ELECTRON PARAMAGNETIC RESONANCE (EPR) SPECTROSCOPY�

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Introduction to EPR Spectroscopy and Its Utilities

• Electron Paramagnetic Resonance (EPR) spectroscopy is an absorption spectroscopy.
• Involves absorption of radiation in the microwave region (10⁴-10⁶ MHz) under the influence of

a magnetic field.

• Also known as Electron Spin Resonance spectroscopy.
• Involves transition between electronic spin states via resonance phenomenon.
• Specific for paramagnetic substances.

Roessler and Salvadori, Chem. Soc. Rev., 2018, 47, 2534-2553

WHICH COMPOUNDS CAN BE ANALYZED VIA EPR?

EPR Spectroscopy

(Suitable for Paramagnetic Species)

Stable Paramagnetic Species:

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• persistent species with unpaired electron(s).
• Examples:- simple molecules eg. NO,O₂, NO₂

- transition metal ions and their complexes:

eg. Fe⁺³, [Fe CN ₆]⁻³ etc.

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Unstable Paramagnetic Species:

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• Free radicals or radical ions.
• Formed as intermediates in chemical reactions or by irradiation of molecules with energetic UV or X-rays or nuclear particulate beam.
• Study possible if lifetime greater than about 10⁻⁶ seconds.

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Bunce J. Chem. Educ. 1987, 64, 907

WHICH COMPOUNDS CAN BE ANALYZED VIA EPR?

EPR Spectroscopy

(Suitable for Paramagnetic Species)

Unstable Paramagnetic Species:

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• Free radicals or radical ions.
• Formed as intermediates in chemical reactions or by irradiation of molecules with energetic UV or X-rays or nuclear particulate beam.
• Study possible if lifetime greater than about 10⁻⁶ seconds.

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Study possible at low temperatures via a technique called “Matrix Isolation” !!

Radicals to be a) generated at low temperatures (cryogenic); or

b) produced in solid state or frozen solution state; or

c) trapped in a solid matrix of host material (e.g. solid inert gases, zeolites, etc.)

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Bunce J. Chem. Educ. 1987, 64, 907

PIETER ZEEMAN

OTTO STERN

YEVGENY

ZAVOISKY

WALTHER GERLACH

GEORGE UHLENBECK

SAMUEL GOUDSMIT

Study of splitting of spectral lines in the presence of an external magnetic field

The atomic beam split into two upon passage of a beam of silver atoms via inhomogeneous magnetic field (SPACE QUANTIZATION)

Spinning motion of electron as its new degree of freedom

First observation of EPR spectra of CuCl₂.2H₂O IN 1944.

History en route to EPR spectroscopy

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Lower energy state (more stable) with spin

magnetic moment μ_𝑒 aligned with applied field

Higher energy state (less stable) with spin

magnetic moment μ_𝑒 opposing applied field

Working principle behind epr spectroscopy: zeeman splitting

Basu J. Chem. Educ. 2001, 78, 666

Shin et al. Bull. Korean Chem. Soc. 2024, 45, 835–862

• Absorption frequency varies with applied magnetic field strength as hν = ΔE = g.β. 𝐇_𝟎.
• ESR absorption position must be expressed in a form independent of field strength

• Rearranging above eqn,

g = hν/ β. 𝐇_𝟎

DPPH

g = 2.0036

• Measuring g-value: by measuring the field separation between the centre of the spectrum of the unknown sample and the reference sample.

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ESR ABSORPTION POSITIONS : IMPORTANCE OF g- FACTOR

Similar to Chemical Shift!

Kovacs et al. RSC Adv., 2012, 2, 12812-12817

DEPENDENCE OF g-FACTOR ON ORIENTATION:- g-ANISOTROPY

• g value depends on the orientation of the species containing an unpaired electron with respect to the applied magnetic field.

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• Depends also on the physical state of the sample:-
• Gas and liquid states:- free tumbling motion.

- g value averaged over all orientations.

2. Solid crystal lattice:-
1. If a perfectly symmetrical lattice, the g value is the same in all directions. This is an isotropic effect.

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• If the crystal has low symmetry, g depends on the crystal orientation (value of g may vary along x, y, z axes). This is called g-anisotropy.

