Inversions of thermal systems in density functional theory

Warm dense matter is an important area of study for many fields, from astrophysics to clean energy, one that has been supported by density functional theory--based computations for experimental design, interpretation of results, and theoretical investigations. To further improve the efficacy of density functional theory at the high temperatures and pressures of the warm dense matter regime, better approximations to the exchange-correlation potential are needed. Density-to-potential inversions can be used to obtain the exact Kohn-Sham potential, from which we can extract the exact exchange-correlation potential. Inversions of finite-temperature densities can expose the temperature dependence of the exchange-correlation potential, which can inform construction and analysis of finite-temperature exchange-correlation approximations. In this work, I will present results from inverting finite-temperature densities for model systems using the thermal analogue to the Wang-Parr inversion method and discuss how this method can give glimpses into how thermal systems evolve over time.