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© 2012, K.S. Suslick
Electron Paramagnetic Resonance (EPR) = Electron Spin Resonance (ESR)
I. Origins of EPR: Zeeman Interaction
II. Experimental considerations, Spectral presentation
III. Anisotropy and Spin-Orbit Coupling Components
IV. Hyperfine and Superhyperfine Splittings
V. Uses & ApplicationsA. Inorganic Spin DistributionB. d-orbital splittings & EX EnergiesC. Bioinorganic examplesD. Spin Labelling
© 2012, K.S. Suslick
Survey of Spectroscopic Techniquescm-1 108 107 105 104 103 102 10 1 0.1 0.01 0.001
thz
mag momentof nuclei
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© 2012, K.S. Suslick
E R
Paramagnetic
Most substances do not contain paramagnetic speciesand are hence EPR silent
DisadvantageFewer accessible systems
Advantages1) Easier to tell the source of EPR.
2) Introduction of “spin labels”
N
O
H2NOH
N
O
S S
O
O
+ Protein-SH
N
O
SS
Protein
© 2012, K.S. Suslick
EPR Pros & Cons
What EPR can tell us:
• What types of paramagnetic species are present
• What is the local structure/symmetry of these species
• What is the nature of the wavefunc0on containing the unpaired spin (i.e., where are the unpaired spins localized ).
• For organic radicals, sub-µM; for TM complexes, mM to 10 µM;300 µL volume. i.e., 10-1000 X more sensitive than NMR
Major disadvantages:
• Typically requires odd integer spins (i.e., S = 1/2, 3/2, 5/2, 7/2, etc…)
• Resolution is not as good as in NMR (broad features)
• Often requires very low temps for good resolution (10 K typical)
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© 2012, K.S. Suslick
The Spin Hamiltonian
“sp
in H
amilt
on
ian
”kinetic energy, e─ - nuclear attraction, e─ - e─
repulsion, nucl.-nucl. replusion, ligand field
Nuclear Zeeman (NMR)
Electronic Zeeman (EPR)
Zero Field Splitting (ZFS) from spin-orbit coupling of angular mom.
Hyperfine Coupling of e─ & nuclear moments (NMR & EPR)
© 2012, K.S. Suslick
1. An unpaired electron has a magnetic moment: µe→
Zeeman Interactions: Energy Splittings
2. In an applied magnetic field, H0, along the z directionclassically,
3. For one free electron:
B = Bohr magneton= 9.27×10−24 J/T
define: -eħ = ge
cf. EI = - mIħH0 (nucleus)
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© 2012, K.S. Suslick
Zeeman Interactions: Energy Splittings
B = Bohr magneton= 9.27×10−24 J/T
4. For one free electron, the selection rule:
∆ ms = ± 1 electric dipole forbidden, mag dipole allowed only.
5. Energy difference: gβ(+½)H - gβ(-½)H = gβH = h
© 2012, K.S. Suslick
Zeeman Interactions: Energy Splittings for 1 e-
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© 2012, K.S. Suslick
Zeeman Interactions: Energy Splittings
Microwave frequency is fixed by the generator (“Klystron”),so the magnetic field (H or B) is “scanned” until resonance found:
© 2012, K.S. Suslick
Zeeman Interactions: Energy Splittings
Microwave frequency is fixed by the generator (“Klystron”),so the magnetic field (H or B) is “scanned” until resonance found:
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© 2012, K.S. Suslick
The g-value
Ezee = - μe H0 = geemSH0
ge
In the case of a free electron inspace, the e- is the only sourceof magnetism in the sample:
When unpaired electron couples to
1) Empty orbital (e.g., d1), g < ge
2) Occupied orbital (e.g., d9), g > ge
Generally 1.3 < g < 9
In the case of an e- in a molecule, SOC (spin-orbit coupling constant ) adds or subtracts orbital angular momentum to that of free electronand we lump that into “gobs” or “g”:
Ezee = - (μe + aλ) H0
= gobsemSH0
© 2012, K.S. Suslick
• For most organic radicals, g ≈ ge
• For transition metals, large deviations from ge possible
• g can be measure to high accuracy (±0.0001)
• g is the “chemical shift” equivalent of EPR
• g depends on structure of radical, excitation energies, strengths of spin-orbit couplings
Note for later: g is anisotropic and not a scalar but a tensor.
