			15min:

SPECTROSCOPY OF X₂Y₄ (D_2h) MOLECULES: TENSORIAL FORMALISM ADAPTED TO THE \mathbfO(3) \supset D_2h CHAIN, HAMILTONIAN AND TRANSITION MOMENT OPERATORS. APPLICATION TO THE

₁₂ and

₂ BANDS OF C₂H₄..

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.

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A tensorial formalism adapted to the case of X₂Y₄ asymmetric molecules with D_2h symmetry has been developed in the same way as in the previous works on XY₄ (T_d) and XY₆ (O_h) spherical tops, XY₅Z (C_4v) symmetric tops^, or XY₂Z₂ (C_2v) asymmetric tops. We use the \mathbfO(3) \supset D_2h group chain. The method is similar to that already outlined by Sartakov et al. . 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 ₁₂ band of the C₂H₄ molecule and the other the Raman active ₂ band.