AbstractThe electron–phonon interaction is central to condensed matter, e.g. through electrical resistance, superconductivity or the formation of polarons, and has a strong impact on observables such as band gaps or optical spectra. The most common framework for band energy corrections is the Fröhlich model, which often agrees qualitatively with experiments in polar materials, but has limits for complex cases. A generalized version includes anisotropic and degenerate electron bands, and multiple phonons. In this work, we identify trends and outliers for the Fröhlich models on 1260 materials. We test the limits of the Fröhlich models and their perturbative treatment, in particular the large polaron hypothesis. Among our extended dataset most materials host perturbative large polarons, but there are many instances that are non-perturbative and/or localize on distances of a few bond lengths. We find a variety of behaviors, and analyze extreme cases with huge zero-point renormalization using the first-principles Allen-Heine-Cardona approach.