# Electron Spin Resonance (ESR) Spectroscopy

This is a spectroscopic technique related to NMR that makes use of the fact that electrons also have an intrinsic spin angular momentum. For electrons, the spin quantum number, S, is equal to ½. This number specifies the magnitude of the total spin angular momentum for an electron to have the numerical value / 2 (in precisely the same way that a spin angular momentum quantum number of I = ½ specifies the spin angular momentum of a proton or other spin-½ nucleus to have magnitude / 2.)

The component of the spin angular momentum on an arbitrary axis (usually designated as the z axis) is equal to m_{S} , where the quantum number m_{S} can have values of ± ½. (Again note the close analogy with the spin angular momentum of nuclei, which will be apparent throughout.)

The energy levels of an electron spin in a magnetic field of strength B are given by:

μ_{B} is the Bohr magneton, a fundamental constant, and g_{e} is another fundamental constant called the g-value of an electron, with a value of approximately 2.0023 .

Thus we can see that upon the application of a magnetic field, the energy of an α electron (m_{S} = +½) is increased and the energy of a β electron (m_{S} = -½) is lowered. The separation of the two energy levels can be seen to be equal to g_{e}μ_{B}B . When a sample containing such electron spins is put in a magnetic field and then exposed to electromagnetic radiation, absorption of radiation at a frequency ν occurs, where ν is a value which satisfies this resonance condition:

i.e. when the frequency is such that each photon has energy equal to the gap between energy levels.

Electron spin resonance spectroscopy is the study of species that contain an unpaired electron by observing the conditions of magnetic field strength and frequency of radiation at which they come into resonance. Typically, the magnetic field strength is around 0.3 T and the radiation then falls into the microwave portion of the spectrum.

Note that the species to be studied must contain an unpaired electron, as if all the electrons in the sample are paired then their opposing spin angular momenta cancel each other out and there is no overall spin angular momentum to create an overall magnetic moment. This limits the use of ESR to radicals, some d-metal complexes, and molecules that are in an excited electronic state.

As in NMR, the electronic spins interact with local magnetic fields within the molecule or complex, which leads to the resonance condition being more commonly written as:

where g is the g-value of the specific radical or complex. They are normally very close in value to g_{e}.

ESR spectra contain hyperfine structure, which is the name given to the splitting of the individual resonance lines into components. As in NMR the analysis of this splitting can yield much useful data. The source of this hyperfine structure is the magnetic interaction between the electron spin and any magnetic nuclei in the sample species.

In general, the presence of a single spin-I nucleus splits the resonance line into 2I + 1 hyperfine lines of equal intensity. When there are several magnetic nuclei present, they all contribute to the hyperfine structure. If equivalent magnetic nuclei are present, then some of the split lines are coincident, and the lines are no longer all of equal intensity. In simple cases it is possible to predict the appearance of the spectrum using the splitting diagrams introduced in the consideration of the splitting patterns in NMR.