SPECTROSCOPY OF X_{2}Y_{4} (D_{2h}) MOLECULES: TENSORIAL FORMALISM ADAPTED TO THE O(3) ⊃ D_{2h} CHAIN, HAMILTONIAN AND TRANSITION MOMENT OPERATORS. APPLICATION TO THE ν_{12} and ν_{2} BANDS OF C_{2}H_{4}.

\underline{M. ROTGER}, W. RABALLAND, V. BOUDON and M. LOËTE, Laboratoire de Physique de l’Université de Bourgogne, UMR CNRS 5027, 9, Avenue Alain Savary, B.P. 47 870, F-21078 DIJON Cedex, France.

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_{d}) 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) ⊃ 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 ν_{12} band of the C_{2}H_{4} molecule and the other the Raman active ν_{2} band.

aW. Raballand, M. Rotger, V. Boudon and M. Loëte, J. Mol. Spectrosc., accepted (2003).

bJ.-P. Champion, M. Loëte 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).

cM. Rotger, V. Boudon and M. Loëte, J. Mol. Spectrosc., 200, 123-130, (2000).

dM. Rotger, V. Boudon and M. Loëte, J. Mol. Spectrosc., 200, 131-137, (2000).

eM. Rotger, V. Boudon and M. Loëte, J. Mol. Spectrosc., 216, 297-307, (2002).

fB. G. Sartakov, J. Oomens, J. Reuss and A. Fayt, J. Mol. Spectrosc., 185, 31-47 (1997).