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
2010 Physical Review B  
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
more » ... m. 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.
doi:10.1103/physrevb.81.121106 fatcat:rw7aojcawrdqpe7gwupqj7r3ay