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The exclusion rule

المؤلف:  Peter Atkins, Tina Overton, Jonathan Rourke, Mark Weller, and Fraser Armstrong

المصدر:  Shriver and Atkins Inorganic Chemistry ,5th E

الجزء والصفحة:  188

2025-08-30

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The exclusion rule

The three-atom nonlinear molecule H₂O has 3x3 – 6 = 3 vibrational modes (Fig. 6.14). It should be intuitively obvious (and can be confirmed by group theory) that all three vibrational displacements lead to a change in the dipole moment. It follows that all three modes of this C_2v molecule are IR active. It is much more difficult to judge intuitively whether or not a mode is Raman active because it is hard to know whether a particular distortion of a molecule results in a change of polarizability (although modes that result in a swelling of the molecule such as the symmetric stretch of CO₂ are good prospects). This difficulty is partly overcome by the exclusion rule, which is sometimes helpful: If a molecule has a centre of inversion, none of its modes can be both IR and Raman active. (A mode may be inactive in both.)

Figure 6.14 An illustration of the counting procedure for displacements of the atoms in a nonlinear molecule.