Vibronic intensities in centrosymmetric coordination compounds of the rare earths Part II. A vibronic crystal field-closure-ligand polarisation model and applications to the PrCl6 and UBr6 complex ions in octahedral symmetry

A symmetry adapted formalism to evaluate the vibronic intensities induced by the ungerade vibrational modes in centrosymmetric coordination compounds of the rare earths is put forward and applied to several selected electronic transitions of the PrCl³⁻₆ and UCl²⁻₆ complex ions in octahedral symmetry. This current model is based upon a modified symmetry adapted version of the combined vibronic crystal field-closure-ligand polarisation approach. This model differs from that developed in Part I of this series, in that for the vibronic crystal field contribution to the total transition dipole moment, the closure procedure is employed rather than the utilisation of a truncated basis set for the central metal intermediate electronic states. A criterion is introduced to choose an appropriate set of phases for both the electronic and the vibrational coordinates so that to ensure the right sign for the interference term (which couples together both the vibronic crystal field and the vibronic ligand polarisation contributions to the total transition dipole moment). We have focused our attention on the modulation of the intermolecular force field and a version of a modified general valence force field has been adopted. The reasons for using this formalism rather than the superposition model (SM) are fully discussed in the text. Finally, it is shown that the agreement with experiment is satisfactory for most of the components of the transitions studied, despite the apparent simplicity of our model calculation. General master equations applicable to any f^N electronic configurations are derived to show the utility and flexibility of this current formalism.