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)].

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• Extraction of the frequency moments of spectral densities from imaginary-time correlation function data
• Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter
• Quantum version of the integral equation theory based dielectric scheme for strongly coupled electron liquids
• Revisiting the Vashishta-Singwi dielectric scheme for the warm dense uniform electron fluid
• Energy response and spatial alignment of the perturbed electron gas
• Ion core effect on transport characteristics in warm dense matter
• Density-Functional-Theory Perspective on the Non-Linear Response of Correlated Electrons Across Temperature Regimes
• Nonlinear electronic density response of the warm dense electron gas: multiple perturbations and mode coupling