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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.
Gupta et al. (Mon,) studied this question.