A normal mode of vibration is a collective motion of nuclei. The nuclei oscillate in phase about the equilibrium geometry of the molecule. However, each nucleus has a potentially different magnitude and extent of motion. In general for a non-linear molecule with N atoms there are 3N total degrees of freedom and 3N - 6 vibrational degrees of freedom. We can subtract out the 3 translational and 3 rotational degrees of freedom about the center of mass of the molecule. There is a normal mode that corresponds to each vibrational degree of freedom.
Internal coordinates
It is most convenient to describe molecular motions in terms of a set of internal coordinates. These are:
Bond stretching
Angle bending
Torsions
Wags
The internal degrees of freedom describe localized collective motions that have chemical significance. Bond stretching has a relationship to the stiffness of a spring force cosntant between two atoms. While this is not exactly the same as bond strength, it is related. The force constant of a diatomic bond stretch is equal to the curvature (second derivative) of the potential energ profile of the bond.
Nomenclature of normal modes
There is an enitre vocabulary devoted to the description of molecular normal modes.
