Orbital-free Molecular Dynamics Research Articles

Equation of state of dense plasmas: Orbital-free molecular dynamics as the limit of quantum molecular dynamics for high-Z elements

The applicability of quantum molecular dynamics to the calculation of the equation of state of a dense plasma is limited at high temperature by computational cost. Orbital-free molecular dynamics, based on a semiclassical approximation and possibly on a gradient correction, is a simulation method available at high temperature. For a high-Z element such as lutetium, we examine how orbital-free molecular dynamics applied to the equation of state of a dense plasma can be regarded as the limit of quantum molecular dynamics at high temperature. For the normal mass density and twice the normal mass density, we show that the pressures calculated with the quantum approach converge monotonically towards those calculated with the orbital-free approach; we observe a faster convergence when the orbital-free approach includes the gradient correction. We propose a method to obtain an equation of state reproducing quantum molecular dynamics results up to high temperatures where this approach cannot be directly implemented. With the results already obtained for low-Z plasmas, the present study opens the way for reproducing the quantum molecular dynamics pressure for all elements up to high temperatures.

Integral equation model for warm and hot dense mixtures.

In a previous work [C. E. Starrett and D. Saumon, Phys. Rev. E 87, 013104 (2013)] a model for the calculation of electronic and ionic structures of warm and hot dense matter was described and validated. In that model the electronic structure of one atom in a plasma is determined using a density-functional-theory-based average-atom (AA) model and the ionic structure is determined by coupling the AA model to integral equations governing the fluid structure. That model was for plasmas with one nuclear species only. Here we extend it to treat plasmas with many nuclear species, i.e., mixtures, and apply it to a carbon-hydrogen mixture relevant to inertial confinement fusion experiments. Comparison of the predicted electronic and ionic structures with orbital-free and Kohn-Sham molecular dynamics simulations reveals excellent agreement wherever chemical bonding is not significant.

A simple method for determining the ionic structure of warm dense matter

A model for dense homo-nuclear plasmas that couples an average atom model for the calculation of the electronic structure to the quantum Ornstein–Zernike equations describing the ionic structure is summarized and described pedagogically. The model is applied to the calculation of ion–ion pair distribution functions gII(r) for tungsten in the warm and hot dense matter regimes. These results are compared to orbital-free molecular dynamics simulations and excellent agreement is found. Calculations of gII(r) with a simple version of the model (which we call the ion-sphere model) are in remarkable agreement with those of the full model. This ion-sphere model provides a simple and efficient method of calculating accurate gII(r) for warm and hot dense matter for many applications involving low- to high-Z elements with a modest investment of effort.

Thomas-FermiZ-scaling laws and coupling stabilization for plasmas

Extending the well-known Thomas-Fermi Z-scaling laws to the Coulomb coupling parameter, we investigate the stabilization of the ionic coupling in isochoric heating [Clérouin et al., Phys. Rev. E 87, 061101 (2013)]. This stabilization is restricted to a domain in atomic number Z, temperature, and density, including strong limitations on high couplings, that can only be obtained for high-Z elements. Contact is made with recent isochoric heating experiments. The consequences for corresponding states with respect to ionic coupling are also quantified via orbital free molecular dynamics simulations. This opens avenues for future isochoric heating experiments.

The melting point of lithium: an orbital-free first-principles molecular dynamics study

The melting point of liquid lithium near zero pressure is studied with large-scale orbital-free first-principles molecular dynamics (OF-FPMD) in the isobaric-isothermal ensemble. We adopt the Wang-Govind-Carter (WGC) functional as our kinetic energy density functional (KEDF) and construct a bulk-derived local pseudopotential (BLPS) for Li. Our simulations employ both the ‘heat-until-melts’ method and the coexistence method. We predict 465 K as an upper bound of the melting point of Li from the ‘heat-until-melts’ method, while we predict 434 K as the melting point of Li from the coexistence method. These values compare well with an experimental melting point of 453 K at zero pressure. Furthermore, we calculate a few important properties of liquid Li including the diffusion coefficients, pair distribution functions, static structure factors, and compressibilities of Li at 470 K and 725 K in the canonical ensemble. Our theoretically-obtained results show good agreement with known experimental results, suggesting that OF-FPMD using a non-local KEDF and a BLPS is capable of accurately describing liquid metals.

