# Reply to comment by Witte et al. on "Isochoric, isobaric, and ultrafast conductivities of aluminum, lithium,and carbon in the warm dense matter regime", Phys. Rev. E $96$, 053206 (2017)

## TL;DR

This paper defends previous conductivity calculations of warm dense aluminum against critiques, presents multi-species DFT results, and finds that certain DFT-MD-KG methods underestimate conductivity compared to experimental values.

## Contribution

It provides multi-species DFT conductivity calculations for warm dense aluminum and addresses limitations of prior DFT-MD-KG methods in estimating conductivity.

## Key findings

- DFT results suggest underestimation of conductivity by DFT-MD-KG methods.
- Multi-species calculations align with experimental melting point conductivity.
- Critiques of structure factor approximation are acknowledged but remain standard practice.

## Abstract

In Phys. Rev. E, $99$, 047201 (2019) Witte {\it et al.} have commented on our conductivity calculations [Phys. Rev. E $96$, 053206 (2017)] for warm dense matter (WDM). (i) They criticize our use of the spherically-averaged structure factor $S(k)$ for calculations of the static conductivity $\sigma$ of FCC aluminum - a common approximation for polycrystalline materials. They themselves give no calculations as their method using density-functional theory (DFT) and molecular dynamics (MD) based Kubo-Greenwood (KG) calculations becomes impractical for cold ions. (ii) We are satisfied that Witte et al. no longer claim a factor of $\sim$ 1.5 change in $\sigma$ on changing the exchange-correlation (XC) functional used. (iii) They have provided computer-intensive calculations of $\sigma$ for aluminum using DFT-MD-KG simulations, for temperatures $T$ up to 15 eV but using only $N$=64 atoms in the simulation, where as a mixture of ionic species needs a far larger $N$ to be credible. We present multi-species conductivity calculations via a parameter-free DFT theory [Phys. Rev. E. $52$, 5352 (1995)] for 5 eV to 50 eV. (iv) The conductivities obtained from well-converged DFT-MD-KG methods show a significant underestimate of $\sigma$; this is especially evident for the isochoric conductivity $\sigma_{\rm ic}$ extrapolating to $\sim3.5\times 10^6$ S/m, i.e, {\it even below} the experimental {\it isobaric} value of 4.1$\times 10^6$ S/m at the melting point, when a value of $\sim 5\times 10^6$ S/m is anticipated.