Lanthanide Crystal Field Theory in the J-Mixing Regime: fⁿ Configurations

The low-energy sector of the lanthanide fⁿ shell is to first approximation governed by the interplay of three interactions: Coulomb repulsion, spin-same-orbit coupling and the ligand crystal field potential. To rationalize the energy landscape in different chemical environments, it is desirable to extract the phenomenological crystal field parameters from experimental data; however, in practice, high-dimensional fitting procedures complicate their routine determination. Here, we present a computational extraction procedure based on real tensorial sets and the $U(7)$ canonical chain that, unlike existing operator equivalent methods, takes all J multiplets of the lowest-energy $LS$ term into account, ensuring meaningful results even in the presence of considerable J-mixing. Two series of lanthanide compounds, [Ln(III)(C₈H₈)₂]⁻} and doped Ln(III):Y₂O₃} (Ln ∈ {Ce, Pr, Nd, Sm, Eu}) serve as examples for high- (D₈ₕ) and low-symmetry (C₂) scenarios. Consequences for the generalisation toward actinides are briefly discussed.