Electron Spin Resonance Spectroscopy
Dylan W. Benningfield
Department of Chemistry
1
Electron Spin Resonance (ESR)

Electron spin resonance (ESR)

Electron paramagnetic resonance (EPR)

Study of paramagnetic materials

Radicals, bi-radicals, triplet states, unfilled conduction bands,
transition metal ions, impurities in semi-conductors, etc.
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
2
Electron Spin Resonance (ESR)

Provides molecular structure information inaccessible by other
analytical methods

Stable paramagnetic species are more easily detected
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
3
ESR Overview

Molecules with one or more unpaired electrons

Unpaired electrons have spin and charge (magnetic moment)

Electronic spin can be in one of two directions

Electron spin states are initially degenerate

Degeneracy lost when exposed to external magnetic field
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
4
ESR Overview

Place sample into magnetic
field (B)

Irradiate sample with
microwave frequencies (GHz)

Scan B at constant frequency to
make spectra
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
http://en.wikipedia.org/wiki/File:EPR_lines.png
http://photonicswiki.org
5
ESR Overview

Microwave source and detector

Modulation of magnetic field and phase-sensitive detection

Spectrum of 1st derivative (shown below)
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
6
ESR Theory

g-value (𝑔) ≈ chemical shift

𝑔𝑒 = 2.00232 for a free electron

Generally 𝑔 = 1.8-2.2

“Resonance” occurs when microwave frequency (GHz) = ∆E
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
7
Energy Levels
∆𝐸 = 𝐸+ − 𝐸− = ℎ𝑣 = 𝑔𝜇𝐵 𝐵
ℎ𝑣
𝑣(𝐺𝐻𝑧)
𝑔=
= 71.4484
𝜇𝐵 𝐵
𝐵(𝑚𝑇)
 g is the g-value
 𝜇𝐵 is the Bohr magneton
(9.274 x 10−28 J/G)
 B is the magnetic field
strength (G = 1x10−1 mT)
http://en.wikipedia.org/wiki/Electron_paramagnetic_resonance
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Paramagnetic_R
esonance/EPR%3A_Interpretation
8
Absorption
http://en.wikipedia.org/wiki/Stimulated_emission#/media/File:Stimulated_Emission.svg
9
Microwaves and Waveguides

Energy in the microwave region

Microwaves handled with a waveguide

Several types of waveguides
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
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X-band Waveguide

X-band waveguides most common

Size = 3.0-3.3 cm

Free electron resonance ≈ 3390 G
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
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Alternative Waveguide
http://en.wikipedia.org/wiki/Electron_paramagnetic_resonance
12
Sensitivity

ESR focuses on absorption of photons by the sample

Net Absorption (𝑁− − 𝑁+ ) can be found using the Boltzmann
distribution seen below:
∆𝐸
ℎ𝑣
𝑔𝜇 𝐵
𝑁+
−𝑘 𝑇
−𝑘 𝑇
− 𝑘 𝐵𝑇
=𝑒 𝐵 =𝑒 𝐵 =𝑒 𝐵
𝑁−
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
13
Sensitivity

For most commonly used temperatures and magnetic fields,
the exponent is very small and can be approximated as the
following:
𝑔𝜇 𝐵
𝑔𝜇𝐵 𝐵
− 𝑘 𝐵𝑇
𝐵
𝑒
≈1−
𝑘𝐵 𝑇

This allows for the following simplification for 𝑁− − 𝑁+ :
𝑁− − 𝑁+ = 𝑁− 1 − 1 −
𝑔𝜇𝐵 𝐵
𝑘𝐵 𝑇
=
𝑁𝑔𝜇𝐵 𝐵
2𝑘𝐵 𝑇
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
14
Sensitivity
𝑁− − 𝑁+ = 𝑁− 1 − 1 −

𝑔𝜇𝑔 𝐵
𝑘𝐵 𝑇
=
𝑁𝑔𝜇𝐵 𝐵
2𝑘𝐵 𝑇
This equations shows that ESR sensitivity (net absorption)
increases with magnetic field strength and decreasing
temperature
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
15
Saturation

Spin-lattice Relaxation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
16
Saturation

Instrument must be temperature controlled
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
17
ESR Instrumentation

An ESR Spectrometer have 6 main parts:
1.
2.
3.
4.
5.
6.
Klystron Tube (microwave generator)
Attenuator
Circulator
Load
Sample Cavity
Diode Detector with μ-Ammeter
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
18
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
19
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
20
Klystron Tube
Electron pathway
Anode
Reflector
electrode
Heated
Filament
Cathode
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
21
Klystron Tube

λ of the microwave = sample cavity size.

