Examination of several exchange-correlation energy functionals by accurate self-consistent atomic calculations

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Abstract
Several local and nonlocal exchange-correlation functionals are tested through accurate Kohn–Sham self-consistent calculations for six nobel gas atoms and three isoelectronic series (with two, four, and ten electrons and atomic numbers up to 20). The calculated exchange, correlation, and total energies have been compared with those from accurate Hartree–Fock calculations and accurate estimates of correlation energies available recently. Improvements over local-density approximation are found for all the tested nonlocal exchange-correlation functionals. In particular, nonlocal correlation energy functionals are shown to perform significantly better than the local approximations when both are used in conjunction with the nonlocal Becke’s exchange energy functional. However, in most cases, all the functionals fail to predict the correct trends of exchange and correlation energies as the atomic charge increases.