2. 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
3. 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
4. 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
5. • 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.
7. • 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
8. • 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.
9. • 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.
10. What causes the energy
levels?
Resulting energy levels of an electron
in a magnetic field
11. • 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
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. 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
14. • 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
15. 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
16. Spin – Spin relaxation (T2)
• Excess energy given to neighbouring
electron.
• Independent of temperature
• Has two components
Dipolar interaction
Direct interaction
17. 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.
18. • 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
19. 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
20. • 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
21. 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
22. 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
23. • 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
24. 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
26. 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
28. 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)
+
29. 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
30. • 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, …
31. Hyperfine Interactions
• 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
32. 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
37. Hyperfine Interactions
• 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
39. 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
41. 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
42. Hyperfine Interactions
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
44. 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.
45. • 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|]
46.
47. 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
49. • 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||
50. • 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||
51. Fine structure of esr spectra
• Zero Field Splitting
• Kramer’s theorem
• Effective spin state
• Break down of selection rule
52. 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
Electron spin resonance (ESR) spectroscopy, also referred to as electron paramagnetic resonance (EPR) spectroscopy, is a versatile, nondestructive analytical technique which can be used for a variety of applications including: oxidation and reduction processes, biradicals and triplet state molecules, reaction kinetics, as well as numerous additional applications in biology, medicine and physics.
However, this technique can only be applied to samples having one or more unpaired electrons.
As we know, spectroscopy is the measurement and interpretation of the energy difference between atomic or molecular states. 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.
Shown is a block diagram for a typical EPR spectrometer. The radiation source usually used is called a klystron. Klystrons are vacuum tubes known to be stable 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. The radiation may be incident on the sample continuously (i.e., continuous wave, abbreviated cw) 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 and absorption lines then be detected when the separation of the energy levels is equal or very close to the frequency of the incident microwave photons. 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.
When an electron is placed within an applied magnetic field, B o , the two possible spin states of the electron have different energies. This energy difference is a result of the Zeeman effect. The lower energy state occurs when the magnetic moment of the electron is aligned with the magnetic field and a higher energy state where m is aligned against the magnetic field. The two states are labeled by the projection of the electron spin, M S , on the direction of the magnetic field, where M S = -1/2 is the parallel state, and M S = +1/2 is the antiparallel state.
So for a molecule with one unpaired electron in a magnetic field, the energy states of the electron can be defined as: E = g B B o M S = ±1/2gm B B o where g is the proportionality factor (or g-factor), B is the Bohr magneton, B o is the magnetic field, and M S is the electron spin quantum number. From this relationship, there are two important factors to note: the two spin states have the same energy when there is no applied magnetic field and the energy difference between the two spin states increases linearly with increasing magnetic field strength.
As mentioned earlier, an EPR spectrum is obtained by holding the frequency of radiation constant and varying the magnetic field. Absorption occurs when the magnetic field “tunes” the two spin states so that their energy difference is equal to the radiation. This is known as the field for resonance. As spectra can be obtained at a variety of frequencies, the field for resonance does not provide unique identification of compounds. The proportionality factor, however, can yield more useful information. For a free electron, the proportionality factor is 2.00232. For organic radicals, the value is typically quite close to that of a free electron with values ranging from 1.99-2.01. For transition metal compounds, large variations can occur due to spin-orbit coupling and zero-field splitting and results in values ranging from 1.4-3.0.
acac = acetylacetonate
In addition to the applied magnetic field, unpaired electrons are also sensitive to their local environments. Frequently the nuclei of the atoms in a molecule or complex have a magnetic moment, which produces a local magnetic field at the electron. The resulting interaction between the electron and the nuclei is called the hyperfine interaction. Hyperfine interactions can be used to provide a great deal of information about the sample including providing information about the number and identity of nuclei in a complex as well as their distance from the unpaired electron. This interaction expands the previous equation to: E = gm B B o M S + aM S m I where a is the hyperfine coupling constant and mI is the nuclear spin quantum number for the neighboring nucleus. It is important to note that if a signal is split due to hyperfine interactions, the center of the signal (which is used to determine the proportionality factor) is the center of the splitting pattern. So for a doublet, the center would be half way between the two signals and for a triplet, the center would be the center of the middle line.
So a single nucleus with a spin ½ will split each energy level into two, as shown above, and then two transitions (or absorptions) can be observed. The energy difference between the two absorptions is equal to the hyperfine coupling constant.
The rules for determining which nuclei will interact are the same as for NMR. For every isotope of every element, there is a ground state nuclear spin quantum number, I , which has a value of n/2, where n is an integer. For isotopes which the atomic and mass numbers are both even, I =0, and these isotopes have no EPR (or NMR) spectra. For isotopes with odd atomic numbers but even mass numbers, the value of n is even leading to values of I which are integers, for example the spin of 14 N is 1. Finally for isotopes with odd mass numbers, n is odd, leading to fractional values of I, for example the spin of 1 H is ½ and the spin of 51 V is 7/2.
The coupling patterns that are observed in EPR spectra are determined by the same rules that apply to NMR spectra. However, in EPR spectra it is more common to see coupling to nuclei with spins greater than ½. The number of lines which result from the coupling can be determined by the formula: 2 NI + 1 where N is the number of equivalent nuclei and I is the spin. It is important to note that this formula only determines the number of lines in the spectrum, not their relative intensities.
The relative intensities of the lines is determined by the number of interacting nuclei. Coupling to a single nucleus gives lines each of equal intensity.
Relative intensities of splitting patterns observed due to hyperfine coupling with a nucleus with I = ½. The splitting patterns are named similar to those in NMR: 2 lines = doublet 3 lines = triplet 4 lines = quartet 5 lines = quintet 6 lines = sextet 7 lines = septet
Computer simulations of EPR spectra for interactions with N equivalent nuclei of spin 1/2.
Relative intensities of splitting patterns observed due to hyperfine coupling with a nucleus with I = 1.
Computer simulations of EPR spectra for interactions with N equivalent nuclei of spin 1.
An example is shown by the EPR spectrum of the radical anion of benzene, [C6H6•]-, in which the electron is delocalized over all six carbon atoms and therefore exhibits coupling to six equivalent hydrogen atoms. As a result, the EPR spectrum shows seven lines with relative intensities of 1:6:15:20:15:6:1.
If an electron couples to several sets of nuclei, then the overall pattern is determined by first applying the coupling to the nearest nuclei, then splitting each of those lines by the coupling to the next nearest nuclei, and so on.
An example of this can be seen in the radical anion of pyrazine. Where coupling to two equivalent 14 N ( I = 1) nuclei gives a quintet with the relative intensities of 1:2:3:2:1 which are further split into quintets with relative intensities of 1:4:6:4:1 by coupling to four equivalent hydrogens.
