Physical Methods in Inorganic Chemistry Magnetic Resonance

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Physical Methods in Inorganic ChemistryMagnetic
Resonance
Lecture Course Outline Lecture 1 A quick
reminder A few trends in Inorganic NMR A
little more on Chemical Exchange Essential NMR
Methods Spin Decoupling Spin Relaxation
Measurements (again and more) Lecture 2 NMR
Methods continued 2D and others Correlated
Spectroscopy (COSY) Nuclear Overhauser
(NOE) Magic Angle Spinning (MAS) Lecture 3
Electron Paramagnetic Resonance The why and
when of EPR in Inorganic Chemistry EPR
methods (ENDOR, DEER)
Physical Methods Magnetic Resonance
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Physical Methods in Inorganic ChemistryMagnetic
Resonance
Literature H. Friebolin One and Two Dimensional
NMR Spectroscopy H. Günther NMR Spectroscopy P.
J. Hore Nuclear Magnetic Resonance (primer) A. K.
Brisdon Inorganic Spectroscopic Methods
(primer) C. P. Slichter Principles of Magnetic
Resonance R. Freeman Spin Choreography
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Website and e-mail http//timmel.chem.ox.ac.uk t
immel_at_physchem.ox.ac.uk
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Magnetic Resonance
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Selected NMR properties of some elements
Gyromagnetic ratio (107 rad T-1s-1)
26.75 8.58 6.72 1.93 -2.71 29.18 6.98 -5.31 10.84
7.05 6.35 5.12 -0.85 -1.25 -10.02 6.43 -8.50 1.12
0.50 5.80 4.82
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Trends in Chemical Shifts
Remember The diamagnetic shielding generally
becomes smaller as the electron density at the
nucleus decreases.
Thus electronegative substituents, positive
charge or increase in oxidation state usually
result in decreased shielding and increased shift.
Physical Methods Magnetic Resonance
Opposite effects may be observed for transition
metals (ligand effects).
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Effect of Charge, Substituents and Oxidation
State
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The effect of coordination on the chemical shift
of a transition metal

• Remember
• The paramagnetic shielding contribution sp 1/DE
  
• 2. paramagnetic currents AUGMENT the magnetic
  field (sp is negative, hence a DESHIELDING
  parameter!)

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Typically, shifts follow the spectrochemical
series strong field ligands give small or
negative chemical shifts whilst halogens give
larger chemical shifts.
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Chemical Exchange
Remember
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• Examples of Fluxional inorganic systems.
• Axial-equatorial exchange in trigonal
  bipyramidal systems
• (PF5, SF4, PF4NMe2 , Fe(CO)5)
• Bridging/axial exchange in carbonyls.
• Bridging terminal exchange in boranes (B2H6
  etc.)borohydrides (Al(BH4)3)
• Ring-whizzing in ?1-cyclopentadienides (Cu(PMe3)(
  ?1-C5H5)
• Interchange of ring bonding modes in compounds
  with mixed heptacity
• ( e.g. (?1-C5H5)2(?5C5H5)2Ti
  (?4-C6H6)(?6-C5H5)Os

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17O spectrum of Co4(CO)12
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The 31P spectrum of PF4N(Me)2
All 19F equivalent at high Temperature
Physical Methods Magnetic Resonance
I(31P) (19F) 1/2
19Fe and 19Fea not equivalent at low Temperature
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13CH spectrum of (CH3)3C 6Li4
Recall multiplets 2nI 1
I(6Li) 1
n 4
Jav (5.4 Hz x 3 0)/4 4.1 Hz
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J(13C-6Li) 5.4 Hz
n 3
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NMR Acronyms
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Methods
Continuous wave
E
hn
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B
B
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Spin Lattice Relaxation and The
Inversion-Recovery Experiment
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Inversion Recovery Method
p/2
t1
t2
t3
t4
z
z
z
z
y
y
y
y
x
x
x
x
NMR Signal I(t)
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Spin Spin Relaxation and theSpin Echo Experiment
echo