Wide range equation of state for fluid hydrogen from density functional theory

Wide range equation of state (EOS) for liquid hydrogen is ultimately obtained by combining two kinds of density functional theory (DFT) molecular dynamics simulations, namely, first-principles molecular dynamics simulations and orbital-free molecular dynamics simulations. Specially, the present introduction of short cutoff radius pseudopotentials enables the EOS to be available in the range from 9.82 × 10−4 to 1.347 × 103 g/cm3 and up to 5 × 107 K. By comprehensively comparing with various attainable experimental and theoretical data, we derive the conclusion that our DFT-EOS can be readily and reliably applied to hydrodynamic simulations of the inertial confinement fusion.

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.

Equation of state of dense plasmas by ab initio simulations: Bridging the gap between quantum molecular dynamics and orbital-free molecular dynamics at high temperature

The applicability of quantum molecular dynamics to the calculation of the equation of state of a dense plasma is limited at high temperature by computational cost. Orbital-free molecular dynamics, based on the Thomas-Fermi semiclassical approximation and possibly on a gradient correction, is the only simulation method currently available at high temperature. We show in the case of a dense boron plasma that the two approaches give pressures differing by a few percent even at temperatures as high as a few tens of electron-volts. We indicate how the pressures obtained by orbital-free molecular dynamics can be corrected in order to appear as a limit of the quantum molecular dynamics results as temperature increases. We thus obtain a method to calculate the equation of state of a dense plasma up to high temperatures where quantum molecular dynamics cannot be directly implemented.

Plastic ablator and hydrodynamic instabilities: A first-principles set of microscopic coefficients

We have performed orbital-free and quantum molecular dynamics simulations on plastic ablator along two isochores, namely 7 and 9 g cm(-3), from 5 to 40 eV. These thermodynamic conditions correspond to those encountered during inertial confinement fusion capsule implosion when hydrodynamic instabilities can take place. The coupling between orbital-free and quantum approaches allowed us to compute an exhaustive set of microscopic coefficients, i.e., equation-of-state, ionic diffusion coefficients, thermal and electrical conductivities, spanning phenomena that can mitigate the growth of classical Rayleigh-Taylor instability. Comparisons to widely used models in hydrodynamics codes are developed.

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.

The equation of state, electronic thermal conductivity, and opacity of hot dense deuterium-helium plasmas

Thermophysical properties of dense deuterium-helium plasmas along the 160 g/cm3 isochore with temperatures up to 800 electron-volt are reported. From Kubo-Greenwood formula, the electronic thermal conductivity and Rosseland mean opacity are determined by means of quantum molecular dynamics (QMD) simulations. Equation of states is obtained by QMD and orbital free molecular dynamics. The electronic heat conductance is compared with several models currently used in inertial confinement fusion designs. Our results indicate that only in the weak coupling regime, the opacity is sensitive to the concentration of helium.

An investigation of the local structure and dynamic properties of undercooled liquid silicon using the orbital-free ab-initio molecular dynamics method

We present results for the static and dynamic structural properties of undercooled liquid Si, at several temperatures between 1550 K and 1100 K, obtained through orbital-free ab-initio molecular dynamics simulations. The local bond angle distributions show a modest increase in the tetrahedral order upon decreasing the temperature. We also analyze the variation of several dynamic magnitudes and transport properties with temperature, showing a tendency to sustain shear waves for some wavevectors as undercooling is deepened. We compare our orbital-free ab-initio results with the limited experimental data available, as well as with results of other ab-initio simulations.

