First-principles analysis method for the multiplet structures of rare-earth ions in solids

A first-principles fully relativistic multielectron method based on molecular orbital (MO) theory is applied to the analysis for the 4f5d configurations of Pr³⁺-doped LaF₃, LiYF₄ (YLF), and CaF₂ crystals. The formation of MOs between the Pr 5d orbitals and the ligand fluorine 2p orbitals is considered using a (PrF ₁₁)^8- and (PrF₈)^5- molecular models. The energy of the lowest level of 4f5d configuration decreases in the order LaF₃, LiYF₄, and CaF₂ (O_h symmetry). The high energy in Pr³⁺:LaF₃ is ascribed to the smaller ligand-field splitting due to the large coordination number. The analysis of many-electron wave functions shows the mixtures between the spin-orbit splitting of the 4f-level MOs and the ligand-field splitting of the 5d-level MOs. Configuration interaction with one-electron excitations gives transition probability to the originally forbidden two-electron excitations, which produce satellite structures in spectra.