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What is the effect of relaxation on the echo
amplitude?
Spin spin Relaxation
random magnetic fields destroy phase coherence
and are not refocused by p pulse
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NMR Echo of each signal
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Echo Trains
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The Method of Spin Decoupling
FACT SpinSpin Coupling yields important
information but NMR data interpretation
complicated by line splittings.
A SOLUTION simplify spectra by removing some
(chosen) splittings and learn about which nuclei
couple to which.
HOW apply a second Radiofrequency source (S2)
with strength B2 in addition to transmitter S1
used for detection of spectrum (a so-called
double resonance experiment). S2 is positioned at
the resonance of a particular nucleus.
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RESULT decoupled spectra are less crowded and
have much higher sensitivity as all available NMR
intensity concentrated into single line (and
Nuclear Overhauser).
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The Origin of the Spin Decoupling Effect
I(X) I(A) 1/2
A X
J
Irradiation of X at its resonance frequency
induces rapid transitions from X( ) to X( ) and
vice versa. A sees a single, averaged field.
nA
nX
X( ) X( )
A( ) A( )
B2 of same order as 2pJAX nX should be
sufficiently far away from nA
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Notation AX
nA
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The Method of Spin Decoupling
FeFa
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FaFe
I(A) I(X) 0
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31P(CH3CH2O)3
irrad
31P(CH3CH2O)3
31P(CH3CH2O)3
I(31P)1/2
irrad
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31P(CH3CH2O)3
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Recall Exercise
B 1.41T
Electron
Can we transfer this polarisation?
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1H
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The Nuclear Overhauser Effect
1) Enhancement of Sensitivity
ie, the heteronuclear (13C H) Nuclear
Overhauser Effect
g(1H) 26.75 107 rad T-1 s-1 g(13C) 6.72 107
rad T-1 s-1
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2) Information about proximity of two nuclei (ie,
protons)
3) Dependent on Cross Relaxation between
different spins. Prerequisite for this cross
relaxation experiment is that the spin lattice
relaxation of the nuclei is dominated by
dipole-dipole interaction with the other nuclear
spins.
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The origin of the Nuclear Overhauser Effect
Result saturated proton transitions, 13C
population difference increased 3-fold
Irradiate proton resonances
2
1
0
13C
H
sat
1
3
4
1
2
4
H
sat
13C
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4
3
Boltzmann
Protons saturated
Cross Relaxation
Takes spins from top to bottom level, competition
with 13C relaxation (restoring Boltzmann in 13C
population)
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The maximum attainable enhancement (the
fractional increase in intensity)
hmax 1/2 gI/gS
where I is the saturated spin and S is the
observed spin.
Physical Methods Magnetic Resonance

• Maximum effect occurs when there is no leakage
  as a result of relaxation mechanisms other than
  the dipole-dipole interaction (a through space
  interaction!).
• For homonuclear systems, maximum enhancement is
  50.
• Remember that 15N and 29Si have negative g.

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Selective Nuclear Overhauser enhancements
g
a
d
b
Difference Spectrum
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d
g
a
b
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29SiH(Ph)3
gSi - 5.31 107 rad T-1s-1
Magnitude 1hmax 11/2 gI/gS -1.5
gH 26.75 107 rad T-1s-1
29Si1H
Proton Decoupled
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Coupled
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Principles of 2-Dimensional NMR
Father of 2D NMR Jeener, Belgium Main
Developers RR Ernst (Switzerland), R Freeman
(UK, Oxford)
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What we know from FT NMR
p/2
FT
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2D NMR is a domain of FT and pulsed spectroscopy
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Principles of 2-Dimensional NMR
The time-intervals of 2D NMR
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A 2-Dimensional Experiment
evolution
Series of one-dimensional NMR spectra must be
recorded
t1
evolution
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t1
evolution
t1
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Amplitude Modulation
Phase Modulation
t1
t1
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Fourier transformation of FID signal, S(t1, t2)
must be performed to obtain 2D spectrum as
function of two frequency variables S(F1, F2)
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Spin-spin coupling was active during t1, hence F1
contains coupling constant
Larmor precession active during t2, hence F2
contains chemical shift
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What happens during the pulse sequences?
Pulse Sequence
?
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What happens during the second p/2x Pulse?
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Pulse Sequence
t2
?
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A Simple 2D NMR Spectrum results
F2
F1
W
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W
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Correlated Spectroscopy (COSY)
Pulse Sequence
p/2x
p/2x
Aim To discover spin-spin couplings in a
molecule. Answer Which resonance belongs to
which nucleus?
t2
t1
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Schematic COSY spectrum of an AX system
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Use of COSY to assign 11B NMR of B10H14.
(no couplings via H-bridges)
2
2
2
4
a
34 12 5678 910
d
b
c
a 2B coupled to all kinds of B 3,4
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b 4B coupled to 2 kinds of B 5,6,7,8
c 2B coupled to 1 kind of B 9,10
d 2B coupled to 2 kinds of B 1,2
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2D-Nuclear Overhauser Spectroscopy
D
I S
WI
WS
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And the resulting spectrum
D
I S
WI
WS
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Cross Peaks tell us about interacting spins.
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2D NOESY vs 1D NMR
69 amino acids, M 7688
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2 D NOESY Why?

