A sufficiently damped iteration of the Kohn-Sham (KS) equations with the exact functional is proven to always converge to the true ground-state density, regardless of the initial density or the strength of electron correlation, for finite Coulomb systems. We numerically implement the exact functional for one-dimensional continuum systems and demonstrate convergence of the damped KS algorithm. More strongly correlated systems converge more slowly.
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Wagner et al. (2013) studied this question.
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