Electrical and thermal conductivity of liquid sodium from first-principles calculations

We report on the electrical and thermal conductivity of liquid sodium at 400 K, calculated using density functional theory with the local density approximation (LDA) and the Kubo-Greenwood formula. We extensively tested system-size errors and k-point sampling, using simulation cells containing up to 2000 atoms. We find that convergence of the results with respect to the size of the system is slow, and at least 1024-atom systems are required to obtain conductivities converged to within a few percent. Γ-point sampling does not seem to be accurate enough, even for the very largest 2000-atom system. We performed calculations at three densities, including the experimental density ρₑₓₚₜ=921 kg m^-3, the LDA density ρLDA=1046 kg m^-3, and a higher density ρ=1094 kg m^-3. At the experimental density, the electrical conductivity is underestimated by ~35%, at the LDA density it is overestimated by ~18%, and at the largest density it is higher than the experimental one by ~50%. At the experimental density, we also used the Perdew-Burke-Ernzerhof functional, and found that the conductivity is overestimated by only ~6%.