Consistency between the Green-Kubo formula and the Lorentz model for predicting the infrared dielectric function of polar materials

Accurate prediction of infrared dielectric functions in polar materials is fundamental for thermal and photonic applications, yet it remains unexplored whether the two main methods, the Green-Kubo formula and Lorentz model, can give unified predictions. In this work, we present a detailed comparison of these two approaches using MgO and LiH as prototypical cases employing both the empirical rigid ion model (RIM) and machine learning potential (MLP). We demonstrate that the conventional Lorentz model fails to capture the multiphonon absorption inherent in the Green-Kubo method, which can be resolved using the phonon self-energy as a generalization of the usual linewidth. In addition, with RIM, a correction factor of ${\ensuremath{\varepsilon}}_{\ensuremath{\infty}}$ is required in the ionic contribution to the infrared response to account for the electronic polarization effect, which is yet captured by MLP using the Born effective charges for calculating the dipole moment. The present benchmark study thus enables cross-validation of dielectric function calculations while providing mechanistic insights into the polarization dynamics.