)(
)(
)(
)( 48.71407145.0
gauss
GHz
T
GHz
HHH
hg
Energy of the Zeeman transition (and hence the “g-value”) is determined at a fixed microwave frequency with H0 being scanned. The “g-value”is a unique property of the molecule as a whole and independent of any electron – nuclear spin interactions.
The g-value
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© 2012, K.S. Suslick
What is the origin of g‐values different from 2.0?
Deviations from g = 2.0 due primarily to Spin‐Orbit Coupling. SOC constant, ζ, is metal‐ion dependent: can be small (150 cm‐1; Ti3+) or large (830 cm‐1; Cu2+).
An electron acquires orbital motion so to favorably experience the magnetic field of a nucleus, hence lowering its overall energy.
Specifically, an electron in an orbital (e.g., xy), can, via SOC, gain orbital angularmomentum via mixing with other orbital trajectories defined by rotationaloperators. Hence, an electron in xy can gain xz character via rotation about X, where such a rotation has a barrier, Δx.
For an electron that rotates into an empty orbital, the "current" created by the rotating electron leads to a magnetic field that opposes the applied magnetic fieldB0. This requires a larger applied field to achieve resonance, and hence a loweringof g.
For an electron that rotates into an occupied orbital, the sense of the current created by the rotating electron leads to a magnetic field that aligns with the applied magnetic field B0. This requires a smaller applied field to achieve resonance, and hence a raising of g.
© 2012, K.S. Suslick
What is the origin of g‐values different from 2.0?
For an electron that rotates into an empty orbital, the "current" created by the rotating electron leads to a magnetic field that opposes the applied magnetic field B0. This requires a larger applied field to achieve resonance, and hence alowering of g.
Mo(CN)8 3‐
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© 2012, K.S. Suslick
EPR Spectra
Problems in observing EPR transitions:
H0
So, one must be careful to avoid “power saturation”: i.e., driving the populations into exactly equal fractions by driving transitions faster than spin relaxationand therefore losing all net change in magnetization.
© 2012, K.S. Suslick
EPR Spectra
Problems in observing EPR transitions:
2. Zeeman transitions are magnetic dipole coupled only:ms = ±1 therefore only small transition probability.
3. Transitions are often broad relative to energy of transition.Line broadening from site inhomogeneity,
leads to Gaussian shapes.
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© 2012, K.S. Suslick
EPR Spectra
Solution to observing EPR transitions:
To enhance S/N and locate broad signals, EPR spectrometers use modulation detection 1st Derivative spectra: Signal Ampl / mag field
Instrumentally, the mag field is modulated using coils aligned with mag field (Helmholtz coils) to oscillate H0 a bit (0.01 to 20 G) at ~100 kHz. Detection is then phase locked to that frequency.
© 2012, K.S. Suslick
EPR Spectra typically given as 1st Derivative
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© 2012, K.S. Suslick
EPR Spectra typically given as 1st Derivative
Absorption Derivative
increasing g decreasing g
© 2012, K.S. Suslick
EPR QM
“sp
in H
amilt
on
ian
”
kinetic energy, e─ - nuclear attraction, e─ - e─
repulsion, nucl.-nucl. replusion, ligand field
Nuclear Zeeman (NMR)
Electronic Zeeman (EPR)
Zero Field Splitting (ZFS) from spin-orbit coupling of angular mom.
Hyperfine Coupling of e─ & nuclear moments (NMR & EPR)
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© 2012, K.S. Suslick
g-value Anisotropy
© 2012, K.S. Suslick
Anisotropic Interactions always complicate things(solids, frozen solutions, membranes etc.)
• with the applied field
• with surrounding magnetic nuclei
• among electron spins (if more than one, obviously)
Recall: Description of physical quantities
Isotropic: scalars Directional: vectors Interactions between vectorial quantities: tensors
g-value Anisotropy
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© 2012, K.S. Suslick
g is Anisotropic and Varies with Direction
''' xxg ''' yxg''' zxg
''' xyg ''' yyg ''' zyg
''' xzg ''' yzg''' zzg
where jiij gg ''
Diagonalisexxg
yyg
zzg
0 0
0 0
0 0
xg
yg
zg
Principal values
Anisotropy:
Asymmetry:
isozz ggg
ggg xxzz
)(
© 2012, K.S. Suslick
For an arbitrary orientation of a crystal in a magnetic field
2/122
222
222
)cos
sinsin
cossin(
zz
yy
xx
g
g
gg
In spherical coordinates:
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© 2012, K.S. Suslick
Electronic Zeeman Hamiltonian (g is actually a tensor)
g-value Anisotropy
© 2012, K.S. Suslick
Uses & Applications of EPR
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© 2012, K.S. Suslick
In a frozen solution, an ensemble of all possible orientations of the metal site with respect to mag field vector.
