Unlocking the power of orbital-free density functional theory to explore the electronic structure under extreme conditions

Cheng Ma; Qiang Xu; Zhenhao Zhang; Ke Wang; Ying Sun; Wenhui Mi; Zhandos A. Moldabekov; Tobias Dornheim; Jan Vorberger; Sebastian Schwalbe; Xuecheng Shao

doi:10.1063/5.0331238

Volume 11 Issue 5

Sep. 2026

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Cheng Ma, Qiang Xu, Zhenhao Zhang, Ke Wang, Ying Sun, Wenhui Mi, Zhandos A. Moldabekov, Tobias Dornheim, Jan Vorberger, Sebastian Schwalbe, Xuecheng Shao. Unlocking the power of orbital-free density functional theory to explore the electronic structure under extreme conditions[J]. Matter and Radiation at Extremes, 2026, 11(5): 057205. doi: 10.1063/5.0331238

Citation:

Cheng Ma, Qiang Xu, Zhenhao Zhang, Ke Wang, Ying Sun, Wenhui Mi, Zhandos A. Moldabekov, Tobias Dornheim, Jan Vorberger, Sebastian Schwalbe, Xuecheng Shao. Unlocking the power of orbital-free density functional theory to explore the electronic structure under extreme conditions[J]. Matter and Radiation at Extremes, 2026, 11(5): 057205. doi: 10.1063/5.0331238

Citation:

Cheng Ma, Qiang Xu, Zhenhao Zhang, Ke Wang, Ying Sun, Wenhui Mi, Zhandos A. Moldabekov, Tobias Dornheim, Jan Vorberger, Sebastian Schwalbe, Xuecheng Shao. Unlocking the power of orbital-free density functional theory to explore the electronic structure under extreme conditions[J]. Matter and Radiation at Extremes, 2026, 11(5): 057205. doi: 10.1063/5.0331238

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Unlocking the power of orbital-free density functional theory to explore the electronic structure under extreme conditions

doi: 10.1063/5.0331238

Cheng Ma^{1, 2
,},
Qiang Xu^1
,,
Zhenhao Zhang¹,
Ke Wang¹,
Ying Sun^{1, 2},
Wenhui Mi^{1, 2
,
,
,},
Zhandos A. Moldabekov^{3
,
,
,},
Tobias Dornheim^{3, 4
,},
Jan Vorberger^3
,,
Sebastian Schwalbe^3
,,
Xuecheng Shao^{1, 2, 5
,
,
,}

1.
Key Laboratory of Material Simulation Methods and Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, China
2.
State Key Lab of High Pressure and Superhard Materials, College of Physics, Jilin University, Changchun 130012, China
3.
Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden D-01328, Germany
4.
Center for Advanced Systems Understanding (CASUS), Görlitz D-02826, Germany
5.
International Center of Future Science, Jilin University, Changchun 130012, China

More Information

Corresponding author: a)Authors to whom correspondence should be addressed: mwh@jlu.edu.cn; z.moldabekov@hzdr.de; and shaoxc@jlu.edu.cn
Received Date: 2026-02-24
Accepted Date: 2026-06-14

Available Online: 2026-09-28

Publish Date: 2026-09-01

Abstract

Abstract

Recent advances in X-ray free-electron laser diagnostics have enabled direct probing of electronic properties 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 describing the electronic density and the electron–ion structure factor. Overcoming this limitation, we present a non-empirical KS-assisted orbital-free density functional framework for calculations under 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 of the order of 100 eV, quantum nonlocality remains essential for correctly describing the electron–ion structure factor in dense hydrogen.

The authors have no conflicts to disclose.
Conflict of Interest
Cheng Ma: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Qiang Xu: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Zhenhao Zhang: Data curation (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Ke Wang: Data curation (supporting); Methodology (supporting); Validation (supporting); Visualization (supporting). Ying Sun: Data curation (supporting); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Resources (equal); Validation (supporting); Visualization (equal); Writing – review & editing (equal). Wenhui Mi: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Zhandos A. Moldabekov: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Tobias Dornheim: Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jan Vorberger: Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Sebastian Schwalbe: Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Xuecheng Shao: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (lead); Resources (equal); Software (equal); Writing – original draft (equal); Writing – review & editing (equal).
Author Contributions
The data supporting the findings of this study are available according to the FAIR principles in the Rossendorf Data Repository (RODARE) at https://doi.org/10.14278/rodare.4738, Ref. 86.

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References(87)

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