Group Theory for Chemists, 2nd Edition

3

Reducible Representations

In this opening chapter of Part II you will see how the techniques of Part I can be applied to the analysis of vibrational spectra. The translations and rotations of a whole molecule were used in Chapter 2 as the basis for determining the irreducible representations of the point group. This is not the total extent to which symmetry governs the movements of the atoms within a molecule, as the vibrational motions – bond stretches and bends – must also obey the point group symmetry.

The problem we will tackle in this chapter is to predict the vibrational spectrum of the simple molecule SO₂ (C_2v), using group theory and the demands of point group symmetry to identify which vibrational modes are allowed. This will give ...