Anharmonicity of vibration in molecules

Summary

The presence of anharmonicity entails the interactions of the normal modes of vibrations, which are independent in the harmonic oscillator approximation. The method of Hartree has been applied to study the mutual interaction of the normal modes, each assumed to be moving in the average potential field of the rest, and to evaluate their wave functions and eigenvalues. It is shown that, to a first order of approximation, normal vibrations belonging to the antisymmetric species do not interact with the rest and suffer no anharmonicity at all. The wave functions and eigenvalues of the different normal modes have been evaluated correct to the second order. The question of degeneracy has been considered and expressions have been given for the energy values of the different sublevels into which an overtone level of a degenerate system may be expected to split up according to group-theoretical considerations.