Jahn-Teller active normal mode

If one quantum of a Jahn-Teller active normal vibration in the benzene cation (these are the modes with 62g symmetry) is excited, the linear dynamic Jahn-Teller coupling leads to a splitting into two vibronic states with j = ll2 (E g symmetry) and... 

The symmetry of the normal mode of vibration that can take the molecule out of the degenerate electronic state will have to be such as to satisfy Eq. (6-7). The direct product of E with itself (see Table 6-11) reduces to A + A 2 + E. The molecule has three normal modes of vibration [(3 x 3) - 6 = 3], and their symmetry species are A + E. A totally symmetric normal mode, A, does not reduce the molecular symmetry (this is the symmetric stretching mode), and thus the only possibility is a vibration of E symmetry. This matches one of the irreducible representations of the direct product E E therefore, this normal mode of vibration is capable of reducing th eZ)3/, symmetry of the H3 molecule. These types of vibrations are called Jahn-Teller active vibrations. 

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