Unlocking the Power of Orbital-Free Density Functional Theory to Explore the Electronic Structure Under Extreme Conditions

TL;DR

This work tackles the challenge of accurately modeling electronic structure under extreme conditions where KSDFT is computationally costly. It introduces SKANEX, a non-empirical KSDFT-assisted OFDFT framework that optimizes a non-interacting free-energy functional with a density-driven inversion guided by KSDFT, achieving KSDFT-level accuracy for electron densities, electron–ion structure factors, and EOS across a broad range of temperatures and densities. Benchmarking against KSDFT, PIMC, and Rayleigh-weight data on dense hydrogen and beryllium demonstrates high fidelity and speedups of up to several hundred times over KSDFT, while highlighting the continued importance of quantum non-locality at temperatures around $100$ eV. The method provides a scalable, robust platform for OFDFT-based electronic-structure calculations in warm dense matter and dense plasmas, with potential extensions to heavier elements, transport properties, and time-dependent regimes, and is ready for integration into open-source tools like DFTpy.

Abstract

Recent advances in X-ray free-electron laser diagnostics have enabled direct probing of the electronic structure under extreme pressures and temperatures, such as those encountered in stellar interiors and inertial confinement fusion experiments, challenging theoretical models for interpreting experimental data. Kohn-Sham density functional theory (KSDFT) has been successfully applied to analyze experimental X-ray scattering measurements, but its high computational cost renders routine application impractical. Orbital-free DFT (OFDFT) is a substantially more efficient alternative, with computational cost scaling linearly with system size and a weak temperature dependence, yet it often lacks the accuracy required for electronic structure description. Overcoming this limitation, we present a non-empirical Kohn-Sham-assisted orbital-free density functional framework for calculations at extreme conditions, which enables efficient OFDFT simulations with KSDFT-level accuracy for electron densities, electron-ion structure factors, and equations of state across a broad range of conditions. Benchmark comparisons with quantum Monte Carlo data for dense hydrogen and validation against Rayleigh weight measurements of hot dense beryllium demonstrate the reliability of the framework and speedups of up to several hundred times compared with KSDFT. We further show that even at temperatures on the order of 100 eV, quantum non-locality remains essential for correctly describing the electronic structure of dense hydrogen.

Figures (4)

• Figure 1: (a) Temperature–density plane showing the 50% ionization line evaluated using the Thomas–Fermi average-atom (TFAA) model MORE1985305. Also shown are thermodynamic conditions relevant to neutron-star atmospheres 10.1063/1.5097885, the interiors of Saturn Preising_2023 and Jupiter French_2012refId0, exoplanets Fortov_2009, the solar interior solar_interior_2022, white dwarfs 10.1063/1.5097885, inertial confinement fusion (ICF) experiments ICFDATA, and hydrogen jet experiments H_jet_prlFletcher_2022. (b) Illustration depicting the change in the localization degree of electron density around protons with the change in density, while keeping the electron degeneracy degree constant at $\theta = 1$. The data were generated performing KSDFT calculations at $r_s=1$, $r_s=2$, and $r_s=3.23$. (c) Electron-ion static structure factors $S_{ie}(q)$ calculated using PIMC, KSDFT, and OFDFT, for $r_s=1$, $r_s=2$, and $r_s=3.23$ at $\theta=1$. (d) Electron density distribution along the [110] direction of the cubic simulation cell for the proton configurations shown in panel (b), obtained from KSDFT simulations and OFDFT calculations using different non-interacting free-energy functionals.
• Figure 2: Electron-ion static structure factor in dense hydrogen plasmas. (a) Comparison of OFDFT results using the TF model and SKANEX at $r_s=1$ ($\rho=2.7~{\rm g/cm^3}$) for $\theta=2$ ($T= 100.1~{\rm eV}$) and $\theta=4$ ($T= 200.4~{\rm eV}$). (b) Comparison of the results calculated using SKANEX with different numbers of atoms at $r_s=2$ ($\rho = 0.34~\mathrm{g/cm^3}$) and $\theta=1$ ($T= 12.5~{\rm eV}$).
• Figure 3: Electronic pressure for hydrogen atoms arranged in a face-centered cubic lattice, computed using KSDFT and OFDFT at different electron temperatures and at densities of (a) $\rho = 2.7~\mathrm{g/cm^3}$ , (b) $\rho = 0.34~\mathrm{g/cm^3}$ , and (c) $\rho = 0.08~\mathrm{g/cm^3}$ .
• Figure 4: Rayleigh weight of strongly compressed beryllium at temperatures of 150 eV. Shown are OFDFT results and experimental data from NIF measurements Tilo_Nature_2023Dornheim_pop_2025.