Transition metal (TM) and Rare Earth (RE) ions are introduced to various compounds to activate light emission, to compensate defects, generate magnetic properties, etc. For TM ions and II-VI compounds Ludwig-Woodbury model was introduced, which correctly explained spin multiplicity of states. However, several experimental results indicated that this simple model cannot explain optical properties of these ions. For example, it was very puzzling why Cr ion in GaAs is observed in three charge states despite relatively small band gap of this compound. Also energies of different multiplets could not be described by a simple crystal field model.

Similar situation was then found for RE ions. Intra-shell transitions of RE ions should be very weak since f-f processes are parity forbidden. It was puzzling how to explain relatively bright emission of RE ions.

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