Selection Rules for Vibrational Spectroscopy
The fundamental modes of vibration of a molecule are active (observable) by IR or Raman spectroscopy if they meet the appropriate selection rules.
A vibration is IR active if there is a change in dipole moment during the vibration. Fortunately this information is also found in the character tables. Vibrations which occur with a change in dipole moment have the same symmetry properties as translations - corresponding to the x, y or z in the molecular properties column. In our example (water) for A1 there is a z and for B1 an x in the column - so all three vibrations are IR active and observable. We would expect to see three peaks in the IR spectrum - two with A1 symmetry and one with B1.
Raman spectroscopy involves inelastic light scattering and the selection rules are different from those of IR. For a vibration to be Raman active there must be a change in polarizability of the molecule. These vibrations correspond to symmetry species which have a product of two translations. the products are found in the far right hand column of the character table and can be simple cross products (e.g. z.y ) or squares (x2). For water all three vibrations will be Raman active.
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