Ionic and electronic transport properties in dense plasmas by orbital-free density functional theory

We validate the application of our recent orbital-free density functional theory (DFT) approach [Phys. Rev. Lett. 113, 155006 (2014);] for the calculation of ionic and electronic transport properties of dense plasmas. To this end, we calculate the self-diffusion coefficient, the viscosity coefficient, the electrical and thermal conductivities, and the reflectivity coefficient of hydrogen and aluminum plasmas. Very good agreement is found with orbital-based Kohn-Sham DFT calculations at lower temperatures. Because the computational costs of the method do not increase with temperature, we can produce results at much higher temperatures than is accessible by the Kohn-Sham method. Our results for warm dense aluminum at solid density are inconsistent with the recent experimental results reported by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)].

Figure 1

Self-diffusion coefficient of hydrogen plasmas at $2 \mathrm{g}/\mathrm{cm}{}^3$ and lower temperatures, where comparison with Kohn-Sham is possible. In (a) our results show excellent agreement with Kohn-Sham while the Thomas-Fermi approach exhibits $\sim 20$%–30% difference. In (b) we see that for hydrogen at these temperatures and densities, there is minimal difference in using LDA or PBE exchange-correlation functionals. Also using a Nose-Hoover chain (NHC) thermostat [12], we find negligible difference with the isokinetic thermostat used in all other calculations discussed in this paper.

Figure 2

Self-diffusion coefficient (a) and shear viscosity coefficient (b) for hydrogen plasmas at 2 and $8 \mathrm{g}/\mathrm{cm}{}^3$ in the range of temperatures from 1 to 100 eV. Very good agreement is shown with Kohn-Sham at lower temperatures. As expected the shorter mean-free-path associated with higher density leads to lower diffusion and higher viscosity.

Figure 3

Self-diffusion coefficient for aluminum plasmas at 2.7 and $8.1 \mathrm{g}/\mathrm{cm}{}^3$ and from 0.5 to 10 eV. Again good agreement is shown with Kohn-Sham calculations at 0.5 and 1 eV. A smooth fit to the orbital-free calculations is shown.

Figure 4

Self-diffusion coefficient for liquid aluminum near melt compared with experimental results. Our results are close to those for Kohn-Sham for both PBE and LDA. None of the simulations are in agreement with Experiment no. 1 [17] and Experiment no. 2 [18] suggesting inaccuracy due to the exchange-correlation functional (for more discussion, see Ref. [15])

Figure 5

Electrical (a) and thermal (b) conductivities for hydrogen at 10, 5, 2, $1 \mathrm{g}/\mathrm{cm}{}^3$ (decreasing from top to bottom curves) from 1000 to 2 000 000 K. For a baseline comparison we show the commonly used model results of Kitamura and Ichimaru [26].

Figure 6

Electrical conductivity (a), thermal conductivity (b) and reflectivity coefficient (c) of aluminum plasmas at 2.7 and $2.35 \mathrm{g}/\mathrm{cm}{}^3$. Previous Kohn-Sham and experimental results at the liquid density agree with our calculations.

Figure 7

Electrical conductivity of aluminum. Recent experimental results for $2.7 \mathrm{g}/\mathrm{cm}{}^3$ [2] are not consistent with DFT calculations and other experimental measurements.

Figure 8

Convergence of the electrical and thermal conductivity for aluminum at $2.7 \mathrm{g}/\mathrm{cm}{}^3$ and $T=5$ eV with respect to the width of the Lorentzian smearing, $\mathrm{\Gamma }$. The value of the ${\sigma }_0$ and ${\kappa }_0$ relative to the converged values is shown.

Figure 9

Optical conductivity evaluated at each ionic configuration and averaged over the 10 configurations at $2.7 \mathrm{g}/\mathrm{cm}{}^3$ and 5 eV.