  We discuss a method to calculate with quantum molecular dynamics simulations
the rate of energy exchanges between electrons and ions in two-temperature
plasmas, liquid metals and hot solids. Promising results from this method were
recently reported for various materials and physical conditions [J. Simoni and
J. Daligault, Phys. Rev. Lett. 122, 205001 (2019)]. Like other ab-initio
calculations, the approach offers a very useful comparison with the
experimental measurements and permits an extension into conditions not covered
by the experiments. The energy relaxation rate is related to the friction
coefficients felt by individual ions due to their non-adiabatic interactions
with electrons. Each coefficient satisfies a Kubo relation given by the time
integral of the autocorrelation function of the interaction force between an
ion and the electrons. These Kubo relations are evaluated using the output of
quantum molecular dynamics calculations in which electrons are treated in the
framework of finite-temperature density functional theory. The calculation
presents difficulties that are unlike those encountered with the Kubo formulas
for the electrical and thermal conductivities. In particular, the widely used
Kubo-Greenwood approximation is inapplicable here. Indeed, the friction
coefficients and the energy relaxation rate diverge in this approximation since
it does not properly account for the electronic screening of electron-ion
interactions. The inclusion of screening effects considerably complicates the
calculations. We discuss the physically-motivated approximations we applied to
deal with these complications in order to investigate a widest range of
materials and physical conditions.
