Vibronic coupling model for the intensities of f-f transitions in octahedral lanthanide (III) complexes

A general theory of vibronically induced electric-dipole intensity in the f-f transitions of octahedral (Oh ) six-coordinate trivalent lanthanide ion complexes is developed. The theory is based on a model in which both static (point-charge crystal field) and dynamic (transient ligand dipoles) coupling between the metal ion and the ligands are included. Electric-dipole intensity is introduced into the vibronic components of the parity-forbidden Ln3+ f-f transitions via a vibronic coupling mechanism involving the chromophoric f-electrons and the ν 3(t 1u ), ν 4(t 1u ), and ν 6(t 2u ) skeletal vibrational modes of the octahedral LnL6 system. Calculations based on the theoretical model are carried out for the 7F0→5D1, 7F0→5D2, and 7F1→5D1 transitions of EuCl6 3-, and the results are compared with experimental data reported for Cs2NaEuCl6. Good agreement between the calculated and observed total dipole strengths is achieved, and excellent agreement between theory and experiment is obtained for the distribution of (relative) intensity among the vibronic components of the transitions. The general applicability, utility, and limitations of the theory are discussed.