Predicting hot-electron free energies from ground-state data

Machine-learning interatomic potentials, while extremely successful in describing condensed phases, are usually trained on ground-state electronic-structure calculations depending exclusively on the atomic positions and ignoring the electronic temperature. Hence, they are limited in their ability to describe thermally excited electrons. We introduce a rigorous framework to calculate the finite-temperature electron free energy based exclusively on ground-state total energy and electronic density of states, while allowing to sample on-the-fly the electronic free energy at any temperature. Our physically-motivated approach facilitates modeling material properties in extreme conditions with a fraction of the usual cost. We demonstrate it by computing the equation of state and heat capacity of hydrogen at planetary conditions. This approach demonstrates the impact of a universal model describing structural and electronic properties inexpensively and its ability to enable more accurate and predictive materials modeling and design.