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

TL;DR

This paper provides an analytical parametrization of the local field correction within the effective static approximation for the uniform electron gas, covering a wide range of densities and temperatures, with high accuracy in warm dense matter applications.

Contribution

It introduces a new analytical parametrization of the LFC within ESA applicable across various densities and temperatures, with an accessible Python implementation.

Findings

ESA accurately describes quantities in warm dense matter regime.

Inaccuracy arises only at very high r_s values (~20).

Exact asymptotic limits improve accuracy over neural-net models.

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 ($0.7\leq r_s \leq20$) and temperatures ($0\leq \theta\leq 4$) 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 ($r_s\sim20$). 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)].