Statistical calculation of jellium surface properties

Abstract

The consequences and importance of incorporating the second kinetic-energy-density gradient correction in metal-surface calculations are demonstrated by extending the statistical calculations of Smith for jellium metal to include this contribution. The results for the surface energy thus obtained are essentially exact when compared to those of Lang and Kohn. The errors in the work function are greater than those obtained by considering only the first gradient correction in the surface energy functional, but these results closely approximate the high-density polycrystalline metal experimental values. The variation of the work function for densities higher than those existing in metals is also plotted. Results are determined both by application of the Rayleigh-Ritz variational principle for the energy and satisfaction of the Budd-Vannimenus constraint. The work functions reach a maximum and then decrease, but do not asymptotically approach the infinite-density-limit result predicted by Peuckert, but rather vanish at some finite value of the density as in our previous work. A more rigorous method for the determination of the high-density work function is also indicated.