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 wavefunction mixing. The phenomenon was first explained by the Italian physicist Enrico Fermi.
Two conditions must be satisfied for the occurrence of Fermi resonance:
Fermi resonance most often occurs between fundamental and overtone excitations, if they are nearly coincident 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 lead to additional bands in the spectrum, but rather shifts in bands that would otherwise exist.
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 cm<sup>âÂÂ1</sup>. This splitting arises from the mixing of ý<sub>CO</sub> and the overtone of HCH bending modes.
In CO<sub>2</sub>, the bending vibration ý<sub>2</sub> (667 cm<sup>âÂÂ1</sup>) has symmetry à<sub>u</sub>. The first excited state of ý<sub>2</sub> is denoted 01<sup>1</sup>0 (no excitation in the ý<sub>1</sub> mode (symmetric stretch), one quantum of excitation in the ý<sub>2</sub> bending mode with angular momentum about the molecular axis equal to ñ1, no excitation in the ý<sub>3</sub> mode (asymmetric stretch)) and clearly transforms according to the irreducible representation à<sub>u</sub>. Putting two quanta into the ý<sub>2</sub> mode leads to a state with components of symmetry (à<sub>u</sub> àà<sub>u</sub>)<sub>+</sub> = ã<sup>+</sup><sub>g</sub> + à<sub>g</sub>. These are called 02<sup>0</sup>0 and 02<sup>2</sup>0 respectively. 02<sup>0</sup>0 has the same symmetry (ã<sup>+</sup><sub>g</sub>) and a very similar energy to the first excited state of v<sub>1</sub> denoted 100 (one quantum of excitation in the ý<sub>1</sub> symmetric stretch mode, no excitation in the ý<sub>2</sub> mode, no excitation in the ý<sub>3</sub> mode). The calculated unperturbed frequency of 100 is 1337 cm<sup>âÂÂ1</sup>, and, ignoring anharmonicity, the frequency of 02<sup>0</sup>0 is 1334 cm<sup>âÂÂ1</sup>, twice the 667 cm<sup>âÂÂ1</sup> of 01<sup>1</sup>0. The states 02<sup>0</sup>0 and 100 can therefore mix, producing a splitting and also a significant increase in the intensity of the 02<sup>0</sup>0 transition, so that both the 02<sup>0</sup>0 and 100 transitions have similar intensities.