A wide-range temperature-dependent deep potential for sodium with near-experimental accuracy from melting to the critical point
Abstract
We construct temperature-dependent deep potentials for sodium using finite-temperature DFT data obtained with the PBE, AM05, and r2SCAN exchange-correlation functionals and investigate the thermophysical properties of sodium from room temperature to the critical region. The predicted critical parameters show a dependence on the exchange-correlation functional. The model based on the r2SCAN functional gives a critical temperature Tc=2.508(8) kK, density ρc=0.203(4) g/cm3, and pressure Pc=0.249(6) kbar, in close agreement with the recommended values. This model is then used to reconstruct the normal-pressure and critical isobars and to calculate the enthalpy, heat capacities, thermal expansion coefficient, bulk moduli, Grüneisen parameter, and speed of sound. The calculated normal-pressure bcc density differs by only 0.06% from the experimental value. Direct solid-liquid coexistence simulations give a melting temperature of 346(2) K, 25 K below the recommended value, consistent with the sensitivity expected from meV/atom free-energy errors. Liquid-vapor coexistence simulations reproduce the binodal and yield a surface tension that approaches zero near the critical point. The calculated self-diffusion coefficient and shear viscosity extend the available transport-property data into the expanded-liquid and near-critical regions, where direct experimental information is sparse. We also demonstrate the thermodynamic consistency of the results by comparing the speed of sound obtained from direct acoustic simulations with that calculated from the equation of state.
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BibTeX
@misc{demyanov2026widerange,
title = {{A wide-range temperature-dependent deep potential for sodium with near-experimental accuracy from melting to the critical point}},
author = {G. S. Demyanov and D. V. Minakov and V. B. Fokin and P. R. Levashov},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29826},
eprint = {2608.29826},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29826},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A wide-range temperature-dependent deep potential for sodium with near-experimental accuracy from melting to the critical point
AU - G. S. Demyanov
AU - D. V. Minakov
AU - V. B. Fokin
AU - P. R. Levashov
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29826
UR - https://arxiv.org/abs/2608.29826
AB - We construct temperature-dependent deep potentials for sodium using finite-temperature DFT data obtained with the PBE, AM05, and r^2SCAN exchange-correlation functionals and investigate the thermophysical properties of sodium from room temperature to the critical region. The predicted critical parameters show a dependence on the exchange-correlation functional. The model based on the r^2SCAN functional gives a critical temperature T_c=2.508(8) kK, density ρ_c=0.203(4) g/cm^3, and pressure P_c=0.249(6) kbar, in close agreement with the recommended values. This model is then used to reconstruct the normal-pressure and critical isobars and to calculate the enthalpy, heat capacities, thermal expansion coefficient, bulk moduli, Grüneisen parameter, and speed of sound. The calculated normal-pressure bcc density differs by only 0.06% from the experimental value. Direct solid-liquid coexistence simulations give a melting temperature of 346(2) K, 25 K below the recommended value, consistent with the sensitivity expected from meV/atom free-energy errors. Liquid-vapor coexistence simulations reproduce the binodal and yield a surface tension that approaches zero near the critical point. The calculated self-diffusion coefficient and shear viscosity extend the available transport-property data into the expanded-liquid and near-critical regions, where direct experimental information is sparse. We also demonstrate the thermodynamic consistency of the results by comparing the speed of sound obtained from direct acoustic simulations with that calculated from the equation of state.
ER -