TENSORIAL DEVELOPMENT FOR THE ROVIBRONIC HAMILTONIAN AND TRANSITION MOMENTS OF OCTAHEDRAL $XY_{6}$ MOLECULES IN A FOURFOLD DEGENERATE ELECTRONIC STATE.
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Date
2000
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Ohio State University
Abstract
Some transition-metal hexafluorides like $ReF_{6}, OsF_{6}$ or $IrF_{6}$ 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 $spectra^{a,b}$ 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 $O^{s}_{h}$ group as the octahedron point group with its spinorial representations. We also presented a systematic tensorial development in the $SU(2) \otimes C_{1} \supset O^{s}_{h}$ group chain for the vibronic Hamiltonian of an octahedral molecule in a fourfold degenerate electronic $state^{d}$ of symmetry $G^{\prime 1}_{g}$. 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 $G^{\prime 1}_{g}$ electronic state. A construction of the form $\[ \tilde{H} = \sum_{i} \tilde{t}_{i}((E^{(\Gamma_{\epsilon})}\otimes V^{(\Gamma_{\nu})})^{(\Gamma)}\otimes R^{(\Gamma)})^{(A_{1_{g}})} \]$ 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.
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$^{a}$R.S. McDowell and L.B. Asprey J. Mol. Spectrosec. 45, 491-493 (1973). $^{b}$V. Boudon, M. Rotger and D. Avignant J. Mol. Spectrosc. 175, 327-339 (1996). $^{c}$V. Boudon, and F. Michelot J. Mol. Spectrosc. 165, 554-579 (1994). $^{d}$V. Boudon, F. Michelot, and J. Moret-Bailly J. Mol. Spectrosc, 166, 449-470 (1994).
Author Institution: Laboratoire de Physique de l'Universit\'{e} de Bourgogne
Author Institution: Laboratoire de Physique de l'Universit\'{e} de Bourgogne