Exchange-correlation potential for inhomogeneous electron systems at finite temperatures

The basis for a density-functional theory of inhomogeneous electron systems at finite temperatures is a suitable exchange-correlation potential. A local potential is presented here for a wide range of densities and temperatures based on the first-order exchange and sum of ring diagrams for the interacting homogeneous electron gas. The validity of this scheme in the different temperature-density regions is discussed. It is found that the correlations dominate over the first-order exchange contributions over a wide range of temperatures for a given density.