QUANTUM-MECHANICS OF ASYMPTOTIC EFFECTIVE POTENTIAL AND IMAGE CHARGE AT METAL-SURFACES

Electrons are confined within a metal and about its surface by a local effective potentials as described by Hohenberg-Kohn-Sham density-func tional theory. The asymptotic structure of this potential in the class ically forbidden vacuum region is that of the 'exchange-correlation' p otential V-XC(KS)(r) defined mathematically as the functional derivati ve of the 'exchange-correlation' energy functionalE(XC)(KS) [rho] of t he density rho(r). This functional and its derivative represent electr on correlations due to the Pauli exclusion principle, Coulomb repulsio n, and the correlation contribution to the kinetic energy. The functio nal and derivative also have a rigorous quantum-mechanical interpretat ion in terms of a sum of two fields whose source distributions are exp ectations of Hermitian operators taken with respect to the system wave function. These fields separately represent the Pauli-Coulomb and corr elation-kinetic contributions. This article is concerned with our pres ent understanding of the asymptotic structure of V-XC(KS)(r) in the cl assically forbidden region, and of the electron correlations which con tribute to it. The description is within the context of both conventio nal density-functional theory as well as its physical interpretation i n terms of fields. The physics of the 'image' charge localized to the surface region, a property intrinsic to the nonuniform electron densit y system at a metal surface, is also described.