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We propose a non-perturbative $ab$ $initio$ approach to calculate theelectrical conductivity of a liquid metal. Our approach is based on the Kuboformula and the theory of electron-phonon coupling (EPC), and unlike theconventional empirical approach based on the Kubo-Greenwood formula, fullytakes into account the effect of coupling between electrons and moving ions. Weshow that the electrical conductivity at high temperature is determined by anEPC parameter $\lambda_{\mathrm{tr}}$, which can be inferred,non-perturbatively, from the correlation of electron scattering matricesinduced by ions. The latter can be evaluated in a molecular dynamicssimulation. Based on the density-functional theory and pseudopotential methods,we implement the approach in an $ab$ $initio$ manner. We apply it to liquidsodium and obtain results in good agreement with experiments. This approach isefficient and based on a rigorous theory, suitable for applying to generalmetallic liquid systems.

Non-perturbative $ab$ $initio$ approach for calculating the electrical conductivity of a liquid metal