Equation of state of warm dense deuterium and its isotopes from density-functional theory molecular dynamics.

Of the two approaches of density-functional theory molecular dynamics, quantum molecular dynamics is limited at high temperature by computational cost whereas orbital-free molecular dynamics, based on an approximation of the kinetic electronic free energy, can be implemented in this domain. In the case of deuterium, it is shown how orbital-free molecular dynamics can be regarded as the limit of quantum molecular dynamics at high temperature for the calculation of the equation of state. To this end, accurate quantum molecular dynamics calculations are performed up to 20 eV at mass densities as low as 0.5g/cm^{3} and up to 10 eV at mass densities as low as 0.2g/cm^{3}. As a result, the limitation in temperature so far attributed to quantum molecular dynamics is overcome and an approach combining quantum and orbital-free molecular dynamics is used to construct an equation of state of deuterium. The thermodynamic domain addressed is that of the fluid phase above 1 eV and 0.2g/cm^{3}. Both pressure and internal energy are calculated as functions of temperature and mass density, and various exchange-correlation contributions are compared. The generalized gradient approximation of the exchange-correlation functional, corrected to approximately include the influence of temperature, is retained and the results obtained are compared to other approaches and to experimental shock data; in parts of the thermodynamic domain addressed, these results significantly differ from those obtained in other first-principles investigations which themselves disagree. The equations of state of hydrogen and tritium above 1 eV and above, respectively, 0.1g/cm^{3} and 0.3g/cm^{3}, can be simply obtained by mass density scaling from the results found for deuterium. This ab initio approach allows one to consistently cover a very large domain of temperature on the domain of mass density outlined above.

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 C(2)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 1-10 eV and 0.6-10 g/cm(3) for quantum molecular dynamics, and 5-1000 eV and 1-10 g/cm(3) for orbital-free molecular dynamics. Simulations for the full C(2)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.

Numerical convergence of the self-diffusion coefficient and viscosity obtained with Thomas-Fermi-Dirac molecular dynamics.

Computations of the self-diffusion coefficient and viscosity in warm dense matter are presented with an emphasis on obtaining numerical convergence and a careful evaluation of the standard deviation. The transport coefficients are computed with the Green-Kubo relation and orbital-free molecular dynamics at the Thomas-Fermi-Dirac level. The numerical parameters are varied until the Green-Kubo integral is equal to a constant in the t→+∞ limit; the transport coefficients are deduced from this constant and not by extrapolation of the Green-Kubo integral. The latter method, which gives rise to an unknown error, is tested for the computation of viscosity; it appears that it should be used with caution. In the large domain of coupling constant considered, both the self-diffusion coefficient and viscosity turn out to be well approximated by simple analytical laws using a single effective atomic number calculated in the average-atom model.

Orbital-free molecular dynamics simulations of a warm dense mixture: examination of the excess-pressure matching rule.

A form of the linear mixing rule involving the equality of excess pressures is tested with various mole fractions and various types of orbital-free molecular dynamics simulations. For all the cases considered, this mixing rule yields, within statistical error, the pressure of a mixture of helium and iron obtained by a direct simulation. In an attempt to interpret the robustness of the mixing rule, we show that it can be derived from thermodynamic stability if the system is regarded as a mixture of independent effective average atoms. The success of the mixing rule applied with equations of state including various degrees of approximation leads us to suggest its use in the thermodynamic domain where quantum molecular dynamics can be implemented.

Direct verification of mixing rules in the hot and dense regime.

We perform orbital-free molecular dynamics simulations in the hot and dense regime for two mixtures: equimolar helium-iron and asymmetric deuterium-copper plasmas. For thermodynamic properties, we test two isobaric-isothermal mixing rules whose definitions involve either the equality of total pressures or the equality of the so-defined excess pressures of the components; the pressure and internal energy obtained by direct simulations are in very good agreement with those given by the mixing rule involving the equality of excess pressures. The viscosity of the deuterium-copper mixture is also extracted from a direct simulation and compared to the result given by a mixing rule applied to the viscosities of the pure elements. Finally, for structural properties, the effective charges given by the isobaric-isothermal mixing rule for the average atom model, used in the binary ionic mixture model, yield partial pair distribution functions in good agreement with those obtained by a direct simulation.