PRINCIPLES OF ESR

Electron Spin Resonance
Spectroscopy

V.Santhanam
Department of chemistry
SCSVMV
Enathur

ESR Spectroscopy
• Electron Spin Resonance Spectroscopy
• Also called EPR Spectroscopy
– Electron Paramagnetic Resonance
Spectroscopy
• Non-destructive technique
• Applications
– Extensively used in transition metal
complexes
– Deviated geometries in crystals

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

Energy of Transitions
• ESR measures the transition between the
electron spin energy levels
– Transition induced by the appropriate
frequency radiation
• Required frequency of radiation dependent
upon strength of magnetic field
– Common field strength 0.34 and 1.24 T
– 9.5 and 35 GHz
– Microwave region

• The absorption of energy causes a
transition of an electron from a lower
energy state to a higher energy state.

• In EPR spectroscopy the radiation used is in
the gigahertz range.

• Unlike most traditional spectroscopy
techniques, in EPR spectroscopy the
frequency of the radiation is held constant
while the magnetic field is varied in order to
obtain an absorption spectrum.

How does the
spectrometer work?

• The radiation source usually used is called a
klystron

• They are high power microwave sources
which have low-noise characteristics and
thus give high sensitivity

• A majority of EPR spectrometers operate at
approximately 9.5 GHz, which corresponds
to about 32 mm ( Q-band)

• The radiation may be incident on the sample
continuously or pulsed

• The sample is placed in a resonant cavity
which admits microwaves through an iris.

• The cavity is located in the middle of an
electromagnet and helps to amplify the
weak signals from the sample.

• Numerous types of solid-state diodes are
sensitive to microwave energy

• Absorption lines are detected when the
separation of the energy levels is equal to
the energy of the incident microwave.

• In practice, most of the external
components, such as the source and
detector, are contained within a microwave
bridge control.

• Additionally, other components, such as an
attenuator, field modulator, and amplifier,
are also included to enhance the
performance of the instrument.

What causes the energy
levels?

Resulting energy levels of an electron
in a magnetic field

• When an electron is placed within an applied
magnetic field, Bo, the two possible spin
states of the electron have different
energies (Zeeman effect)

• The lower energy state occurs when the
magnetic moment of the electron is aligned
with the magnetic field.

• The two states are labeled by the projection
of the electron spin, MS, on the direction of
the magnetic field, where MS = -1/2 is
parallel and MS = +1/2 is anti parallel state

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)

How ESR is different?
• According to uncertainty principle

∆ E . ∆ t ≈ h/4∏

Since ∆ E = h ∆ν

∆ν = h/4∏ . ∆ t

• So when the life time of electron in the
excited state decreases the lines broaden

• Due to many reasons the absorption lines are very
broad.
• To get finer information ∂A/∂H is plotted against H
to get the first derivative curve. When phase-
sensitive detection is used, the signal is the first
derivative of the absorption intensity

Spin-Lattice relaxation (T1)
• Excess energy given to either the lattice or
the tumbling solvent molecules.

• Depends on temperature.

• If temperature increases then all these
motions increase leading to effective
relaxation

• To minimize this effect esr spectrum is
always recorded at LNT 77 K when thermal
energy is minimum

Spin – Spin relaxation (T2)
• Excess energy given to neighbouring
electron.

• Independent of temperature

• Has two components

Dipolar interaction

Direct interaction

Dipolar interaction
• Spinning e- produces a magnetic field which
affects the neighbouring e-

• Since esr spectra are taken in frozen state
spins are locked and this effect becomes
important.

• This leads to low T2 values and hence very
broad lines.

• The interaction includes a 1/r3 term. Where r
is the distance between two neighbouring
electrons.

• If the concentration of unpaired e-
increases then r value decreases leading to
low T2 and hence broad lines. This is called
concentration broadening
• The r value is increased by diluting the
sample with isomorphous diamagnetic
materials

Direct interaction of e-
• In dipolar interaction e-s interact through
the magnetic fields.

• If concentration of unpaired e- is high then
the spin of e-s can directly interact leading
to line broadening.

• If the hyperfine splitting is of the same
order then only a single broad line is
observed. This is called concentration
narrowing

• Same electron undergoes resonance at
different fields with different operating
frequencies.

• So mentioning the field of resonance may be
misleading.

• g is used to mention the position of the line
E = mBB0MS

g = h ∆ν / mBB0MS

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

POSITION OF THE SIGNAL
• Already mentioned g value gives the
position of the signal.