A “powder spectrum” is then observed:
2g
3g
Powder absorbancespectrum
1st derivative
1g
rhombic Powder absorbancespectrum
1st derivative
axial(tetragonal)
g-value Anisotropy
© 2012, K.S. Suslick
yyxx ggg
Often the g tensor has axial symmetry
Then:zzgg
║
┴
2/12222 )cossin( ggg ║┴
And:
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© 2012, K.S. Suslick
Axial g-value Anisotropy
Absorption Derivative
Axial hyperfine (later): often a|| >> a┴ ~ 0
© 2012, K.S. Suslick
Axial g-value Anisotropy
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© 2012, K.S. Suslick
Zero Field Splitting
Zero Field Splitting (also a tensor)
© 2012, K.S. Suslick
Zero Field Splitting (ZFS) vs. Zeeman Splitting
Kramer’sDoublets
Kramer’s Doublets: Effective half-integer spin states (S = 5/2, 3/2, 1/2, etc.) that are split under an applied magnetic field to the ±Ms microstates (Zeeman Splitting).
Example: A 4T1 state is split under axial zero-field splitting into three sets of Kramer’s doublets (S = 5/2, 3/2, and 1/2), which are separated by Zeeman splitting to the ±3/2 and ±1/2 microstates.
axial rhombicityZeeman
ZeemanSplittings
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© 2012, K.S. Suslick
Zero Field Splitting
© 2012, K.S. Suslick
ZFS from Ligand Field Distortions
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Uses & Applications of EPR
FeIII, d5
© 2012, K.S. Suslick
Allowed Transitions for N nuclei with spins Ii
For k sets of equivalent nucleiwith ni nuclei per setwith Ii nuclear spin per nuclei,
Total number of Hyperfine lines:
“Hyperfine” (HF) and “Superhyperfine” (SHF) are both due tocoupling between electron/paramagnetic spin and nuclear spins:
Hyperfine refers to interaction of a metal nucleuswith “its own” unpaired electron spin density.
Superhyperfine refers to interaction of unpaired electron spin densitywith ligand nuclei.
k
kiihf InN
1
)12(
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© 2012, K.S. Suslick
Hyperfine Interactions
= interaction of paramagnetic spins with nuclear spins
ElectronicZeeman
Splittings
Hyperfine (e- spin-nuclear spin)Splittings
For an isotropic coupling between electron &
nucleus I = ½
© 2012, K.S. Suslick
S S
SS
S
S
I
I
S I
I
aiso/4
aiso/4
aiso/4
aiso/4
Isotropic Coupling between e- & nucleus I = ½
I
I
Recall:
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© 2012, K.S. Suslick
ElectronicZeeman
Splittings
Hyperfine (e- spin-nuclear spin)Splittings
Hyperfine Interactions
a = hyperfinecouplingconstant
© 2012, K.S. Suslick
Hyperfine with More than One Nucleus
SISI
Sb Sb
1 spin ½ nucleus
SI1I2 SI1I2
2 eq. spin ½ nuclei
SI1I2 SI1I2
SI1I2 SI1I2
SI1I2 SI1I2
isoISI amm )(
SI1I2I3 SI1I2I3
SI1I2I3 SI1I2I3
SI1I2I3 SI1I2I3
SI1I2I3 SI1I2I3
SI1I2I3 SI1I2I3
SI1I2I3 SI1I2I3
SI1I2I3 SI1I2I3
SI1I2I3 SI1I2I3
3 eq. spin ½ nuclei
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© 2012, K.S. Suslick
Allowed Transitions for N nuclei with spins Ii
k
kiihf InN
1
)12(
For k sets of equivalent nucleiwith ni nuclei per setwith Ii nuclear spin per nuclei,
Total number of Hyperfine lines:
e.g., benzene radical anion
1 set of 6 H (I=1/2)
Nhf = 2*6*½ +1 = 7 lines
© 2012, K.S. Suslick
Allowed Transitions for N nuclei with spins Ii
k
kiihf InN
1
)12(
For k sets of equivalent nucleiwith ni nuclei per setwith Ii nuclear spin per nuclei,
Total number of Hyperfine lines:
e.g., [BH3●]— 1set of 3 H (I=1/2)and 1 set of 1 11B (I=3/2)
Nhf = (2*3*½ +1)*(2*1*3/2+1) = 16 lines
EPR spectrum of [BH3●]— in solution.
