Classical Theory of Molecular Vibrations

Abstract

Normal vibrations are characterized as having particle motions which are all either in-phase or out-of-phase at the same instant in time, in other words, for a given normal vibration each atom in the molecule oscillates along a line at the same frequency. For a diatomic molecule only one vibration occurs, only one vibrational energy level pattern exists, and only one fundamental transition occurs. The frequency of this transition is proportional to the force constant and the reduced mass of the vibration. For a polyatomic molecule there are 3N-6 normal modes of vibration (or 3N-5 for a linear molecule) and the vibrational energy level diagram can be very complicated, and overtones, combination and difference bands may be observed. It is necessary then to see how the frequencies of these transitions can be used to determine the force constants and provide an understanding of how the molecule vibrates.