STRUCTURE OF THE PAULI AND CORRELATION-KINETIC COMPONENTS OF THE KOHN-SHAM EXCHANGE POTENTIAL AT A METAL-SURFACE

According to the rigorous physical interpretation of Kohn-Sham (KS) de nsity-functional theory in terms of the components of the true wavefun ction, the KS exchange potential nu(x)(KS)(r) = delta E-x(KS)[rho]/del ta rho(r), where E-x(KS)[rho] is the exchange energy functional, is th e work done to move an electron in a conservative field R(r). This fie ld comprises a component E-x(KS)(r) representative of Pauli correlatio ns and another Z(tc)((1))(r) that constitutes part of the correlation contribution to the kinetic energy. The field E-x(KS)(r) is derived vi a Coulomb's law from the KS Fermi hole charge, and the field Z(tc)((1) )(r) from thp kinetic-energy-density tensor involving the first-order correction to the KS single-particle density matrix. For systems in wh ich the curls of these component fields separately vanish, the potenti al nu(x)(KS)(r) is the sum of the work done W-x(KS)(r) and W-tc((1))(r ) in the fields E-x(KS)(r) and Z(tc)((1))(r) respectively. In this pap er we study the structure of the work W-x(KS)(r) and W-tc((1))(r) at a simple-metal surface as represented by the jellium and structureless- pseudopotential models for which the work W-x(KS)(r) and W-tc((1))(r) are separately path-independent. A general expression for the field E- x(KS)(r) is derived in terms of momentum-space integrals of the electr on orbitals. This enables its easy determination, and thereby determin ation of the potential W-x(KS)(r). The field expression further allows for the derivation of the exact analytical asymptotic structure of th e potential W-x(KS)(r) in the vacuum region, a result valid for the fu lly self-consistently determined orbitals of both models. With the exa ct analytical asymptotic structure of nu(x)(KS)(r) in the vacuum known , that of the potential W-tc((1))(r) in this region is then determined analytically. As is the case for nu(x)(KS)(r) which decays asymptotic ally in the vacuum as -alpha(KS)/x, the potentials W-x(KS)(r) and W-tc ((1))(r) also decay as -alpha(w)/x and alpha(tc)((1))/x, respectively, the decay coefficients depending upon the metal Fermi energy and barr ier height. It is further shown that for metallic densities, W-x(KS)(r ) does not approach the nu(x)(KS)(r) asymptotic metal-bulk value of (- k(F)/pi), so that W-tc((1))(r) is also finite in this region. Thus, at a metal surface, the KS exchange potential nu(x)(KS)(r) comprises pri ncipally its Pauli component W-x(KS)(r), with the correlation-kinetic part W-tc((1))(r) being finite and long-ranged in both the Vacuum and metal-bulk regions, its contribution diminishing with increasing metal density. (C) 1998 Academic Press.