Numerical Estimates of Temperature-Dependent Bounds on the Exchange-Correlation Free Energy

In density functional theory, the Lieb-Oxford bound has been used to constrain popular approximations of the exchange-correalation density functional.  Preliminary evidence from thermal density functional theory supports the existence of a similar, temperature-dependent bound. A well-known parameterization of the exchange-correlation free energy of the uniform electron gas is used to generate adiabatic connection curves and generate estimates of these bounds in various temperature and density regimes.  Connections to known limiting behaviors of the exchange-correlation will be discussed.