Orbital-free Molecular Dynamics Research Articles

Multicomponent mutual diffusion in the warm, dense matter regime

We present a study in the warm, dense matter regime of transport properties for a ternary mixture of the isotopes of hydrogen at 5 g/cm3 at temperatures between 50 and 400 eV as well as for a quaternary system with added carbon at 20 g/cm3 and 10 eV. We determine the properties from a series of orbital-free molecular dynamics simulations and calculate the diffusion coefficients in the Maxwell–Stefan (MS) formulation. The Darken approximation, which includes only time correlations between the same atom of the same species, gives reasonable agreement with the full MS results. However, we find that the reasons for this concurrence rest with more complex, and somewhat subtle, details within the MS prescription.

Reduced ionic diffusion by the dynamic electron–ion collisions in warm dense hydrogen

The dynamic electron–ion collisions play an important role in determining the static and transport properties of warm dense matter (WDM). The electron force field (EFF) method is applied to study the ionic transport properties of warm dense hydrogen. Compared with the results from quantum molecular dynamics and orbital-free molecular dynamics, the ionic diffusions are largely reduced by involving the dynamic collisions of electrons and ions. This physics is verified by the quantum Langevin molecular dynamics (QLMD) simulations, which includes electron–ion collision-induced friction (EI-CIF) into the dynamic equation of ions. Based on these new results, we proposed a model including the correction of collision-induced friction of the ionic diffusion. The CIF model has been verified to be valid in a wide range of densities and temperatures. We also compare the results with the Yukawa one-component plasma (YOCP) model and Effective OCP (EOCP) model. We proposed to calculate the self-diffusion coefficients using the EOCP model modified by the CIF model to introduce the dynamic electron–ion collision effect.

Unified first-principles equations of state of deuterium-tritium mixtures in the global inertial confinement fusion region

Accurate knowledge of the equation of state (EOS) of deuterium–tritium (DT) mixtures is critically important for inertial confinement fusion (ICF). Although the study of EOS is an old topic, there is a longstanding lack of global accurate EOS data for DT within a unified theoretical framework. DT fuel goes through very wide ranges of density and temperature from a cold condensed state to a hot dense plasma where ions are in a moderately or even strongly coupled state and electrons are in a partially or strongly degenerate state. The biggest challenge faced when using first-principles methods for obtaining accurate EOS data for DT fuel is the treatment of electron–ion interactions and the extremely high computational cost at high temperatures. In the present work, we perform extensive state-of-the-art ab initio quantum Langevin molecular dynamics simulations to obtain EOS data for DT mixtures at densities from 0.1 g/cm3 to 2000 g/cm3 and temperatures from 500 K to 2000 eV, which are relevant to ICF processes. Comparisons with average-atom molecular dynamics and orbital-free molecular dynamics simulations show that the ionic strong-coupling effect is important for determining the whole-range EOS. This work can supply accurate EOS data for DT mixtures within a unified ab initio framework, as well as providing a benchmark for various semiclassical methods.

Static and dynamic properties of multi-ionic plasma mixtures.

Complex plasma mixtures with three or more components are often encountered in astrophysics or in inertial confinement fusion (ICF) experiments. For mixtures containing species with large differences in atomic number Z, the modeling needs to consider at the same time the kinetic theory for low-Z elements combined with the theory of strongly coupled plasma for high-Z elements, as well as all the intermediate situations that can appear in multicomponent systems. For such cases, we study the pair distribution functions, self-diffusions, mutual diffusion, and viscosity for ternary mixtures at extreme conditions. These quantities can be produced from first principles using orbital free molecular dynamics at the computational expense of very intensive simulations to reach good statistics. Utilizing the first-principles results as reference data, we assess the merit of a global analytic model for transport coefficients, "pseudo-ions in jellium" (PIJ), based on an isoelectronic assumption (iso-n_{e}). With a multicomponent hypernetted-chain integral equation, we verify the quality of the iso-n_{e}prescription for describing the static structure of the mixtures. This semianalytical modeling compares well with the simulation results and allows one to consider plasma mixtures not accessible to simulations. Applications are given for the mix of materials in ICF experiments. A reduction of a multicomponent mixture to an effective binary mixture is also established in the hydrodynamic limit and compared with PIJ estimations for ICF relevant mixtures.

