Pseudoatom molecular dynamics

Spectral-partitioned Kohn-Sham density functional theory

We introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics

Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/cm^{3} to 16 g/cm^{3} and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. We find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.

Random-walk shielding-potential viscosity model for warm dense metals

We develop a model, called the "random-walk shielding-potential viscosity model" (RWSP-VM) that introduces the statistics of random-walk ions and the Debye shielding effect to describe the viscosities of warm dense metals. The viscosities of several metals with low to high atomic numbers (Be, Al, Fe, and U) are calculated using the analytical expression of RWSP-VM. Additionally, we simulate the viscosities of Fe and Be by employing the Langevin molecular dynamics (MD) and classical MD, while the MD data for Al and U are obtained from a previous work. The results of the RWSP-VM are in good agreement with the MD results, which validates the proposed model. Furthermore, we compare the RWSP-VM with the one-component plasma model and Yukawa viscosity model and show that the three models yield results in excellent agreement with each other in the regime where the RWSP-VM is applicable. These results indicate that the RWSP-VM is a universal, accurate, and highly efficient model for calculating the viscosity of metals in the warm dense state. The code of the proposed RWSP-VM is provided, and it is envisaged that it will have broad application prospects in numerous fields.

Dense plasma opacity via the multiple-scattering method

The calculation of the optical properties of hot dense plasmas with a model that has self-consistent plasma physics is a grand challenge for high energy density science. Here we exploit a recently developed electronic structure model that uses multiple scattering theory to solve the Kohn-Sham density functional theory equations for dense plasmas. We calculate opacities in this regime, validate the method, and apply it to recent experimental measurements of opacity for Cr, Ni, and Fe. Good agreement is found in the quasicontinuum region for Cr and Ni, while the self-consistent plasma physics of the approach cannot explain the observed difference between models and the experiment for Fe.

Effect of ionic disorder on the principal shock Hugoniot

The effect of ionic disorder on the principal Hugoniot is investigated using multiple scattering theory to very high pressure (Gbar). Calculations using molecular dynamics to simulate ionic disorder are compared to those with a fixed crystal lattice, for both carbon and aluminum. For the range of conditions considered here we find that ionic disorder has a relatively minor influence. It is most important at the onset of shell ionization and we find that, at higher pressures, the subtle effect of the ionic environment is overwhelmed by the larger number of ionized electrons with higher thermal energies.

Bound electron screening effect on ion-ion potential of warm and hot dense matter

The effects of bound electron screening in warm and hot dense matter are investigated analytically and a theoretical description of screened short-range repulsion is given meanwhile. An empirical ion-ion potential including the classic charge screening and chemical bond attraction at various temperatures and densities is proposed. By solving hypernetted chain equations and comparing the obtained radial distribution function (RDF) with ab initio simulations, the proposed ion-ion potential is found to be promising over a wide range of temperatures and densities for warm dense aluminum and iron. The elastic scattering amplitude and the x-ray absorption near the edge structure of warm dense aluminum calculated from the obtained RDF are in good agreement with experiment results.

Equation of state modeling with pseudoatom molecular dynamics

Using a modified version of the pseudoatom molecular-dynamics approach, the silicon and oxygen equations of state were generated and then employed to construct the equation of state of silicon dioxide. The results are supported by the close agreement with ab initio simulations of the silicon pressure and experimental shock Hugoniot of silicon dioxide. Ion thermal contributions to thermodynamic functions provided by the PAMD simulations are compared to their counterparts obtained with the one-component plasma and charged-hard-sphere approximations.

Multiple scattering theory for dense plasmas

Dense plasmas occur in stars, giant planets, and in inertial fusion experiments. Accurate modeling of the electronic structure of these plasmas allows for prediction of material properties that can in turn be used to simulate these astrophysical objects and terrestrial experiments. But modeling them remains a challenge. Here we explore the Korringa-Kohn-Rostoker Green's function (KKR-GF) method for this purpose. We find that it is able to predict equation of state in good agreement with other state-of-the-art methods, where they are accurate and viable. In addition, it is shown that the computational cost does not significantly change with temperature, in contrast with other approaches. Moreover, the method does not use pseudopotentials-core states are calculated self consistently. We conclude that KKR-GF is a very promising method for dense plasma simulation.

Atom-in-jellium equations of state in the high-energy-density regime

Recent path-integral Monte Carlo and quantum molecular dynamics simulations have shown that computationally efficient average-atom models can predict thermodynamic states in warm dense matter to within a few percent. One such atom-in-jellium model has typically been used to predict the electron-thermal behavior only, although it was previously developed to predict the entire equation of state (EOS). We report completely atom-in-jellium EOS calculations for Be, Al, Si, Fe, and Mo, as elements representative of a range of atomic number and low-pressure electronic structure. Comparing the more recent method of pseudoatom molecular dynamics, atom-in-jellium results were similar: sometimes less accurate, sometimes more. All these techniques exhibited pronounced effects of electronic shell structure in the shock Hugoniot which are not captured by Thomas-Fermi based EOS. These results demonstrate the value of a hierarchical approach to EOS construction, using average-atom techniques with shell structure to populate a wide-range EOS surface efficiently, complemented by more rigorous three-dimensional multiatom calculations to validate and adjust the EOS.

Path integral Monte Carlo simulations of warm dense aluminum

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of 0.1-32.4gcm^{-3} and 10^{4}-10^{8} K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multishock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multishock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and 〈Z〉 to reveal the evolution of the plasma structure and ionization behavior.

