An estimator for the Coulomb repulsion parameter U to generate vacuum referred binding energy schemes for lanthanides in compounds

The U-value defined as the energy difference between the Eu^4+/3+ and Eu^3+/2+ charge transition levels (CTLs) is the most important parameter in constructing vacuum referred binding energy diagrams (VRBEs) with all the lanthanide CTLs with respect to the vacuum level of energy. The parameter is difficult to determine from experiment and the aim of this work is to establish a method to estimate the U-value from the average electronegativity of the cations in the compound. Since the U-value is controlled by the same physical processes, i.e., covalence and anion polarizability, as the centroid shift ϵ_c of the Ce³⁺ 5d configuration, one may estimate the U-value from that centroid shift. That method provides already good values for U for about 175 different compounds. Those U-values are compared with the average cation electronegativity χ_av, and relations will be established from which the U-value can be estimated with about ±0.1 eV accuracy from just the composition of the compound. It can be applied to all types of stoichiometric inorganic compounds like the halides (F, Cl, Br, I), chalcogenides (O, S, Se), and nitrides (N). The U-value complemented with the bandgap and the energy needed for electron transfer from the valence band top to a trivalent lanthanide dopant is then sufficient to construct a VRBE diagram with all lanthanide levels with respect to the vacuum level and the host valence and conduction bands.