ESR Spectra- Principle-Hyperfine Splitting and structure- g-factor - Factors affecting g-value - Anisotropic system- Triplet state - Kramer's degeneracy - Zero Field Splitting

1. ELECTRON SPIN RESONANCE
SPECTROSCOPY
Dr.P.GOVINDARAJ
Associate Professor & Head , Department of Chemistry
SAIVA BHANU KSHATRIYA COLLEGE
ARUPPUKOTTAI - 626101
Virudhunagar District, Tamil Nadu, India

2. ELECTRON SPIN RESONANCE SPECTRA (ESR Spectra)
Definition
The interaction between the electron spin energy levels of a molecule and the
microwave radiation causes transition between the electron spin energy levels by the
absorption of microwave radiation is called Electron Spin Resonance Spectra (ESR
Spectra)
Condition
 Molecules having unpaired electrons gives ESR Spectra.
Example: Free radicals, transition metal ions and paramagnetic molecules
like Nitric oxide, Oxygen etc.,
 ESR Spectra obtained in the Microwave region: 2000-9600 MHz

3. Principle of ESR Spectra
The spinning charged electron can generate spin magnetic moment μs given
by
μs = -geμ 𝐵 𝒔 --------(1)
Where
ge ---- g-factor
μB ---- Bohr magneton =
𝑒ℎ
4𝜋me
(e – charge of electron & me – mass of electron)
s ---- spin of the electron (½)

4. When an electron spin having magnetic moment (μs) is placed in a magnetic field Bz ,
the interaction energy is
E = - μs Bz cosθ --------(2)
Where
θ ---- Angle between μs and Bz
Principle of ESR Spectra
Substitute cosθ =
𝑚 𝑠
𝑠
and μs = -geμBs in equation (2) we get
E = -(- geμBs) Bz
𝑚 𝑠
𝑠
= geμB Bz 𝑚 𝑠
E = geμB Bz 𝑚 𝑠 --------(3)

5. For an electron of spin s = ½ , the spin angular momentum quantum number will
have values of 𝑚 𝑠 = ± ½ and substituting the values of 𝑚 𝑠 = ± ½ in equation in (3)
we get two energy levels E -½ and E +½
Principle of ESR Spectra
E -½ = - ½ geμBBz ---------(4)
E +½ = + ½ geμBBz ---------(5)

6. • In the absence of Magnetic field (Bz = 0), the two values of 𝑚 𝑠 will gives rise to a
doubly degenerate spin energy state. If a magnetic field is applied, this degeneracy
is removed by splitting the energy level as E -½ and E +½ shown in the diagram
• The low energy state will have the spin magnetic moment aligned with the field and
correspond to quantum number, 𝑚 𝑠 = - ½ . The high energy state will have the spin
magnetic moment opposed to the field and corresponds to the quantum number,
𝑚 𝑠 = + ½
Principle of ESR Spectra

7. The energy of separation ΔE is obtained by subtracting equation (4) from (5)
ΔE= ½ geμBBz – (– ½ geμBBz )
ΔE= ½ geμBBz + ½ geμBBz )
Since ΔE= h , equation(6) becomes
ℎ = geμBBz
On substituting all values in the right side of the equation we get
 =
2.0023 𝑥 9.274 𝑥 10−24 𝑥 0.34
6.625 𝑥 10−34
= 9530 MHz
ΔE= geμBBz ---------(6)
 =
geμBBz
ℎ
---------(7)
Principle of ESR Spectra

8. • Since this frequency falls in the microwave region, On passing microwave
radiation causes transition between the electronic spins from lower energy
level to higher energy level shown in the diagram resulted ESR spectrum.
Principle of ESR Spectra

9. HYPERFINE SPLITTING AND HYPERFINE STRUCTURE IN ESR SPECTRA
Definition:
The splitting of ESR spectra of an electron by the interactions between the magnetic
spinning electron and adjacent spinning magnetic nuclei is called Hyperfine
splitting and the resulted splitting ESR signals are called Hyperfine structure
Number of peaks in ESR and Selection rule:
In general, if a single electron interacts magnetically with “n” equivalent nuclei,
the electron signal is split up into a (2nI +1) multiplet.
Where
n ---- No. of nuclei
I ---- spin quantum number of the nucleus = ½
• For H
.
radical , n=1 & I = ½ and No. of Signals = (2 X 1 X ½ + 1) = 2
• For CH3
.
radical , n=3 & I = ½ and No. of Signals = (2 X 3 X ½ + 1) = 4
Example:
The selection rule for hyperfine transition is Δms = ± 1 , ΔmI = 0

10. ESR spectra of free radicals in solution (or) Hyperfine structure of free
radicals in solution
• The ESR spectra of free radicals in solution are very much useful for getting details of
electron distribution and structure of the radicals
• The free radical must be produced in a concentration of about 10-13 moldm-3 for getting
good ESR spectrum
ESR spectrum for H
. (H-atom) free radical
• For H
.
radical , S = ½ , I= ½ , ms = ± ½ and mI = ± ½
• In the absence of magnetic field (Bz = 0), the electron spin energy levels are degenerate
• In the presence of magnetic field (Bz ≠ 0), the ms = -½ sublevel going down and the
ms = + ½ sublevel going up (shown in the diagram)

