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

To be published in Physical Review Research. 29 pages, 15 figures. Derivation of Hamiltonian clarified since v3 and added appendix B on computation of free energy

References in corpus (20)

• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• Electronic transport coefficients from ab initio simulations and application to dense liquid hydrogen
• DFT: A Theory Full of Holes?
• {\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit
• All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas
• Tetrahedral clustering in molten lithium under pressure
• 'Hartree-exchange' in ensemble density functional theory: Avoiding the non-uniqueness disaster
• Quantum-mechanical calculation of ionization potential lowering in dense plasmas
• Finite-temperature orbital-free DFT molecular dynamics: coupling Profess and Quantum Espresso
• A step in the direction of resolving the paradox of Perdew-Zunger self-interaction correction
• A self-interaction-free local hybrid functional: Accurate binding energies vis-à-vis accurate ionization potentials from Kohn-Sham eigenvalues
• Carbon ionization at Gbar pressures: an ab initio perspective on astrophysical high-density plasmas
• Gradient corrections to the exchange-correlation free energy
• Equation of state for partially ionized carbon at high temperatures
• Path Integral Monte Carlo and Density Functional Molecular Dynamics Simulations of Warm, Dense MgSiO${}_3$
• Fractional occupation in Kohn-Sham density-functional theory and the treatment of non-pure-state v-representable densities
• Reconciling ionization energies and band gaps of warm dense matter derived with ab initio simulations and average atom models
• Finite Temperature Scaling in Density Functional Theory
• Higher Ionization Energies of Atoms in Density Functional Theory

Cited by in corpus (7)

• Current challenges in the physics of white dwarf stars
• Electronic Density Response of Warm Dense Matter
• First principles simulations of dense hydrogen
• Improving dynamic collision frequencies: impacts on dynamic structure factors and stopping powers in warm dense matter
• Improved calculations of mean ionization states with an average-atom model
• Physics-enhanced neural networks for equation-of-state calculations
• atoMEC: An open-source average-atom Python code