Faulkner-Richardson vibronic intensity

The model which has been most widely applied to the calculation of vibronic intensities of the Cs2NaLnCl6 systems is the vibronic coupling model of Faulkner and Richardson [67]. Prior to the introduction of this model, it was customary to analyse one-phonon vibronic transitions using Judd closure theory, Fig. 7d, [117] (see, for example, [156]) with the replacement of the Tfectromc (which is proportional to the above Q2) parameters by T bromc, which include the vibrational integral and the derivative of the CF with respect to the relevant normal coordinate. The selection rules for vibronic transitions under this scheme therefore parallel those for forced electric dipole transitions (e.g. A/ <6 and in particular when the initial or final state is /=0, then A/ =2, 4, 6). 

Faulkner and Richardson (1978a) assumed isotropic ligands, for which n = 0. Thus the rank k in expression (95) is limited to 3. After making various estimates of the charges, polarizabilities, and bond lengths, they were able to obtain reasonably good values for the relative intensities of the three vibronic lines... 

Faulkner TR, Richardson PS (1978) Vibronic coupling model for the intensities of f-f transitions in octahedral lanthanide (111) complexes. Mol Phys 35 1141-1161... 

Spectral bands of an aquated lanthanide ion arising from vibronic contributions were reported first by Haas and Stein (1971) in their study of the emission spectrum of aquated Gd. These bands are termed vibronic because they arise from a simultaneous change in the electronic state of the metal ion and the vibrational state of a coordinated ligand. Stavola et al. (1981) noted additional examples of such bands and presented a theoretical model based on the importance of electronic factors for calculating the intensities of lanthanide-ion vibronic transitions. Their theoretical model also predicts selection rules for such transitions. The intensities of observed bands assigned by these workers as being vibronic typically were at least 50 times weaker than the parent purely electronic band. Faulkner and Richardson (1979) have... 

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