Enhancement factor of nuclear reactions in partially ionized plasmas and asymmetric mixtures

When hydrogen is mixed with heavy (high‐Z) elements, even as traces, such as iron in the sun, the plasma mixture transits from a weakly coupled state to the intermediate coupling regime of simultaneous weak and strong couplings due to charge asymmetry. In those circumstances, partial ionization is an important aspect to consider. We present a global approach for evaluating enhancement factors for thermonuclear reactions in such mixtures. We grounded our approach on extensive orbital free molecular dynamics (OFMD) simulations of hydrogen‐silver mixtures, chosen as a prototype of hydrogen—high‐Zmixtures, in a large range of temperature (100 < T < 1600 eV). By comparing a series of OFMD simulations to hyper‐netted chain calculations of effective binary ionic mixtures (eBIM), we set a general procedure for computing enhancement factors. The electron screening contribution is also included implicitly in the definition of the effective ionizations within the average atom framework. The agreement between the pair distribution functions of OFMD and eBIM validates a prescription in which each average atom representing a given species shares the same external electron density with the others (iso‐nerule). We checked that an interpolation formula between weak and strong couplings in BIM, due to Chugunov and DeWitt, is accurate enough to address the limit of extreme dilution of a heavy element.

Checking the Salpeter enhancement of nuclear reactions at intermediate coupling in asymmetric mixtures

We investigate the plasma enhancement of nuclear reactions in the intermediate coupling regime using orbital free molecular dynamics (OFMD) simulations. Mixtures of H-Cu and H-Ag serve as prototypes of simultaneous weak and strong couplings due to the charge asymmetry. Of particular importance is the partial ionization of Cu and Ag and the free electron polarization captured by OFMD simulations. By comparing a series of OFMD simulations at various concentrations and constant pressure to multi-component hyper-netted chain (MCHNC) calculations of effective binary ionic mixtures, we set a general procedure for computing enhancement factors. The MCHNC procedure allows extension to very low concentrations (5% or less) and to very high temperatures (few keV) unreachable by the simulations. Enhancement factors for nuclear reaction rates extracted from the MCHNC approach are compared with the Salpeter theory in the weak and strong coupling regimes, and a new interpolation is proposed.

Equation of state of carbon in the warm dense matter regime from density-functional theory molecular dynamics

We show 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 of carbon. As a result, we construct an approach that allows to reproduce the quantum molecular dynamics equation of state of carbon at high temperature by combining quantum and orbital-free molecular dynamics. We apply this approach to a wide range of density and temperature conditions of the liquid or plasma state: $30\ensuremath{\ge}\ensuremath{\rho}\ensuremath{\ge}0.8\phantom{\rule{0.16em}{0ex}}\mathrm{g}/{\mathrm{cm}}^{3}, T\ensuremath{\ge}1$ eV. Then we test the sensitivity of the equation of state obtained to the choice of the exchange-correlation functional. We retain the generalized gradient approximation of this functional, corrected to approximately include the influence of temperature, and compare the results obtained to published first-principles calculations and to experimental shock data.

Transport properties of warm and hot dense iron from orbital free and corrected Yukawa potential molecular dynamics

The equation of states, diffusions, and viscosities of strongly coupled Fe at 80 and 240 eV with densities from 1.6 to 40 g/cm3 are studied by orbital-free molecular dynamics, classical molecular dynamics with a corrected Yukawa potential and compared with the results from average atom model. A new local pseudopotential is generated for orbital free calculations. For low densities, the Yukawa model captures the correct ionic interaction behavior around the first peak of the radial distribution function (RDF), thus it gives correct RDFs and transport coefficients. For higher densities, the scaled transformation of the Yukawa potential or adding a short range repulsion part to the Yukawa potential can give correct RDFs and transport coefficients. The corrected potentials are further validated by the force matching method.

