Analytical representation of the local field correction of the uniform electron gas within the effective static approximation

The description of electronic exchange--correlation effects is 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 local field correction (LFC), which allows highly accurate estimation properties such as interaction energy structure factor. present work, we give an analytical parametrization LFC within ESA that valid any wave number, available entire range densities ($0.7\leq r_s \leq20$) temperatures ($0\leq \theta\leq 4$) are relevant both ground state warm dense matter regime. A short implementation Python provided, can easily be incorporated into existing codes. addition, extensive analysis performance regarding various quantities like dynamic factor, dielectric function, electronically screened ion-potential, also stopping power medium. summary, find gives excellent all these regime, only becomes inaccurate when electrons start form strongly correlated electron liquid ($r_s\sim20$). Moreover, note exact incorporation asymptotic limits often leads superior accuracy compared neural-net representation [\textit{J.~Chem.~Phys.}~\textbf{151}, 194104 (2019)].