The finite-temperature adiabatic connection formula, which gives interaction free energies in terms of the potential energy alone, is cast as an integral over the temperature and has been used to write new relations between correlation components in terms of temperature and the coupling constant. Using the results of a new linear response proof for thermal ensembles, the thermal connection formula and the fluctuation-dissipation theorem are combined to produce a method for generating entirely new exchange-correlation free energy approximations.
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