Electron spin resonance (ESR) spectroscopy, also known as electron paramagnetic resonance (EPR) spectroscopy, is a technique used to study materials with unpaired electrons. It detects transitions between spin energy levels of unpaired electrons when exposed to microwave radiation under a static magnetic field. ESR is sensitive to electronic structure and can provide information about defects, impurities, and reactive intermediates. The technique is complementary to nuclear magnetic resonance (NMR) but uses microwave radiation rather than radio waves and detects electron rather than nuclear spins.

1. Electron Spin Resonance
Electron Paramagnetic Resonance
BY- KANHAYA LAL KUMAWAT
INSTITUTE OF CHEMICAL TECHNOLOGY MUMBAI

2. 2
ESR Spectroscopy
• Electron Spin Resonance Spectroscopy
• Also called EPR Spectroscopy
• Electron Paramagnetic Resonance Spectroscopy
• Non-destructive technique

3. NMR and ESR/EPR
• EPR focuses on the interactions between an external magnetic field and the unpaired electrons
of whatever system it is localized to, as opposed to the nuclei of individual atoms.
• The electromagnetic radiation used in NMR typically is confined to the radio frequency range
between 300 and 1000 MHz, whereas EPR is typically performed using microwaves in the 3 -
400 GHz range.
• In EPR, the frequency is typically held constant, while the magnetic field strength is varied. This
is the reverse of how NMR experiments are typically performed, where the magnetic field is
held constant while the radio frequency is varied.
• Due to the short relaxation times of electron spins in comparison to nuclei, EPR experiments
must often be performed at very low temperatures, often below 10 K, and sometimes as low
as 2 K. This typically requires the use of liquid helium as a coolant.
• EPR spectroscopy is inherently roughly 1,000 times more sensitive than NMR spectroscopy due
to the higher frequency of electromagnetic radiation used in EPR in comparison to NMR.

4. Applications of ESR
• Electronic state of magnetic materials and semiconductors
• Electron state of semiconductor lattice defects and impurities (dopants)
• Structure of glass and amorphous materials
• Tracking of catalytic reactions, changes in charge state
• Photo-catalytic reactivity and photochemical reaction mechanisms
• Radicals of polymer polymerization processes (photo-polymerization, graft polymerization)
• Active oxygen radicals related to aging in disease in living organisms
• Oxidative degradation of lipids (food oils, petroleum, etc.)
• Detection of foodstuffs exposed to radiation
• Measurement of the age of fossils and geological features using lattice defects

5. 5
What compounds can you analyze?
• Applicable for species with one or more unpaired electrons
• Free radicals
• Transition metal compounds
• Useful for unstable paramagnetic compounds generated in situ
• Electrochemical oxidation or reduction

6. An electron is a negatively charged particle with certain mass, it mainly has two kinds of
movements.
1. Spinning around the nucleus, which brings orbital magnetic moment.
2. "spinning" around its own axis, which brings spin magnetic moment.
Magnetic moment of the molecule is primarily contributed by unpaired electron's spin
magnetic moment.
MS=√S(S+1) h/2π
•MS is the total spin angular moment,
•S is the spin quantum number and
•h is Planck’s constant.

7. In the z direction, the component of the total spin angular moment can only assume two values:
MSZ=mS⋅h/2π
The term ms have (2S + 1) different values: +S, (S − 1), (S − 2),.....-S. For single unpaired electron,
only two possible values for ms are +1/2 and −1/2.
The magnetic moment, μe is directly proportional to the spin angular momentum and one may
therefore write
μe=−geμBMs
The appearance of negative sign is due to the fact that the magnetic momentum of electron
is antiparallel to the spin itself. The term (geμB) is the magnetogyric ratio. The Bohr magneton,
μB, is the magnetic moment for one unit of quantum mechanical angular momentum:
μB=eh/4πme
where e is the electron charge, me is the electron mass, the factor ge is known as the free
electron g-factor with a value of 2.002 319 304 386 (one of the most accurately known physical
constant).