Anode = coarse correction for the λ of the microwave.

Voltage = fine correction for the λ of the microwave
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
22
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
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Attenuator

The attenuator homogenizes the power of the incoming
microwaves

Does not change frequency

Reduces noise
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
24
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
25
Circulator

The circulator is used to direct the microwaves

Keeps microwaves from reflecting back towards the source
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
26
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
27
Load

Completely absorb any reflected microwaves

Turns microwaves to heat energy
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
28
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
29
Sample Cavity


An oscillating magnetic field is super-imposed on the d.c.
Adds a.c. component in the diode current
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
30
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
31
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
32
𝒗 Resonance
𝑄 = (𝑣𝑟𝑒𝑠 )/(∆𝑣)
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
33
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
34
Diode Detector and μ-Ammeter

Current is proportional to microwave power reflected from the
sample cavity

Plain d.c. measurements have too much noise

a.c. component is added in the sample cavity
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
35
ESR Instrumentation
www.auburn.edu/~duinedu/epr/2_pracaspects.pdf
36
ESR Spectra

This a.c. component is amplified
using a frequency selective
amplifier

Modulation amplitude is less than
the line width

Detected a.c. signal is
proportional to the change in
sample absorption
http://en.wikipedia.org/wiki/Electron_paramagnetic_resonance#/media/File:EPR_lines.png
37
ESR Spectra

Absorbance = Too Noisy

1st derivative = better
apparent resolution

2nd derivative = even better
resolution, but less sensitive
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
38
Coalescence

Similar to NMR, ESR
signals can coalesce at
higher temperatures
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
39
Nuclear Hyperfine Interactions
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Param
agnetic_Resonance/Hyperfine_Splitting
40
Hyperfine Coupling Constant
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Param
agnetic_Resonance/Hyperfine_Splitting
41
Nuclear Hyperfine Interactions
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Param
agnetic_Resonance/Hyperfine_Splitting
42
Nuclear Hyperfine Interactions
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Param
agnetic_Resonance/Hyperfine_Splitting
43
Nuclear Hyperfine Interactions
𝑎
ℎ𝑣 −
2
𝐵1 =
𝑔𝜇𝐵
𝑎
ℎ𝑣 +
2
𝐵2 =
𝑔𝜇𝐵





B = field strength
a = hyperfine coupling constant
g = g-value
ℎ𝑣 = frequency of radiation
𝜇𝐵 = Bohr magneton
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Param
agnetic_Resonance/Hyperfine_Splitting
44
Nuclear Hyperfine Interactions
𝑎
𝑎
ℎ𝑣 +
ℎ𝑣 −
2
2
∆𝐵 = 𝐵2 − 𝐵1 =
−
𝑔𝜇𝐵
𝑔𝜇𝐵
𝑔𝜇𝐵
𝑎=
∆𝐵





B = field strength
a = hyperfine coupling constant
g = g-value
ℎ𝑣 = frequency of radiation
𝜇𝐵 =
Bohr magneton
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Param
agnetic_Resonance/Hyperfine_Splitting
45
Superhyperfine Splitting

Further splitting from hyperfine interactions

Very small

Due to neighboring nuclei
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
46
Isotropic and Anisotropic Interactions
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Param
agnetic_Resonance/Hyperfine_Splitting
47
Number of Peaks

For equivalent nuclei:
# 𝑝𝑒𝑎𝑘𝑠 = 2𝑀𝐼 + 1

M = number of equivalent nuclei

I = nuclear spin number
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
48
Number of Peaks

For more than one set of equivalent nuclei:
# 𝑝𝑒𝑎𝑘𝑠 = 2𝑀1 𝐼1 + 1 2𝑀2 𝐼2 + 1 2𝑀3 𝐼3 + 1 …

M = number of equivalent nuclei

I = nuclear spin number
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
49
Number of Peaks
http://www.auburn.edu/~duinedu/epr/3%20theory.pdf
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Common Nuclear Spins
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Param
agnetic_Resonance/EPR%3A_Interpretation
51
Common Nuclear Spins
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Param
agnetic_Resonance/EPR%3A_Interpretation
52
Number of Peaks

