principles of esr

Electron Spin Resonance Electron Spin Resonance SpectroscopySpectroscopy

V.Santhanam

Department of chemistry

SCSVMV

Enathur

ESR SpectroscopyESR 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 What compounds can you analyze?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 TransitionsEnergy 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 What causes the energy levels? 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 (TSpin-Lattice relaxation (T11))• 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 (TSpin – Spin relaxation (T22))• Excess energy given to neighbouring

electron.

• Independent of temperature

• Has two components

Dipolar interaction

Direct interaction

Dipolar interactionDipolar 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 lineE = mBB0MS

g = h ∆ν / mBB0MS

Proportionality FactorProportionality 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 SIGNALPOSITION 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 usedReference 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 FactorProportionality FactorMoO(SCN)5

2- 1.935

VO(acac)2 1.968

e- 2.0023

CH3 2.0026

C14H10 (anthracene) cation

2.0028

C14H10 (anthracene) anion

2.0029

Cu(acac)2 2.13

Hyperfine InteractionsHyperfine 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 nucleiE = gmBB0MS + aMsmI

a = hyperfine coupling constant

mI = nuclear spin quantum number

Hyperfine InteractionsHyperfine Interactions

Interaction with a single nucleus of spin ½

Z E R O F IE L D

F I E L D B Z

m S = + 1 /2

m S = - 1 /2

m I

- ( 1 /2 )

+ ( 1 /2 )

- ( 1 /2 )

+ ( 1 /2 )

e

N

N

2

1

Which nuclei will interact?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, …

Hyperfine InteractionsHyperfine Interactions• Coupling patterns same as in NMR• More common to see coupling to nuclei with

spins greater than ½• The number of lines:

2NI + 1N = number of equivalent nucleiI = spin

• Only determines the number of lines--not the intensities

Hyperfine InteractionsHyperfine 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

Relative Intensities for Relative Intensities for II = ½ = 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 Relative Intensities for II = ½ = ½

Relative Intensities for Relative Intensities for II = 1 = 1N 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 Relative Intensities for II = 1 = 1

Hyperfine InteractionsHyperfine 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

Hyperfine InteractionsHyperfine Interactions

EPR spectrum of vanadyl acetylacetonate

Hyperfine InteractionsHyperfine 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

Hyperfine InteractionsHyperfine Interactions

EPR spectrum of benzene radical anion

Hyperfine InteractionsHyperfine 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

Hyperfine InteractionsHyperfine InteractionsPyrazine anionElectron delocalized over ringExhibits coupling to two equivalent N

(I = 1)2NI + 1 = 2(2)(1) + 1 = 5Then couples to four equivalent H (I = ½)2NI + 1 = 2(4)(1/2) + 1 = 5So 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

Hyperfine InteractionsHyperfine Interactions

EPR spectrum of pyrazine radical anion

Hyperfine splitting and anisotropyHyperfine 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 systemsAnisotropic 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 spectraFine structure of esr spectra• Zero Field Splitting• Kramer’s theorem• Effective spin state• Break down of selection rule

ESR spectra of metal complexesESR 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

Specific examplesSpecific examples