Thermal density functional theory (DFT) is commonly used in simulations of warm dense matter, a highly-energetic phase characterized by strongly correlated electrons, thermal effects, and quantum effects of electrons. Currently, numerous approximations exist for the exchange-correlation (XC) energy component of the total energy in DFT at zero temperature, and these approximations are often erroneously used for finite-temperature DFT. The adiabatic connection is a useful tool for analyzing and constraining approximations of the XC energy in zero-temperature theory. Here, its temperature-dependent extension is demonstrated and analyzed using a well-known parametrization of the uniform electron gas free energy. Inspired by the Lieb-Oxford inequality, which provides a lower bound for the ground-state XC energy, upper and lower bounds for the XC free energy are explored in this work and demonstrated for the finite-temperature adiabatic connection.

Numerical estimates of bounds on the exchange-correlation free energy

ACS Spring 2022

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