Example: radical CO2

2 Oxygen, I =
3
2

# 𝑝𝑒𝑎𝑘𝑠 = 2𝑀𝐼 + 1

#𝑝𝑒𝑎𝑘𝑠 = (2)(2)
3
2
+ 1 = 7 peaks
53
Number of Peaks

Example: radical NH3

1 Nitrogen, I = 1

3 Hydrogen, I =
1
2

# 𝑝𝑒𝑎𝑘𝑠 = (2𝑀𝑁 𝐼𝑁 + 1)(2𝑀𝐻 𝐼𝐻 + 1)

#𝑝𝑒𝑎𝑘𝑠 = ( 2 1 1 + 1)((2)(3)
1
2
+ 1) = 12 peaks
54
Practice ESR Spectra
3
2

Oxygen has an I =

For compounds with equivalent nuclei, #peaks= 2𝑀𝐼 + 1

#𝑝𝑒𝑎𝑘𝑠 = (2)(2)
O
3
2
+1=7
O •+
55
Practice ESR Spectra
O
O •+
Oxygen radical
SDBSWeb : http://sdbs.db.aist.go.jp (National Institute of Advanced Industrial Science and Technology, 3/24/2015)
56
Practice ESR Spectra
1
2

3 H, I =

1 C, I = 0
CH
3

For compounds with equivalent nuclei, #peaks= 2𝑀𝐼 + 1

#𝑝𝑒𝑎𝑘𝑠 = (2)(3)
1
2
+1=4
57
Practice ESR Spectra
CH
3
Methyl radical
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electr
on_Paramagnetic_Resonance/EPR%3A_Interpretation
58
Practice ESR Spectra

2 H with I =


N
(1)(2)
1
2
+1 = 3 peaks
For multiple sets of nuclei:


+1 = 3 peaks
C
H2
1 N with I = 1


(2)(2)
1
2
1
2
# 𝑝𝑒𝑎𝑘𝑠 = 2𝑀1 𝐼1 + 1 2𝑀2 𝐼2 + 1 2𝑀3 𝐼3 + 1 …
Thus, there are (3)(3) = 9 total peaks
59
Practice ESR Spectra
C
H2
N
Acetonitrile radical
SDBSWeb : http://sdbs.db.aist.go.jp (National Institute of Advanced Industrial Science and Technology, 3/24/2015)
60
Practice ESR Spectra


8 H, 2 sets of 4 equivalent nuclei

(4)(2)

(4)(2)
1
2
1
2
+1 = 5 peaks
•-
+1 = 5 peaks
Thus, there are (5)(5) = 25 total peaks
61
Practice ESR Spectra
•-
Naphthalene radical anion
SDBSWeb : http://sdbs.db.aist.go.jp (National Institute of Advanced Industrial Science and Technology, 3/24/2015)
62
Practice ESR Spectra
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
63
Practice ESR Spectra
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
64
Practice ESR Spectra
http://www.chm.bris.ac.uk/emr/Phil/Phil_2/p_2.html
65
Practice Problems

How many ESR peaks would a compound containing one Cu2+
(I=3/2), one N (I=1), and one –OH (I=1/2) have?
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Paramag
netic_Resonance/Hyperfine_Splitting
66
Practice Problems

How many ESR peaks would a compound containing one Cu2+
(I=3/2), one N (I=1), and one –OH (I=1/2) have?

((2*1*3/2+1)(2*1*1+1)(2*1*1/2+1) = 24 peaks
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Paramag
netic_Resonance/Hyperfine_Splitting
67
Practice Problems

How many peaks would a methoxymethyl radical have, and
how would those peaks appear in the spectra (doublets,
triplets, etc.)?
O
C
H2
CH
3
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Paramag
netic_Resonance/Hyperfine_Splitting
68
Practice Problems

How many peaks would a methoxymethyl radical have, and
how would those peaks appear in the spectra (doublets,
triplets, etc.)?

3 H and 2 H
O

(2+1)(3+1)=12 peaks
C
H2

CH
3
Triplet of quartets
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Paramag
netic_Resonance/Hyperfine_Splitting
69
Practice Problems
O
C
H2
CH
3
http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance_Spectroscopies/Electron_Paramag
netic_Resonance/Hyperfine_Splitting
70
Practice Problems

What is the g-value corresponding to a resonance at 9000 MHz
and 3700 G?

𝑔=

1G = 0.1mT
ℎ𝑣
𝜇𝐵 𝐵
= 71.4484
𝑣(𝐺𝐻𝑧)
𝐵(𝑚𝑇)
71
Practice Problems

What is the g-value corresponding to a resonance at 9000 MHz
and 3700 G?

𝑔=
ℎ𝑣
𝜇𝐵 𝐵
= 71.4484
9(𝐺𝐻𝑧)
370(𝑚𝑇)
= 1.738
72
Questions?
73