The equation of state of partially ionized hydrogen and deuterium plasma revisited

Abstract

We present novel first-principle fermionic path integral Monte Carlo (PIMC) simulation results for a dense partially ionized hydrogen (deuterium) plasma, for temperatures in the range $15,000$K $\le T\le 400,000$K and densities $7\cdot 10^{-7}$g/cm${}^3\le {\rho }_H\le 0.085$ g/cm${}^3$ ($1.4\cdot 10^{-6}$g/cm${}^3\le {\rho }_D\le 0.17$ g/cm${}^3$), corresponding to $100\ge r_s\ge 2$, where $r_s=\bar{r}/a_B$ 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 [A. Filinov \textit{et al.}, Contrib. Plasma Phys. \textbf{61}, e202100112 (2021)] 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 re-evaluate the accuracy of the RPIMC simulations for hydrogen by Hu \textit{et al.} [Phys. Rev. B \textbf{84}, 224109 (2011)] and of various chemical models. The deviations are generally found to be small, but for the lowest temperature, $T=15,640$~K they reach several percent. We present detailed tables with our first principles results for the pressure and energy isotherms.

References in corpus (44)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Path Integral Monte Carlo Calculation of the Deuterium Hugoniot
• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• The Uniform Electron Gas at Warm Dense Matter Conditions
• A Massive Core in Jupiter Predicted From First-Principles Simulations
• FPEOS: A First-Principles Equation of State Table of Deuterium for Inertial Confinement Fusion Applications
• Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions
• Hydrogen-Helium Mixtures in the Interiors of Giant Planets
• A new equation of state for dense hydrogen-helium mixtures
• {\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit
• Equation of state of fully ionized electron-ion plasmas
• Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of Brown Dwarfs
• \textit{Ab Initio} Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter
• Ab initio thermodynamic results for the degenerate electron gas at finite temperature
• Path Integral Monte Carlo Simulation of the Low-Density Hydrogen Plasma
• Gradient Symplectic Algorithms for Solving the Schroedinger Equation with Time-Dependent Potentials
• Temperature-dependent quantum pair potentials and their application to dense partially ionized hydrogen plasmas
• Thermodynamics of hot dense H-plasmas: Path integral Monte Carlo simulations and analytical approximations
• X-Ray Thomson scattering without the Chihara decomposition
• First-Principles Equation of State Database for Warm Dense Matter Computation
• Cooling sequences and color-magnitude diagrams for cool white dwarfs with hydrogen-atmospheres
• Crystallization in two-component Coulomb systems
• Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen
• High order Chin actions in path integral Monte Carlo
• Saturn layered structure and homogeneous evolution models with different EOSs
• Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes
• Finite-temperature orbital-free DFT molecular dynamics: coupling Profess and Quantum Espresso
• Electron-ion scattering in dense multi-component plasmas: application to the outer crust of an accreting neutron star
• Fast and accurate quantum molecular dynamics of dense plasmas across temperature regimes
• \emph{Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas
• Ab Initio Quantum Monte Carlo Simulations of the Uniform Electron Gas without Fixed Nodes II: Unpolarized Case
• Monte Carlo results for the hydrogen Hugoniot
• Structural characteristics of strongly coupled ions in a dense quantum plasma
• Phase Transition in Strongly Degenerate Hydrogen Plasma
• Towards ab initio thermodynamics of the electron gas at strong degeneracy
• High-order Path Integral Monte Carlo methods for solving quantum dot problems
• Fermion Sign Problem in Path Integral Monte Carlo Simulations: Grand-canonical ensemble
• Wide range equation of state for fluid hydrogen within density functional theory
• Equation of state for dense hydrogen and plasma phase transition
• Interacting electrons in a one-dimensional random array of scatterers - A Quantum Dynamics and Monte-Carlo study
• Prediction of a roton-type feature in warm dense hydrogen
• On the quantum statistics of bound states within the Rutherford model of matter
• Analysis of dynamical effects in the uniform electron liquids with the self-consistent method of moments complemented by the Shannon information entropy and the path-integral Monte-Carlo simulations
• Dynamic properties and the roton mode attenuation in the liquid 3He: an ab initio study within the self-consistent method of moments

Cited by in corpus (9)

• First principles simulations of dense hydrogen
• Ionization potential depression and Fermi barrier in warm dense matter--a first--principles approach
• Ionisation Calculations using Classical Molecular Dynamics
• Virial coefficients of the Uniform Electron Gas from Path Integral Monte Carlo Simulations
• Statistical theory of charged particle systems including triple bound states -- and the Collaboration Lviv-Rostock
• The virial expansion of the Hydrogen equation of state in comparison to PIMC simulations: the quasiparticle concept, IPD, and ionization degree
• Modeling partially-ionized dense plasma using wavepacket molecular dynamics
• Unlocking the Power of Orbital-Free Density Functional Theory to Explore the Electronic Structure Under Extreme Conditions
• On the statistical theory of strong electrolytes and high-temperature plasmas: new applications of the work of Yukhnovskii and Kelbg