Origin of Molecular Vibrations

The force constant K is a measure of bond strength, and r is the distance between two nuclei after displacement. Such vibration motion is considered as harmonic. The potential energy of a harmonic vibration is expressed as Evti i. 

Commonly, the vibrational spectroscopy covers a wavenumber range from 200 to 4000 cm-1. We should know that crystalline solids also generate lattice vibrations in addition to molecular vibrations. The lattice vibrations refer to the vibrations of all the atoms in crystal lattice in a synchronized way. Such vibrations exhibit lower frequencies compared with those of common molecular vibrations and have a wavenumber range of about 20-300 cm-1. Coupling between lattice and molecular vibrations can occur if the molecular vibrations lie in such a low wavenumber range. Molecular vibrations can be distinguished from the lattice vibrations because they are not as sensitive to temperature change as lattice vibrations. 

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