SPECTROSCOPY OF $X_{2}Y_{4} (D_{2h})$ MOLECULES: TENSORIAL FORMALISM ADAPTED TO THE $O(3) \supset D_{2h}$ CHAIN, HAMILTONIAN AND TRANSITION MOMENT OPERATORS. APPLICATION TO THE $\nu_{12}$ and $\nu_{2}$ BANDS OF $C_{2}H_{4}$.
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Date
2003
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Ohio State University
Abstract
A tensorial formalism adapted to the case of $X_{2}Y_{4}$ asymmetric $molecules^{a}$ with $D_{2h}$ symmetry has been developed in the same way as in the previous works on $XY_{4} (T_{b})$ and $XY_{6} (O_{h})$ spherical $tops^{b}, XY_{5}Z (C_{4v})$ symmetric $tops^{c,d}$ or $XY_{2}Z_{2} (C_{2v})$ asymmetric $tops^{e}$. We use the $O(3) \supset D_{2h}$ group chain. The method is similar to that already outlined by Sartakov $et al.^{f}$. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain. Such relations are then expressed in the $D_{2h}$ group itself. We also present a development of the Hamiltonian, dipole moment, and polarizability operators for this type of molecules. Expressions of the matrix elements are derived for these operators. Two preliminary applications are presented. One concerns the infrared active $\nu_{12}$ band of the $C_{2}H_{4}$ molecule and the other the Raman active $\nu_{2}$ band.
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$^{a}$W. Raballand, M. Rotger, V. Boudon and M. Lo\""{e}te, J. Mol. Spectrosc., accepted (2003). $^{b}$J.-P. Champion, M. Lo\""{e}te and G. Pierre, in ""Spectroscopy of the Earth's Atmosphere and Interstellar Medium"" (K. N. Rao and A. Weber, Eds.) pp. 339-422, Academic Press, Inc., San Diego (1992). $^{c}$M. Rotger, V. Boudon and M. Lo\""{e}te, J. Mol. Spectrosc., 200, 123-130, (2000). $^{d}$M. Rotger, V. Boudon and M. Lo\""{e}te, J. Mol. Spectrosc., 200, 131-137, (2000). $^{e}$M. Rotger, V. Boudon and M. Lo\""{e}te, J. Mol. Spectrosc., 216, 297-307, (2002). $^{f}$B. G. Sartakov, J. Oomens, J. Reuss and A. Fayt, J. Mol. Spectrosc., 185, 31-47 (1997).
Author Institution: Laboratoire de Physique de I'Universit\'{e} de Bourgogne
Author Institution: Laboratoire de Physique de I'Universit\'{e} de Bourgogne