TENSORIAL DEVELOPMENT FOR THE ROVIBRONIC HAMILTONIAN AND TRANSITION MOMENTS OF OCTAHEDRAL XY_{6} MOLECULES IN A FOURFOLD DEGENERATE ELECTRONIC STATE

\underline{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}^{,}^{b} A few years ago, we have elaborated a tensorial formalism adapted to octahedral molecules with an odd number of electrons^{c} (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) ⊗ C_{I} ⊃ O_{h}^{S} group chain for the vibronic Hamiltonian of an octahedral molecule in a fourfold degenerate electronic state^{d} 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

H̃ = ∑_{i} t̃_{i} ((E^{(Γ_{e})} ⊗ V^{(Γ_{v})})^{(Γ)} ⊗ R^{(Γ)})^{(A_{1g})}

is proposed, where we define electronic operators E^{(Γ_{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.

aR. S. McDowell and L. B. Asprey J. Mol. Spectrosc. 45, 491–493 (1973).

bV. Boudon, M. Rotger and D. Avignant J. Mol. Spectrosc. 175, 327–339 (1996).

cV. Boudon, and F. Michelot J. Mol. Spectrosc. 165, 554–579 (1994).

dV. Boudon, F. Michelot, and J. Moret-Bailly J. Mol. Spectrosc. 166, 449–470 (1994).