Comparisons of density-functional average-atom models and measures of the mean ionization state

Density-functional average-atom (AA) models are an important tool in simulations of the warm dense matter (WDM) regime, because they account for quantum interactions at favourable computational cost. AA models are typically based on a common premise - namely, an atom immersed in a plasma environment - but use a range of different assumptions and approximations, leading to inconsistent predictions for various properties. We compare results across several models, differing for example in their choice of boundary conditions and exchange-correlation functional, focussing on the mean ionization state (MIS), an important property in WDM. Furthermore, we compare different methods for evaluating the MIS: a simple energy threshold, and approaches based on the inverse participation function and electron localization function. We evaluate the relative merits of these approaches and, time-permitting, compare our AA results with full Kohn-Sham density-functional theory calculations.