Fermi Resonance
Definition and meaning of Fermi Resonance in chemistry.
Fermi resonance is a quantum mechanical interaction between two vibrational states of a molecule that have nearly equal energy and the same symmetry, causing the states to mix, repel each other in energy, and share spectral intensity.
In more detail
It arises from anharmonic terms in the molecular potential that couple a fundamental vibration to an overtone or combination band lying close in energy, provided both belong to the same irreducible representation of the molecule's point group. The coupling pushes the two energy levels further apart than a simple harmonic model predicts (level repulsion) and mixes their wavefunctions, so intensity normally carried only by the strong fundamental is redistributed to the otherwise weak overtone or combination band. Consequently, both bands appear with comparable, anomalously enhanced intensity in the infrared or Raman spectrum rather than one strong line and one nearly invisible one.
Key facts
| Type | Vibrational level-mixing effect in spectroscopy |
|---|---|
| Requires | Near-degenerate energy and matching symmetry species |
| Classic example | CO2 Fermi diad (v1 with 2v2, Σg+) |
| Field | Physical Chemistry |
In carbon dioxide, the symmetric stretch v1 (harmonic estimate near 1333 cm⁻¹) and the first overtone of the bending mode, 2v2 (near 1334 cm⁻¹), share Σg+ symmetry and undergo Fermi resonance, producing the observed Raman doublet at 1388 and 1286 cm⁻¹ known as the Fermi diad.
Frequently asked questions
What two conditions must be met for Fermi resonance to occur?
The interacting vibrational states must lie close in energy (near-degenerate) and must belong to the same symmetry species of the molecule's point group, so the anharmonic coupling matrix element between them is nonzero.
How can you recognize Fermi resonance in a spectrum?
An overtone or combination band that should be weak instead appears with intensity comparable to a nearby fundamental, and the two bands are shifted apart in frequency relative to their unperturbed positions.