Fast and accurate quantum molecular dynamics of dense plasmas across temperature regimes

Framework for Laplacian-Level Noninteracting Free-Energy Density Functionals

A framework for orbital-free Laplacian-level meta-generalized-gradient approximation (meta-GGA) for the noninteracting free-energy-density functionals based upon analysis of the fourth-order gradient expansion is developed. The framework presented here provides a new tool for developing advanced orbital-free thermal functionals at the meta-GGA level of theory. A nonempirical meta-GGA functional, which in the slowly varying density limit correctly reduces to the finite-temperature fourth-order gradient expansion for the noninteracting free energy, is constructed. Application to warm dense helium demonstrates that the developed meta-GGA functional drastically increases the accuracy of orbital-free-density functional theory simulations at temperatures below 40 eV as compared to the lower Thomas-Fermi and GGA rungs.

Stochastic density functional theory combined with Langevin dynamics for warm dense matter

This study overviews and extends a recently developed stochastic finite-temperature Kohn-Sham density functional theory to study warm dense matter using Langevin dynamics, specifically under periodic boundary conditions. The method's algorithmic complexity exhibits nearly linear scaling with system size and is inversely proportional to the temperature. Additionally, a linear-scaling stochastic approach is introduced to assess the Kubo-Greenwood conductivity, demonstrating exceptional stability for dc conductivity. Utilizing the developed tools, we investigate the equation of state, radial distribution, and electronic conductivity of hydrogen at a temperature of 30 000 K. As for the radial distribution functions, we reveal a transition of hydrogen from gaslike to liquidlike behavior as its density exceeds 4g/cm^{3}. As for the electronic conductivity as a function of the density, we identified a remarkable isosbestic point at frequencies around 7 eV, which may be an additional signature of a gas-liquid transition in hydrogen at 30 000 K.

Kohn-Sham accuracy from orbital-free density functional theory via Δ-machine learning

We present a Δ-machine learning model for obtaining Kohn-Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine-learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn-Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas-Fermi-von Weizsäcker orbital-free energies and forces by more than two orders of magnitude but is also more accurate than MLFFs based solely on Kohn-Sham DFT while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al0.88Si0.12, the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn-Sham study performed at an order of magnitude smaller length and time scales.

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.

Equation of state of partially ionized hydrogen and deuterium plasma revisited

We present improved first-principle fermionic path integral Monte Carlo (PIMC) simulation results for a dense partially ionized hydrogen (deuterium) plasma, for temperatures in the range 15000K≤T≤400000K and densities 7×10^{-7}g/cm^{3}≤ρ_{H}≤0.085g/cm^{3} (1.4×10^{-6}g/cm^{3}≤ρ_{D}≤0.17g/cm^{3}), corresponding to 100≥r_{s}≥2, where r_{s}=r[over ¯]/a_{B} is the ratio of the mean interparticle distance to the Bohr radius. These simulations are based on the fermionic propagator PIMC (FP-PIMC) approach in the grand canonical ensemble [Filinov et al., Contrib. Plasma Phys. 61, e202100112 (2021)0863-104210.1002/ctpp.202100112] and fully account for correlation and quantum degeneracy and spin effects. For the application to hydrogen and deuterium, we develop a combination of the fourth-order factorization and the pair product ansatz for the density matrix. Moreover, we avoid the fixed node approximation that may lead to uncontrolled errors in restricted PIMC (RPIMC). Our results allow us to critically reevaluate the accuracy of the RPIMC simulations for hydrogen by Hu et al. [Phys. Rev. B 84, 224109 (2011)1098-012110.1103/PhysRevB.84.224109] and of various chemical models. The deviations are generally found to be small, but for the lowest temperature, T=15640 K they reach several percent. We present detailed tables with our first principles results for the pressure and energy isotherms. We expect our updated results will serve as a valuable benchmark for comparison with other methods.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Equilibrium properties of warm dense deuterium calculated by the wave packet molecular dynamics and density functional theory method

A joint simulation method based on the wave packet molecular dynamics and density functional theory (WPMD-DFT) is applied to study warm dense deuterium (nonideal deuterium plasmas). This method was developed recently as an extension of the wave packet molecular dynamics (WPMD) in which the equations of motion are solved simultaneously for classical ions and semiclassical electrons represented as Gaussian wave packets. Compared to the classical molecular dynamics and WPMD simulations, the method of WPMD-DFT provides a more accurate representation of quantum effects such as electron-ion coupling and electron degeneracy. It allows studying nonadiabatic dynamics of electrons and ions in equilibrium and nonequilibrium states while being more accurate and efficient at high densities than WPMD and classical molecular dynamics. In the paper, we discuss particular features of the method such as special boundary conditions and the procedure of isentrope calculation as well as the results obtained by WPMD-DFT for the shock-compressed deuterium. The compression isentrope and principal Hugoniot curves obtained by WPMD-DFT are compared with available experimental data and other simulation approaches to validate the method. It opens up a possibility of further application of the method to study nonequilibrium states and relaxation processes.

