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

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.

Transport properties of a quasisymmetric binary nitrogen-oxygen mixture in the warm dense regime

Transport properties of mixtures in the warm dense matter (WDM) regime play an important role in natural astrophysics. However, a physical understanding of ionic transport properties in quasisymmetric liquid mixtures has remained elusive. Here, we present extensive ab initio molecular dynamics (AIMD) simulations on the ionic diffusion and viscosity of a quasisymmetric binary nitrogen-oxygen (N-O) mixture in a wide warm dense regime of 8-120 kK and 4.5-8.0 g/cm^{3}. Diffusion and viscosity of N-O mixtures with different compositions are obtained by using the Green-Kubo formula. Unlike asymmetric mixtures, the change of proportions in N-O mixtures slightly affects the viscosity and diffusion in the strong-coupling region. Furthermore, the AIMD results are used to build and verify a global pseudo-ion in jellium (PIJ) model for ionic transport calculations. The PIJ model succeeds in reproducing the transport properties of N-O mixtures where ionization has occurred, and provides a promising alternative approach to obtaining comparable results to AIMD simulations with relatively small computational costs. Our current results highlight the characteristic features of the quasisymmetric binary mixtures and demonstrate the applicability of the PIJ model in the WDM regime.

Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma

Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (<50  eV). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

Benchmarking the effective one-component plasma model for warm dense neon and krypton within quantum molecular dynamics simulation

The effective one-component plasma (EOCP) model has provided an efficient approach to obtaining many important thermophysical parameters of hot dense matter [J. Clérouin, et al., Phys. Rev. Lett. 116, 115003 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.115003]. In this paper, we perform extensive quantum molecular dynamics (QMD) simulations to determine the equations of state, ionic structures, and ionic transport properties of neon and krypton within the warm dense matter (WDM) regime where the density (ρ) is up to 12 g/cm^{3} and the temperature (T) is up to 100 kK. The simulated data are then used as a benchmark to explicitly evaluate the EOCP and Yukawa models. It is found that, within present ρ-T regime, the EOCP model can excellently reproduce the diffusion and viscosity coefficients of neon and krypton due to the fact that this model defines a system which nearly reproduces the actual physical states of WDM. Therefore, the EOCP model may be a promising alternative approach to reasonably predicting the transport behaviors of matter in WDM regime at lower QMD computational cost. The evaluation of Yukawa model shows that the consideration of the energy level broadening effect in the average atom model is necessary. Finally, with the help of EOCP model, the Stokes-Einstein relationships about neon and krypton are discussed, and fruitful plasma parameters as well as a practical ρ-T-dependent formula of the effective coupling parameter are obtained. These results not only provide valuable information for future theoretical and experimental studies on dense neon and krypton but also reveal the applicability of the EOCP model and the limitation of the Yukawa model in WDM regime and further support the continuing search for a unified description of ionic transport in dense plasma.

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.

Quantum molecular dynamics study on the proton exchange, ionic structures, and transport properties of warm dense hydrogen-deuterium mixtures

Comprehensive knowledge of physical properties such as equation of state (EOS), proton exchange, dynamic structures, diffusion coefficients, and viscosities of hydrogen-deuterium mixtures with densities from 0.1 to 5 g/cm^{3} and temperatures from 1 to 50 kK has been presented via quantum molecular dynamics (QMD) simulations. The existing multi-shock experimental EOS provides an important benchmark to evaluate exchange-correlation functionals. The comparison of simulations with experiments indicates that a nonlocal van der Waals density functional (vdW-DF1) produces excellent results. Fraction analysis of molecules using a weighted integral over pair distribution functions was performed. A dissociation diagram together with a boundary where the proton exchange (H_{2}+D_{2}⇌2HD) occurs was generated, which shows evidence that the HD molecules form as the H_{2} and D_{2} molecules are almost 50% dissociated. The mechanism of proton exchange can be interpreted as a process of dissociation followed by recombination. The ionic structures at extreme conditions were analyzed by the effective coordination number model. High-order cluster, circle, and chain structures can be founded in the strongly coupled warm dense regime. The present QMD diffusion coefficient and viscosity can be used to benchmark two analytical one-component plasma (OCP) models: the Coulomb and Yukawa OCP models.

Structural and transport properties of ammonia along the principal Hugoniot

We investigate, via quantum molecular dynamics simulations, the structural and transport properties of ammonia along the principal Hugoniot for temperatures up to 10 eV and densities up to 2.6 g/cm³. With the analysis of the molecular dynamics trajectories by use of the bond auto-correlation function, we identify three distinct pressure-temperature regions for local chemical structures of ammonia. We derive the diffusivity and viscosity of strong correlated ammonia with high accuracy through fitting the velocity and stress-tensor autocorrelation functions with complex functional form which includes structures and multiple time scales. The statistical error of the transport properties is estimated. It is shown that the diffusivity and viscosity behave in a distinctly different manner at these three regimes and thus present complex features. In the molecular fluid regime, the hydrogen atoms have almost the similar diffusivity as nitrogen and the viscosity is dominated by the kinetic contribution. When entering into the mixture regime, the transport behavior of the system remarkably changes due to the stronger ionic coupling, and the viscosity is determined to decrease gradually and achieve minimum at about 2.0 g/cm³ on the Hugoniot. In the plasma regime, the hydrogen atoms diffuse at least twice as fast as the nitrogen atoms.

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.

Method to manage integration error in the Green-Kubo method

The Green-Kubo method is a commonly used approach for predicting transport properties in a system from equilibrium molecular dynamics simulations. The approach is founded on the fluctuation dissipation theorem and relates the property of interest to the lifetime of fluctuations in its thermodynamic driving potential. For heat transport, the lattice thermal conductivity is related to the integral of the autocorrelation of the instantaneous heat flux. A principal source of error in these calculations is that the autocorrelation function requires a long averaging time to reduce remnant noise. Integrating the noise in the tail of the autocorrelation function becomes conflated with physically important slow relaxation processes. In this paper we present a method to quantify the uncertainty on transport properties computed using the Green-Kubo formulation based on recognizing that the integrated noise is a random walk, with a growing envelope of uncertainty. By characterizing the noise we can choose integration conditions to best trade off systematic truncation error with unbiased integration noise, to minimize uncertainty for a given allocation of computational resources.

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.

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.