* V. BOUDON*, M. REY, M. LOËTE, F. MICHELOT, Laboratoire de Physique de l'Université de Bourgogne, UMR CNRS 5027, 9 Av. A. Savary, BP 4780, F-21078 DIJON Cedex, FRANCE.

Some transition-metal hexafluorides like ReF_{6}, OsF_{6} or IrF_{6} have the particularity to posses a incomplete electronic subshell leading to low-lying degenerate electronic states. The ground electronic state is generally also degenerate. This implies the existence of very complex rovibronic couplings and thus the observation of unsual spectra^{,}

A few years ago, we have elaborated a tensorial formalism adapted to octahedral molecules with an odd number of electrons ( *i.e.\/* with half-integer angular momenta), defining the O_{h}^{S} group as the octahedron point group with its spinorial representations. We also presented a systematic tensorial development in the SU(2)øtimes C_{I}\supset O_{h}^{S} group chain for the vibronic Hamiltonian of an octahedral molecule in a fourfold degenerate electronic state of symmetry G'_{g}. However, this development had the disadvantage to lead to infinite matrices, due to the particular form of the vibronic coupling terms (Jahn-Teller, ... ). Moreover, the molecular rotation was not included. In this talk, we present a systematic tensorial development of the full effective rovibronic Hamiltonian for a given vibronic polyad in a G'_{g} electronic state. A construction of the form H=\sum_{i} t_{i} ((E^(
_{e})øtimes V^(
_{v}))^(
)øtimes R^(
))^(A_{1g}) is proposed, where we define electronic operators E^(
_{e}). This Hamiltonian has now finite matrices in the basis of the considered polyad. A similar construction is also given for the transition moment operators (dipole moment and polarizability) which are necessary to calculate transition intensities.