11. • Each electron sublevel interacts with nucleus of mI = + ½ and - ½ giving
four sublevels designated by the value of mI . This is called hyperfine
interaction.
• On passing microwave radiation into the H
.
system two transitions are
possible as per the selection rule ∆ms = +1; ∆mI = 0 resulted two ESR lines,
i.e., a doublet shown in the diagram.
• The two ESR lines are equally intense, the spacing between them is called
hyperfine coupling constant (a), expressed in tesla (or) milli tesla units.
ESR spectrum for H
. (H-atom) free radical

12. • In the presence of magnetic field (Bz ≠ 0), the electron spin energy level ms= -½
going down and the electron spin energy level ms = +½ going up (shown in the
diagram)
• Each electron spin energy levels interacts with four nucleus spin energy levels:
mI =
+3
2
,
+1
2
,
−1
2
,
−3
2
resulted eight sublevels designated by the values of mI
ESR spectrum or Hyperfine structure for .CH3 radical
• For
.CH3 , S= ½ , ms= + ½ and - ½
• Since for a proton , I = ½ , mI values for three equivalent protons are :
mI =
+3
2
,
+1
2
,
−1
2
,
−3
2
• In the absence of magnetic field (Bz = 0) , the electron spin energy levels
(ms = ± ½ ) are degenerate

13. • On passing microwave radiation into the
.CH3 system four transition are possible as per
the selection rule ∆ms = +1 and ∆mI = 0 resulted four ESR lines called quartet.
ESR spectrum or Hyperfine structure for .CH3 radical

14. The position of an ESR signal is defined by the
effective g-value, i.e., by
Since h and μB (Bohr magneton) are constant, g-
factor is a measure of the ration between
frequency () and magnetic field(Bz), i.e.,
g-factor in ESR spectra
g =
h
μBBz
g 

Bz

15. Factors affecting g-value
• For free electron and organic radicals such as the methyl radical, the g-value
depends upon the spin angular momentum of the electron itself and its value
was found to be 2.0023 (ge)
• In the case of the transition metal ion and their complexes, g-value depends
upon the spin and the orbital motion of the electron. So that, the g-value
departs from the ge value.
• In solution, because of free rotating motion, the g-factor is isotropic, i.e., it is
the average of the three g-value in the x, y and z directions.
• In solid state, because of restricted motion, the g-value is anisotropic, i.e., its
magnitude depends upon the direction of measurement.

16. ESR of Anisotropic system
• Anisotropic systems in ESR is the free radicals (or) paramagnetic materials in the
form of crystalline states (or) frozen solutions in which the interactions of applied
magnetic field with the spin angular momentum ( 𝑆 ) and orbital angular momentum
( 𝐿 ) of the electron must be depends on the orientation of the sample.
• For Anisotropic systems having axial symmetry, one of these terms gll is different
from the other two g terms.
• For Anisotropic systems having lower symmetries, the three terms gxx , gyy and gzz
are all different.
i.e., g-factor for anisotropic system must be directional property and represented
as gxx , gyy and gzz . gzz is designated as gll and gxx & gyy are designated as g

17. • Shapes of ESR absorption curves and first derivatives curves for
anisotropic system having (a) an axis of symmetry and (b) no symmetry
shown below
ESR of Anisotropic system

18. ESR for Triplet state
• Molecules having diamagnetic ground states but which possess excited triplet
states (with two unpaired electrons) which have lifetimes long enough to
record ESR spectra.
_________ Excited state _____ and ______ Triplet state
ms = +1 ms = -1
Singlet ________ Ground state ____________
ms = 0
• In the presence of a magnetic field, a triplet state splits into its three
components shown in the diagram, giving two possible transition,
• ms = -1 → 0 and ms = 0 → +1, whose energies are identical.
↑↑ ↓↓
↑↓

19. ESR for Triplet state

20. Kramer’s degeneracy and Zero Field Splitting
• In a crystal (or) frozen sample, dipole-dipole interactions being anisotropic , the
energy levels with ms = ± 1 are shifted relative to that with ms = 0 even in the
absence of an applied magnetic filed.
This is shown in the following diagram
• For a two electrons system, there are three possible spin orientations:
i.e., The splitting of energy levels in anisotropic systems in
the absence of applied magnetic field is called zero field is called Zero Field
Splitting (ZFS).
↓↓↑↑↑↓
ms = +1 ms = -1ms = 0

21. • For a three electrons system, there are four possible spin orientations
↑↑↑
ms = +
3
2
↑↑↓ ↓↓↑ ↓↓↓
ms = +
1
2
ms = -
1
2
ms = -
3
2
Kramer’s degeneracy and Zero Field Splitting

22. • Kramer’s rule states that for a system having an even number of unpaired
electron spins, the lowest energy state will be that with ms = 0 and all higher
energy states in the even number electron system & all states for systems with
an odd number of unpaired electron spin, will be doubly degeneracy
i.e., ms = +1 & -1 has same energy
ms = +
1
2
& -
1
2
has same energy
ms = +
3
2
& -
3
2
has same energy
ms = +
5
2
& -
5
2
has same energy
..
..
This degeneracy is known as Kramer’s degeneracy
Kramer’s degeneracy and Zero Field Splitting

23. • For an even number of electron system (Two electrons) the Kramer’s
degeneracy (ms = ± 1 has same energy) is removed by an applied magnetic
field, which shifts the two levels ms = -1 and ms = + 1 in opposite directions
shown in the diagram. As a result, two allowed transitions (ms = -1 → 0 and
ms = 0 → +1) occurred at different energy.
Kramer’s degeneracy and Zero Field Splitting