Fermi resonance

Fermi resonance

A Fermi resonance is a splitting of lines in an infrared spectrum or Raman spectrum, the theory of which is one of the many contributions of the Italian-American physicist Enrico Fermi. It occurs when two different vibrational states of a molecule transform according to the same irreducible representation of the molecular point group and have almost the same energy. This can occur for triatomic and larger molecules, the spectrum of CO2 providing a good example.

In CO2, the bending vibration ν2 (667 cm-1) has symmetry Πu. The first excited state of ν2 is denoted 0110 (no excitation in ν1, one quantum of excitation in ν2 with angular momentum about the molecular axis equal to ±1, no excitation in ν3) and clearly transforms according to the irreducible representation Πu. Putting two quanta into ν2 leads to a state with components of symmetry (Πu × Πu)+ = Σ+g + Δ g. These are called 0200 and 0220, respectively. 0200 has the same symmetry (Σ+g) as, and a very similar energy to, state 100 (a single excitation in the ν1 symmetric stretch (calculated unperturbed frequency 1337 cm-1), no excitation in ν2, no excitation in ν3). The similarity in energy may be thought of as an accidental near-degeneracy. The states 0200 and 100 can therefore mix together, producing a splitting and also a significant increase in the intensity of the 0200 transition, so that both the 0200 and 100 transitions have similar intensities.


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