Chemical Sciences: A Manual for CSIR-UGC National Eligibility Test for Lectureship and JRF/Fermi resonance

A Fermi resonance is the shifting of the energies and intensities of absorption bands in an infrared or Raman spectrum. It is a consequence of quantum mechanical mixing. The phenomenon was explained by the Italian-American physicist Enrico Fermi.

Selection rules and occurrence
Two conditions must be satisfied for the occurrence of Fermi Resonance:
 * the two vibrational states of a molecule transform according to the same irreducible representation of the molecular point group.
 * The energies of the transitions (accidentally) have almost the same energy.

Since the normal modes of a molecule are generally of disparate energies, they do not mix. Thus, Fermi resonance most often occurs between normal and overtone modes, which are often nearly coincidental in energy.

Fermi resonance leads to two effects. First, the high energy mode shifts to higher energy and the low energy mode shifts to still lower energy. Second, the weaker mode gains intensity (becomes more allowed) and the more intense band decreases in intensity. The two transitions are describable as a linear combination of the parent modes. Fermi resonance does not really lead to additional bands in the spectrum.

Ketones
High resolution IR spectra of most ketones reveal that the "carbonyl band" is split into a doublet. The peak separation is usually only a few wavenumbers. This splitting arises from the mixing of νCO and the overtone of HCH bending modes.

CO2
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.