Relaxation of non-isothermal hot dense plasma parameters

The relaxation of temperature, coupling parameters, the excess part of equation of state, and the correlation energy of the non-isothermal hot dense plasmas are considered on the basis of the method of effective interaction potentials. The electron–ion effective interaction potential for the hot dense plasma is discussed. The accuracy of description of the dense plasma properties by the effective electron–ion interaction potential is demonstrated by the agreement of the derived quantities like stopping power and transport coefficients calculated using our methodology with the results of the finite-temperature Kohn-Sham density-functional theory molecular dynamics, and orbital-free molecular dynamics results as well as with the data obtained using other theoretical approaches.

Correlation and transport properties for mixtures at constant pressure and temperature.

Transport properties of mixtures of elements in the dense plasma regime play an important role in natural astrophysical and experimental systems, e.g., inertial confinement fusion. We present a series of orbital-free molecular dynamics simulations on dense plasma mixtures with comparison to a global pseudo ion in jellium model. Hydrogen is mixed with elements of increasingly high atomic number (lithium, carbon, aluminum, copper, and silver) at a fixed temperature of 100 eV and constant pressure set by pure hydrogen at 2g/cm^{3}, namely, 370 Mbars. We compute ionic transport coefficients, such as self-diffusion, mutual diffusion, and viscosity for various concentrations. Small concentrations of the heavy atoms significantly change the density of the plasma and decrease the transport coefficients. The structure of the mixture evidences a strong Coulomb coupling between heavy ions and the appearance of a broad correlation peak at short distances between hydrogen atoms. The concept of an effective one component plasma is used to quantify the overcorrelation of the light element induced by the admixture of a heavy element.

Validity boundary of orbital-free molecular dynamics method corresponding to thermal ionization of shell structure

With $^{6}\mathrm{Li}\text{D}$ as an example, we show that the applicable region of the orbital-free molecular dynamics (OFMD) method in a large temperature range is determined by the thermal ionization process of bound electrons in shell structures. The validity boundary of the OFMD method is defined roughly by the balance point of the average thermal energy of an electron and the ionization energy of the lowest localized electronic state. This theoretical proposition is based on the observation that the deviation of the OFMD method originates from its less accurate description to the charge density in partially ionized shells, as compared with the results of the extended first-principles molecular dynamics method, which well reproduces the charge density of shell structures.

First-principles prediction of the softening of the silicon shock Hugoniot curve

Shock compression of silicon (Si) under extremely high pressures (>100 Mbar) was investigated by using two first-principles methods of orbital-free molecular dynamics (OFMD) and path integral Monte Carlo (PIMC). While pressures from the two methods agree very well, PIMC predicts a second compression maximum because of 1s electron ionization that is absent in OFMD calculations since Thomas-Fermi-based theories lack shell structure. The Kohn-Sham density functional theory is used to calculate the equation of state (EOS) of warm dense silicon for low-pressure loadings (P < 100 Mbar). Combining these first-principles EOS results, the principal shock Hugoniot curve of silicon for pressures varying from 1 Mbar to above 10 Gbar was derived. We find that silicon is 20% or more softer than what was predicted by widely-used EOS models. Existing high-pressure experimental data (P = 1 - 2 Mbar) seem to indicate this softening behavior of Si, which calls for future strong-shock experiments (P > 10 Mbar) to benchmark our results.

Transport properties of an asymmetric mixture in the dense plasma regime.

We study how concentration changes ionic transport properties along isobars-isotherms for a mixture of hydrogen and silver, representative of turbulent layers relevant to inertial confinement fusion and astrophysics. Hydrogen will typically be fully ionized while silver will be only partially ionized but can have a large effective charge. This will lead to very different physical conditions for the H and Ag. Large first principles orbital free molecular dynamics simulations are performed and the resulting transport properties are analyzed. Comparisons are made with transport theory in the kinetic regime and in the coupled regime. The addition of a small amount of heavy element in a light material has a dramatic effect on viscosity and diffusion of the mixture. This effect is explained through kinetic theory as a manifestation of a crossover between classical diffusion and Lorentz diffusion.

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.

