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We discuss a method to calculate with quantum molecular dynamics simulationsthe rate of energy exchanges between electrons and ions in two-temperatureplasmas, liquid metals and hot solids. Promising results from this method wererecently reported for various materials and physical conditions [J. Simoni andJ. Daligault, Phys. Rev. Lett. 122, 205001 (2019)]. Like other ab-initiocalculations, the approach offers a very useful comparison with theexperimental measurements and permits an extension into conditions not coveredby the experiments. The energy relaxation rate is related to the frictioncoefficients felt by individual ions due to their non-adiabatic interactionswith electrons. Each coefficient satisfies a Kubo relation given by the timeintegral of the autocorrelation function of the interaction force between anion and the electrons. These Kubo relations are evaluated using the output ofquantum molecular dynamics calculations in which electrons are treated in theframework of finite-temperature density functional theory. The calculationpresents difficulties that are unlike those encountered with the Kubo formulasfor the electrical and thermal conductivities. In particular, the widely usedKubo-Greenwood approximation is inapplicable here. Indeed, the frictioncoefficients and the energy relaxation rate diverge in this approximation sinceit does not properly account for the electronic screening of electron-ioninteractions. The inclusion of screening effects considerably complicates thecalculations. We discuss the physically-motivated approximations we applied todeal with these complications in order to investigate a widest range ofmaterials and physical conditions.

Calculation of electron-ion temperature equilibration rates and friction coefficients in plasmas and liquid metals using quantum molecular dynamics