Multicomponent mutual diffusion in the warm, dense matter regime.

We present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.

First-principles equation-of-state table of silicon and its effects on high-energy-density plasma simulations.

Using density-functional theory-based molecular-dynamics simulations, we have investigated the equation of state for silicon in a wide range of plasma density and temperature conditions of ρ=0.001-500g/cm^{3} and T=2000-10^{8}K. With these calculations, we have established a first-principles equation-of-state (FPEOS) table of silicon for high-energy-density (HED) plasma simulations. When compared with the widely used SESAME-EOS model (Table 3810), we find that the FPEOS-predicted Hugoniot is ∼20% softer; for off-Hugoniot plasma conditions, the pressure and internal energy in FPEOS are lower than those of SESAME EOS for temperatures above T ≈ 1-10 eV (depending on density), while the former becomes higher in the low-T regime. The pressure difference between FPEOS and SESAME 3810 can reach to ∼50%, especially in the warm-dense-matter regime. Implementing the FPEOS table of silicon into our hydrocodes, we have studied its effects on Si-target implosions. When compared with the one-dimensional radiation-hydrodynamics simulation using the SESAME 3810 EOS model, the FPEOS simulation showed that (1) the shock speed in silicon is ∼10% slower; (2) the peak density of an in-flight Si shell during implosion is ∼20% higher than the SESAME 3810 simulation; (3) the maximum density reached in the FPEOS simulation is ∼40% higher at the peak compression; and (4) the final areal density and neutron yield are, respectively, ∼30% and ∼70% higher predicted by FPEOS versus the traditional simulation using SESAME 3810. All of these features can be attributed to the larger compressibility of silicon predicted by FPEOS. These results indicate that an accurate EOS table, like the FPEOS presented here, could be essential for the precise design of targets for HED experiments.

First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions.

Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. With first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions (ρ=0.1to100g/cm(3) and T=1000 to 4,000,000 K). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic target implosions on OMEGA using the FPEOS table of CH have predicted ∼30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ∼5% reduction in implosion velocity that is caused by the ∼10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered light from ICF implosions.

Dynamical and transport properties of liquid gallium at high pressures.

Quantum molecular dynamics (QMD) simulations are used to calculate the equation of state, structure, and transport properties of liquid gallium along the principal shock Hugoniot. The calculated Hugoniot is in very good agreement with experimental data up to a pressure of 150 GPa as well as with our earlier classical molecular dynamics calculations using a modified embedded atom method (MEAM) potential. The self-diffusion and viscosity calculated using QMD agree with experimental measurements better than the MEAM results, which we attribute to capturing the complexity of the electronic structure at elevated temperatures. Calculations of the DC conductivity were performed around the Hugoniot. Above a density of 7.5 g/cm(3), the temperature increases rapidly along the Hugoniot, and the optical conductivity decreases, indicating simple liquid metal behavior.

First-principles thermal conductivity of warm-dense deuterium plasmas for inertial confinement fusion applications.

Thermal conductivity (κ) of both the ablator materials and deuterium-tritium (DT) fuel plays an important role in understanding and designing inertial confinement fusion (ICF) implosions. The extensively used Spitzer model for thermal conduction in ideal plasmas breaks down for high-density, low-temperature shells that are compressed by shocks and spherical convergence in imploding targets. A variety of thermal-conductivity models have been proposed for ICF hydrodynamic simulations of such coupled and degenerate plasmas. The accuracy of these κ models for DT plasmas has recently been tested against first-principles calculations using the quantum molecular-dynamics (QMD) method; although mainly for high densities (ρ > 100 g/cm3), large discrepancies in κ have been identified for the peak-compression conditions in ICF. To cover the wide range of density-temperature conditions undergone by ICF imploding fuel shells, we have performed QMD calculations of κ for a variety of deuterium densities of ρ = 1.0 to 673.518 g/cm3, at temperatures varying from T = 5 × 103 K to T = 8 × 106 K. The resulting κQMD of deuterium is fitted with a polynomial function of the coupling and degeneracy parameters Γ and θ, which can then be used in hydrodynamic simulation codes. Compared with the "hybrid" Spitzer-Lee-More model currently adopted in our hydrocode lilac, the hydrosimulations using the fitted κQMD have shown up to ∼20% variations in predicting target performance for different ICF implosions on OMEGA and direct-drive-ignition designs for the National Ignition Facility (NIF). The lower the adiabat of an imploding shell, the more variations in predicting target performance using κQMD. Moreover, the use of κQMD also modifies the shock conditions and the density-temperature profiles of the imploding shell at early implosion stage, which predominantly affects the final target performance. This is in contrast to the previous speculation that κQMD changes mainly the inside ablation process during the hot-spot formation of an ICF implosion.

