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In this paper, we investigate the energy minimization model of the ensembleKohn-Sham density functional theory for metallic systems, in which apseudo-eigenvalue matrix and a general smearing approach are involved. We studythe invariance and the existence of the minimizer of the energy functional. Wepropose an adaptive double step size strategy and the correspondingpreconditioned conjugate gradient methods for solving the energy minimizationmodel. Under some mild but reasonable assumptions, we prove the globalconvergence of our algorithms. Numerical experiments show that our algorithmsare efficient, especially for large scale metallic systems. In particular, ouralgorithms produce convergent numerical approximations for some metallicsystems, for which the traditional self-consistent field iterations fail toconverge.

Mathematical Analysis and Numerical Approximations of Density Functional Theory Models for Metallic Systems