Question

1) Under C4v symmetry, which of the following irreducible representations, if any, correspond to a Raman active vibration?

A1,A2,B1,B2,E

2) Under C4v symmetry, which of the following irreducible representations, if any, correspond to an IR active vibration?

A1,A2,B1,B2,E

Please explain!

Answer 1

1) Under C_4v symmetry, which of the following irreducible representations, if any, correspond to a Raman active vibration?

A₁,A₂,B₁,B₂,E

Answer:

Vibration is Raman active ..............................change in the polarizability of the molecule.

In terms of group theory,

Vibration is Raman active .............symmetry is the same as x², y², z².

See the Character Table:

A₁,B₁,B₂,E

2) Under C_4v symmetry, which of the following irreducible representations, if any, correspond to an IR active vibration?

A₁,A₂,B₁,B₂,E

Answer:

Vibration is IR active .............................change in the dipole moment of the molecule.

Vibration is IR active......... ......................symmetry is the same as x, y, z coordinate.

A₁, E