First principles nonequilibrium plasma mixing.

We have performed nonequilibrium classical and quantum-mechanical molecular dynamics simulations that follow the interpenetration of deuterium-tritium (DT) and carbon (C) components through an interface initially in hydrostatic and thermal equilibrium. We concentrate on the warm, dense matter regime with initial densities of 2.5-5.5 g/cm3 and temperatures from 10 to 100 eV. The classical treatment employs a Yukawa pair-potential with the parameters adjusted to the plasma conditions, and the quantum treatment rests on an orbital-free density functional theory at the Thomas-Fermi-Dirac level. For times greater than about a picosecond, the component concentrations evolve in accordance with Fick's law for a classically diffusing fluid with the motion, though, described by the mutual diffusion coefficient of the mixed system rather than the self-diffusion of the individual components. For shorter times, microscopic processes control the clearly non-Fickian dynamics and require a detailed representation of the electron probability density in space and time.

Transport properties of lithium hydride at extreme conditions from orbital-free molecular dynamics.

We have performed a systematic study of lithium hydride (LiH), using orbital-free molecular dynamics, with a focus on mass transport properties such as diffusion and viscosity by extending our previous studies at the lower end of the warm, dense matter regime to cover a span of densities from ambient to 10-fold compressed and temperatures from 10 eV to 10 keV. We determine analytic formulas for self- and mutual-diffusion coefficients, and viscosity, which are in excellent agreement with our molecular dynamics results, and interpolate smoothly between liquid and dense plasma regimes. In addition, we find the orbital-free calculations begin to agree with the Brinzinskii-Landau formula above about 250 eV at which point the medium becomes fully ionized. A binary-ion model based on a bare Coulomb interaction within a neutralizing background with the effective charges determined from a regularization prescription shows good agreement above about 100 eV with the orbital-free results. Finally, we demonstrate the validity of a pressure-based mixing rule in determining the transport properties from the pure-species quantities.

Quantum molecular dynamics simulations of transport properties in liquid and dense-plasma plutonium.

We have calculated the viscosity and self-diffusion coefficients of plutonium in the liquid phase using quantum molecular dynamics (QMD) and in the dense-plasma phase using orbital-free molecular dynamics (OFMD), as well as in the intermediate warm dense matter regime with both methods. Our liquid metal results for viscosity are about 40% lower than measured experimentally, whereas a previous calculation using an empirical interatomic potential (modified embedded-atom method) obtained results 3-4 times larger than the experiment. The QMD and OFMD results agree well at the intermediate temperatures. The calculations in the dense-plasma regime for temperatures from 50 to 5000 eV and densities about 1-5 times ambient are compared with the one-component plasma (OCP) model, using effective charges given by the average-atom code INFERNO. The INFERNO-OCP model results agree with the OFMD to within about a factor of 2, except for the viscosity at temperatures less than about 100 eV, where the disagreement is greater. A Stokes-Einstein relationship of the viscosities and diffusion coefficients is found to hold fairly well separately in both the liquid and dense-plasma regimes.

Viscosity and mutual diffusion of deuterium-tritium mixtures in the warm-dense-matter regime.

We have calculated viscosity and mutual diffusion of deuterium-tritium (DT) in the warm, dense matter regime for densities from 5 to 20 g/cm{3} and temperatures from 2 to 10 eV, using both finite-temperature Kohn-Sham density-functional theory molecular dynamics (QMD) and orbital-free molecular dynamics (OFMD). The OFMD simulations are in generally good agreement with the benchmark QMD results, and we conclude that the simpler OFMD method can be used with confidence in this regime. For low temperatures (3 eV and below), one-component plasma (OCP) model simulations for diffusion agree with the QMD and OFMD calculations, but deviate by 30% at 10 eV. In comparison with the QMD and OFMD results, the OCP viscosities are not as good as for diffusion, especially for 5 g/cm{3} where the temperature dependence is significantly different. The QMD and OFMD reduced diffusion and viscosity coefficients are found to depend largely, though not completely, only on the Coulomb coupling parameter Γ , with a minimum in the reduced viscosity at Γ≈25 , approximately the same position found in the OCP simulations. The QMD and OFMD equations of state (pressure) are also compared with the hydrogen two-component plasma model.

