-Platz 4, 24098 Kiel, Germany. 
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Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Schneider, Reinhold. Best $N$-term approximation in electronic structure calculations I. One-electron reduced density matrix. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 1, pp. 49-61. doi : 10.1051/m2an:2006007. https://www.numdam.org/articles/10.1051/m2an:2006007/

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