Question

How many IR and Raman peaks would be observed from the following irredeuciple representation ?

Answer 1

There are some rules to find out the IR active and Raman active mode in an irreducible representation. These rules are as follows:

(1) If an irreducible representation in a vibration mode is associated with x, y, or z in the character table, then the mode is IR active.

(2)) If an irreducible representation in vibration mode is associated with a product term (x2, xy) in the character table, then the mode is Raman active.

(3) If a molecule having a center of symmetry. So according to mutual exclusion rule, we can say any vibration in the molecule is IR active and that vibration is Raman inactive.

These rule number (1) and (2) are based on the character table portion III where x, y, z, Rx, Ry, Rz, xy, yz, xz etc. are given.

This rule number (3) is based on the symmetry of the molecule.

Using the above rules, we can say that C_2v molecule does not have a center of symmetry hence rule #3 is not valid here.

All the irreducible representation in C_2v has associated with either of one or more x, y, z, Rx, Ry, Rz. Hence all irreducible representations are IR active.

Similarly, all the irreducible representation contains product term here. Hene all the Raman active also.

Hence the IR active and Raman active modes here are 15. (6A₁+A₂+4B₁+4B₂)