Ab InitioSimulations of Dense Helium Plasmas

We study the thermophysical properties of dense helium plasmas by using quantum molecular dynamics and orbital-free molecular dynamics simulations, where densities are considered from 400 to 800 g/cm3 and temperatures up to 800 eV. Results are presented for the equation of state. From the Kubo-Greenwood formula, we derive the electrical conductivity and electronic thermal conductivity. In particular, with the increase in temperature, we discuss the change in the Lorenz number, which indicates a transition from strong coupling and degenerate state to moderate coupling and partial degeneracy regime for dense helium.

Orbital-free molecular dynamics simulations of transport properties in dense-plasma uranium

We have calculated the self-diffusion coefficients and shear viscosity of dense-plasma uranium using orbital-free molecular dynamics (OFMD) at the Thomas–Fermi–Dirac level. The transport properties of uranium in this regime have not previously been investigated experimentally or theoretically. The OFMD calculations were performed for temperatures from 50 to 5000 eV and densities from ambient to 10 times compressed. The results are compared with the one-component-plasma (OCP) model, using effective charges given by the average-atom code INFERNO and by the regularization procedure from the OFMD method. The latter generally showed better agreement with the OFMD for viscosity and the former for diffusion. A Stokes–Einstein relationship of the OFMD viscosities and diffusion coefficients is found to hold fairly well with a constant of 0.075 ± 0.10, while the OCP/INFERNO model yields 0.13 ± 0.10.

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.

KINETIC ENERGY FUNCTIONALS: EXACT ONES FROM ANALYTIC MODEL WAVE FUNCTIONS AND APPROXIMATE ONES IN ORBITAL-FREE MOLECULAR DYNAMICS

We consider the problem of constructing kinetic energy functionals in density functional theory. We first discuss the functional generated through the application of local-scaling transformations to the exact analytic wavefunctions for the Hookean model of 4He (a finite mass three-particle system), and contrast this result with a previous one for ∞He (infinite mass system). It is shown that an exact non-Born-Oppenheimer treatment not only leads to mass-correction terms in the kinetic energy, but to a basically different functional expression. In addition, we report and comment on some recently advanced approximate kinetic energy functionals generated in the context of the constraint-based approach to orbital-free molecular dynamics. The positivity and non-singularity of a new family of kinetic energy functionals specifically designed for orbital-free molecular dynamics is discussed. Finally, we present some conclusions.

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.

Transport properties of lithium hydride from quantum molecular dynamics and orbital-free molecular dynamics

We have performed a systematic study of lithium hydride in the warm-dense-matter regime for a density range from one to four times ambient solid and for temperatures from 2 to 6 eV using both finite-temperature density-functional theory quantum molecular dynamics (QMD) and orbital-free molecular dynamics (OFMD) with a focus on dynamical properties such as diffusion and viscosity. The validity of various mixing rules, especially those utilizing pressure, were checked for composite properties determined from QMD/OFMD simulations of the pure species against calculations on the fully interacting mixture. These rules produce pressures within about 10% of the full-mixture values but mutual-diffusion coefficients as different as 50%. We found very good agreement overall between the QMD, employing a three-electron pseudopotential, and the OFMD in the local-density approximation, especially at the higher temperatures and densities.

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.

Melting transition in rotating sodium clusters

We investigate the possible influence of a global cluster rotation on the melting-like transition of Na$_{30}$, Na$_{55}$ and Na$_{147}$, by means of orbital-free density-functional molecular dynamics simulations. The results reveal that very large angular momenta L are needed to significantly alter the results of simulations performed on nonrotating clusters, and therefore validate the usual L=0 approximation made in computer simulations of cluster thermal properties. However, a global rotation might have a more profound influence on the thermal properties in the limit of very small cluster sizes, when the ratio of rotational to vibrational degrees of freedom is not negligible. For those clusters which are in a highly excited rotational state, we find enhanced isomerization rates and even depressed melting points.