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Best N-term approximation in electronic structure calculations I.One-electron reduced density matrix
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- Journal:
- ESAIM: Mathematical Modelling and Numerical Analysis / Volume 40 / Issue 1 / January 2006
- Published online by Cambridge University Press:
- 23 February 2006, pp. 49-61
- Print publication:
- January 2006
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- Article
- Export citation
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We discuss best N-term approximation spaces for one-electron wavefunctions $\phi_i$
and reduced density matrices ρemerging from Hartree-Fock and density functional theory. The approximation spaces $A^\alpha_q(H^1)$ 
for anisotropicwavelet 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 toproof that both $\phi_i$ and ρ 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.
