A long-standing puzzle in density functional theory is the issue of the long-range behavior of the Kohn- Sham exchange-correlation potential at metal surfaces. As an important step toward its solution, it is proven here, through a rigorous asymptotic analysis and an accurate numerical solution of the optimized-effectivepotential integral equation, that the Kohn-Sham exact exchange potential decays as ln z / z far into the vacuum side of an extended semi-infinite jellium. In contrast with the situation in localized systems, such as atoms, molecules, and slabs, this dominant contribution does not arise from the so-called Slater potential. This exact exchange result provides a strong constraint on the suitability of approximate correlation-energy functionals.

C.M.H. acknowledges financial support from CONICET of Argentina. C.R.P. was supported by the EC’s Marie Curie IIF (Grant No. MIF1-CT-2006-040222). J.M.P. acknowledges partial support by the University of the Basque Country, the Basque Unibertsitate eta Ikerketa Saila, and the Spanish Ministerio de Educación y Ciencia (Grants No. FIS2006-01343 and No. CSD2006-53).

4 páginas, 2 figuras.-- PACS number(s): 71.15.Mb, 31.15.eg, 71.10.Ca.-- et al.

Peer reviewed