Eleven density functionals, including some of the most widely used ones, are tested on their ability to predict nonrelativistic, electron correlation energies for the 17 atoms from He to Ar, the 17 cations from Li(+) to K(+), and 11 (1)S state atoms from Ca to Rn. They all lead to relatively poor predictions for the heavier atoms. Reparametrization of these functionals improves their performance for light atoms 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 new functionals lead to qualitatively improved predictions for the heavier atoms without unreasonably compromising accuracy for the lighter atoms. Further progress would be facilitated by reliable estimates of electron correlation energies for more atoms, particularly heavy ones.

All-electron correlation energies E(c) are not very well-known for atoms with more than 18 electrons. Hence, coupled-cluster calculations in carefully designed basis sets are combined with fully converged second-order Møller-Plesset perturbation theory (MP2) computations to obtain fairly accurate, nonrelativistic E(c) values for the 12 closed-shell atoms from Ar to Rn. These energies will be useful for the evaluation and parameterization of density functionals. The results show that MP2 overestimates ∣E(c)∣ for heavy atoms. Spin-component scaling of the MP2 correlation energy is used to provide a simple explanation for this overestimation.

Reparametrization of Wigner's correlation energy density functional yields a very close fit to the correlation energies of the helium isoelectronic sequence. However, a quite different reparametrization is required to obtain an equally close fit to the isoelectronic sequence of Hooke's atom. In an attempt to avoid having to reparametrize the functional for different choices of the one-body potential, we propose a parametrization that depends on global characteristics of the ground-state electron density as quantified by scale-invariant combinations of expectation values of local one-body operators. This should be viewed as an alternative to the density-gradient paradigm, allowing one to introduce the nonlocal dependence of the density functional on the density in a possibly more effective way. Encouraging results are obtained for two-electron systems with one-body potentials of the form r(zeta) with zeta=-12,+12,1, which span the range between the Coulomb potential (zeta=-1) and the Hooke potential (zeta=2).

All-electron correlation energies E(c) are not very well known for open-shell atoms with more than 18 electrons. The complete basis-set (CBS) limits of second-order Møller-Plesset (MP2) perturbation theory energies are obtained for open-shell atoms by computations in large basis sets combined with a knowledge of the MP2/CBS limit for the next larger closed-shell atom with the same valence shell structure. Then higher-order correlation corrections are found by coupled-cluster calculations using basis sets that are not quite as large. The method is validated for the open-shell atoms from Al to Cl for which E(c) is reasonably well established. Then, the method is used to obtain non-relativistic E(c) values, probably accurate to 3%, for the open-shell atoms of the fourth period: K, Sc-Cu, and Ga-Br. These energies are compared with the predictions of 19 density functionals and may be useful for the parameterization of new ones. The results show that MP2 overestimates |E(c)| for atoms heavier than Fe.

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