Localized versus extended systems in density-functional theory: some lessons from the Kohn-Sham exact exchange potential

C. M. HOROWITZ; C. R. PROETTO; J. M. PITARKE

PHYSICAL REVIEW B - CONDENSED MATTER AND MATERIALS PHYSICS

The American Physical Society

Año: 2010 vol. 81 p. 1211061 - 1211064

0163-1829

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 towards its solution, it is proved here, through a rigurouos asymptotic analysis and accurate numerical solution of the Optimized-Effective-Potential integral equation, that the Kohn-Sham exact exchange potential decays as $ln(z)/z$ far into the vacuum side of an {it extended} semi-infinite jellium. In contrast to the situation in {it localized} systems, like 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.