Application of Q-DFT to the Metal–Vacuum Interface

Abstract

In this chapter we study select properties of the inhomogeneous electron gas at a metal–vacuum interface in the context of Local Effective Potential Energy Theory. The metal surface problem differs in fundamental ways from the atomic, ionic, and molecular systems studied thus far. The latter are few-electron, finite, discrete energy spectrum systems, whereas the physical system at hand is an extended, many-electron system with a continuous energy spectrum. Metal surface physics is a field unto itself. Here we are going to be concerned with certain intrinsic aspects of the subject. The model employed in the calculations is one in which the lattice of positive ions in the metal is smeared out and replaced by a uniform positive charge background or “jellium.” The jellium model is appropriate for the “simple” metals whose conduction band arises only from s and p shells. The semi-infinite jellium metal is confined to the negative half-space, the metal surface being defined as the position where the uniform positive background charge ends abruptly. In the plane parallel to the surface, the jellium extends to infinity. The positive half-space is the vacuum region. (The semi-infinite jellium metal surface model is distinct from the jellium slab metal model in which the positive charge background is finite. We will be concerned only with the semi-infinite jellium metal model.) Thus, in the case of the metal–vacuum interface, the external potential energy of the electrons is due to the half-space positive jellium charge distribution. As a consequence of the translational symmetry in the plane parallel to the surface, the electron density is nonuniform only in the direction perpendicular to the surface. It approaches the bulk-metal density value deep in the crystal, exhibits the Bardeen-Friedel [1, 2] oscillations at and about the surface due to the “impurity” which in this case is the surface, and vanishes asymptotically in the classically forbidden vacuum region. The semi-infinite jellium metal is charge neutral. In the jellium model of a metal surface, lattice properties recede in significance, and it is the electronic properties that are to the fore.