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 of paramount importance for many applications in physics, chemistry, and beyond. In a recent paper, Dornheim et al. [Phys. Rev. Lett. 125, 235001 (2020)] have presented the 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 this 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 <= r(s) <= 20) and temperatures (0 <= theta <= 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 the stopping power in an 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) similar to 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 [T. Dornheim et al., J. Chem. Phys. 151, 194104 (2019)].