Hydrogen Chemisorption by the Spin-density Functional Formalism. I

Abstract

We discuss the use of the density functional formalism in the problem of hydrogen chemisorption on metal surfaces and present support for the use of the Kohn-Sham (KS) scheme with the local spin-density approximation for exchange and correlation. The calculation by Smith, Ying and Kohn with the Hohenberg-Kohn formalism is discussed. We argue that two of their approximations, a gradient expansion for the kinetic energy and a linearization of their equations, are severe. We derive, using the KS formalism, a new, practical scheme, in which these approximations are avoided. Our formalism can be applied to various models for the metal. When solving the equations of the Kohn-Sham scheme, we utilize the fact that the adatom-induced changes are localized around the adatom. We make an expansion of these changes in a finite basis set, which is approximately complete around the adatom. Subsidiary conditions on the overcomplete basis set of pure metal plus localized functions are used to eliminate complicating sums over pure metal states. The approximations made are discussed, and the errors are shown to decrease as the size of the localized basis is increased. We give expressions for the binding energy and the electron distribution from which one can calculate the dipole moment, the location of the adsorbed atom and other ground state properties.