Eleven density functionals, including some of the most widely used ones, are tested on their abilityto predict nonrelativistic, electron correlation energies for the 17 atoms from He to Ar, the 17 cationsfrom Li+ to K+, and 11 1S state atoms from Ca to Rn. They all lead to relatively poor predictions forthe heavier atoms. Reparametrization of these functionals improves their performance for lightatoms but does not alleviate their problems with the heavier, closed-shell atoms. Several novel,few-parameter, density functionals for the correlation energy are developed heuristically. Four newfunctionals lead to qualitatively improved predictions for the heavier atoms without unreasonablycompromising accuracy for the lighter atoms. Further progress would be facilitated by reliableestimates of electron correlation energies for more atoms, particularly heavy ones.
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