The stick diagram marks the resonancesfor the 11B(I=3/2) and the three protons.
(The remaining very weak resonances aredue to the radicals containing 10B (I=3).)
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© 2012, K.S. Suslick
Oxidation of a Chromium(III) porphyrin to CrVPorph(isotropic in solution)
S(Cr5+) = ½ I(14N) = 1
I(52Cr) = 0 (84% abundant)
Nhf = (2*4*1+1) = 9 lines
but also
I(53Cr) = 3/2 (9.6% abundant) (2*1*3/2+1) = 4 sets of 9 lines, weak
Allowed Transitions for N nuclei with spins Ii
© 2012, K.S. Suslick
Two Spin Nuclei: Li+(13CO2─)
I(13C) = ½, I(7Li) = 3/2
12C
A(13C)>>A(7Li): Spin density mainly on 13C
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© 2012, K.S. Suslick
Origins of Hyperfine Coupling
© 2012, K.S. Suslick
But Hyperfine can (is) also anisotropic
dipolariso AAA
Fermi contact Interaction Density of unpaired electronat nucleus (s-orbital characterin semi-occupied MO (SOMO).
ISOTROPIC,“Through-bond”
Dipolar Interaction p,d,f orbital character
in SOMO.Averages out in soln.
ANISOTROPIC“Through Space”
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© 2012, K.S. Suslick
A Model Cu2+ systemAxial symmetry
I(65Cu) = 3/2 d9, S=1/2
gg║ ┴
Axial hyperfine: often a|| >> a┴ ~ 0
© 2012, K.S. Suslick
Uses & Applications of EPR
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© 2012, K.S. Suslick
HFS for Identification of Metal
© 2012, K.S. Suslick
Uses & Applications of EPR: Metal Identification
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© 2012, K.S. Suslick
HFS for Identification of Metal
© 2012, K.S. Suslick
HFS for Identification of Metal
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© 2012, K.S. Suslick
HFS for Identification of Metal
© 2012, K.S. Suslick
I = 3/2
HFS for Identification of Metal
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© 2012, K.S. Suslick
HFS for Identification of Metal
© 2012, K.S. Suslick
HFS for Identification of Metal
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© 2012, K.S. Suslick
Identification of Ligands: “Superhyperfine”
© 2012, K.S. Suslick
Identification of Ligands
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© 2012, K.S. Suslick
Transition Metal EPR
• Complicated by the fact that transition metal systems might have several unpaired electrons and several approximately degenerate orbitals
• 3d elements important: only moderate spin-orbit coupling
• Ability to distinguish between high spin and low spin complexes (in ligand fields): coordination number and geometry accessible via EPR
• Difficult to observe EPR on systems w/ integer S systems
• Most common:
Ti3+(d1)S=1/2
Fe3+(d5) S=5/2 (high spin) often high anisotropy, S=1/2 (low spin)
Cu2+(d9) S=1/2 I=3/2 for 63Cu and 65Cu
Co2+(d7) S= 3/2 (high spin) S=1/2 (low spin)
© 2012, K.S. Suslick
ZFS in EPR
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ZFS in EPR
© 2012, K.S. Suslick
Uses & Applications of EPR: Heme Proteins
Easy to tell L.S. Fe(III) from H.S. Fe(III)
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powder spectrum for a rhombic g-tensor
xxg yygzzg
Low spin Fe3+ in cytochrome P450
Powder spectrum
1st derivative s3
© 2012, K.S. Suslick
Uses & Applications of EPR
Slide 63
s3 There are many Cytochrome P450 enzymes, and they catalyse oxidation of various organic substrates (e.g. medicines) in living organisms. At the centre of these enzymes is a haem centre (iron porphyrin), bonded to the protein through an Fe-S bond to a cysteine side-chain. In the resting state of the enzyme, the iron centre is in the +III oxidation state. Successive one-electron reduction, binding of dioxygen, one-electron reduction, addition of two protons, and loss of water, leads to formal transfer of an oxygen atom to the iron atom. The resulting key intermediate, referred to as "Compound I", formallyhas an iron atom in the +V oxidation state (in fact, part of this charge is delocalised on the porphyrin ring and the oxygen atom, so that the iron is better described as being in the +IV or even +III oxidation state).stuart, 2/22/2006
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© 2012, K.S. Suslick
Uses & Applications of EPR
Blumberg and Peisach’s plot of a large family of low spin hemes showing howdata cluster into five domains. The first four (C, B, H, O) have similar rhombicdistorHons but increasing axial fieldstrength. These assigned with histidine (axial 5th site) but 6th ligand is methionineC, neutral histidine H, anionic histidine B, and oxide O. The fifth family (P) are the P450 heme enzymes, with cysteine andwater as the axial ligands.
