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4 páginas, 2 figuras.-- PACS number(s): 71.15.Mb, 31.15.eg, 71.10.Ca.-- et al.A long-standing puzzle in density functional theory is the issue of the long-range behavior of the Kohn-\udSham exchange-correlation potential at metal surfaces. As an important step toward its solution, it is proven\udhere, through a rigorous asymptotic analysis and an accurate numerical solution of the optimized-effectivepotential\udintegral equation, that the Kohn-Sham exact exchange potential decays as ln z  / z far into the vacuum\udside of an extended semi-infinite jellium. In contrast with the situation in localized systems, such as atoms,\udmolecules, and slabs, this dominant contribution does not arise from the so-called Slater potential. This exact\udexchange result provides a strong constraint on the suitability of approximate correlation-energy functionals.C.M.H. acknowledges financial support from CONICET\udof Argentina. C.R.P. was supported by the EC’s\udMarie Curie IIF (Grant No. MIF1-CT-2006-040222). J.M.P.\udacknowledges partial support by the University of the\udBasque Country, the Basque Unibertsitate eta Ikerketa Saila,\udand the Spanish Ministerio de Educación y Ciencia\ud(Grants No. FIS2006-01343 and No. CSD2006-53).Peer reviewe

Theory of highly charged ion energy gain spectroscopy of molecular collective excitations