8. This magnetic moment interacts with the applied magnetic field. The interaction between
the magnetic moment (μ) and the field (B) is described by
E=−μ⋅B
For single unpaired electron, there will be two possible energy states, this effect is called
Zeeman splitting.
E+1/2=1/2gμBB
E−1/2=−1/2gμBB
In the absence of external magnetic field,
E+1/2=E−1/2=0
However, in the presence of external magnetic field , the difference between the two
energy states can be written as
ΔE=hv=gμBB

9. 9
energy levels
Resulting energy levels of an electron in a magnetic
field

10. 10
Energy Transitions
• ESR measures the transition between the electron spin energy levels
• Transition induced by the appropriate frequency radiation
• Required frequency of radiation is dependent upon strength of
magnetic field
• Common field strength 0.34 and 1.24 T
• 9.5 and 35 GHz
• Microwave region
Because of electron-nuclear mass differences, the magnetic moment of an electron is substantially larger than
the corresponding quantity for any nucleus, so that a much higher electromagnetic frequency is needed to bring
about a spin resonance with an electron than with a nucleus, at identical magnetic field strengths. For example,
for the field of 3350 G, spin resonance occurs near 9388.2 MHz for an electron compared to only about 14.3 MHz
for 1H nuclei.

12. 12
Describing the energy levels
• Based upon the spin of an electron and its associated magnetic
moment
• For a molecule with one unpaired electron
• In the presence of a magnetic field, the two electron spin energy levels are:
E = gmBB0MS
g = proportionality factor mB = Bohr magneton
MS = electron spin B0 = Magnetic field
quantum number
(+½ or -½)

13. EPR is often used to investigate systems in which electrons have both orbital and spin
angular momentum, which necessitates the use of a scaling factor to account for the
coupling between the two momenta. This factor is the g-factor, and it is roughly equivalent
in utility how chemical shift is used in NMR. The g factor is associated with the quantum
number J, the total angular momentum, where J=L+S.
gJ = 1+[J(J+1)+S(S+1)-L(L+1)]/2J(J+1)
Here, gL is the orbital g value and gs is the spin g value. For most spin systems with angular
and spin magnetic momenta, it can be approximated that gL is exactly 1 and gs is exactly 2.
This equation reduces to what is called the Landé formula:
gJ = 3/2−L(L+1)−S(S+1)/2J(J+1)
And the resultant electronic magnetic dipole is:
μJ=−gJμBJ
In practice, these approximations do not always hold true, as there are many systems in
which J-coupling does occur, especially in transition metal clusters where the unpaired spin
is highly delocalized over several nuclei. But for the purposes of a elementary examination
of EPR theory it is useful for the understanding of how the g factor is derived. In general this
is simply referred to as the g-factor or the Landé g-factor.

14. The g-factor for a free electron with zero angular momentum still has a small quantum mechanical
corrective g value, with g=2.0023193. In addition to considering the total magnetic dipole moment of
a paramagnetic species, the g-value takes into account the local environment of the spin system. The
existence of local magnetic fields produced by other paramagnetic species, electric quadrupoles,
magnetic nuclei, ligand fields (especially in the case of transition metals) all can change the effective
magnetic field that the electron experiences such that
Beff=B0+Blocal
The g-factor must then be replaced by a variable g factor geff such that:
Beff=B0⋅(g/geff)
• Many organic radicals and radical ions have unpaired electrons with L near zero, and the total
angular momentum quantum number J becomes approximately S. As a result, the g-values of these
species are typically close to 2.
• In contrast, unpaired spins in transition metal ions or complexes typically have larger values of L
and S, and their g values diverge from 2 accordingly.
After all of this, the energy levels that correspond to the spins in an applied magnetic field can now be
written as:
Ems=msgeμBB0
And thus the energy difference associated with a transition is given as:
ΔEms=ΔmsgeμBB

