Chapter 9, Drago
Electron Paramagnetic Resonance Spectroscopy
EPR is the same as ESR,
different names same process
In EPR the electron spin moment interacts with
the magnetic field, this is called the Zeeman effect.
This is defined by
g is the value for the free electron,
beta is the bohr magneton
and S is the spin operator.
In EPR the ground state is the ms = -1/2 state because the
electron has the opposite charge as the proton has.
The energy difference is defined by
The energy difference in an EPR expt
corresponds to approx. 2000 gauss and
frequencies in the microwave region.
This is greater than the energy required for a nuclear expt because
the magnetic moment for an electron is -9.3x10-21 erg/gauss and is
1.4x10-23 erg/gauss for a proton.
A difference of apprx. 660 times
The EPR expt is dependent on the population
difference between excited and ground states
EPR is commonly a CW expt with constant r.f. pulse and
varying magnetic field.
The two common frequencies are
X-band 9.5 gigahertz and Q-band 35 gigahertz
Mega is 106 and Giga is 109
Higher the frequency
the better the resolution.
Key points in running an EPR expt,
The solvent should form a good glass (separates molecules better)
The tube should be quartz (absorbs less microwave power and
has less metallic impurities)
Note a critical difference between NMR and EPR
In EPR changes in g value represent changes
in energy and in NMR changes the shielding
represent changes in energy.
For this reason, there are two g-values in EPR, the g-value that is
effected by spin orbit coupling (ie free electron) and the transition g-
For a free electron these are one and the same.
Nuclear hyperfine Splitting
Remember that the hyperfine interaction is
dependent of the contact coupling, A.
H = A I•S
A is dependent on the “contact” between
the electron and the nucleus.
This contact is greatest when the electron can interact
with the s orbital of the nucleus (same as NMR).
When this occurs the electron
can be split by the nucleus.
This is seen for organic radicals, because have sharp lines
Example: An organic radical split by a H atom (I=1/2)
Zeeman Hyperfine Coupling
This gives a doublet and coupling to a
nucleus of I=1 gives a triplet.
Note that the beta is g.s. for the electron and
alpha is the g.s. for the nucleus
Anisotropic Interactions: The g-tensor
The free electron has a g-value of ge=2.0023
There may be spin-orbit coupling
which will effect the ge
We have discussed this before with metals
but lets look at the simple case of Boron, 2p1.
All the p orbitals are degenerate thus a radical on B
can have spin orbit coupling to all the p-orbitals.
If all the orbitals have same energy then the spin orbit coupling
energy averages to zero over the x,y, and z coordinate.
However, if the atom is placed in a crystal which
removes the degeneracy then the spin orbit
coupling becomes asymmetric
px = py but do not equal pz
Now the observed g-value will depend upon
orientation of the crystal in the magnetic field.
gpara = gz and gperp = gx = gy
Basically, the g value tells you how strong the electron
magnetic tensor is in a given direction.
Therefore if you orientate the crystal in a different direction the
energy to resonate changes and thus the absorption will shift.
This effect is similar to shielding in the NMR experiment.
The spin-orbit coupling gives a gperp < gpara = ge
What happens if the crystal is ground into a powder?
All orientations are present however there are more chances
that the gperp will be aligned with the field than gpara.
Axis orientations wrt Ho
How do we combine a hyperfine coupling with
a g-tensor anisotropy in the powder sample?
A < (gpara - gperp)bH
and I = 1 so Mi = -1, 0 , 1
Three separate spectra
The EPR of Triplet states
How do we deal with systems that have
more than one electron?
This is similar to metals but simplier because
they are organic radicals
UV irradiated napthalene
The spectrum has three peaks which change resonance
drastically with changes of crystal orientation.
The spectra could not be fitted
with anisotropic g-tensors
This un-explained anisotropy is
due to spin-spin interaction!
This is what we deal with in metal systems all the time,
multiple spins occupying multiple orbitals
The magnitude of this coupling depends on the
energies of the MO’s that the electron resides in.
When the two MO’s are far in energy then
a singlet is the g.s., no interaction.
When they are close in energy, the pairing energy is
greater and thus a stable triplet is formed.
With a triple state, if the electrons did not couple
then the three states would be degenerate
However, magnetic dipole-dipole interactions
the two electrons removes the degeneracy in the absence
of a magnetic field as seen in Fig. 9.23
The splitting energy between these states is D,
the zero-field parameter
Depending on the strength of D, the number
of transitions seen will be different.
Allowed transitions are Dm=+/-1, but if they are close
enough then can see the forbidden Dm = 2.
Note that when the D is small then the states mix
and forbiddeness of a transition can be removed.
Only when D is large do the values
become valid quantum numbers
The electron-electron interaction can be described by a zero-field
splitting tensor which has the following Hamiltonian
This is the famous equation that uses E and D as parameters.
In EPR of metals we always talk in terms of E/D.
E/D =0 is an axial system
E/D = 0.33 is a rhombic system.
Remember that D is a Dz component and
E is a Dx or Dy component of the zero-field vector D.
This is how E/D can describe symmetry
in terms of x, y, and z.
Dz + Dx + Dy = 0
Electron Paramagnetic Resonance of Metalloproteins
EPR probes the environment of a paramagnetic center by defining
the size and shape of the magnetic moment
produced by the unpaired electron.
Two Objectives when considering the use of EPR
1) A quantitative measure of the amount of
paramagnetic species present in ones sample.
2) Determine the structural domain in which the paramagnet
resides by probing the interaction of local electric and magnetic
fields with the unpaired electrons of the metal ion.
The fundamental property that is measured in EPR is
the magnetic moment (m) of the paramagnetic center.
We measure m indirectly via the parameter g,
which is the spectroscopic manifestation of m.
m can also be determined with magnetic susceptibility
however EPR has a number of advantages.
1) Not a bulk method, see individual species.
2) Shape of magnetic moment gives information
3) Paramagnetic center interacts with other nuclei.
4) EPR is 1000 fold more sensitive.
Here are a number of examples of metalloproteins that have been
The g-values relate to the orientation of
the magnetic field relative to the molecule.
There are typically three g-values and they
correspond to structural axis of the molecule, gx, gy,
The orientation dependence of the g-value has a profound effect on
the shape of the EPR and it is critical that you learn these
This will help you determine if there are multiple species or not.
What factors are responsible for the great diversity of the EPR
These variations reflect the differences in the size and shape of the
local electric and magnetic fields that are present in the molecule.
Local electric fields originate in the electrons on the ligands.
They create the zero-filed splitting.
Local magnetic fields originate from parent nuclei and/or hyperfine
With this general view of paramagnetic centers, lets now back up
and think about the fundamental principles of EPR.