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Shin et al. Bull. Korean Chem. Soc. 2024, 45, 835–862

• The g value deviation ( δg ) from the free electron ( g₀ ) along any direction can be explained by

the following relation :-

g = g₀ ± n.λ/ ΔE

where, n = defines amount of orbital mixing.

λ = ground state spin-orbit coupling constant.

ΔE = transition energy.

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• + sign for mixing with a filled orbital and – sign with an empty orbital.
• g value for less than half-filled configurations < 2.0023 and for more than half-filled

configurations > 2.0023.

• n value to be taken from the magic pentagon:-

Derivation of g-factor for transition metal complexes:

the magic pentagon

Shin et al. Bull. Korean Chem. Soc. 2024, 45, 835–862

Derivation of g-factor for transition metal complexes:

the magic pentagon using few Ni(III) complexes

Shin et al. Bull. Korean Chem. Soc. 2024, 45, 835–862

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SCHEMATIC DIAGRAM OF AN ESR SPECTROMETER

instrumentation

• ESR spectra usually recorded as derivative spectrum.

Reason:- instrumental considerations associated with better signal-to-noise ratio.

- Broader spectral lines in absorption mode due to shorter relaxation times; hence poor resolution.

- Easy determination of resonant magnetic value at the point of x-axis bisection.

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Output spectrum

Absorption spectrum:-

• plot of intensity versus strength of magnetic field.
• Observed as soon as resonant magnetic field value is approached.

Derivative spectrum:-

• dispersion curve.
• plot of derivative signal against strength of magnetic field.
• Better resolution and clearer data interpretation.

• Sample:- single crystal/solid powder/liquid/solution/frozen state.
• Tube diameter ~ 5mm.
• Samples with low dielectric constant :- amount ~ 0.15-0.5 mL.
• Samples with high dielectric constant :- amount ~ 0.05 mL.
• Solvents like water, alcohol etc with high dielectric constant not preferred.

Reason:- strong absorption in microwave region.

• Sample as frozen solution :- solvent freezes to form glass to trap paramagnetic species.
• Solvents and mixtures forming good glasses:- methylcyclohexane, isooctane, toluene, glycerol ,

sulfuric acid, nujol etc.

propane + propene, toluene + acetone, toluene+ chloroform.

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Sample handling

SENSITIVITY OF AN ESR SPECTROMETER

Sensitivity of an ESR spectrometer given as :-

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Sensitivity increases with increase in magnetic field strengths.

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Variation in EPR spectrum of TEMPO nitroxide radical with change in microwave band.

𝑁_𝑚𝑖𝑛 = 1 * 10¹¹ δH/√τ

Where, 𝑁_𝑚𝑖𝑛 = minimum number of detectable spins per gauss.

δH = width between deflection points on the derivative absorption curve.

τ = time constant of the detecting system

1/α band width of the detection circuit.

1. FINE STRUCTURE:-
• For substances with more than one unpaired electron.
• Result of electron-electron coupling.
• Let we have a crystal with molecules/ions with two parallel electron spins.

→ Total spin S = ½ + ½ = 1; Spin multiplicity = 2S + 1 = 3 (triplet state) .

→ Angular momentum S for S = 1 :- S = √𝑆(𝑆 + 1) * h/2∏ = √2 units.

→ Possible spin states = 2S+1 = 2*1 + 1= 3.

Allowed orientations of two parallel electron spins in applied field.

Splitting of energy into 3 levels and dipolar shift, D, raising 𝑆_𝑧 = ±1 levels.

Multiplet structures in epr spectroscopy

The zero-field

splitting of a

triplet state

(“KRAMER’S

DEGENERACY”)

The effect of applied magnetic field and allowed transitions between levels.

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S_Z = ±1

states

diverge

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Two fine structure lines

Fine structure separation ~ 0.1-0.2 T, line width ~ 10^-3 -10^-4 T

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Zero field splitting

Or

CRYSATL FIELD EFFECT

Dipolar Interaction

Spin-Orbit Coupling

Strong Internal Electric Field

Hyperfine coupling

ESR spectrum of free electron with single transition

n between Zeeman-splitted states.

