Bent molecules XY2 using the C2v character table

The SO2 molecule belongs to the 2 point group, and in this section we look again at the three normal modes of vibration of SO2, but this time use the C2v character table to determine  

The C2V character table is shown below, along with a diagram that relates the SO2 molecule to its C2 axis and two mirror planes we saw earlier that the z axis coincides with the C2 axis, and the molecule lies in the yz plane. 

This is known as a reducible representation and can be rewritten as the sum of rows of characters from the C2v character table. Inspection of the character table reveals that summing the two rows of characters for the Ai and B2 representations gives us the result we require, i.e.  

This allows us to assign Ai symmetry to the scissoring mode. 

Finally, how can we use a character table to determine whether a particular mode of vibration is IR or Raman active At the right-hand side of a character table, there are two columns containing functions x, y and/or z, or products of these functions (e.g. x, xy, yz, (x - y ), etc.). We will not detail the origins of these terms, but will focus only on the information that they provide  

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