A short introduction
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 Last Updated on Thursday, 22 November 2012 22:35
What is EPR?
ESR or EPR is a spectroscopy that is used to study the structure and the dynamics of selected systems that have a paramagnetic center.
In most cases the paramagnetism derives only from the angular spin momentum S of unpaired electrons, then the acronym ESR (Electron Spin Resonance) is also encountered.
Paramagnetic centres can be naturally found in many systems but, at request, they can also be introduced on purpose; for this reason EPR is used in many different fields: chemistry, physics, biology, medicine,…
Analysis of the spectra allow to obtain information that often other techiques can not obtain.

Structural information 
Information that can 


Dynamical information 
Ingredients

Ingredients required to run an EPR experiment are: a paramagnetic centre, a microwave cavity, a magnetic field, a microwave radiation (and a temperature controller).

Paramagnetic centres can be found naturally anywhere. Some examples of paramagnetic centres are: free radicals, metal centres in proteins, and in organometallics, defects in materials, paramagnetic centres in semiconductors and electrons in metals.
If not naturally present, there are some possibilities of introducing a paramagnetic centre on purpose. Here is a list of systems normally studied by EPR after introduction of a paramagnetic centres in the systems.
Systems with paramagnetic centres

Condensed phases: liquid, crystalline or liquid crystalline 
Proteins 
Membranes 
Materials 
Photoexcited molecules in solution and in solid phase 
Transient radicals produced by irradiation 
The free electron case
The classical example is that of an unpaired electron, with quantum number S=1/2.
For this system there is a magnetic moment μ associated with the spin S which is oriented by the magnetic field because of the Zeeman interaction. For this quantum system the projection of the magnetic moment along the field is quantized; the quantization is given by the quantum number m_{s} so that:
where β is the Bohr magneton and g_{e} is the gfactor of the electron.
The two states m_{s} =±1/2 interact with the field and the strength of the interaction is given by the Zeeman term:
A transition between the two levels can be induced by a radiation that fulfil the requirement:
EQ.3
this is the resonance condition.
A continuous wave (cw) EPR spectrum is normally acquired by measuring the absorption of microwaves while sweeping the magnetic field. Most EPR spectrometers use lockin detection, and the spectra are in derivative form.
Unpaired electrons in molecules
With respect to the free electron case, electrons in molecules are characterized by the presence of a) a small orbital magnetic moment summing to the spin contribution, and b) the presence of coupled paramagnetic nuclei.
a) The gvalue
Mostly, the orbital contribution is small, and it is possible to show that it is generated by the mixing of orbitals through the spinorbit interaction.
In this case the term can be taken into account for through a newly defined gfactor.
g in general is a tensor: the interaction depends on the direction of application of the magnetic field with respect to the molecule.
The most general Zeeman Hamiltonian for a species is then:
In solution the tumbling motion of the molecules averages the principal values of the tensor, and a single value is obtained.
b) Interactions with paramagnetic nuclei
Paramagnetic nuclei act as perturbation on the unpaired electron(s) because of the presence of two types of interactions: a contact (isotropic) interaction, and a dipolar (anisotropic) interaction,
The Hamiltonian for the hyperfine interaction is normally written as:
where A is the hyperfine (hf) tensor and is the nuclear spin operator.
The simpler case is that of a fast tumbling radical (S=1/2) in a fluid solution, for which the tumbling motion of the molecule averages to zero the dipolar interaction; in this case the hf tensor reduces to a contant, a_{iso}.
For small values of a_{iso} the hyperfine spin Hamiltonian is simplified to:
thus the EPR line due to magnetic electron spin transition is split in two or more lines according to the nuclear angular momentum quantum number I, and this can be understood in terms of the different values of the quantum number m_{I} (relative to the nuclear spin component along the magnetic field direction) value.
Splitting of the line due to an interaction of a radical (S=1/2) with a nuclear spin I=1/2.
Experimental methods and more information
There are two families of spectroscopies b
ased on the fact that the microwaves can be continously irradiating the sample (cwEPR), or that the microwaves can be pulsed (pulseEPRmethods).
cwEPR

Pulse EPR

Xband EPR

 High Field EPR

 ENDOR

Hyperfine spectroscopies
 Spectroscopies for the study of the
relaxation properties 
Besides the very first principles introduced here, a good knowledge of the methodologies needs a study in depth.
We recommend very much to attend the available Schools on the subject, in particular
 The GIRSE School for an introduction to basic EPR
 The EFEPR School for advanced topics, especially for Pulse EPR
Follow the News for the announcements.
Books are also available on the subject.
A recent book covering most aspects of EPR, both cw and pulse methods, together with examples, is:
M. Brustolon, E. Giamello Ed.'s Electron Paramagnetic Resonance. A pratictioner's toolkit. Wiley 2009.
More references are available at the Bibliography section.
For WEB resources go to the Links section.