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¹H

S = 1/2

.Methyl radical (𝑪^̇𝑯_𝟑) :-

Energy level diagram illustrating coupling between unpaired electron and one nucleus with spin I = 1

• Number of peaks of multiplet given

by (2*n*1/2) + 1 = n + 1 rule.

• Intensities of component peaks are coefficients of binomial expansion of (𝑥 + 1)^𝑛.

• Number of peaks of multiplet given by

(2*n*1) + 1 = 2n+1 rule.

• Modified pascal’s triangle to obtain intensities of component peaks.

Mnemonic for intensity ratio of multiplet peaks

• Examples:- 1) Ethyl radical :-
• Splitting into 1:2:1 triplet by CH₂ (lines 1,2,4)and

1:3:3:1 (lines 1,3,6,9)quartet by CH₃.

• 𝑎^CH2 = 22.4 G , 𝑎^CH3 = 26.9 G

2) CH𝐅_𝟐 radical:-

• Splitting into 1:2:1 triplet by 2 Fs and then doublet by single H.
• 𝑎^𝐹 = 84 G ; 𝑎^𝐻 = 22 G

3) C𝐇_𝟑C𝐇_𝟐OCHC𝐇_𝟑 radical :-

β

𝛼 γ

𝑎^𝐻 = 13.8 G, 𝑎^𝐻 = 21.9 G, 𝑎^𝐻= 1.4 G.

Hyperfine constants due to adjacent spin active nuclei: dependency on local spin intensity

Delocalized organic free radicals:-

1) Butadiene radical anion:-

• Quintet of triplets ( 4 equivalent CH₂

protons and 2 equivalent CH protons).

• 𝑎_1,4 = 7.6 G , 𝑎_2,3 = 2.8 G

Reason :- a ∝ electron density at that

position.

2) Benzyl radical :-

a_CH2 = 16.4 G

a_{𝑜𝑟𝑡ℎ𝑜} = 5.1 G a_{𝑝𝑎𝑟𝑎} = 6.3 G a_{𝑚𝑒𝑡𝑎} = 1.6 G

3) Naphthalene radical anion :-

Splitting into 25 lines by 4 equivalent α and 4 equivalent β protons

ClCHCO₂H radical:-

nuclear quadrupole moment

• Nuclei with I ≥ 1 have property of i.e. the nuclear charge distribution

taking an ellipsoid shape.

• In NMR time scale (MHz) , the magnetic effects of various possible spin states average out to zero.
• In ESR time scale (GHz) , such nuclei do not get sufficient time to cycle through all spin states.

CONSEQUENCE :-

Quadrupolar nuclei with spin I

≥

1 cause splitting of electron resonance in ESR ;

while no such splitting of spectra is experienced in case of NMR

.

Quadrupolar coupling

PhC=OĊHNO radical:-

Anion radical of pyrazine:-

Proton NMR spectrum of methanol

ESR spectrum of hydroxymethyl radical

• On NMR time scale exchange of hydroxyl proton takes place too fast via H-bonding.
• Hence ,methyl protons are not split by OH proton into doublet ( until temperature is too low to slow

down exchange phenomenon).

• OH group remains static in ESR timescale.
• Hence, averaging out of spin states does not occur.
• Doublet splitting is observed due to OH proton for CH₂ protons in ĊH₂OH radical.

Exchangeable protons: observed in epr or not?

N C

• Splitting into 6 lines of equal intensity by single Re nucleus (I=5/2).

• Further splitting of each peak

by 4 N (I=1) into 9 lines.

• 63_Cu = natural abundance – 69.17% magnetic moment β_N = 2.43
• 65_Cu = natural abundance – 30.83%

magnetic moment β_N = 2.54

Epr spectra of few transition metal complexes

EPR spectrum of binuclear mixed valence oxovanadium (IV/V) complexes of general formula 𝑽_𝟐𝑶_𝟑L

• 50_𝑉 → Natural abundance = 0.25% magnetic moment β_N = 3.61 nuclear spin = 6
• 51_𝑉 → Natural abundance = 99.75% magnetic moment β_N = 5.83 nuclear spin = 7/2

Hence, splitting of the ESR pattern

by 2 V into (2*2*7/2)+1=15 lines.

