PHYSICAL REVIEW B VOLUME 1, NUMBER 12 15june1970 Theory of Metal Surfaces: Charge Density and Surface Energy* N. D. Langt and.Kohn Department of Physics, University of California, San Diego, La Jolla, Califoria 92037 (Received 28 January 1970) The first part of this paper deals with the jellium model of a metal surface. The theory of the inhomogeneous electron relation energies, is used. Self- consistent electron density distrib ace energy is found to be neg- ative for high densities (rg2.5).In are calculated which arise ections to the surtace energy is replaced by a pseudopotential model of the ions. One c tralized lattice, the other an interaction ener Both of these correc- tions are essential at higl t rgy is in semiquan- titative agreement with surface-t eight simple metals (Li, Na, K, Rb, Cs, Mg, Zn, Al), typical errors being about 25%. For Pb there is a serious disagree- ment. I. INTRODUCTION ment over a wide range of densities. The calcu- The electron theory of metals has lated surface energy, however, while in fair agreement with experiment at low electron den- primarily concerned with properties of the m sities, fails completely-to the point of giving the interior. These bulk properties are, of course, of great fundamental interest, and, wrong sign -for higher-density metals such as Al The present paper is aimed particularly at the the theorist, the translati problem of the surface energy. In Sec. II, we ing inside the metal introdu of simplicity into describe fully self-consistent calculation for the years there has been exce round(or jellium) model of metal using the theory of Refs. 7 and 8. Nu- ments of both electr interactions, so that merical results for density distributions (including of giving quantita oscillations), potentials, and surface en- wide classes of m Theories of dy remarked, the uniform speaking, lagged primarily to the ground model is totally inadequate for de- bing the surface energy of high-density metals. duced by th In Sec. III, we supplement this model by first-or- near the su: using the zero- symmetry stributions of the uniform back- was animp and by the addition of the appropri- an appr Na. I energies. The r esulting gies are found to be in rather good very tey ith experiment over the entire range problem tion of elect In a subsequent paper we shall describe the ef- with systems nic lattice on the work function, par- was put forward ticularly on the anisotropies associated with dif- This formulation ferent crystal faces. roreatsns II. UNIFORM POSITIVE BACKGROUND MODEL formed approx using this the A. Mathematical Formulation surface in which torm seml-intinite po We address ourselves to the problem of deter- fully self-consister mining the surface electronic structure in the lines has been repo model of a metal in which the positive charges are rs. These studies give, the work replaced by a uniform charge background of den- function, good qualitative agreement with experi- sity 4555