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Thermal density functional theory calculations often use the Mermin-Kohn-Shamscheme, but employ ground-state approximations to the exchange-correlation (XC)free energy. In the simplest solvable nontrivial model, an asymmetric Hubbarddimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Shamfunctionals for this system and extract the exact XC free energy. For moderatetemperatures and weak correlation, we find this approximation to be excellent.We extract various exact free-energy correlation components and the exactadiabatic connection formula.

physical review. b./physical review. b

Exact thermal density functional theory for a model system: Correlation  components and accuracy of the zero-temperature exchange-correlation  approximation