The Density-Functional Formalism and the Electronic Structure of Metal Surfaces

Abstract

Publisher Summary A prerequisite to analysis of the electronic structure of metal surfaces is a procedure for studying large, strongly inhomogeneous systems of electrons. Two such procedures that have been widely used in the past are the Thomas–Fermi method and the Hartree method. Not long ago, a general theory of inhomogeneous electron gases in their ground state, which we shall refer to as the density-functional formalism, was introduced by Hohenberg, Kohn, and Sham. The central quantity in this theory is the electron density, whose basic role is established by the theorem that the properties of the system, in particular the groundstate energy, are functionals only of this density. With the density as the varied function, a variational principle is established for the energy. The associated Euler equation is formulated in two ways—both in principle exact—that are particularly convenient for the study of strongly inhomogeneous systems. One formulation is similar to the Thomas–Fermi method, the other to the Hartree method; in their various approximate versions, they represent systematic ways of extending the classic methods which they resemble. This chapter outlines the density-functional formalisms and discusses its application to two of the most basic static properties of a surface: the work function and the surface energy.