• Advantages wrt 1D 1H1H NOE
• Simplification of crowded spectra
• No need for selective excitation of individual
  resonances
• Higher efficiency

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NMR in Solids

• Problems
• Through Space dipolar coupling not averaged out
  (broadened spectra)
• Hence, long spin lattice relaxation times T1
  (lack of modulation of dipolar coupling) and
  therefore restriction of pulse repetition rate,
  consequently, poor S/N
• Fast spin-spin relaxation times T2 (line
  broadening)
• Chemical Shift anisotropy not averaged out (line
  broadening)

Distance dependent information on spin
separations!
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Often broad, structureless resonance
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Temperature dependence of line width
Proton resonance line
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Solid complex adduct
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The Dipolar Coupling-Through Space Coupling
S
N
N
S
N
N
S
S
attraction
repulsion
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Anisotropic quantity
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In a single crystal, this is simple
Recall
D
A X
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KAX splitting in spectrum of X caused by dipolar
coupling to A
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Magic Angle Spinning
0 for q 54.7o
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At this angle all dipolar interactions disappear!
Recall here that the resonance frequency of a
given nucleus X coupled to a nucleus A is
determined by the total field it experiences in
z-direction, ie, B0 BAmz where BAmz is the
dipolar field generated by A on X.
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But what about a powder?

• Every molecule AX has a unique q but different
  molecules
• have different q. We need a trick.

54.7o
54.7o
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A powder sample is mounted for magic angle
spinning and gives the internuclear vectors an
average orientation at the spinning angle.
Also removes chemical shift anisotropy (also
follows the (3cos2q-1) law).
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How fast can you spin?- Or the relevance of the
spinning speed.
Assume Static line width of resonance to be
studied (ie, undesired interaction) is f Hz then
spinning speed must exceed f Hz if all broadening
interaction are to be nullified. Spinning speeds
of up to 35 kHz possible.
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(Ph)331PO
sper
spar
Typical spectrum of a system with axial chemical
shift anisotropy.
static
1.9kHz
At low spinning rates, observation of side bands
(info about principal components of shielding
tensor).
3.8kHz
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At high spinning rate we see a single resonance
at isotropic chemical shift.
siso
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CP-MAS 15N spectrum of (NH4)NO3 CPMAS
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The CP(Cross polarisation)-MAS (Magic Angle
Spinning) 15N spectrum of NH4NO3 shows two
interesting effects 1) the bigger chemical
shift anisotropy for NO3- as compared with
NH4 2) the greater intensity for NH4 due to
magnetisation transfer from 1H.
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2Ca(CH3CO2)2.H2O
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Electron Paramagnetic Resonance (EPR)
Electron Spin Resonance (ESR)
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EPR is developing fast
because its APPLICATIONS so demand
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E R samples
P
Paramagnetic
Most substances do not contain paramagnetic
species and are hence EPR silent

• Advantage
• Easier to interpret
• Introduction of Spin Spies

Disadvantage Fewer accessible systems
a)
b)
O
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S
S
N
O
O
Protein-SH
S
S
Protein
N
O
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Applications of EPRStudy of Electron Transfer
Processes
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Applications of EPRStudy of N_at_C60 (and
others)Quantum Computing
Phase transition temp 260K
4S3/2
(14N) 1
FT-EPR
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K.P. Dinse
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Local StructureENDOR/ESEEM in proteins
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Applications of EPRLong range structureUse of
Spin LabelsLight Harvesting complexes
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Energy Splittings and Selection Rule
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The g-value
The g-value is a unique property of the molecule
as a whole and independent of any electron
nuclear hyperfine interactions.
E mSgemBB0
E mSgmBB0
SO coupling (SO constant l) leads to derivation
of g from that of free electron
ge 2.00232
In case the electron is the only source of
magnetism in the sample
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When unpaired electron couples to
1) Empty orbital (e.g., d1), gltge
2) Occupied orbital (e.g., d9), ggtge
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• 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 of NMR

Physical Methods Magnetic Resonance
g depends on structure of radical, excitation
energies, strengths of spin-orbit couplings
Note later, we will discuss that g is
anisotropic and not actually a scalar but a
tensor.
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Isotropic Coupling between an electron and a
nuclear spin 1/2
Hyperfine Coupling
S in field
wS
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More than one nucleus
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Allowed Transitions for N nuclei with spins Ik
N nuclei couple to S
Total Number of states
Total number of allowed transitions
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Frequencies of allowed transitions
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The EPR signal is typically in the first
derivative form
Employ modulation technique
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EPR of a Simple Isotropic C-centred radical
1mT
e
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Another isotropic system in solution BH3-.
EPR spectrum of BH3? in solution. The stick
diagram marks the resonances for the 11B(I3/2)
and the three protons. The remaining weak
resonances are due to the radicals containing
10B(I3).
Physical Methods Magnetic Resonance
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Oxidation of a Chromium (III) porphyrine
derivative (still, isotropic in solution)
S(Cr5) 1/2 I(14N) 1 I(53Cr) 3/2 (9.6
abundant)

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But nothing is ever that simple
Anisotropic Interactions (of significance in
solids, frozen solutions, membranes etc.)

