Abstract
The rotation-vibrational states of a methane-shaped molecule may be divided into vibrational components (S. G. Larsen and S. Brodersen, J. Mol. Spectrosc. 157, 220-236, 1993). each characterized by a symmetry indicated as an irreducible representation of the full rotational group O 3. A simple group-theoretical method is presented, yielding the possible symmetries of the vibrational components for any vibrational state of a given symmetry. The method also indicates which changes may occur in the symmetries of two interacting vibrational components. Finally, local symmetry indices are introduced, and it is demonstrated that they represent an alternative description of the symmetry of vibrational components, leading to the same results for the possible symmetries and for the changes in these. The results are immediately valid for any T d molecule. but the general ideas should be easy to transfer to other molecules.
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