The Blumberg analysis tends to work best when V/Δ is quite large. These are knownas “Truth Tables”.
© 2012, K.S. Suslick
Uses & Applications of EPR
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© 2012, K.S. Suslick
Uses & Applications of EPR
© 2012, K.S. Suslick
Uses & Applications of EPR
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© 2012, K.S. Suslick
Uses & Applications of EPR
© 2012, K.S. Suslick
Uses & Applications of EPR
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© 2012, K.S. Suslick
Uses & Applications of EPRg values
© 2012, K.S. Suslick
Uses & Applications of EPR
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© 2012, K.S. Suslick
Uses & Applications of EPR
© 2012, K.S. Suslick
Uses & Applications of EPR
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© 2012, K.S. Suslick
Uses & Applications of EPR
Each nucleus experiences the hyperfine fieldof only one electron.
Each (spin 1/2) nucleus then gives rise to two resonanceconditions depending on whether the electron hyperfine
field opposes or augments the applied field.
A strong radiofrequency (NMR) field induces NMR transitions which are observed as a change in the
intensity of an electron resonance condition.
Electron Nuclear Double Resonance (ENDOR)
© 2012, K.S. Suslick
Uses & Applications of EPR
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© 2012, K.S. Suslick
Uses & Applications of EPR
© 2012, K.S. Suslick
Uses & Applications of EPR
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© 2012, K.S. Suslick
ENDOR
© 2012, K.S. Suslick
aE Is 4
1
2
1
2
12
aE Is 4
1
2
1
2
13
aE Is 4
1
2
1
2
11
aE Is 4
1
2
1
2
14
Recall:
1
2
3
4
Thermal Equil.
1
1
11
IS|
IS|
IS|
IS|
EPR 1-3saturated.
1
1
11
sat
The ENDOR experiment (simplified)
aI 2
1
NMR transition(3-4) at
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© 2012, K.S. Suslick
ENDOR
Relative populations are given by Boltzmann at thermal equilibrium (I<<S, hence populations of 1 & 2, 3 & 4 assumed identical)
Irradiate 1-3 transition (saturate at high power): that will give same populations in 1 & 3.
Irradiate system with RF (NMR) and sweep frequency while continually saturating EPR transition; observe the intensity of its absorption
When RF frequency matches |I-a/2|, transition 3-4 will be induced, restoring some population difference between levels 1&3
More EPR absorption now possible: that is ENDOR signal
Equally, when RF frequency matches |I + a/2| (1-4 transition), this time a pumping from 1-4 occurs (as 4 has the higher population) and a population difference between 1&3 is again achieved and EPR transition enhance – the second ENDOR signal
In practice, need to consider spin lattice relaxation processes
© 2012, K.S. Suslick
Toluene Solvent
Hyperfinecouplings not
resolved
EPR
1H ENDOR
Two wide doublets which give the hyperfine couplings to protons in the C8H8 and C5H5 rings directly.
Orientation Selection
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© 2012, K.S. Suslick
Electron Nuclear Double Resonance
© 2012, K.S. Suslick
Tetracene cations in sulphuric acid
EPR spectrum
ENDOR 1H (3 types of protons)