• Actually g is not a constant. It is a tensor
quantity- changes with environment.

• Many systems show g values close to that of
free e-, but deviations are also common.

• Deviations in the order±0.05 may be the
mixing of low lying e.s with the g.s

• g values for the d metal ions (3d)
ranges from 0.2 – 8.
• The wide range is attributed to many
reasons.
 L-S coupling
 Crystal field Splitting
 Presence of inherent magnetic field in the
crystal.
 But L-S coupling and oxidation state of the metal
ion make the g value characteristic

Reference used
• When the operating
frequency of the
instrument is not known
precisely then DPPH radical
is used as standard.
• It gives five extremely
sharp peaks with intensity
ratio 1:2:3:2:1 (in solid
state one sharp line)
• g= 2.0036[1-∆H/H]
• ∆H – diff between std and
sample
• H – sample field

Proportionality Factor
MoO(SCN)52- 1.935
VO(acac)2 1.968

e- 2.0023
CH3 2.0026
C14H10 (anthracene)
2.0028
cation
C14H10 (anthracene)
2.0029
anion
Cu(acac)2 2.13

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


Interaction with a single nucleus of spin ½

m I

-(1/2)
m S = + 1 /2 νN
(1/2)
+

ν2
νe F IE L D B Z
Z E R O F IE L D ν1
-(1/2)

m S = -1 /2 νN
(1/2)
+

Which nuclei will interact?
• Measured as the distance
between the centers of
two signals
• Selection rules same as
for NMR
• Every isotope has a
ground state nuclear spin
quantum number, I
– has value of n/2, n is
an integer

• Isotopes with even atomic number and even
mass number have I = 0, and have no EPR
spectra
– 12C, 28Si, 56Fe, …

• Isotopes with odd atomic number and even
mass number have n even
– 2H, 10B, 14N, …

• Isotopes with odd mass number have n odd
– 1H, 13C, 19F, 55Mn, …

• Coupling patterns same as in NMR
• 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

• 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

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

Relative Intensities for I = ½

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

Relative Intensities for I = 1

• Example:
– VO(acac)2
– 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


EPR spectrum of vanadyl
acetylacetonate

• 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


EPR spectrum of benzene radical anion

• 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

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


EPR spectrum of pyrazine radical anion

Hyperfine splitting and anisotropy
• In solution the molecules are under
continuous motion so interactions in
all directions are same
• So hyperfine interaction is said to be
isotropic.
• In the case of solid state depending
upon the orientation of the crystal
field experienced will change
indifferent direction so A is
anisotropic.

• Usually field is considered to be
applied along Z axis. So A along Z axis
is called A||
• A values along X and Y directions
called A|

•A ave = 1/3[A|| + A|]

Anisotropic systems
• Anisotropy is shown by solids, frozen
solutions, radicals prepared by irradiation of
crystalline materials, radical trapped in host
matrices, paramagnetic point defect in
single crystals.
• For systems with spherical or cubic
symmetry g is isotropic
• For systems with lower symmetry,
g ==> g‖ and g┴ ==> gxx, gyy, gzz

• ESR absorption line shapes show distinctive
envelope

system with an axis of symmetry no symmetry

• Spin Hamiltonian of an unpaired e- if it is present in a
cubic field is

H = g β | Hx.Sx + Hy.Sy + Hz.Sz|

• If the system lacks a spherical symmetry and possess at
least one axis ( Distorted Oh,SP or symmetric tops) then

H = β |gxx Hx.Sx +gyy Hy.Sy + gzz Hz.Sz|

• Usually symmetry axis coincides with the Z axis and H is
applied along Z axis then
gxx = gyy = gL ; gzz = g||

• When the symmetry axis coincides with Z
axis determination of g is simple.

• The crystal is mounted on a sample cavity
and rotated across the field

• The g value varies between gL and g||

Fine structure of esr spectra
• Zero Field Splitting
• Kramer’s theorem
• Effective spin state
• Break down of selection rule

ESR spectra of metal complexes
• Factors affecting g value
 Operating frequency
 Concentration of unpaired e-
 Ground term of the ion
 Direction of measurement
 Symmetry of the field
 Inherent magnetic field
 Sustaining effect
 Crystal field splitting
 Jahn – Teller distortion
 Zero field splitting
 Mixing of gs and es

PRINCIPLES OF ESR

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