Symmetry Considerations for Vibrations

Unless otherwise noted, all art on this page is Cengage Learning 2014. 

FIGURE 14.31 The (/j normal vibration of HjO, and the effects of the symmetry elements of the Cjv point group on the vibration. In this case, operation of all symmetry elements yields a motion that is exactly the same as the original motion. Therefore, the eigenvalues of the operations are all 1, and this vibration can be labeled with the A, irreducible representation of the Qv point group. 

The degeneracy of a vibration is related to its character of the identity element of its irreducible representation label. Doubly degenerate vibrations always have an irreducible representation label having Xe 2. Triply degenerate vibrations always have an irreducible representation label having Xe 3. There are no higher degeneracies for vibrations. 

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