Journal
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
Volume 46, Issue 2, Pages 341-388Publisher
EDP SCIENCES S A
DOI: 10.1051/m2an/2011038
Keywords
Electronic structure calculation; density functional theory; Thomas-Fermi-von Weizsacker model; Kohn-Sham model; nonlinear eigenvalue problem; spectral methods
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Funding
- ANR [LN3M]
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In this article, we provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsacker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the electronic density, and allows for a comprehensive analysis. This is not the case for the Kohn-Sham LDA model, for which the uniqueness of the ground state electronic density is not guaranteed. We prove that, for any local minimizer Phi(0) of the Kohn-Sham LDA model, and under a coercivity assumption ensuring the local uniqueness of this minimizer up to unitary transform, the discretized Kohn-Sham LDA problem has a minimizer in the vicinity of Phi(0) for large enough energy cut-offs, and that this minimizer is unique up to unitary transform. We then derive optimal a priori error estimates for the spectral discretization method.
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