15. 15
Proportionality Factor
• Measured from the center
of the signal
• For a free electron
• 2.00232
• For organic radicals
• Typically close to free-
electron value
• 1.99-2.01
• For transition metal compounds
• Large variations due to spin-orbit coupling and zero-
field splitting
• 1.4-3.0

16. 16
Spectra
signal is the first derivative of the absorption intensity

17. 17
Proportionality Factor
MoO(SCN)5
2- 1.935
VO(acac)2 1.968
e- 2.0023
CH3 2.0026
C14H10 (anthracene) cation 2.0028
C14H10 (anthracene) anion 2.0029
Cu(acac)2 2.13

18. 18
How does the spectrometer work?

20. KLYSTRONS
• Klystron tube acts as the source of radiation.
• It is stabilized against temperature fluctuation by immersion in an oil
bath or by forced air cooling.
• The frequency of the monochromatic radiation is determined by the
voltage applied to klystron.
• It is kept a fixed frequency by an automatic control circuit and
provides a power output of about 300 milli watts.

21. WAVE GUIDE OR WAVEMETER
•The wave meter is put in between the oscillator and attenuator.
•To know the frequency of microwaves produced by klystron oscillator.
•The wave meter is usually calibrated in frequency unit (megahertz) instead of wavelength.
•Wave guide is a hollow, rectangular brass tube. It is used to convey the wave radiation to
the sample and crystal.
ATTENUATORS
•The power propagated down the wave guide may be continuously decreased by inserting a
piece of resistive material into the wave guide. This piece is called variable attenuator.
•It is used in varying the power of the sample from the full power of klystron to one
attenuated by a force 100 or more.

22. ISOLATORS
•It’s device which minimizes vibrations in the frequency of microwaves produced by klystron oscillator.
•Isolators are used to prevent the reflection of microwave power back into the radiation source.
•It is a strip of ferrite material which allows micro waves in one direction only.
•It also stabilizes the frequency of the klystron.
SAMPLE CAVITIES
•The heart of the ESR spectrometer is the resonant cavity containing the sample.
•Rectangular cavity and cylindrical cavity have widely been used.
•In most of the ESR spectrometers, dual sample cavities are generally used. This is done for
simultaneous observation of a sample and a reference material.
•Since magnetic field interacts with the sample to cause spin resonance the sample is placed where
the intensity of magnetic field is greatest.

23. MODULATION COIL
•The modulation of the signal at a frequency consistent with good signal noise ratio in the crystal
detector is accomplished by a small alternating variation of the magnetic field.
•The variation is produced by supplying an A.C. signal to modulation coil oriented with respect the
sample in the same direction as the magnetic field.
•If the modulation is of low frequency (400 cycles/sec or less), the coils can be mounted outside the
cavity and even on the magnet pole pieces.
•For higher modulation frequencies, modulation coils must be mounted inside the resonant cavity or
cavities constructed of a non-metallic material e.g., Quartz with a tin silvered plating.

24. CRYSTAL DETECTORS
•Silicon crystal detectors, which converts the radiation in D.C has widely been used as a detector of
microwave radiation.
MAGNET SYSTEM
•The resonant cavity is placed between the poles pieces of an electromagnet.
•The field should be stable and uniform over the sample volume.
•The stability of field is achieved by energizing the magnet with a highly regulated power supply.
•The ESR spectrum is recorded by slowly varying the magnetic field through the resonance
condense by sweeping the current supplied to the magnet by the power supply.

