Ionic and electronic transport properties in dense plasmas by orbital-free density functional theory

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Manufacturing process of short carbon fiber reinforced Al matrix with preformless and their properties

The conventional manufacturing process of fiber-reinforced metal matrix composites via liquid infiltration processes, preform manufacturing using inorganic binders is essential. However, the procedure involves binder sintering, which requires high energy and long operating times. A new fabrication process without preform manufacturing is proposed to fabricate short carbon fiber (SCF)-reinforced aluminum matrix composites using a low-pressure infiltration method. To improve the wettability between fiber and matrix, fibers were plated copper using an electroless plating process. The low-pressure infiltration method with preformless succeeded in manufacturing a composite with a volume fraction of about 30% of carbon fibers.The fiber orientation of the composite material manufactured without preform and the fiber orientation of the composite material manufactured using an inorganic binder was almost the same. The manufactured composites with preformless have high hardness and high thermal conductivity.

Multifidelity regression of sparse plasma transport data available in disparate physical regimes

Physical data are typically generated by experiments and computations in limited parameter regimes. When datasets generated using such disparate methods are combined into one dataset, the resulting dataset is typically sparse, with dense "islands" in a potentially high-dimensional parameter space, and predictions must be interpolated among such islands. Using plasma transport data as our example, we propose a multifidelity Gaussian-process regression framework that incorporates physical data from multiple sources at multiple fidelities. The impact of the proposed framework varies from little improvement over simpler approaches to qualitatively changing the prediction with consistently increased confidence in regions lacking high-fidelity data. By varying low- and high-fidelity data sources, we demonstrate an approach for determining when multifidelity Gaussian-process regression adds value over single-fidelity regression and therefore when its additional computational costs are merited. We also examine the case in which the outputs of the low- and high-fidelity models correspond to different physical quantities, one of which may be intrinsically computationally cheaper to compute. We conclude by analyzing strategies for sampling high-fidelity data for use in this framework, and we develop a simple sampling approach for reducing regression error across large gaps in data.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

Consistent approach for electrical resistivity within Ziman's theory from solid state to hot dense plasma: Application to aluminum

The approach presented in this work allows a consistent calculation of electrical conductivity of dense matter from the solid state to the hot plasma using the same procedure, consisting in dropping elastic scattering contributions to solid's and liquid's structure factors in the framework of the Ziman theory. The solid's structure factor was computed using a multiphonon expansion. The elastic part is the zero-phonon term and corresponds to Bragg peaks, thermally damped by Debye-Waller attenuation factors. For the liquid, a similar elastic contribution to the structure factor results from a long-range order persisting during the characteristic electron-ion scattering time. All the quantities required for the calculation of the resistivities are obtained from our average-atom model, including the total hypernetted-chain structure factor used from the liquid state to the plasma. No interpolation between two limiting structure factors is required. We derive the correction to apply to the resistivity in order to account for the transient long-range order in the liquid and show that it improves considerably the agreement with quantum-molecular dynamics simulations and experimental aluminum's isochoric and isobaric conductivities. Our results suggest that the long-range order in liquid aluminum could be a slightly compressed fcc one. Two series of ultrafast experiments performed on aluminum were also considered, the first one by Milchberg et al. using short laser pulses and the second one by Sperling et al. involving x-ray heating and carried out on the Linac Coherent Light Source facility. Our attempts to explain the latter assuming an initial liquid state at an ion temperature much smaller than the electron one suggest that the actual initial state before main heating is neither perfectly solid nor a normal liquid.

Particle-in-cell simulation method for macroscopic degenerate plasmas

Nowadays hydrodynamic equations coupled with external equation of states provided by quantum mechanical calculations is a widely used approach for simulations of macroscopic degenerate plasmas. Although such an approach is proven to be efficient and shows many good features, especially for large scale simulations, it encounters intrinsic challenges when involving kinetic effects. As a complement, here we have invented a fully kinetic numerical approach for macroscopic degenerate plasmas. This approach is based on first principle Boltzmann-Uhling-Uhlenbeck equations coupled with Maxwell's equation, and is eventually achieved via an existing particle-in-cell simulation code named LAPINS. In this approach, degenerate particles obey Fermi-Dirac statistics and nondegenerate particles follow the typical Maxwell-Boltzmann statistics. The equation of motion of both degenerate and nondegenerate particles are governed by long range collective electromagnetic fields and close particle-particle collisions. Especially, Boltzmann-Uhling-Uhlenbeck collisions ensure that evolution of degenerate particles is enforced by the Pauli exclusion principle. The code is applied to several benchmark simulations, including electronic conductivity for aluminium with varying temperatures from 2 eV to 50 eV, thermalization of alpha particles in a cold fuel shell in inertial confinement fusion, and rapid heating of solid sample by short and intense laser pulses.

Nature of Non-Adiabatic Electron-Ion Forces in Liquid Metals

An accurate description of electron-ion interactions in materials is crucial for our understanding of their equilibrium and nonequilibrium properties. Here we assess the properties of frictional forces experienced by ions in noncrystalline metallic systems, including liquid metals and warm dense plasmas, that arise from electronic excitations driven by the nuclear motion due to the presence of a continuum of low-lying electronic states. To this end, we perform detailed ab initio calculations of the full friction tensor that characterizes the set of friction forces. The non-adiabatic electron-ion interactions introduce hydrodynamic couplings between the ionic degrees of freedom, which are sizable between nearest neighbors. The friction tensor is generally inhomogeneous, anisotropic, and nondiagonal, especially at lower densities.

Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations

We present an accurate and efficient real-space formulation of the Hellmann-Feynman stress tensor for O(N) Kohn-Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi-Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O(N) methods. We then describe its evaluation within the O(N) infinite-cell Clenshaw-Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. We employ the new formulation to compute the viscosity of hydrogen at 10⁶ K from Kohn-Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

Model of electron transport in dense plasmas spanning temperature regimes

We present a new model of electron transport in warm and hot dense plasmas which combines the quantum Landau-Fokker-Planck equation with the concept of mean-force scattering. We obtain electrical and thermal conductivities across several orders of magnitude in temperature, from warm dense matter conditions to hot, nondegenerate plasma conditions, including the challenging crossover regime between the two. The small-angle approximation characteristic of Fokker-Planck collision theories is mitigated to good effect by the construction of accurate effective Coulomb logarithms based on mean-force scattering, which allows the theory to remain accurate even at low temperatures, as compared with high-fidelity quantum simulation results. Electron-electron collisions are treated on equal footing as electron-ion collisions. Their accurate treatment is found to be essential for hydrogen, and is expected to be important to other low-Z elements. We find that electron-electron scattering remains influential to the value of the thermal conductivity down to temperatures somewhat below the Fermi energy. The accuracy of the theory seems to falter only for the behavior of the thermal conductivity at very low temperatures due to a subtle interplay between the Pauli exclusion principle and the small-angle approximation as they pertain to electron-electron scattering. Even there, the model is in fair agreement with ab initio simulations.

First-Principles Determination of Electron-Ion Couplings in the Warm Dense Matter Regime

We present first-principles calculations of the rate of energy exchanges between electrons and ions in nonequilibrium warm dense plasmas, liquid metals, and hot solids, a fundamental property for which various models offer diverging predictions. To this end, a Kubo relation for the electron-ion coupling parameter is introduced, which includes self-consistently the quantum, thermal, nonlinear, and strong coupling effects that coexist in materials at the confluence of solids and plasmas. Most importantly, like other Kubo relations widely used for calculating electronic conductivities, the expression can be evaluated using quantum molecular dynamics simulations. Results are presented and compared to experimental and theoretical predictions for representative materials of various electronic complexity, including aluminum, copper, iron, and nickel.

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.

Isochoric, isobaric, and ultrafast conductivities of aluminum, lithium, and carbon in the warm dense matter regime

We study the conductivities σ of (i) the equilibrium isochoric state σ_{is}, (ii) the equilibrium isobaric state σ_{ib}, and also the (iii) nonequilibrium ultrafast matter state σ_{uf} with the ion temperature T_{i} less than the electron temperature T_{e}. Aluminum, lithium, and carbon are considered, being increasingly complex warm dense matter systems, with carbon having transient covalent bonds. First-principles calculations, i.e., neutral-pseudoatom (NPA) calculations and density-functional theory (DFT) with molecular-dynamics (MD) simulations, are compared where possible with experimental data to characterize σ_{ic}, σ_{ib}, and σ_{uf}. The NPA σ_{ib} is closest to the available experimental data when compared to results from DFT with MD simulations, where simulations of about 64-125 atoms are typically used. The published conductivities for Li are reviewed and the value at a temperature of 4.5 eV is examined using supporting x-ray Thomson-scattering calculations. A physical picture of the variations of σ with temperature and density applicable to these materials is given. The insensitivity of σ to T_{e} below 10 eV for carbon, compared to Al and Li, is clarified.

Pair potentials for warm dense matter and their application to x-ray Thomson scattering in aluminum and beryllium

Ultrafast laser experiments yield increasingly reliable data on warm dense matter, but their interpretation requires theoretical models. We employ an efficient density functional neutral-pseudoatom hypernetted-chain (NPA-HNC) model with accuracy comparable to ab initio simulations and which provides first-principles pseudopotentials and pair potentials for warm-dense matter. It avoids the use of (i) ad hoc core-repulsion models and (ii) "Yukawa screening" and (iii) need not assume ion-electron thermal equilibrium. Computations of the x-ray Thomson scattering (XRTS) spectra of aluminum and beryllium are compared with recent experiments and with density-functional-theory molecular-dynamics (DFT-MD) simulations. The NPA-HNC structure factors, compressibilities, phonons, and conductivities agree closely with DFT-MD results, while Yukawa screening gives misleading results. The analysis of the XRTS data for two of the experiments, using two-temperature quasi-equilibrium models, is supported by calculations of their temperature relaxation times.

Dynamic conductivity and plasmon profile of aluminum in the ultra-fast-matter regime

We use an explicitly isochoric two-temperature theory to analyze recent x-ray laser scattering data for aluminum in the ultra-fast-matter (UFM) regime up to 6 eV. The observed surprisingly low conductivities are explained by including strong electron-ion scattering effects using the phase shifts calculated via the neutral-pseudo-atom model. The difference between the static conductivity for UFM-Al and equilibrium aluminum in the warm-dense matter state is clearly brought out by comparisons with available density-fucntional+molecular-dynamics simulations. Thus the applicability of the Mermin model to UFM is questioned. The static and dynamic conductivity, collision frequency, and the plasmon line shape, evaluated within the simplest Born approximation for UFM aluminum, are in good agreement with experiment.

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.