First-principles derivation and properties of density-functional average-atom models

TL;DR

This paper derives a first-principles average-atom model from many-body theory to improve warm dense matter simulations, analyzing assumptions, choices, and errors in existing models and their impact on key properties.

Contribution

It provides a rigorous derivation of the average-atom model from fundamental principles and examines how different modeling choices affect accuracy in warm dense matter applications.

Findings

Impact of boundary conditions on equation-of-state data

Effect of exchange-correlation functionals on ionization levels

Analysis of errors and strategies for improvement in KS-AA models

Abstract

Finite-temperature Kohn--Sham density-functional theory (KS-DFT) is a widely-used method in warm dense matter (WDM) simulations and diagnostics. Unfortunately, full KS-DFT-molecular dynamics models scale unfavourably with temperature and there remains uncertainty regarding the performance of existing approximate exchange-correlation (XC) functionals under WDM conditions. Of particular concern is the expected explicit dependence of the XC functional on temperature, which is absent from most approximations. Average-atom (AA) models, which significantly reduce the computational cost of KS-DFT calculations, have therefore become an integral part of WDM modelling. In this paper, we present a derivation of a first-principles AA model from the fully-interacting many-body Hamiltonian, carefully analysing the assumptions made and terms neglected in this reduction. We explore the impact of different choices within this model -- such as boundary conditions and XC functionals -- on common properties in WDM, for example equation-of-state data, ionization degree and the behaviour of the frontier energy levels. Furthermore, drawing upon insights from ground-state KS-DFT, we discuss the likely sources of error in KS-AA models and possible strategies for mitigating such errors.