• Steady state concentrations of free radicals are often too low for detection.

e.g. - no cyclohexyl radicals seen by ESR during free radical chlorination of cyclohexane.

reason :- C₆H₁^̇ ₁ + Cl₂ → C₆H₁₁Cl + Cl^̇ reaction is very fast ; [C₆H₁^̇ ₁] at steady state is very low.

• Solution :-

SPIN TRAPPING TECHNIQUE.

• Method :- To solution containing expected free radicals , a “spin trap” is added.
• SPIN TRAP :- A diamagnetic substance with which radicals R^̇ react readily and form spin adducts ( TR^̇ ).

T + R^̇ → TR^̇

• SPIN ADDUCT:- Also a free radical, less reactive than R^̇.

- comparatively higher and detectable steady state concentration.

• Examples of spin traps :-

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These are substances containing N=O functional group.

2-methyl-2-

nitrosopropane

nitrosodurene

Phenyl tert-butyl nitrone

Spin trapping

→ Example:- 1) 2-methyl-2-nitrosopropane + CH^̇₃ →

2) phenyl tert-butyl nitrone + C^̇₄H₉ →

(adduct 1)

(adduct 2)

ESR spectrum of adduct 1

• Characteristic 1:1:1 splitting due to β

nitrogen.

• Further splitting of each component peak into quartet by 3 γ protons in the ratio 1:3:3:1.

ESR spectrum of adduct 2

• Characteristic 1:1:1 splitting due to β nitrogen.
• Further splitting of each component peak into

doublet by the single γ proton in the ratio 1:1.

Shin et al. Bull. Korean Chem. Soc. 2024, 45, 835–862

• Useful in structure elucidation of radicals.
• Common substitutions:- a) deuterium (I = 1) in place of protium (I = ½).

b) 15_𝑁 (I = ½) in place of 14_𝑁 (I = 1).

• Examples:-

1)

• ESR spectrum of adduct of C𝐇^̇_𝟑 with 2- methyl-2-nitrosopropane.
• 1:1:1 splitting by nitrogen followed by

splitting of component peaks in ratio 1:3:3:1

by 3 protons.

• ESR spectrum of adduct of C𝐃^̇_𝟑 with 2- methyl-2-nitrosopropane.
• Splitting into triplet 1:1:1 by nitrogen

followed by splitting into septet of each

peak by 3 deuterium (I =1).

𝑎^𝑁 same for both ; 𝑎^𝐷

< 𝑎^𝐻

Isotopic substitution

2) Reduction of potassium nitroform in NaOH solution to elucidate structure of the radical formed:-

ESR spectrum when reaction carried out in 𝐇_𝟐O

• Main 1:2:3:2:1 splitting due to 2 14_𝑁 (I=1).

• Doublet splitting due to one proton (I=1/2).
• 𝑎^𝑁= 9.6 G, 𝑎^𝐻= 4.1 G.

ESR spectrum when reaction carried out in 𝐃_𝟐O

• Main 1:2:3:2:1 splitting due to 2 14_𝑁 (I=1).

• Triplet splitting 1:1:1 due to one D (I=1).
• 𝑎^𝑁= 9.6 G, 𝑎^𝐷= 0.6 G.

_𝐂̇

𝐇

[(

𝐍𝐎

𝟐

)

𝟐

]

𝐂

𝐃[(

𝐍𝐎

𝟐

)

𝟐

]

3) Structure determination of product of reaction of azide radicals with nitrosodurene

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Two nitrogens are equivalent (proved by labelling with N-15 and taking ESR data.

• NMR and ESR share same fundamental principles.
• Both are Magnetic Spin Resonance spectroscopies.
• Both probe the interaction of magnetic dipoles with an applied magnetic field and electromagnetic

radiation of appropriate wavelength.

Splitting of electronic spin states.

Splitting of nuclear spin states

Esr vs nmr

• Total local field including hyperfine splitting is given as :- 𝐵_𝑙𝑜𝑐 = 𝐵₀ + a. 𝑚_𝐼

( a = hyperfine splitting constant )

• Origin of hyperfine splitting :- 1) Dipole-dipole interaction:-
• electron in p orbital experiences this.
• anisotropic; averaged out by tumbling motion.
• observed for radicals trapped in solids.

2) Fermi-contact interaction:-

• valid when point dipole approximation fails for s-orbital electrons

due to its penetration into the nucleus.

• isotropic.

