Ab initio calculations of the Hubbard U for the early lanthanides using the constrained random-phase approximation

In this work we have calculated U from first principles for the early lanthanides (Ce-Gd) using the constrained random phase approximation (cRPA). We compare the static limit of U with experimental estimations from x-ray photoemission spectroscopy (XPS) and bremsstrahlung isochromat spectroscopy (BIS) spectra and also discuss the frequency dependence of U across the series. The localized subspace is constructed using maximally localized Wannier functions (MLWFs). We discuss the choice of parameters used to construct the Wannier functions and show that in the case of Eu and Gd, where the local density approximation does not yield the correct position of the 4f bands, a physically motivated choice gives better agreement with experiment.