dc.creator Hilico, J. C. en_US dc.creator Morrt-Bailly, Jacques en_US dc.date.accessioned 2006-06-15T13:17:53Z dc.date.available 2006-06-15T13:17:53Z dc.date.issued 1970 en_US dc.identifier 1970-B-3 en_US dc.identifier.uri http://hdl.handle.net/1811/8368 dc.description Author Institution: Facult\'{e} des Sciences, Laboratoire de Spectroscopic Mol\'{e}culaire en_US dc.description.abstract In all states in which vibrational quanta of $\nu_{1}$ ($A_{1}$), $\nu_{3}$ and $\nu_{1}$ (both $F_{2}$) are excited, the theory of vibration-rotational perturbations in tetrahedral $XY_{4}$ molecules is usually examined in the light of the modern theory of angular momentum coupling in the full rotation group 0(3), the wave-functions associated with these oscillators having spherical symmetry. On the other hand, the E symmetry associated with the doubly-degenerate oscillator $\nu_{1}$ corresponds to no representation of 0(3). To study the combination level $\nu_{2}+\nu_{3}$, one can first couple the tetrahedral tensor functions $^{(2)}\Psi^{(E)}$ and $^{({3})}\Psi^{(F_{1})}$ to obtain the vibrational functions $^{(V)}\Psi^{(F_{1})}$ and $^{(V)}\Psi^{(F_{1})}$ associated with the two vibrational sub-levels ($E\times F_{2}= F_{1}+ F_{2}$). By a tensorial extension from $T_{4}$ to 0(3), these tensor functions are considered as spherical tensors $D^{(1_{g})}$ and $D^{(2_{a})}$ respectively. Then, vibration-rotation functions are obtained by spherical coupling. This coupling scheme for wave-functions implies an adapted form for the tensorial expression of the hamiltonian operator: H^{(A_{2})}=H^{(2g)}_{A_{1}}+H^{(4g)}_{A_{1}}+H^{(6g)}_{A_{1}}+\ldots+H^{(3u)}_{A_{1}}+H^{(2u)}_{A_{1}}+\ldots. where $H^{(\int_{g})}_{A_{1}}$ accounts for each individual vibrational sub-level, whereas $H^{(J_{u})}_{A_{1}}$ accounts for the interaction between these sub-levels. The detailed calculations use the tetrahedral as well as the spherical tensor formalism. This method makes possible definite assignments for about one hundred observed lines, a determination of good approximate values for the molecular parameters involved, a qualitative explanation of the general structure of the observed high-resolution spectra, and a satisfactory interpretation of the whole spectrum. en_US dc.format.extent 136929 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title THE $\nu_{2}+\nu_{3}$ BAND OF $CH_{4}$---THEORY AND INTERPRETATION en_US dc.type article en_US
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