Energy levels of paramagnetic ions: Algebra. IV. The case of fN ions in cubical symmetry

The symmetry-adapted formalism and the weak-field model described in the first three papers of this series are applied to the case of a configuration nf^N in octahedral symmetry. In this case, the latter weakfield model is restricted to a 30-parameter model which accounts for isotropic and anisotropic Coulomb (repulsion) interactions, isotropic and anisotropic spin-orbit interactions, and crystal-field interactions. A comparison between this 30-parameter weak-field model and a 33-parameter strong-field model is established. Equivalence between these two models requires three constraint relations to be satisfied for some strong-field parameters. The three relations are examined on various viewpoints.