Density-functional calculations of transport properties in the nondegenerate limit and the role of electron-electron scattering

We compute electrical and thermal conductivities of hydrogen plasmas in the nondegenerate regime using Kohn-Sham density functional theory (DFT) and an application of the Kubo-Greenwood response formula, and demonstrate that for thermal conductivity, the mean-field treatment of the electron-electron (e-e) interaction therein is insufficient to reproduce the weak-coupling limit obtained by plasma kinetic theories. An explicit e-e scattering correction to the DFT is posited by appealing to Matthiessen's Rule and the results of our computations of conductivities with the quantum Lenard-Balescu (QLB) equation. Further motivation of our correction is provided by an argument arising from the Zubarev quantum kinetic theory approach. Significant emphasis is placed on our efforts to produce properly converged results for plasma transport using Kohn-Sham DFT, so that an accurate assessment of the importance and efficacy of our e-e scattering corrections to the thermal conductivity can be made.

Figure 1

${\epsilon }_{\max }\to \infty$ scaling fit to the thermal conductivity for $T=$ 500, 700, and 900 eV and $\rho =$ 40 g/${\mathrm{cm}}^3$.

Figure 2

${\epsilon }_{\max }\to \infty$ scaling fit to the electrical conductivity for $T=$ 500, 700, and 900 eV and $\rho =$ 40 g/${\mathrm{cm}}^3$.

Figure 3

(a) Electrical conductivity of hydrogen at $\rho =$ 40 g/${\mathrm{cm}}^3$ as computed by Kohn-Sham DFT, extrapolated to an infinite number of single-particle states, ${\sigma }_{\mathrm{DFT}}$ (solid green circles) and as computed by the QLB equation using the prescription outlined in Ref. [22] (blue curve), and the electrical conductivity in the absence of e-e collisions from the QLB calculations, ${\sigma }_{ei}$ (open blue circles). (b) Thermal conductivity of hydrogen at $\rho =$ 40 g/${\mathrm{cm}}^3$ extrapolated to an infinite number of single-particle states, ${\kappa }_{\mathrm{DFT}}$ (solid green circles), and as computed by the QLB equation using the prescription outlined in Ref. [22] (blue curve).

Figure 4

Thermal conductivity of hydrogen at $\rho =40$ g/${\mathrm{cm}}^3$ as computed within a number of approximations. QLB result for $\kappa$ (blue curve); ${\kappa }_{\mathrm{DFT}}$ extrapolated to an infinite number of single-particle states (solid green circles); $S_{\kappa }{\kappa }_{ei}$ as determined from QLB (solid black diamonds); $S_{\sigma }{\kappa }_{ei}$ as determined from QLB (open diamonds); ${\kappa }_{\mathrm{DFT}}$ corrected with ${\kappa }_{ee}$ from QLB using Eq. (10) (solid blue squares).