Knowledge Bank

Some transition-metal hexafluorides like $ReF6,OsF6$ or $IrF6$ have the particularity to posses a incomplete electronic sub-shell 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 $spectraa,b$ A few years ago, we have elaborated a tensorial formalism adapted to octahedral molecules with an odd number of $electronsc$ (i.e. with half-integer angular momenta), defining the $Ohs$ group as the octahedron point group with its spinorial representations. We also presented a systematic tensorial development in the $SU(2)\otimes C1\supset Ohs$ group chain for the vibronic Hamiltonian of an octahedral molecule in a fourfold degenerate electronic $stated$ of symmetry $Gg\prime 1$. 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 $Gg\prime 1$ electronic state. A construction of the form $\backslash [H~=\sum it~i((E(\Gamma ϵ)\otimes V(\Gamma \nu ))(\Gamma )\otimes R(\Gamma ))(A1g)\backslash ]$ is proposed, where we define electronic operators $E\prime (\Gamma e)$. 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.