A basic vibration of a polyatomic molecule. All vibrational motion of a polyatomic molecule can be treated as a superposition of the normal modes of vibration of the molecule. If N is the number of atoms in a molecule, the number of modes of vibration is 3N – 5 for a linear molecule and 3N – 6 for a nonlinear molecule. Each of these vibrational modes has a characteristic frequency, although it is possible for some of them to be degenerate. For example, in a linear triatomic molecule there are four normal modes of vibration since 3N – 5 = 4 for N = 3. These vibrational modes are:

1. (a) symmetric stretching (breathing) vibrations;

2. (b) antisymmetric stretching vibrations; and

3. (c) two bending vibrations, which are degenerate.

The theoretical analysis of normal modes of vibrations of polyatomic molecules is greatly facilitated by the use of group theory.