Planar-surface charge densities and energies beyond the local-density approximation

We present a self-consistent calculation of the ground-state properties of simple metallic planar surfaces using density-functional theory with nonlocal exchange-correlation effects included. Our calculational scheme closely follows the classic work of Lang and Kohn for the jellium model, except that the exchange-correlation energy and potential within the local-density approximation (LDA) are replaced by the corresponding nonlocal functionals of Langreth and Mehl (LM). We also include the discrete-lattice effects, following the variational scheme of Perdew and Monnier. The physical properties considered include the one-electron effective potential, charge-density profile, surface energy, and work function. For each of the most densely packed surfaces of seven simple metals with fcc or bcc structure, we find that, when compared with results in the LDA, the Friedel oscillation in the electron density near the surface is systematically depressed as a result of positive LM contributions to the effective potential at places where the LDA density oscillation is peaked. We find a systematic increase in surface energies, with bigger increases for higher-density metals. Increases are also found in the work functions. Our results and those from other density-functional calculations are compared with results from variational treatments of the ground-state wave function, and with experiment. We also comment upon the Fermi hypernetted-chain jellium surface energies and work functions.