| In this thesis we study the nonuniform electron density system at a metal-vacuum interface via the corresponding local effective potential confining the electrons, the metal being represented by the jellium and structureless pseudopotential models. The study is performed within conventional Kohn-Sham (KS) density-functional theory and its recently derived quantum-mechanical interpretation. In the latter, properties are determined in terms of the separate electron correlations due to the Pauli exclusion principle, Coulomb repulsion and the correlation contribution to the kinetc energy. We have derived the exact analytical structure, valid for self-consistent orbitals, of the KS theory exchange potential in the classically forbidden region. This structure is image-potential-like of the form {dollar}-alphasb{lcub}KS,x{rcub}(beta)chi{dollar} where the parameter {dollar}betasp2{dollar} is the ratio of the surface barrier height to the metal Fermi energy. For a Wigner-Seitz radius of {dollar}rsb{lcub}s{rcub}{dollar} = 4.1, which is approximately that for which jellium metal is stable, the decay coefficient is precisely 1/4. Over the metallic range of densities {dollar}rsb{lcub}s{rcub}{dollar} = 2-6, the coefficient ranges from 0.195 to 0.274. Thus, if the asymptotic structure of the KS exchange-correlation potential is the image potential, then this structure is due principally to KS exchange effects, the KS correlation contribution being an order of magnitude smaller. These results, then lead to the concept of an 'image' charge localized to the surface region for asymptotic positions of the electron. We have further derived the exact analytical structure in the vacuum of the Slater exchange potential, and of the Pauli-correlation and correlation-kinetic components of the KS exchange potential. These structures are all image-potential-like, decaying respectively as {dollar}-alphasb{lcub}S{rcub}(beta)chi, -alphasb{lcub}W{rcub}(beta)chi{dollar} and {dollar}alphasbsp{lcub}tsb{lcub}c{rcub}{rcub}{lcub}(1){rcub}(beta)/chi{dollar}. The Pauli-correlation component constitutes the major fraction of the KS exchange potential asymptotically, but there is a finite correlation-kinetic contribution. It is only for metals of high density that the KS exchange potential is the same as its Pauli component. We have also determined the structure of the Pauli-correlation and correlation-kinetic components about the surface extending into the metal bulk. Once again, the KS exchange potential is comprised primarily of its Pauli component, the correlation-kinetic part being an order of magnitude smaller. Similar calculations for atoms then show the intershell bumps in the KS exchange potential to be due to correlation-kinetic effects. We have also constructed an approximate KS exchange potential for the metal surface via the concept of restricted functional differentiation developed by us. This potential is then shown to satisfy essentially all integral and differential sum rules for this property, as well as possess the correct asymptotic structure in the metal bulk and vacuum regions. Finally, we have constructed separate approximate KS exchange and correlation energy functionals such that the potentials improve upon the local density approximation by possessing the correct asymptotic structure in the vacuum. |
