Fermi and Coriolis Perturbations

Perturbations between close-lying energy levels can occur for all types of molecules. These perturbations may be caused by either Fermi resonance or Coriolis interaction. Both phenomena can produce either vibrational or rotational perturbations. The rotational perturbations will affect only levels of the same over-all species and the same J value. The restriction to the same species also holds true for vibrational perturbations in the case of Fermi resonance, but in the case of Coriolis interaction perturbation can occur between vibrational levels of different species. We shall discuss Fermi resonance first. 

The rule limiting perturbation effects of the Fermi resonance type to vibrational levels of the same species restricts the occurrence of this phenomenon in many molecules. Fermi resonance has been observed between fundamental, combination, and overtone bands in some molecules. If two sublevels exist which have the same energy but different species, only the sublevel with the same species as the perturbing vibration will be excited. This will be illustrated below for CO2. 

Fermi resonance can produce a vibrational or a rotational perturbation. The former involves a shift of a vibrational level from its normal position. In addition, the vibrational change will alter the rotational constant B for the two interacting energy levels. Although the change in the rotational constant B could be thought of as a rotational perturbation, we shall restrict the use of this term to cases for which a rotational perturbation occurs without a vibrational disturbance and consider the vibrational level shift as a vibrational perturbation. 

Fermi Resonance (Rotational Perturbation). A rotational perturbation of the Fermi resonance type can occur even if the interaction between two vibrational levels of the same species is slight. If the two vibrational energy states are near each other, then some lines of the rotational fine-line structure may be perturbed. The rotational lines which have nearly the same energy will be the ones which perturb each other. We shall not give an example of such a perturbation here however, examples of this type of perturbation will be found in the spectra interpreted in the later sections of this chapter. 

When a molecule rotates and vibrates simultaneously, two forces can appear. One is the apparent centrifugal force present whenever a mass is rotated the second is the Coriolis force. The coupling which has been observed between a rotation and a vibration has been related to this Coriolis force. 

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