25. 25
Hyperfine Interactions
• EPR signal is ‘split’ by neighboring nuclei
• Called hyperfine interactions
• Can be used to provide information
• Number and identity of nuclei
• Distance from unpaired electron
• Interactions with neighboring nuclei
E = gmBB0MS + aMsmI
a = hyperfine coupling constant
mI = nuclear spin quantum number
• Measured as the distance between the centers of two
signals

26. 26
Which nuclei will interact?
Selection rules same as for NMR
• Isotopes with even atomic number and even mass
number have I = 0, and have no EPR spectra
• 12C, 28Si, 56Fe, …
• For isotopes with odd atomic numbers and even mass
numbers, the values of I are integers.
2H, 10B, 14N, …
• For isotopes with odd mass numbers, the values
of I are fractions. For example the spin of 1H is 1/2
and the spin of 23Na is 7/2.
1H, 13C, 19F, 55Mn, …

27. 27
Hyperfine Interactions
Interaction with a single nucleus of spin ½

28. 28
Hyperfine Interactions
More common to see coupling to nuclei with spins greater than ½
• The number of lines:
2NI + 1
N = number of equivalent nuclei
I = spin
• Only determines the number of lines--not the intensities

29. 29
Hyperfine Interactions
• Relative intensities determined by the number of interacting nuclei
• If only one nucleus interacting
• All lines have equal intensity
• If multiple nuclei interacting
• Distributions derived based upon spin
• For spin ½ (most common), intensities follow binomial distribution

30. 30
Relative Intensities for I = ½
N Relative Intensities
0 1
1 1 : 1
2 1 : 2 : 1
3 1 : 3 : 3 : 1
4 1 : 4 : 6 : 4 : 1
5 1 : 5 : 10 : 10 : 5 : 1
6 1 : 6 : 15 : 20 : 15 : 6 : 1

31. 31
Relative Intensities for I = ½

32. 32
Relative Intensities for I = 1
N Relative Intensities
0 1
1 1 : 1 : 1
2 1 : 2 : 3 : 2 : 1
3 1 : 3 : 6 : 7 : 6 : 3 : 1
4 1 : 4 : 10 : 16 : 19 : 16 : 10 : 4 : 1
5 1 : 5 : 15 : 20 : 45 : 51 : 45 : 20 : 15 : 5 : 1
6 1 : 6 : 21 : 40 : 80 : 116 : 141 : 116 : 80 : 40 : 21 : 6 : 1

33. 33
Relative Intensities for I = 1

34. 34
Hyperfine Interactions
• Example:
• VO(acac)2 Vanadyl acetylacetonate, C10
• Interaction with vanadium nucleus
• For vanadium, I = 7/2
• So,
2NI + 1 = 2(1)(7/2) + 1 = 8
• You would expect to see 8 lines of equal intensity

35. 35
Hyperfine Interactions
EPR spectrum of vanadyl acetylacetonate

36. 36
Hyperfine Interactions
• Example:
• Radical anion of benzene [C6H6]-
• Electron is delocalized over all six carbon atoms
• Exhibits coupling to six equivalent hydrogen atoms
• So,
2NI + 1 = 2(6)(1/2) + 1 = 7
• So spectrum should be seven lines with relative intensities 1:6:15:20:15:6:1

37. 37
Hyperfine Interactions
EPR spectrum of benzene radical anion

38. 38
Hyperfine Interactions
• Coupling to several sets of nuclei
• First couple to the nearest set of nuclei
• Largest a value
• Split each of those lines by the coupling to the next closest nuclei
• Next largest a value
• Continue 2-3 bonds away from location of unpaired electron

39. 39
Hyperfine Interactions
• Example:
• Pyrazine anion
• Electron delocalized over ring
• Exhibits coupling to two equivalent N (I = 1)
2NI + 1 = 2(2)(1) + 1 = 5
• Then couples to four equivalent H (I = ½)
2NI + 1 = 2(4)(1/2) + 1 = 5
• So spectrum should be a quintet with intensities 1:2:3:2:1 and each of those
lines should be split into quintets with intensities 1:4:6:4:1

40. 40
Hyperfine Interactions
EPR spectrum of pyrazine radical anion

41. 41
Conclusions
• Analysis of paramagnetic compounds
• Compliment to NMR
• Examination of proportionality factors
• Indicate location of unpaired electron
• On transition metal or adjacent ligand
• Examination of hyperfine interactions
• Provides information on number and type of nuclei coupled to the electrons
• Indicates the extent to which the unpaired electrons are delocalized