Example the C—H Stretch Bands of 1,4-Difluorobenzene

With the addition of the selection rules we now have enough tools to use symmetry to decide on the irreducible representations for the vibrations of a particular molecule and then pick out those modes which are IR and/or Raman active. In this example we will apply the general approach above to the C—H stretching modes of 1,4-difluorobenzene. 

Y will take a right-handed screw in the Z-direction). The rotation axes are then labelled according to the direction in space with which they are aligned CziX), C2(Y), CaCZ). 

Reduce the representation. The sums formed in the application of the reduction formula are given in Table 6.6. In this table the symmetry classes that have reducible representation characters of 0 are omitted as they will not contribute to the totals in any irreducible representation. The order of the Da point group h = 8, so that the reduction process yields 

Remove molecular movement/rotation. This basis is designed to include only specific bond vibrations, so no molecular translations or rotations need to be removed. 

Identify IR- and Raman-active modes. From the standard 2h character table in 

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