First-principles derivation and probing the accuracy of an average-atom model in the warm dense matter regime

Modelling the behaviour of materials under warm dense matter (WDM) conditions is important to our understanding of various astrophysical phenomena and inertial confinement fusion (for example). Finite-temperature Kohn--Sham density-functional theory (KS-DFT) can be applied to study materials exposed to WDM conditions --- temperatures of around 1-1000 eV and densities from 10^-2 to 10^4 g/cm3 --- but the usual KS-DFT approach for periodic systems becomes computationally intractable at higher temperatures. In this presentation, we first derive a density-functional average-atom model --- which reduces the full many-body system of electrons and nuclei to a single atom immersed in a plasma --- from first principles. Using this model, we investigate the behaviour of the mean ionization state and pressure (key properties in WDM) for a range of materials, densities and temperatures. Through comparison with higher fidelity simulations and experimental results, we demonstrate that computationally light average-atom models yield accurate results under the right conditions and approximations.