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 (C2v), using group theory and the demands of point group symmetry to identify which vibrational modes are allowed. This will give ...

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