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# ROVIBRONIC COUPLINGS IN A FOURFOLD DEGENERATE ELECTRONIC STATE OF AN OCTAHEDRAL MOLECULE: THE $\nu_{3}$ BAND OF $ReF_{6}$.

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/20459

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 Title: ROVIBRONIC COUPLINGS IN A FOURFOLD DEGENERATE ELECTRONIC STATE OF AN OCTAHEDRAL MOLECULE: THE $\nu_{3}$ BAND OF $ReF_{6}$. Creators: Rey, M.; Boudon, V.; Loete, M. Issue Date: 2002 Abstract: The rhenium hexafluoride ($ReF_{6}$) molecule has the particularity to possess an incomplete electronic d subshell. This open-shell system belongs to the $O_{h}$ group and exhibits a very large spin-orbit coupling leading to a fourfold degenerate electronic ground state of symmetry $G^{\prime}_{g}$. This implies complex couplings between electronic and nuclear motions (vibronic couplings) and between electronic, nuclear and rotational motions (rovibronic couplings) which considerably complicate calculations. Many years ago, some abnormalities in the spectrum of the triply degenerate $\nu_{3}$ band of symmetry $F_{1u}$ (the absence of the usual PQR pattern for such an isolated band, for instance) was attributed to a dynamical quadratic Jahn-Teller $effect^{a}$. But all the theoretical vibronic models developed up to now give matrices with very large sizes when adding the rotational part and this leads in practice to inextricable problems. To solve this, we propose a systematic tensorial development in the $SU(2) \otimes C_{I} \supset O^{S}_{h}$ group chain for the construction of the effective rovibronic $Hamiltonian^{b,c}$. This new theoretical model is based on a polyad scheme and allows a simultaneaous treatment of the four vibronic sublevels $F_{1u} \otimes G^{\prime}_{g}=E^{\prime}_{1u} \oplus E^{\prime}_{2u} \oplus 2G^{\prime}_{u}.$ The corresponding rovibronic energies are obtained by block-diagonalizing the full Hamiltonian for the considered vibronic polyad. The size of each rovibronic block is thus finite. In a previous study, we have successfully tested this model for an electronic triplet state $(V(CO)_{6})^{d}$. Here, we report in a similar way the low resolution band profile of the $\nu_{3}$ band of $ReF_{6}$ and show the agreement between the $observed ^{e}$ and calculated spectrum. URI: http://hdl.handle.net/1811/20459 Other Identifiers: 2002-RC-07