3) Polarization mechanism:-

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McCONNELL EQUATION:-

a = Q.ρ

Where a = hyperfine splitting constant

ρ = spin density

Q = 2.25 mT

INTERPRETATION OF ESR SPECTRA:-

Absorption

position

Intensity

Multiplet

structure

Width of lines

1. Absorption position:-
• Depends on “g” value ( dependent on environment of unpaired electron ).
• Almost same values for free radicals. So, not much useful information revealed regarding their structures.
• Significant for transition metal ions where spin-orbit coupling occurs.
• g values not as important as chemical shifts in NMR.

2. Intensity :-
• ∝ concentration of free radical or paramagnetic substance.
• ∝ number of unpaired electrons.

Hence, ESR suitable for detecting

amount of free radical present.

• ESR is sensitive :- 10⁻¹² moles of free radical can be detected.

Standard sample with known number of unpaired electrons and same line shape as the unknown sample used.

• Most widely used standard :- DPPH (1.53 * 10²¹ unpaired electrons/gram.
• Preferred internal reference :- Cr(III) trapped in ruby crystal clip cemented permanently to sample cell.

- strong absorption at g = 1.4.

• Intensity = area under ESR curve.

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3. Multiplet structure:-
• Fine structure :- n unpaired electronic spins → n equally spaced resonance lines in ESR spectrum.
• Hyperfine structure:- information about neighbouring magnetic nuclei coupling with unpaired electron

in free radical/paramagnetic species.

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4. Width of spectral lines:-
• Depends on relaxation time of spin state under study.
• Typical relaxation time ~ 10⁻⁷ s.
• From modified Heisenberg’s uncertainty equation :- δν = ½.∏. Δt , line width ~ 1MHz.
• Relaxation times can go up to ~ 10 MHz.

Much wider than NMR spectral line, whose normal width ~ 0.1 Hz.

WIDER LINES IN ESR SPECTRA: GOOD OR BAD???

Advantages:- Homogeneity of applied magnetic field is far less critical than that in NMR.

Disadvantages:-

• Lines become difficult to observe and measure than sharp lines.
• Overlapping of signals occurs.

LINE BROADENING:-

• increase in width of spectral lines.
• can be overcome by :- working at low temperatures and using low

concentrations of the sample.

WHY PREFER DERIVATIVE SPECTRUM OVER ABSORPTION SPECTRUM???

Results represented by first derivative spectrum more readily interpretable.

Reason:- 1) The point of absorption maximum difficult to measure accurately with a broad absorption

curve ; but greater precision with derivative curve.

- The no. of peaks in absorption curve – determined from maxima/minima of negative slopes

in derivative curve.

DOUBLE RESONANCE /DOUBLE IRRADIATION IN ESR SPECTROSCOPY

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Applications:

• 1. Useful for revealing desired physical and chemical information from spectra

masked due to broadening.

• Easy observation of nuclear couplings (hyperfine structures).
• Accurate measurements of hyperfine constants.
• Measurement of quadrupole constants in systems with spin number I ≥ 1.

→ Observation of spectrum at one frequency while simultaneously irradiating at another.

1. ENDOR ( Electron Nuclear Double Resonance):-
• A microwave frequency suitable for ESR and a radio frequency suitable for NSR are simultaneously

needed.

• Irradiation with intense microwave radiation to reach ESR saturation.
• Simultaneous sweeping of radio frequency to carry out NMR transition δ𝒎_𝑰= ±𝟏.
• Result :- partial desaturation of ESR transition (δ𝑚_𝑠= ±1)
• Observation of ENDOR signal in ESR spectrum.

ENDOR is special type of NMR where unpaired electron acts as detector.

• ENDOR SIGNAL:- ESR signal height as function of swept radio frequency.

2. ELDOR (Electron- Electron Double Resonance) :-
• Simultaneous irradiation of sample with two microwave frequencies.
• 1^st frequency :- used to observe ESR signal at some part of spectrum.
• 2^nd frequency :- swept through other parts of spectrum.
• ELDOR signal :- ESR signal as function of difference of two microwave frequencies used.

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Applications

:- 1. resolving overlapping multiradical spectra.

2. studying relaxation mechanism.
3. precise measurements of coupling constants of DPPH.