Fermi resonance in benzene

Abstract

The existence of a strong doublet rather than a singlet line in the Raman spectrum of carbon monoxide was explained by Fermi on the theory that when in multi-atomic molecules the frequencies of two independent vibrations are commensurable or nearly so, the vibrations perturb each other, resulting in a mutual repulsion of the two levels and a mixing of eigenfunctions, provided the two vibrations belong to the same symmetry species. Such Fermi resonance is found to occur frequently in many polyatomic molecules, and enables one to explain some characteristic features of Raman and infra-red spectra. For example, it is well known that the Raman spectrum of benzene exhibits two strong lines due to frequencies 1606 cm.^-1 and 1584 cm.^-1, whereas only one at 1596 cm.^-1 is to be expected corresponding to the eg+ vibration. The occurrence of this doublet was shown by Wilson to be due to Fermi resonance between 1596 cm.^-1, which is a pure eg+ frequency, and a binary combination 606 cm.^-1 + 992 cm.^-1 = 1598 cm.^-1, the total eigenfunction of which has again the eg+ symmetry.