Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter.

Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equation of state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. We compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.

Mixed stochastic-deterministic time-dependent density functional theory: application to stopping power of warm dense carbon.

Warm dense matter (WDM) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM is often created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for stopping power, while high temperatures make the traditional tools of condensed matter, e.g. time-dependent density functional theory (TD-DFT), often intractable. We have developed a mixed stochastic-deterministic approach to TD-DFT which provides more efficient computation while maintaining the required precision for model discrimination. Recently, this approach showed significant improvement compared to models when compared to experimental energy loss measurements in WDM carbon. Here, we describe this approach and demonstrate its application to warm dense carbon stopping across a range of projectile velocities. We compare direct stopping-power calculation to approaches based on combining homogeneous electron gas response with bound electrons, with parameters extracted from our TD-DFT calculations.

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.

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.

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime.

We use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n=10^{26}cm^{-3}, T_{i}=10^{5}K, and 10^{7}K

A few selected contributions to electron and photon collisions with H2 and H 2 + .

We discuss a number of aspects regarding the physics of H 2 + and H2. This includes low-energy electron scattering processes and the interaction of both weak (perturbative) and strong (ultrafast/intense) electromagnetic radiation with those systems.

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.

Alternative first-principles calculation of entropy for liquids.

We present an alternative method for interpreting the velocity autocorrelation function (VACF) of a fluid with application to extracting the entropy in a manner similar to the methods developed by Lin et al. [J. Chem. Phys. 119, 11792 (2003)]JCPSA60021-960610.1063/1.1624057 and improved upon by Desjarlais [Phys. Rev. E 88, 062145 (2013)]PLEEE81539-375510.1103/PhysRevE.88.062145. The liquid VACF is decomposed into two components, one gas and one solid, and each contribution's entropic portion is calculated. However, we fit both the gas and solid portions of the VACF in the time domain. This approach is applied to a single-component liquid (a two-phase model of liquid Al at the melt line) and two different two-component systems: a superionic-to-superionic (bcc to fcc) phase transition in H_{2}O at high temperatures and pressures and a metastable liquid state of MgO. For all three examples, comparisons to existing results in the literature demonstrate the validity of our alternative.

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.

Bonding and structure in dense multi-component molecular mixtures.

We have performed finite-temperature density functional theory molecular dynamics simulations on dense methane, ammonia, and water mixtures (CH4:NH3:H2O) for various compositions and temperatures (2000 K ≤ T ≤ 10,000 K) that span a set of possible conditions in the interiors of ice-giant exoplanets. The equation-of-state, pair distribution functions, and bond autocorrelation functions (BACF) were used to probe the structure and dynamics of these complex fluids. In particular, an improvement to the choice of the cutoff in the BACF was developed that allowed analysis refinements for density and temperature effects. We note the relative changes in the nature of these systems engendered by variations in the concentration ratios. A basic tenet emerges from all these comparisons that varying the relative amounts of the three heavy components (C,N,O) can effect considerable changes in the nature of the fluid and may in turn have ramifications for the structure and composition of various planetary layers.

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.

Effect of correlation on viscosity and diffusion in molecular-dynamics simulations.

In the warm dense matter (WDM) regime, material properties like diffusion and viscosity can be obtained from lengthy quantum molecular dynamics simulations, where the quantum behavior of the electrons is represented using either Kohn-Sham or orbital-free density functional theory. To reduce the simulation duration, we fit the time dependence of the autocorrelation functions (ACFs) and then use the fit to find values of the diffusion and viscosity. This fitting procedure avoids noise in the long time behavior of the ACFs. We present a detailed analysis of the functional form used to fit the ACFs, which is always a more efficient means to obtain mass transport properties. We use the fits to estimate the statistical error of the transport properties. We apply this methodology to a dense correlated plasma of copper and a mixture of carbon and hydrogen. Both systems show structure in their ACFs and exhibit multiple time scales. The mixture contains different structural forms of the ACFs for each component in the mixture.

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.

Behavior of the coupling parameter under isochoric heating in a high-Z plasma.

The ion-ion coupling parameter Γ is estimated for tungsten along the ρ=40 g/cm(3) isochore corresponding to twice the normal density with temperatures ranging from 10 eV to 5 keV. Using a variety of approaches from a spherical Thomas-Fermi ion to a full three-dimensional orbital-free method, we show that along an isochore the effective ionic coupling parameter is almost constant over a wide range of temperatures (in our case Γ~/=20) due to the competition between rising temperatures and increased ionization. This Γ-plateau effect depends on the chosen density and is well delineated at normal density but almost disappears at five times the normal density. This effect could be used to obtain well-defined and predictable experimental conditions.

Thomas-Fermi Z-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.

Parallel solver for the time-dependent linear and nonlinear Schrödinger equation.

A solution of the time-dependent Schrödinger equation is required in a variety of problems in physics and chemistry. These include atoms and molecules in time-dependent electromagnetic fields, time-dependent approaches to atomic collision problems, and describing the behavior of materials subjected to internal and external forces. We describe an approach in which the finite-element discrete variable representation (FEDVR) is combined with the real-space product (RSP) algorithm to generate an efficient and highly accurate method for the solution of the time-dependent linear and nonlinear Schrödinger equation. The FEDVR provides a highly accurate spatial representation using a minimum number of grid points while the RSP algorithm propagates the wave function in operations per time step. Parallelization of the method is transparent and is implemented here by distributing one or two spatial dimensions across the available processors, within the message-passing-interface scheme. The complete formalism and a number of three-dimensional examples are given; its high accuracy and efficacy are illustrated by a comparison with the usual finite-difference method.