• with the applied field
• with surrounding magnetic nuclei
• between electron spins (if more than one,
  obviously)

Physical Methods Magnetic Resonance
Description of physical quantities
Recall

• Isotropic scalars
• Directional vectors
• Interactions between vectorial quantities
  tensors

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g is anisotropic and varies with direction
0
0
Diagonalise
0
0
0
0
where
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For an arbitrary orientation of a crystal in a
magnetic field
In spherical coordinates
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And the resulting powder spectrum for a rhombic
g-tensor
Low spin Fe3 in cytochrome P450
Powder spectrum
1st derivative
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Often the g tensor has axial symmetry
Then

-
And

-
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ESR spectrum of a simple d1 system

-
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But things are not that easy
The hyperfine couplings can also be anisotropic
(and often are!)
Recall Fermi contact Interaction (discussion
of J) Density of unpaired electron at nucleus
(s-orbital character in SOMO) ISOTROPIC
Recall Dipolar Interaction, D p,d,f orbital
character in SOMO Averages out in
solution ANISOTROPIC
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A Model Cu2 system
Axial symmetry
I(65Cu) 3/2
d9, S1/2
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Li(13CO2-)
I(13C) ½, I(7Li) 3/2
12C
Physical Methods Magnetic Resonance
A(13C)gtgtA(7Li) Spin density mainly on 13C
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Transition Metal EPR

• Complicated by the fact that transition metal
  systems might have several unpaired electrons and
  several approximately degenerate orbitals
• 3d elements important as 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 with integer S

Physical Methods Magnetic Resonance
Systems
Ti3(d1)S1/2
Fe3(d5) S5/2 (high spin) often high anisotropy,
S1/2 (low spin)
Cu2(d9) S1/2 I3/2 for 63Cu and 65Cu
Co2(d7) S 3/2 (high spin) S1/2 (low spin)
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Multiple Resonance Techniques
EPR spectrum of the phenalenyl radical
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Physical Methods Magnetic Resonance
The problems of resolving the hyperfine lines
may be linked to that of a man with several
telephones on his desk all of which ring at the
same time. If he tries to answer them all, he
hears a jumble of conversations as all callers
speak to him at once. Of course his callers have
no problem they only hear one voice.
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This is analogous to recognising
that each nucleus experiences the hyperfine
field of only one electron. Each (spin-1/2)
nucleus then gives rise to two resonance
conditions depending on whether the electron
hyperfine field opposes or augments the applied
field.
Physical Methods Magnetic Resonance
How?
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)
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Electron Nuclear Double Resonance
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Isotropic Coupling between an electron and a
nuclear spin 1/2
Recall
wS
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The ENDOR experiment (simplified)
Recall
EPR 1-3 saturated.
4
3
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2
1
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Previous overhead

• Relative populations are given by Boltzmann at
  thermal equilibrium (wIltltwS, hence populations of
  1 2, 3 4 assumed identical)
• Irradiate 1-3 transition (saturate at high power)
  same populations in 13 now
• Irradiate system with RF (NMR) and sweep
  frequency whilst continually saturating EPR
  transition observe the intensity of its
  absorption
• When RF frequency matches wI-a/2, transition
  3-4 will be induced, restoring some population
  difference between levels 13
• More EPR absorption now possible this is an
  ENDOR signal
• Equally, when RF frequency matches wI a/2
  (1-4 transition), this time a pumping from 1-4
  occurs (as 4 has the higher population) and a
  population difference between 13 is again
  achieved and EPR transition enhance the second
  ENDOR signal
• In practice, need to consider spin lattice
  relaxation processes

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Tetracene cations in sulphuric acid
EPR spectrum
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ENDOR
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Orientation Selection
EPR
Hyperfine couplings not resolved
1H ENDOR
Toluene Solvent
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Two wide doublets which give the hyperfine
couplings to protons in the C8H8 and C5H5 rings
directly. Repeat for parallel components and find
spin densities.