Rayleigh-Ritz variational calculations of real-metal-surface properties

One-parameter variational calculations, employing different Kohn-Sham-type energy functionals of the density, are performed to determine the surface energy, relaxation dipole barrier, and work function for the most densely packed crystal faces of 12 simple metals (Al, Pb, Zn, Mg, Li, Ca, Sr, Ba, Na K, Rb, and Cs). The variational single-particle wave functions used are those generated from the linear-potential model, and the surface-energy functionals considered are those within the local-density approximation (LDA) for exchange and correlation, and the LDA with wave-vector analysis and gradient-expansion corrections. Both the first density-gradient correction coefficients due to Geldart-Rasolt, and the first and second gradient coefficients of Gupta-Singwi are employed in the determination of these properties. A comparative study of these gradient expansions and wave-vector-analysis corrections to the LDA exchange-correlation energy is also performed for jellium metal surfaces. The ions of the crystal are included via the Ashcroft pseudopotential, and a general and exact expression for the work function, including band-structure effects, is derived for the case when the ionic lattice is represented by such local pseudopotentials. The results of the primarily analytic calculations indicate that the bounds obtained within the LDA are superior to the perturbative results of Lang and Kohn, and that it is necessary to include corrections to the LDA value of the exchange-correlation energy if results comparable to existing experimental values are to be obtained. For medium- and low-density metals, the energy functionals with the wave-vector and gradient-expansion corrections lead to essentially equivalent results and closely approximate the experimental values. Although all three energy functionals lead to accurate results for the high-density metals (with the exception of Pb), the gradient-expansion values are generally superior. The results for the surface dipole barrier demonstrate that the density profile at real-metal surfaces is substantially different from that at the surface of jellium metal. The corresponding work functions obtained are, however, similar to the jellium-model values and fairly insensitive to the choice of energy functional employed. These results for the work functions compare well with polycrystalline metal experimental values.