The performance of approximations to the Hohenberg-Kohn-Sham density functionals is tested by comparing with essentially exact results for light atoms (the He isoelectronic series, Be, and Ne). The approximation schemes considered here are the effective gradient schemes due to Langreth and Mehl (LM), and the ‘‘modified weighted-density’’ (MWD) approximation due to Gunnarsson and Jones. Compared to the local density approximation the LM schemes give markedly better exchange-correlation energies and a certain improvement in the density profiles, effective potentials, and orbital eigenvalues. The MWD scheme gives good improvements of the exchange-correlation energies but improves the densities, potentials, and eigenvalues only for the He isoelectronic series. The sensitivity of the MWD scheme with respect to the model pair correlation used, as well as some additional approximations used in practical applications of the MWD scheme, are also analyzed.

• Received 30 August 1985

DOI:https://doi.org/10.1103/PhysRevA.33.804