ELECTRON SPIN RESONANCE (ESR/EPR)

Electron spin resonance is also called as Electron Paramagnetic Resonance.
ESR is a spectroscopic technique used to detect “species that have unpaired electrons”. In case of an organic molecule the species are the free radicals and in case of inorganic complexes they are the transition metal ions.
Because most stable molecules have a closed shell configuration with out a suitable unpaired spin, the ESR spectroscopy is less widely used than the NMR(Nuclear Magnetic Resonance) spectroscopy.
ESR was first discovered by a Soviet physicist Yevgeniy Zavoyskiy in 1944.
The basic physical concepts of ESR Spectroscopy are analogous to those of NMR spectroscopy.
Spins of the electron are excited in ESR instead of the spins of the atom’s nuclei as in NMR.
For electrons in a magnetic field of 0.3 tesla, spin resonance occurs at around 10GHz.
ESR is used in solid-state physics, for the identification and quantification of radicals (in chemistry) to identify reaction pathways, as well as in biology and medicine for tagging biological spin probes.
Since radicals are very reactive, they do not normally occur in high concentrations in biological environments. With the help of specifically designed nonreactive radical molecules that attach to specific sites in a biological cell, its possible to obtain information on the environment of these so called spin label or spin probe molecules.
To detect some subtle details of some systems, ‘high field high frequency’ electron spin resonance spectroscopy is required.

UNITS & CONSTANTS :

A magnetic field is described by some constants and units :
· Magnetic induction in teslas (T)
· Magnetic flux density in amperes per meter (A/m)
· The CGS unit for magnetic induction is the gauss (G) which is equivalent to 10-4 T.
Further more, in describing ESR, the following are very important :
Planck’s constant h = 6.63 × 10-34 Js
Boltzmann constant K = 1.38 × 10-23 J/K
Bohr magneton µB = 9.27 × 10-24 J /T

BASICS
An electron has a magnetic moment. When placed in an external magnetic field of strength Bo, this magnetic moment can align itself parallel or antiparallel to the external field. The former is a lower energy state than the latter and the energy separation between the two is ∆E = geµBo, where ge is the gyromagnetic ratio/g factor of the electron .
Gyromagnetic ratio is the raito of electrons magnetic dipole moment to its angular momentum.
To move between the two energy levels, the electron can absorb electromagnetic radiation of the correct energy :

∆E = hν = geµBBo

and this is the fundamental equation of EPR spectroscopy. The paramagnetic centre is placed in a magnetic field and the electron caused to resonate between the two states; the energy absorbed as it does so is monitored, and converted into the EPR spectrum.

A free electron on its own has a value of 2.002319304386. This is ge, the electronic g factor. This means that for radiation at the commonly used frequency of 9.5 GHz (known as X – band microwave radiation, and thus giving rise to X – band spectra), resonance occurs at a magnetic field of about 0.34 tesla / 3400 gauss.
EPR signals can be generated by resonant energy absorption measurements made at different electromagnetic radiation frequencies in a constant external magnetic field (i.e we can scan with a range of different frequency radiation whilst holding the field constant, like in an NMR experiment). Conversely, measurements can be provided by changing the magnetic field B and using a constant frequency radiation; due to technical considerations, this second way is more common. This means that an EPR spectrum is normally plotted with the magnetic field along the X – axis, with peaks at the field that cause resonance (whereas an NMR has peaks at the frequencies that cause resonance).
In practice a single, isolated, paramagnetic centre never occurs, but only a population of a large number centres. If this population of centres is in thermodynamic equilibrium, its statistical distribution is described by the Boltzmann distribution

K is Boltzmann constant
T is temperature in Kelvin
For X – band radiation (ν = 9.75 GHz) at room temperature,

Because the lower level has more electrons than the higher one, transitions from the lower to the higher level are more probable, which is why there is net absorbtion of radiation.

EPR SPECTRAL PARAMETERS

The g Factor :

Knowledge of the g factor gives us information about the paramagnetic center’s electronic structure. When an unpaired electron is in an atom, it is an atom, it feels not only the external magnetic field Bo applied by the spectrometer, but also the effects of any local magnetic fields. Therefore the effective B(eff) felt by the electron is
B(eff) = Bo(1 - σ)
Where σ allows for the effects of the local fields (it can be positive or negative), and therefore the resonance condition is ∆E = hν = geµBB(eff) = geµBBo(1 - σ)
The quantity ge(1 - σ) is called the g factor, given by the symbol g, so

∆E = hν = gµBBo

Give this last equation, you can measure g from the ESR experiments by measuring the field Bo and the frequency ν at which resonance occurs. If g differs from ge (2.0023), this implies that the ratio of the electron’s magnetic momentum to its angular momentum has changed from the free electron value. Since the electrons magnetic moment is constant (its Bohr magneton), then the electron must have gained or lost momentum. It does this through spin – orbit coupling, and because the mechanisms of spin – orbit coupling are well understood, the magnitude of the change can be used to give information about the nature of the atomic or molecular orbital containing the electron. In real life the electrons are associated with atoms. There are three important consequences of this. Firstly the electron may gain or loose angular momentum (through spin – orbit coupling) which will affect the value of the g – factor. Secondly, this change in angular momentum is not the same for all orientations of the atom or molecule in an external magnetic field. It means that the g – factor changes according to the orientation of the paramagnetic atom in the magnetic field – it is anisotropic. This anisotropy depends upon the electronic structure of the atom in question, and so can yield information about the atomic/molecular orbitals containing the unpaired electron. Thirdly, if the atom(s) which the electron is associated with has /have a non – zero nuclear spin, the magnetic field associated with this atom will affect electron too. This leads to the phenomenon of hyperfine coupling, which is analogous to coupling in NMR in splitting the resonance signal into doublets, triplets and so forth.

RESONANCE LINE WIDTH DEFINITION
Resonance line widths are defined in magnetic induction units B and are measured along the axis, from line center to y value crossing chosen point of energy spectrum. These defined widths are called half widths and posses some advantages : for asymmetric lines values of left and right half width can be given. Half width ∆Bh is distance measured from center of line to point in which absorption value has half of maximal absorption curve inclination. In a practical approach, full definition of line width is used. In the case of symmetric lines, half width, and full inclination width ∆Bmax = 2∆B1s .