Simple molecules -- symmetry and vibrations

Let us consider a simple symmetric molecule:

  C Cl₄     (carbon tetrachloride)
The molecule consists of n=5 atoms, thus the number of normal modes (excluding 3 translations and 3 rotations) will be N=3n-6=9. Due to the high symmetry (presence of mirror planes and three-fold axes) there will be doublets and triplets of identical types of vibration (transformed into one another by symmetry operations), with evidently indistinguishable frequencies. This is called degeneracy. In our case, in the point of fact, only 4 out of  9 vibrations are different.

Let us take a  look at these different vibrations in motion...