Equation of state of a dense plasma by orbital-free and quantum molecular dynamics: Examination of two isothermal-isobaric mixing rules

We test two isothermal-isobaric mixing rules, respectively based on excess-pressure and total-pressure equilibration, applied to the equation of state of a dense plasma. While the equation of state is generally known for pure species, that of arbitrary mixtures is not available so that the validation of accurate mixing rules, that implies resorting to first-principles simulations, is very useful. Here we consider the case of a plastic with composition ${\mathrm{C}}_{2}{\mathrm{H}}_{3}$ and we implement two complementary ab initio approaches adapted to the dense plasma domain: quantum molecular dynamics, limited to low temperature by its computational cost, and orbital-free molecular dynamics, that can be implemented at high temperature. The temperature and density range considered is 1\char21{}10 eV and 0.6\char21{}10 ${\mathrm{g}/\mathrm{cm}}^{3}$ for quantum molecular dynamics, and 5\char21{}1000 eV and 1\char21{}10 ${\mathrm{g}/\mathrm{cm}}^{3}$ for orbital-free molecular dynamics. Simulations for the full ${\mathrm{C}}_{2}{\mathrm{H}}_{3}$ mixture are the benchmark against which to assess the mixing rules, and both pressure and internal energy are compared. We find that the mixing rule based on excess-pressure equilibration is overall more accurate than that based on total-pressure equilibration; except for quantum molecular dynamics and a thermodynamic domain characterized by very low or negative excess pressures, it gives pressures which are generally within statistical error or within 1% of the exact ones. Besides, its superiority is amplified in the calculation of a principal Hugoniot.