Spectroscopy of XY 2Z 2 ( C2 v) Molecules: A Tensorial Formalism Adapted to the O(3)⊃ Td⊃ C2 v Chain. Application to the Ground State of SO 2F 2

Abstract

A tensorial formalism adapted to the case of quasi-spherical XY 2Z 2 asymmetric tops such as SO 2F 2 has been developed as an extension of the usual one for the tetrahedral molecules. We use the O(3)⊃ T d ⊃ C 2 v group chain. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain. Such relations are then deduced in the C 2 v group itself. We also present a development of the Hamiltonian, dipole moment, and polarizability operators for the molecules under consideration using this formalism. These operators are involved in the calculation of the energies and intensities of rovibrational transitions and are essential for spectrum simulations. Expressions for the matrix elements are derived for these operators. A first application to the ground state of SO 2F 2 is presented. Programs for spectrum simulation and fit using these methods are freely available at the URL http://www.u-bourgogne.fr/LPUB/c2vTDS.html.