Energy relaxation rates in dense hydrogen plasmas.

A comprehensive study is made of the energy relaxation rates between ions and electrons in a dense hydrogen plasma. Results of classical molecular dynamics (MD) simulations are compared with quantal calculations using the Fermi golden rule and using dimensional continuation. The rates from the molecular dynamics simulations employing a screened potential are found to be in reasonable agreement with the Landau-Spitzer relaxation rates, and are around 30% higher than the Fermi golden rule rates. By inverting the classical MD relaxation rate vs the quantal result, a semiclassical value for the screening length is suggested. We present energy relaxation rates relevant for radiation-hydrodynamic simulations of inertial confinement fusion devices.

Ab initio molecular dynamics and quasichemical study of H+(aq).

The excess proton in water, H(+)(aq), plays a fundamental role in aqueous solution chemistry. Its solution thermodynamic properties are essential to molecular descriptions of that chemistry and for validation of dynamical calculations. Within the quasichemical theory of solutions those thermodynamic properties are conditional on recognizing underlying solution structures. The quasichemical treatment identifies H(3)O(+) and H(2)O(5)(+) as natural inner-shell complexes, corresponding to the cases of n = 1, 2 water molecule ligands, respectively, of a distinguished H(+) ion. A quantum-mechanical treatment of the inner-shell complex with both a dielectric continuum and a classical molecular dynamics treatment of the outer-shell contribution identifies the latter case (the Zundel complex) as the more numerous species. Ab initio molecular dynamics simulations, with two different electron density functionals, suggest a preponderance of Zundel-like structures, but a symmetrical ideal Zundel cation is not observed.

Simulations of the optical properties of warm dense aluminum.

Using quantum molecular dynamics simulations, we show that the optical properties of aluminum change drastically along the nonmetal metal transition observed experimentally. As the density increases and the many-body effects become important, the optical response gradually evolves from the one characteristic of an atomic fluid to the one of a simple metal. We show that quantum molecular dynamics combined with the Kubo-Greenwood formulation naturally embodies the two limits and provides a powerful tool to calculate and benchmark the optical properties of various systems as they evolve into the warm dense matter regime.

Hydration and mobility of HO-(aq).

The hydroxide anion plays an essential role in many chemical and biochemical reactions. But a molecular-scale description of its hydration state, and hence also its transport, in water is currently controversial. The statistical mechanical quasichemical theory of solutions suggests that HO.[H2O]3(-) is the predominant species in the aqueous phase under standard conditions. This result agrees with recent spectroscopic studies on hydroxide water clusters and with the available thermodynamic hydration free energies. In contrast, a recent ab initio molecular dynamics simulation has suggested that HO.[H2O]4(-) is the only dominant aqueous solution species. We apply adiabatic ab initio molecular dynamics simulations and find good agreement with both the quasichemical theoretical predictions and experimental results. The present results suggest a picture that is simpler, more traditional, but with additional subtlety. These coordination structures are labile but the tricoordinate species is the prominent case. This conclusion is unaltered with changes in the electronic density functional. No evidence is found for rate-determining activated interconversion of a HO.[H2O]4(-) trap structure to HO.[H2O]3(-) mediating hydroxide transport. The view of HO- diffusion as the hopping of a proton hole has substantial validity, the rate depending largely on the dynamic disorder of the water hydrogen-bond network.

Free energy of liquid water on the basis of quasichemical theory and ab initio molecular dynamics.