Dynamic electron-ion collisions and nuclear quantum effects in quantum simulation of warm dense matter

The structural, thermodynamic and transport properties of warm dense matter (WDM) are crucial to the fields of astrophysics and planet science, as well as inertial confinement fusion. WDM refers to the states of matter in a regime of temperature and density between cold condensed matter and hot ideal plasmas, where the density is from near-solid up to ten times solid density, and the temperature between 0.1 and 100 eV. In the WDM regime, matter exhibits moderately or strongly coupled, partially degenerate properties. Therefore, the methods used to deal with condensed matter and isolated atoms need to be properly validated for WDM. It is therefore a big challenge to understand WDM within a unified theoretical description with reliable accuracy. Here, we review the progress in the theoretical study of WDM with state-of-the-art simulations, i.e. quantum Langevin molecular dynamics and first principles path integral molecular dynamics. The related applications for WDM are also included.

Thomas-Fermi simulations of dense plasmas without pseudopotentials

The Thomas-Fermi model for warm and hot dense matter is widely used to predict material properties such as the equation of state. However, for practical reasons current implementations use pseudopotentials for the electron-nucleus interaction instead of the bare Coulomb potential. This complicates the calculation and quantities such as free energy cannot be converged with respect to the pseudopotential parameters. We present a method that retains the bare Coulomb potential for the electron-nucleus interaction and does not use pseudopotentials. We demonstrate that accurate free energies are obtained by checking variational consistency. Examples for aluminum and iron plasmas are presented.

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.

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 dense plasmas with pseudoatom molecular dynamics

We present an approximation for calculating the equation of state (EOS) of warm and hot dense matter that is built on the previously published pseudoatom molecular dynamics (PAMD) model of dense plasmas [Starrett et al., Phys. Rev. E 91, 013104 (2015)PLEEE81539-375510.1103/PhysRevE.91.013104]. While the EOS calculation with PAMD was previously limited to orbital-free density functional theory (DFT), the new approximation presented here allows a Kohn-Sham DFT treatment of the electrons. The resulting EOS thus includes a quantum mechanical treatment of the electrons with a self-consistent model of the ionic structure, while remaining tractable at high temperatures. The method is validated by comparisons with pressures from ab initio simulations of Be, Al, Si, and Fe. The EOS in the Thomas-Fermi approximation shows remarkable thermodynamic consistency over a wide range of temperatures for aluminum. We calculate the principal Hugoniots of aluminum and silicon up to 500 eV. We find that the ionic structure of the plasma has a modest effect that peaks at temperatures of a few eV and that the features arising from the electronic structure agree well with ab initio simulations.

Ionic Transport Coefficients of Dense Plasmas without Molecular Dynamics

We present a theoretical model that allows a fast and accurate evaluation of ionic transport properties of realistic plasmas spanning from warm and dense to hot and dilute conditions, including mixtures. This is achieved by combining a recent kinetic theory based on effective interaction potentials with a model for the equilibrium radial density distribution based on an average atom model and the integral equations theory of fluids. The model should find broad use in applications where nonideal plasma conditions are traversed, including inertial confinement fusion, compact astrophysical objects, solar and extrasolar planets, and numerous present-day high energy density laboratory experiments.

Models of the elastic x-ray scattering feature for warm dense aluminum

The elastic feature of x-ray scattering from warm dense aluminum has recently been measured by Fletcher et al. [Nature Photonics 9, 274 (2015)]10.1038/nphoton.2015.41 with much higher accuracy than had hitherto been possible. This measurement is a direct test of the ionic structure predicted by models of warm dense matter. We use the method of pseudoatom molecular dynamics to predict this elastic feature for warm dense aluminum with temperatures of 1-100 eV and densities of 2.7-8.1g/cm^{3}. We compare these predictions to experiments, finding good agreement with Fletcher et al. and corroborating the discrepancy found in analyses of an earlier experiment of Ma et al. [Phys. Rev. Lett. 110, 065001 (2013)]PRLTAO0031-900710.1103/PhysRevLett.110.065001. We also evaluate the validity of the Thomas-Fermi model of the electrons and of the hypernetted chain approximation in computing the elastic feature and find them both wanting in the regime currently probed by experiments.

Modified Enskog kinetic theory for strongly coupled plasmas

Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective potential transport theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)] to include an exclusion radius surrounding individual charged particles that is associated with Coulomb repulsion. This is obtained by analogy with the finite size of hard spheres in Enskog's theory. Predictions for the self-diffusion and shear viscosity coefficients of the one-component plasma are tested against molecular dynamics simulations. The theory is found to accurately capture the kinetic contributions to the transport coefficients, but not the potential contributions that arise at very strong coupling (Γ≳30). Considerations related to a first-principles generalization of Enskog's kinetic equation to continuous potentials are also discussed.

Ion-ion dynamic structure factor of warm dense mixtures

The ion-ion dynamic structure factor of warm dense matter is determined using the recently developed pseudoatom molecular dynamics method [Starrett et al., Phys. Rev. E 91, 013104 (2015)]. The method uses density functional theory to determine ion-ion pair interaction potentials that have no free parameters. These potentials are used in classical molecular dynamics simulations. This constitutes a computationally efficient and realistic model of dense plasmas. Comparison with recently published simulations of the ion-ion dynamic structure factor and sound speed of warm dense aluminum finds good to reasonable agreement. Using this method, we make predictions of the ion-ion dynamical structure factor and sound speed of a warm dense mixture-equimolar carbon-hydrogen. This material is commonly used as an ablator in inertial confinement fusion capsules, and our results are amenable to direct experimental measurement.