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

Flad, Heinz-Jürgen; Hackbusch, Wolfgang; Schneider, Reinhold

doi:10.1051/m2an:2006007

Geodesic

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

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.

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 1, pp. 49-61

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Résumé

We discuss best $N$ -term approximation spaces for one-electron wavefunctions $φ_{i}$ and reduced density matrices $ρ$ emerging from Hartree-Fock and density functional theory. The approximation spaces $A_{q}^{α} (H^{1})$ 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 $ℓ_{q}$ spaces of wavelet coefficients to proof that both $φ_{i}$ and $ρ$ are in $A_{q}^{α} (H^{1})$ for all $α > 0$ with $α = \frac{1}{q} - \frac{1}{2}$ . Our proof is based on the assumption that the $φ_{i}$ possess an asymptotic smoothness property at the electron-nuclear cusps.

EuDML MR Zbl

DOI : 10.1051/m2an:2006007

Classification : 41A50, 41A63, 65Z05, 81V70
Keywords: best $N$-term approximation, wavelets, Hartree-Fock method, density functional theory

Affiliations des auteurs :

Flad, Heinz-Jürgen ; Hackbusch, Wolfgang ; Schneider, Reinhold ¹

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     title = {Best $N$-term approximation in electronic structure calculations {I.} {One-electron} reduced density matrix},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {49--61},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {1},
     year = {2006},
     doi = {10.1051/m2an:2006007},
     mrnumber = {2223504},
     zbl = {1100.81050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2006007/}
}

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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: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 1, pp. 49-61. doi: 10.1051/m2an:2006007

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