Introduction
Electron Paramagnetic Resonance (EPR), also known as electron spin resonance (ESR),
is a spectroscopic technique used to investigate paramagnetic (unpaired electron) compounds.
Electrons, like nucleiA*, have charge and spin and therefore have a magnetic moment and are
susceptible to a magnetic field. EPR measures the energy of spin transitions when unpaired
electrons are in a magnetic field. The energy will lead to the characteristic g-factor for
the molecule being analyzed. This technique is analogous to nuclear magnetic resonance (NMR),
but the electron has a much larger magnetic moment and a larger energy gap for spin transitions
than nuclei.
History
EPR was first performed by the Clarendon Laboratory in Oxford, England in 1945.
Using a 25 meter wavelength spectrometer Zavoisky was able to detect faint signals
corresponding to multiple paramagnetic species. Improvements in microwave generation
coinciding with World War II radar development allowed EPR to quickly reach a near-theoretical
limit of sensitivity in only a matter of a few decades. Since then it has become a work horse
technique for a wide varety of chemistry disciplines.
Electron Spin
Free electrons possess an intrinsic angular momentum called spin (S) that generates a
magnetic field through the charge of the electron. From a classical understanding the
free electron has a magnetic dipole with a magnetic moment mu. Without the presence of
an external magnetic field, the directions of the magnetic moment are degenerate in energy.
The introduction of the magnetic field B0 breaks the degeneracy of the magnetic moment which
is observed through the Zeeman Effect.
The magnetic moment of the electron is proportional to the spin projection:
Mu is the Bohr magneton which is equal to 9.274*10-24 J/T and g
e is the spectroscopic g-factor.
The ge for the free electron is known, with high precision, to be 2.0023192778. Typical paramagnetic organic
compounds tend to have g-factors ranging between 1.99 and 2.01 - however transition metals
have a much larger range. The g-factor is unique to each type of paramagnetic center - and
can be used to identify an unknown.
External Magnetic Field
Quantum mechanics shows that the electron spin is quantized to be 1/2 times planck's constant
(which is widely omitted for simplicity). In the presence of an external field along the
z-axis, the projection of the spin, Ms, oriented along the z- axis can only take on the values ±1/2.
The positive M
s corresponds to a antiparallel orientation to the field and a negative
value indicates a parallel orientation to the direction of the field. The energy difference after
the degeneracy is broken is:
Beginning with the hamiltonian for electron spin we have:
We see our expression for ΔE for the spin transition.
Microwave Sources
When a photon of energy equal to ΔE is absorbed, the electron transitions to the
higher energy state. The energy of this transition is similar in magnitude to microwave
radiation. This gives two options for spectroscopy: either the magnetic field can be fixed
and the photon energies can be changed, or the photon energy can be fixed and the magnetic
field varied. Technological limitations make it easier to keep the microwave source
(a klystron or gun diode) fixed.
The approximate microwave band frequencies and names are given in the table below:
Generally speaking, spectra are better resolved at higher frequencies.
Detection
Microwaves propagate to the sample located in a resonator between the two poles of an
electromagnet. The resonator size is chosen such that a standing wave is formed with a
maximal energy density at the sample position. Likewise, the sample location is such that
there is the most uniform external magnetic field. Detectors for EPR employ phase sensitivity
and noise reduction techniques to filter out the unwanted (not at the constant value) photon
frequencies. Likewise, an additional magnetic modulation field is applied in the resonator to
boost resolution - as a result change in absorption is measured relative to the modulation
field which gives a first derivative spectrum.
Furthermore, as spin populations can be related by the Maxwell-Boltzmann distribution,
EPR is normally performed at low temperatures (10-15 K) to ensure that excitation and
absorption are the most probable events. The ground state (n
0) population available to be
EPR observable is shown by:
Generally speaking, keeping T as low as possible results in a large n0, producing a
large EPR signal.
The intensity of absorption by the sample is directly proportional to the relative numbers
of unpaired electrons in the sample. Double integration of the derivative spectrum of
absorbance can be used to estimate concentrations - which is utilized for quantitative
EPR studies, especially those that are characterizing kinetics.
Hyperfine Coupling
Fine structure in EPR arises from hyperfine coupling between the electron and nuclear
spin magnetic moments. The most prominent interaction is from Fermi contact by unpaired
electrons with s character and the nucleus. A nucleus of spin n/2 give (n+1) lines with
equal intensity. Furthermore, an electron can couple to n nuclei giving n+1 lines - the
intensities of which follow a binomial distribution. The distance between these lines are
measured in the change in magnetic field (gauss or tesla) and is called the Hyperfine
Splitting Constant (A).
The g factor of paramagnetic electrons are different from the free electron due to coupling
of the orbital angular momentum and the spin (spin-orbit coupling). The strength of the
coupling is dependent on direction (anisotropic). For low viscosity solutions the effects of
anisotropy are averaged out. However, in crystal EPR the sample molecules are oriented in a
fixed direction and the anisotropy cannot be ignored. Every paramagnetic molecule has a
principal axis system that is a set of unique axes that each have their own g values
(g
x, g
y, and g
z) and hyperfine splitting constants.
Anisotropy causes the g factor to be a second-rank tensor. The principle axis system must
be selected such that the g-tensor 3x3 matrix can be diagonalized to three components g
xx
, g
yy, and g
zz.
For frozen powdered samples anisotropy can play a critical role depending on the system
being studied.
Advantages and Disadvantages
EPR has many useful applications for paramagnetic samples. It very useful for studies
of complex macromolecules - specifically in identifying unknown molecules within
macromolecules (e.g. Fe-S clusters), and is also useful for quantification (e.g. spin
relaxation). EPR is a very sensitive technique and is capable of providing useful data
in volumes as low as 30ΜL and concentrations as low as 1 ΜM. Furthermore, EPR spectra can
be readily taken in 15-20 minutes once the equipment is prepared.
Although EPR has high specificity - that specificity relies on unpaired electrons which
might not be relevant to every system being studied. Most paramagnetic materials need
temperatures as low as 20K for detection which can be an expensive constraint.
EPR is a very useful tool to study proteins with metal clusters, as proteins are usually in low
concentration and volume.
Applications in Biology
Also, it is very popular to spin label sites in a protein for exploration with EPR.
Spin labeling usually takes advantage of the reactivity of protein thiol groups from
cysteines. The most commonly used spin label is a nitroxyl radical bound to a larger
heterocyclic ring. In principle this allows previously EPR silent regions to be explored.
By using complex pulsed EPR techniques, such as double electron-electron resonance, the
distances between spin labels (or natural paramagnetic sites) can be determined - this is
especially useful when crystallographic structures are unavailable.
Consulted Works
Brisdon, A. Inorganic Spectroscopic Methods. Oxford University Press, 1998.
Scott, R. Lukehart, C. Applications of Physical Methods to Inorganic and Bioinorganic Chemistry. Wiley-Interscience. 2007.
Weil, J. Wertz, J. Bolton, J. Electron Paramagnetic Resonance: Elementary Theory and Practical Applications'. McGraw-Hill, John Wiley & Sons, New York, 1994.