First-principles investigations on ionization and thermal conductivity of polystyrene for inertial confinement fusion applications

Using quantum molecular-dynamics (QMD) methods based on the density functional theory, we have performed first-principles investigations of the ionization and thermal conductivity of polystyrene (CH) over a wide range of plasma conditions (ρ = 0.5 to 100 g/cm3 and T = 15 625 to 500 000 K). The ionization data from orbital-free molecular-dynamics calculations have been fitted with a “Saha-type” model as a function of the CH plasma density and temperature, which gives an increasing ionization as the CH density increases even at low temperatures (T &amp;lt; 50 eV). The orbital-free molecular dynamics method is only used to gauge the average ionization behavior of CH under the average-atom model in conjunction with the pressure-matching mixing rule. The thermal conductivities (κQMD) of CH, derived directly from the Kohn–Sham molecular-dynamics calculations, are then analytically fitted with a generalized Coulomb logarithm [(lnΛ)QMD] over a wide range of plasma conditions. When compared with the traditional ionization and thermal conductivity models used in radiation–hydrodynamics codes for inertial confinement fusion simulations, the QMD results show a large difference in the low-temperature regime in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic deuterium–tritium targets with CH ablators on OMEGA and the National Ignition Facility using the QMD-derived ionization and thermal conductivity of CH have predicted ∼20% variation in target performance in terms of hot-spot pressure and neutron yield (gain) with respect to traditional model simulations.

Unified Concept of Effective One Component Plasma for Hot Dense Plasmas.

Orbital-free molecular dynamics simulations are used to benchmark two popular models for hot dense plasmas: the one component plasma (OCP) and the Yukawa model. A unified concept emerges where an effective OCP (EOCP) is constructed from the short-range structure of the plasma. An unambiguous ionization and the screening length can be defined and used for a Yukawa system, which reproduces the long-range structure with finite compressibility. Similarly, the dispersion relation of longitudinal waves is consistent with the screened model at vanishing wave number but merges with the OCP at high wave number. Additionally, the EOCP reproduces the overall relaxation time scales of the correlation functions associated with ionic motion. In the hot dense regime, this unified concept of EOCP can be fruitfully applied to deduce properties such as the equation of state, ionic transport coefficients, and the ion feature in x-ray Thomson scattering experiments.

Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime.

We present simulations of a four-component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5-200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. Additionally, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

Evidence for out-of-equilibrium states in warm dense matter probed by x-ray Thomson scattering.

A recent and unexpected discrepancy between ab initio simulations and the interpretation of a laser shock experiment on aluminum, probed by x-ray Thomson scattering (XRTS), is addressed. The ion-ion structure factor deduced from the XRTS elastic peak (ion feature) is only compatible with a strongly coupled out-of-equilibrium state. Orbital free molecular dynamics simulations with ions colder than the electrons are employed to interpret the experiment. The relevance of decoupled temperatures for ions and electrons is discussed. The possibility that it mimics a transient, or metastable, out-of-equilibrium state after melting is also suggested.

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.

Combining Kohn-Sham and orbital-free density-functional theory for Hugoniot calculations to extreme pressures.

The shock Hugoniot for lithium 6 deuteride ((6)LiD) was calculated via first principles using Kohn-Sham density-functional theory molecular dynamics (KSMD) for temperatures of 0.5-25 eV. The upper limit of 25 eV represents a practical limit where KSMD is no longer computationally feasible due to the number of electronic bands which are required to be populated. To push the Hugoniot calculations to higher temperatures we make use of orbital-free density-functional theory molecular dynamics (OFMD). Thomas-Fermi-Dirac-based OFMD gives a poor description of the electronic structure at low temperatures so the initial state is not well defined. We propose a method of bootstrapping the Hugoniot from OFMD to the Hugoniot from KSMD between 10 and 20 eV, where the two methods are in agreement. The combination of KSMD and OFMD allows construction of a first-principles Hugoniot from the initial state to 1000 eV. Theoretical shock-compression results are in good agreement with available experimental data and exhibit the appropriate high-temperature limits. We show that a unified KSMD-OFMD Hugoniot can be used to assess the quality of the existing equation-of-state (EOS) models and inform better EOS models based on justifiable physics.