Quantum chemical analysis of the bond lengths in fn and fn−1d1 states of Ce3+, Pr3+, Pa4+, and U4+ defects in chloride hosts

It is widely believed that impurity–ligand bond distances in lanthanide (Ln) and actinide (An) doped crystals, are larger in the fn−1d1 energy levels than in the fn ones. This idea, which was not justified and is probably based on the fact that Ln 5d (An 6d) orbitals have a radial extent much larger than Ln 4f (An 5f ) orbitals, has been neither confirmed nor rejected experimentally in spite of the fact that a very large number of absorption/emission spectroscopic studies on f-element doped hosts exist, because the band shapes depend on the square of the bond length offsets between initial and final electronic states. Recent quantum chemical calculations on Ln and An impurities in fluoride and chloride cubic hosts, which considered host embedding, dynamic electron correlation, and relativistic spin–free and spin–orbit coupling effects, have shown that impurity–ligand bond distances are classified in three sets according to their configuration, with the following trend: Re[fn−1d(t2g)1]