Numerical analysis of the planewave discretization of orbital-free and Kohn-Sham models Part I: The Thomas-Fermi-von Weizacker model. (arXiv:0909.1464v1 [math.NA])

We provide {it a priori} error estimates for the spectral and pseudospectral
Fourier (also called planewave) discretizations of the periodic
Thomas-Fermi-von Weizs"acker (TFW) model and of the Kohn-Sham model, within
the local density approximation (LDA). These models allow to compute
approximations of the ground state energy and density of molecular systems in
the condensed phase. The TFW model is stricly convex with respect to the
electronic density, and allows for a comprehensive analysis (Part I). This is
not the case for the Kohn-Sham LDA model, for which the uniqueness of the
ground state electronic density is not guaranteed. Under a coercivity
assumption on the second order optimality condition, we prove in Part II that
for large enough energy cut-offs, the discretized Kohn-Sham LDA problem has a
minimizer in the vicinity of any Kohn-Sham ground state, and that this
minimizer is unique up to unitary transform. We then derive optimal {it a
priori} error estimates for both the spectral and the pseudospectral
discretization methods.

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Original source : http://arxiv.org/abs/0909.1464...