We use ab initio molecular dynamics as a basis for quasichemical theory evaluation of the free energy of water near conventional liquid thermodynamic states. The Perdew-Wang-91 (PW91), Perdew-Burke-Ernzerhof (PBE), and revised PBE (rPBE) functionals are employed. The oxygen radial density distribution using the rPBE functional is in reasonable agreement with current experiments, whereas the PW91 and PBE functionals predict a more structured oxygen radial density distribution. The diffusion coefficient with the rPBE functional is in reasonable accord with experiments. Using a maximum entropy procedure, we obtain x0 from the coordination number distribution xn for oxygen atoms having n neighbors. Likewise, we obtain p0 from pn, the probability of observing cavities of specified radius containing n water molecules. The probability x0 is a measure of the local chemical interactions and is central to the quasichemical theory of solutions. The probability p0, central to the theory of liquids, is a measure of the free energy required to open cavities of defined sizes in the solvent. Using these values and a reasonable model for electrostatic and dispersion effects, the hydration free energy of water in water at 314 K is calculated to be -5.1 kcal/mole with the rPBE functional, in encouraging agreement with the experimental value of -6.1 kcal/mole.

Electrical conductivity for warm, dense aluminum plasmas and liquids.

The electrical conductivity of warm, dense aluminum plasmas and liquids is calculated using ab initio molecular dynamics and the Kubo-Greenwood formula. The density range extends from near solid to one-hundredth of solid density, and the temperature range extends from 6000 K to 30 000 K. This density and temperature range allows direct comparison with experimental results obtained with the tamped exploding wire technique.

Evolution of ultracold neutral plasmas.

We present the first large-scale simulations of an ultracold neutral plasma, produced by photoionization of laser-cooled xenon atoms, from creation to initial expansion, using classical molecular-dynamics methods with open boundary conditions. We reproduce many of the experimental findings such as the trapping efficiency of electrons with increased ion number, a minimum electron temperature achieved on approach to the photoionization threshold, and recombination into Rydberg states of an anomalously low principal quantum number. In addition, many of these effects establish themselves very early in the plasma evolution ( similar ns) before the present experimental observations begin.

Calculation of a deuterium double shock Hugoniot from ab initio simulations.

We calculate the equation of state of dense deuterium with two ab initio simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, in the density range of 0.67 < or = rho < or = 1.60 g cm(-3). We derive the double shock Hugoniot and compare with the recent laser-driven double shock wave experiments by Mostovych et al. [Phys. Rev. Lett. 85, 3870 (2000)]. We find excellent agreement between the two types of microscopic simulations, but a significant discrepancy with the laser-driven shock measurements.

Simulations of fluid hydrogen: comparison of a dissociation model with tight-binding molecular dynamics.

We compare the results of two complementary approaches, tight-binding molecular-dynamics simulations and a dissociation model, for determining the characteristics of dense, fluid hydrogen at pressures extending to megabars and temperatures to 10 000 K. Two tight-binding models were examined: one parametrization emphasized crystalline, molecular, and fluid properties, the other focused more on the intricate molecular interactions involving up to four hydrogen atoms. The two tight-binding cases and the dissociation model agree reasonably well for a variety of properties, including the equation of state, dissociation degree, and proton pair-correlation functions. In simulations of recently reported laser-driven shock experiments, the tight-binding and dissociative models predict different maximum compressions of four and five, respectively. We discuss the sensitivities of the models as well as give estimates for the region of validity of the chemical picture (dissociation model) and the accuracy of the dynamical picture (tight-binding simulations) in cases where molecular hydrogen still dominates the physical behavior.

Mixed direct-iterative methods for boundary integral formulations of dielectric solvation models.

This paper describes a mixed direct-iterative method for boundary integral formulations of dielectric solvation models. We give an example for which a direct solution at thermal accuracy is nontrivial and for which Gauss-Seidel iteration diverges in rare but reproducible cases. This difficulty is analyzed by obtaining the eigenvalues and the spectral radius of the iteration matrix. This establishes that the nonconvergence is due to inaccuracies of the asymptotic approximations for the matrix elements for accidentally close boundary element pairs on different spheres. This difficulty is cured by checking for boundary element pairs closer than the typical spatial extent of the boundary elements and for those pairs performing an 'in-line' Monte Carlo integration to evaluate the required matrix elements. This difficulty are not expected and have not been observed when only a direct solution is sought. Finally, we give an example application of these methods to deprotonation of monosilicic acid in water.