Effects of thermal exchange–correlation functional on thermodynamic quantities of warm dense beryllium

Gao Chang; Zhang Shen; Fu Zhen-Guo; Huang Haijun; He X. T.; Zhang Weiyan; Kang Wei

doi:10.1063/5.0309424

Volume 11 Issue 3

May 2026

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Gao Chang, Zhang Shen, Fu Zhen-Guo, Huang Haijun, He X. T., Zhang Weiyan, Kang Wei. Effects of thermal exchange–correlation functional on thermodynamic quantities of warm dense beryllium[J]. Matter and Radiation at Extremes, 2026, 11(3): 037401. doi: 10.1063/5.0309424

Citation:

Gao Chang, Zhang Shen, Fu Zhen-Guo, Huang Haijun, He X. T., Zhang Weiyan, Kang Wei. Effects of thermal exchange–correlation functional on thermodynamic quantities of warm dense beryllium[J]. Matter and Radiation at Extremes, 2026, 11(3): 037401. doi: 10.1063/5.0309424

Citation:

Gao Chang, Zhang Shen, Fu Zhen-Guo, Huang Haijun, He X. T., Zhang Weiyan, Kang Wei. Effects of thermal exchange–correlation functional on thermodynamic quantities of warm dense beryllium[J]. Matter and Radiation at Extremes, 2026, 11(3): 037401. doi: 10.1063/5.0309424

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Effects of thermal exchange–correlation functional on thermodynamic quantities of warm dense beryllium

doi: 10.1063/5.0309424

Gao Chang^1
,,
Zhang Shen^2
,,
Fu Zhen-Guo^{3, 4
,
,},
Huang Haijun^{1
,
,},
He X. T.^{3, 5},
Zhang Weiyan⁵,
Kang Wei^{5
,
,
,}

1.
School of Physics and Mechanics, Wuhan University of Technology, Wuhan, Hubei 430070, China
2.
College of Science, National University of Defense Technology, Changsha, Hunan 410073, China
3.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
4.
National Key Laboratory of Computational Physics, Beijing 100088, China
5.
HEDPS, Center for Applied Physics and Technology and College of Engineering, Peking University, Beijing 100871, China

More Information

Corresponding author: a)Authors to whom correspondence should be addressed: hjhuang@whut.edu.cn and weikang@pku.edu.cn
Received Date: 2025-10-28
Accepted Date: 2026-01-16

Available Online: 2026-05-28

Publish Date: 2026-05-28

Abstract

Abstract

We report thermodynamic properties, including equation of state, principal Hugoniot, heat capacity, and Grüneisen parameter, for beryllium under density–temperature conditions of ρ = 3.0–9.0 g/cm³ and T = 5–10 000 eV, using an extended first-principles molecular dynamics method together with finite-temperature exchange–correlation functionals. Compared with zero-temperature exchange–correlation models, our results exhibit appreciable differences of about 3% in modeling the equation of state. Thermal excitations of K-shell electrons, delocalization of wave functions, and the merging of energy bands for beryllium along the Hugoniot curve are also presented. In addition to the application of these thermodynamic data to inertial confinement fusion and high-energy-density physics, our results may also serve as useful benchmarks for investigating thermal exchange–correlation effects on thermodynamic properties of warm dense matter, and further help to elucidate the mechanisms of inner-shell electron excitation.

Conflict of Interest
The authors have no conflicts to disclose.
Chang Gao: Investigation (equal); Writing – original draft (equal). Shen Zhang: Investigation (equal); Writing – original draft (equal). Zhen-Guo Fu: Data curation (supporting); Investigation (supporting). Haijun Huang: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal). X. T. He: Investigation (supporting); Project administration (supporting); Supervision (supporting). Weiyan Zhang: Investigation (supporting); Project administration (supporting); Supervision (supporting). Wei Kang: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal).
Author Contributions
H.H. and W.K. conceived the work. C.G. and S.Z. performed the calculations. C.G., S.Z., and Z.G.F. analyzed the data. C.G., S.Z., X.T.H., and W. Z. contributed to the interpretation of the data. C.G. and S.Z. wrote the paper. All co-authors commented critically on the manuscript.
Chang Gao and Shen Zhang contributed equally to this work.
The raw EOS data are provided in supplementary material. Additional data are available from the corresponding author upon reasonable request.

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References(87)

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