RADIATIVE PROCESSES IN CENTROSYMMETRIC LANTHANIDE COMPLEX-IONS .2. A SYMMETRY-ADAPTED VIBRONIC CRYSTAL FIELD-CLOSURE FORMALISM

The formal theory of vibronic coupling in centrosymmetric coordination compounds of the lanthanide complex ions is reviewed on the basis of a crystal field-closure procedure. A formalism is developed on the bas is of a weak field compling scheme and it is applicable to any f-f ele ctronic transition. Throughout the course of the present work, the vib ronic Hamiltonian is expanded to first order in the nuclear Cartesian displacement coordinates. Master equations are derived to account for the transition dipole moments associated with vibronically allowed ele ctronic transitions in centrosymmetric lanthanide complex ions. An int ensive use of the irreducible tenser algebra is performed to express a ll the relevant polyelectronic matrix elements in terms of monoelectro nic matrix elements. The relevant operators and reduced matrix element s are evaluated, in order to facilitate vibronic intensity calculation s in the elpasolite-type systems.