RADIATIVE PROCESSES IN CENTROSYMMETRIC LANTHANIDE COMPLEX-IONS .1. A GENERAL FORMALISM - RELAXATION OF THE CLOSURE APPROXIMATION

The theory of vibronic coupling in centrosymmetric complex ions, such as the LnX(6)(3-) species, which occurs in the hexachloroelpasolite Cs (2)NaLnX(6) (where Ln(3+) is a trivalent lanthanide ion and X = Cl- or Br-), is presented within the framework of a combined vibronic crysta l field-ligand polarization method. We consider a truncated expansion for the intermediate states and general equations are given to calcula te the vibronic intensity distribution associated with a parity forbid den but vibronically allowed electronic transition. Both the Vibronic crystal field and the vibronic ligand polarization coupling constants are evaluated using a standard set of symmetry coordinates. Special ca re concerning the phases of the symmetry coordinates and vibronic oper ators is necessary to ensure the correct signs for the cross terms, wh ich couple together both the vibronic crystal field and ligand polariz ation contribution to the total transition dipole moment. The procedur e is applicable to any f(n) central metal electron configuration.