THEORETICAL APPROACH OF THE ROTATIONAL ENERGY LEVELS OF $SiC_{2}$

Abstract

In the T-shaped $SiC_{2}$ molecule, it is conjectured that the $C_{2}$ fragment is bound to the silicium atom by an ionic essentially non directional bound, and thus could rotate within the $molecule.^{1}$ The $\nu_{3}$ mode, corresponding to this internal rotation, might, therefore, be a large amplitude motion and this could explain the difficulties encountered in fitting the microwave spectrum of this molecule in the ground vibrational $state^{2}$ as well as in the $v_{3}-1$ vibrational $state.^{1}$ In an attempt to calculate the rovibrational energy levels of the $SiC_{2}$ molecule, a formalism will be derived in which the $\nu_{3}$ mode is treated as a large amplitude motion. This requires accounting for the two main features of the $SiC_{2}$ dynamics: the strong dependence of the inverse moment of inertia tensor on the angle of internal rotation and the Coriolis coupling between the large amplitude $\nu_{3}$ mode and the overall rotation of the molecule. The results obtained when using this formalism to fit the microwave $data^{1,2}$ will be discussed. The value obtained for the height of the potential barrier hindering the internal rotation will be reported and compared to the value given by ab initio $calculations.^{3}$