# What is the Difference Between Fermi Resonance and Overtones in IR Spectra

The key difference between fermi resonance and overtones in IR spectra is that fermi resonance is the shifting of the energies and intensities of absorption bands in IR spectra or Raman spectra, whereas overtones in IR spectra are spectral bands that occur in a vibrational spectrum upon the transition of a molecule from the ground state to the second excited state.

IR spectra or IR spectrum is the result of IR spectroscopy, where IR radiation is used to analyze a sample. Here, we can observe the interaction between matter and IR radiation. We can get IR spectra from absorption spectroscopy. IR spectroscopy is used for the identification and analysis of chemical substances in a given sample. This sample can be a solid, liquid or gas. Infrared spectrophotometer is the instrument we use for this process. The IR spectrum is a graph, and it has an absorbance of light by the sample in the y-axis and wavelength or the frequency of IR light in the x-axis. The unit of frequency we use here is reciprocal centimetres (per centimetre or cm-1). If we use wavelength instead of frequency, then the unit of measurement is micrometres.

### CONTENTS

1. Overview and Key Difference
2. What is Fermi Resonance
3. What are Overtones in IR Spectra
4. Fermi Resonance vs Overtones in IR Spectra in Tabular Form
5. Summary – Fermi Resonance vs Overtones in IR Spectra

## What is Fermi Resonance?

Fermi resonance is the shifting of the energies and intensities of the adsorption bands in an IR spectrum or a Raman spectrum. This resonance state is created as a consequence of the quantum mechanical wavefunction mixing. This concept was introduced by the Italian physicist Enrico Fermi, after whom this resonance is named.

If a fermi resonance occurs, there are two conditions that must be satisfied: (1) transformation of the two vibrations modes of a molecule according to the same irreducible representation in the molecular point group (meaning that the symmetry of the two vibrations must be similar) (2) transitions have similar energies coincidentally.

Figure 1: Ideal Appearance of a Normal Mode and an Overtone Before and After the Occurrence of Fermi Resonance

Most often, if the fundamental and overtone excitations nearly coincide with Fermi resonance in energy, Fermi resonance occurs between fundamental and overtone excitations. Moreover, there are two major effects on spectrum lead by Fermi resonance:

1. Shifting of high energy mode to higher energy and shifting of a low energy mode to a lower energy
2. Increasing the intensity of the weaker mode while the more intense band tends to decrease in intensity

## What are Overtones in IR Spectra?

Overtone in IR spectrum is the spectral band that exists in a vibrational spectrum of a molecule when this molecule is transitioning from the ground state to a second excited state. In other words, the transition of the molecule occurs from v=0 to v=2 where v is the vibrational quantum number. We can obtain v from solving the Schrodinger equation for that particular molecule.

Figure 02: Schrodinger Equation

In general, when studying the vibrational spectra of molecules, the chemical bond vibrations tend to be approximable as simple harmonic oscillators. Therefore, we need a quadratic potential to be used in the Schrodinger equation in order to solve the vibrational energy eigenvalues. Usually, these energy states are quantized, and they have only discrete values for energy. If we pass electromagnetic radiation through the sample, the molecules tend to absorb the energy from EMR and change the vibrational energy state of the molecule.

## What is the Difference Between Fermi Resonance and Overtones in IR Spectra?

The key difference between Fermi resonance and overtones in IR spectra is that the Fermi resonance is the shifting of the energies and intensities of absorption bands in IR spectra or Raman spectra, whereas overtones in IR spectra are spectral bands that occur in a vibrational spectrum upon the transition of a molecule from the ground state to the second excited state.

The following table summarizes the difference between Fermi resonance and overtones in IR spectra.

## Summary – Fermi Resonance vs Overtones in IR Spectra

The key difference between Fermi resonance and overtones in IR spectra is that fermi resonance is the shifting of the energies and intensities of absorption bands in IR spectra or Raman spectra, whereas overtones in IR spectra are spectral bands that occur in a vibrational spectrum upon the transition of a molecule from the ground state to the second excited state.