First-principles equation of state database for warm dense matter computation

We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds LiF, B_{4}C, BN, CH_{4}, CH_{2}, C_{2}H_{3}, CH, C_{2}H, MgO, and MgSiO_{3}. For all these materials, we provide the pressure and internal energy over a density-temperature range from ∼0.5 to 50 g cm^{-3} and from ∼10^{4} to 10^{9} K, which are based on ∼5000 different first-principles simulations. We compute isobars, adiabats, and shock Hugoniot curves in the regime of L- and K-shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of H_{2}O, H_{2}O_{2}, Al_{2}O_{3}, CO, and CO_{2} to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their end members. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the Supplemental Material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.

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.

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.

Structure and dynamics of warm dense aluminum: a molecular dynamics study with density functional theory and deep potential

We perform a systematic study on the structure and dynamics of warm dense aluminum (Al) at temperatures ranging from 0.5 to 5.0 eV with molecular dynamics utilizing both density functional theory (DFT) and the deep potential (DP) method. On one hand, unlike the Thomas-Fermi kinetic energy density functional (KEDF), we find that the orbital-free DFT method with the Wang-Teter non-local KEDF yields properties of warm dense Al that agree well with the Kohn-Sham DFT method, enabling accurate orbital-free DFT simulations of warm dense Al at relatively low temperatures. On the other hand, the DP method constructs a deep neural network that has a high accuracy in reproducing short- and long-ranged properties of warm dense Al when compared to the DFT methods. The DP method is orders of magnitudes faster than DFT and is well-suited for simulating large systems and long trajectories to yield accurate properties of warm dense Al. Our results suggest that the combination of DFT methods and the DP model is a powerful tool for accurately and efficiently simulating warm dense matter.

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.

Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions

In a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 117, 156403 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.156403], we presented the first quantum Monte Carlo (QMC) results for the warm dense electron gas in the thermodynamic limit. However, a complete parametrization of the exchange-correlation free energy with respect to density, temperature, and spin polarization remained out of reach due to the absence of (i) accurate QMC results below θ=k_{B}T/E_{F}=0.5 and (ii) QMC results for spin polarizations different from the paramagnetic case. Here we overcome both remaining limitations. By closing the gap to the ground state and by performing extensive QMC simulations for different spin polarizations, we are able to obtain the first completely ab initio exchange-correlation free energy functional; the accuracy achieved is an unprecedented ∼0.3%. This also allows us to quantify the accuracy and systematic errors of various previous approximate functionals.

Crossover from Classical to Fermi Liquid Behavior in Dense Plasmas

We explore the crossover from classical plasma to quantum Fermi liquid behavior of electrons in dense plasmas. To this end, we analyze the evolution with density and temperature of the momentum lifetime of a test electron introduced in a dense electron gas. This allows us (1) to determine the boundaries of the crossover region in the temperature-density plane and to shed light on the evolution of scattering properties across it, (2) to quantify the role of the fermionic nature of electrons on electronic collisions across the crossover region, and (3) to explain how the concept of the Coulomb logarithm emerges at a high enough temperature but disappears at a low enough temperature.

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.

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.

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

We validate the application of our recent orbital-free density functional theory (DFT) approach [Phys. Rev. Lett. 113, 155006 (2014);] for the calculation of ionic and electronic transport properties of dense plasmas. To this end, we calculate the self-diffusion coefficient, the viscosity coefficient, the electrical and thermal conductivities, and the reflectivity coefficient of hydrogen and aluminum plasmas. Very good agreement is found with orbital-based Kohn-Sham DFT calculations at lower temperatures. Because the computational costs of the method do not increase with temperature, we can produce results at much higher temperatures than is accessible by the Kohn-Sham method. Our results for warm dense aluminum at solid density are inconsistent with the recent experimental results reported by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)].

Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements

We extend the applicability range of fermionic path integral Monte Carlo simulations to heavier elements and lower temperatures by introducing various localized nodal surfaces. Hartree-Fock nodes yield the most accurate prediction for pressure and internal energy, which we combine with the results from density functional molecular dynamics simulations to obtain a consistent equation of state for hot, dense silicon under plasma conditions and in the regime of warm dense matter (2.3-18.6  g cm(-3), 5.0×10(5)-1.3×10(8)  K). The shock Hugoniot curve is derived and the structure of the fluid is characterized with various pair correlation functions.

Pseudoatom molecular dynamics

An approach to simulating warm and hot dense matter that combines density-functional-theory-based calculations of the electronic structure to classical molecular dynamics simulations with pair interaction potentials is presented. The method, which we call pseudoatom molecular dynamics, can be applied to single-component or multicomponent plasmas. It gives equation of state and self-diffusion coefficients with an accuracy comparable to orbital-free molecular dynamics simulations but is computationally much more efficient.