Fermi resonance in molecules

2 Fermi resonance interface modes in organic superlattices 9.2.1 Fermi resonance in molecules 

Fermi resonance55 is a phenomenon which can take place in vibrational or electronic spectra of molecules. We already discussed this phenomenon considering 

55 In this section we partly follow (6). The author is deeply grateful to Anatoly Kamchatnov for collaboration. 

Fermi resonance of vibrational excitons with polaritons. In this section we discuss the same effect only for molecular vibrations in multilayers. Below we present a few preliminary remarks which can be useful in the following discussion. 

Let a molecule have two vibrational modes with frequencies uia and uii,. If the second-order resonance condition 2uia uif, is fulfilled, then the huif, transition in the infrared spectrum can split if the interaction is allowed by symmetry of molecule into two lines of comparable intensity. The second line cannot be explained as a result of the interaction of light with the vibrational a mode because the transition with excitation of two hwa quanta is forbidden due to the well-known n — n 1 selection rule for a harmonic oscillator. Fermi explained (7) this experimental observation as a result of a nonlinear resonance interaction of two vibrational modes with each other. Since that time the notion of Fermi resonance has been generalized to processes with participation of different types of quanta (e.g. + iv2 u 3, lo + iv2 — UJ3 — 0J4, and so on) and to elec- 

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