Degrees of freedom and molecular vibrations

At non-zero temperatures, i.e. temperatures above 0 K, all the atoms in a molecule are in motion. The molecule itself also is in translational and rotation motion. In a three dimensional space, an atom in isolation has 3 degrees of freedom, corresponding to the motion along the three independent coordinate axes. A molecule composed of N atoms has a total of 3N degrees of freedom (Figure 10.2).

Figure 10.2 Degrees of rotational freedom for a diatomic (A) and a triatomic (B) molecule

For a non-linear molecule, three of these 3N degrees of freedom correspond to translational motion, three correspond to rotational motion while rest 3N-6 are the vibrational degrees of freedom. For a linear molecule, there are only two rotational degrees of freedom that correspond to the rotation about the two orthogonal axes perpendicular to the bond (Figure 10.2). A linear molecule, therefore, has 3N-5 vibrational degrees of freedom. Let us have a look at the degrees of freedom of a diatomic molecule. A diatomic molecule has a total of 3 × 2 = 6 degrees of freedom. Three of these six degrees of freedom correspond to translational motion of the molecule; two of them define rotational degrees of freedom; while one corresponds to the vibration of the atoms along the bond. The 3N-6 vibrational degrees of freedom (3N-5 for linear molecules) represent the true/fundamental modes of vibration of a molecule. The different types of vibrations are shown in Figure 10.3.