Analytical representation of the Local Field Correction of the Uniform Electron Gas within the Effective Static Approximation

Abstract

The description of electronic exchange--correlation effects is of paramount importance for many applications in physics, chemistry, and beyond. In a recent Letter, Dornheim \textit{et al.} [\textit{Phys. Rev. Lett.}~\textbf{125}, 235001 (2020)] have presented the \emph{effective static approximation} (ESA) to the local field correction (LFC), which allows for the highly accurate estimation of electronic properties such as the interaction energy and the static structure factor. In the present work, we give an analytical parametrization of the LFC within ESA that is valid for any wave number, and available for the entire range of densities ($0.7\le r_s\le 20$) and temperatures ($0\le \theta \le 4$) that are relevant for applications both in the ground state and in the warm dense matter regime. A short implementation in Python is provided, which can easily be incorporated into existing codes. In addition, we present an extensive analysis of the performance of ESA regarding the estimation of various quantities like the dynamic structure factor, static dielectric function, the electronically screened ion-potential, and also stopping power in electronic medium. In summary, we find that the ESA gives an excellent description of all these quantities in the warm dense matter regime, and only becomes inaccurate when the electrons start to form a strongly correlated electron liquid ($r_s\sim 20$). Moreover, we note that the exact incorporation of exact asymptotic limits often leads to a superior accuracy compared to the neural-net representation of the static LFC [\textit{J.~Chem.~Phys.}~\textbf{151}, 194104 (2019)].

References in corpus (26)

• Path Integral Monte Carlo Simulation of the Warm-Dense Homogeneous Electron Gas
• A Massive Core in Jupiter Predicted From First-Principles Simulations
• {\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit
• Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of Brown Dwarfs
• All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas
• Diffusion quantum Monte Carlo study of three-dimensional Wigner crystals
• Effective Static Approximation: A Fast and Reliable Tool for Warm Dense Matter Theory
• Ab Initio Path Integral Monte Carlo Approach to the Static and Dynamic Density Response of the Uniform Electron Gas
• Extended First-Principles Molecular Dynamics Method From Cold Materials to Hot Dense Plasmas
• Nonlinear Electronic Density Response in Warm Dense Matter
• Electron-ion scattering in dense multi-component plasmas: application to the outer crust of an accreting neutron star
• Dynamic properties of the warm dense electron gas: an ab initio path integral Monte Carlo approach
• The Strongly Coupled Electron Liquid: ab initio Path Integral Monte Carlo Simulations and Dielectric Theories
• Gradient corrections to the exchange-correlation free energy
• Configuration Path Integral Monte Carlo Approach to the Static Density Response of the Warm Dense Electron Gas
• Ab initio results for the plasmon dispersion and damping of the warm dense electron gas
• Emergence of an excitonic collective mode in the dilute electron gas
• Permutation Blocking Path Integral Monte Carlo approach to the Static Density Response of the Warm Dense Electron Gas
• A Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study
• Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration
• Restricted configuration path integral Monte Carlo
• First-principles modeling of plasmons in aluminum under ambient and extreme conditions
• The ion potential in warm dense matter: wake effects due to streaming degenerate electrons
• Screening of a test charge in a free-electron gas at warm dense matter and dense non-ideal plasma conditions
• Momentum distribution function and short-range correlations of the warm dense electron gas -- ab initio quantum Monte Carlo results
• Real-space formulation of the stress tensor for $\mathcal{O}(N)$ density functional theory: application to high temperature calculations

Cited by in corpus (31)

• Electronic Density Response of Warm Dense Matter
• First principles simulations of dense hydrogen
• Density Response of the Warm Dense Electron Gas beyond Linear Response Theory: Excitation of Harmonics
• Overcoming finite-size effects in electronic structure simulations at extreme conditions
• Benchmarking Exchange-Correlation Functionals in the Spin-Polarized Inhomogeneous Electron Gas under Warm Dense Conditions
• Effective electronic forces and potentials from ab initio path integral Monte Carlo simulations
• Integral equation theory based dielectric scheme for strongly coupled electron liquids
• Shock Physics in Warm Dense Matter--a quantum hydrodynamics perspective
• Prediction of a roton-type feature in warm dense hydrogen
• Extraction of the frequency moments of spectral densities from imaginary-time correlation function data
• Exchange-correlation effect in the charge response of a warm dense electron gas
• Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter
• Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons
• Quantum version of the integral equation theory based dielectric scheme for strongly coupled electron liquids
• Revealing Non-equilibrium and Relaxation in Warm Dense Matter
• The uniform electron gas at high temperatures: \emph{ab initio} path integral Monte Carlo simulations and analytical theory
• Thermal Signals from Collective Electronic Excitations in Inhomogeneous Warm Dense Matter
• Fourier-Matsubara series expansion for imaginary-time correlation functions
• Multi-Messenger Measurements of the Static Structure of Shock-Compressed Liquid Silicon at 100 GPa
• Revisiting the Vashishta-Singwi dielectric scheme for the warm dense uniform electron fluid
• Applying the Liouville-Lanczos Method of Time-Dependent Density-Functional Theory to Warm Dense Matter
• Estimates of the dynamic structure factor for the finite temperature electron liquid via analytic continuation of path integral Monte Carlo data
• Energy response and spatial alignment of the perturbed electron gas
• Ion core effect on transport characteristics in warm dense matter
• Dynamic properties of the warm dense uniform electron gas with the qSTLS dielectric scheme
• Momentum distribution of the Uniform Electron Gas at finite temperature: Effects of spin-polarization
• Kinetic contribution to the arbitrary order odd frequency moments of the dynamic structure factor
• Nonlinear electronic density response of the warm dense electron gas: multiple perturbations and mode coupling
• The noiseless limit and improved-prior limit of the maximum entropy method and their implications for the analytic continuation problem
• PyLIT: Reformulation and implementation of the analytic continuation problem using kernel representation methods
• Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes