Thermal PBE in warm dense matter: Does it matter and is it accurate?

Conditional probability density functional theory has recently been used to derive the temperature dependence of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) for the exchange-correlation (XC) free energy. We implement and systematically benchmark thermal PBE within Kohn-Sham density functional theory calculations of warm dense matter. Comparisons with the local density approximation (LDA) and PBE functionals, as well as thermal LDA, show that thermal PBE significantly improves the description of warm dense matter properties, including energies, forces, pressures, and electronic charge densities. In particular, thermal PBE exhibits close agreement with path integral Monte Carlo (PIMC) reference data at negligible additional computational cost. This work demonstrates the practical utility of thermal PBE as an accurate semilocal functional for simulations in the warm dense regime.