ANALYTICAL ASYMPTOTIC STRUCTURE OF THE SLATER EXCHANGE AND KOHN-SHAM EXCHANGE AND CORRELATION POTENTIALS AT A METAL-SURFACE

In this paper we consider the semi-infinite jellium and structureless pseudopotential models of a metal surface and derive the exact analyti cal asymptotic structure in the classically forbidden region of (i) th e Slater exchange potential V-x(s)(r), (ii) the Kohn-Sham exchange pot ential nu(x)(r), and thus of the optimized potential method exchange p otential nu(x)(OPM)(r), and show these latter potentials to decay as 1 /2V(x)(s)(r). With the assumption that the Kohn-Sham exchange-correlat ion potential nu(xc)(r) decays asymptotically as the image potential, we thereby derive (iii) the analytical asymptotic structure of the Koh n-Sham correlation potential nu(c)(r). These potentials all decay as - x(-1) with coefficients which depend upon the Fermi energy and surface barrier height. However, it is only nu(x)(r) that is image-potential- like, the coefficient being 1/4 for stable jellium. Thus, with exchang e and correlation effects considered separately, the principal contrib ution to the asymptotic image potential structure arises due to Pauli correlations, the Coulomb correlation contribution being weak. We also show (iv) analytically that for a slab-metal geometry, the potential nu(x)(r) decays as -x(-2) and explain why this is the case. Finally, w e show (nu) analytically that two approximate Kohn-Sham exchange poten tials in the literature possess the correct 1/2V(x)(s)(r) asymptotic s tructure in the vacuum. With exchange and correlation considered toget her, the assumption that the asymptotic image potential structure of n u(xc)(r) is independent of metal parameters provides an alternate ''cl assical'' interpretation of the physical origin of this structure. It is due to those Coulomb correlations which contribute to that part of the Coulomb hole (of charge -e) localized to the surface region, the c omponent (of charge +e) delocalized in the metal bulk screening out th e corresponding delocalized Fermi hole distribution (of charge -e). (C ) 1997 Academic Press.