Physical Methods in Inorganic Chemistry
Magnetic Resonance
Physical Methods – Magnetic 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
Physical Methods in Inorganic
Chemistry
Magnetic Resonance
Literature
H. Friebolin
H. Günther
P. J. Hore
A. K. Brisdon
C. P. Slichter
R. Freeman
One and Two Dimensional NMR Spectroscopy
NMR Spectroscopy
Nuclear Magnetic Resonance (primer)
Inorganic Spectroscopic Methods (primer)
Principles of Magnetic Resonance
Spin Choreography
Website and e-mail:
http://timmel.chem.ox.ac.uk
timmel@physchem.ox.ac.uk
Magnetic
Resonance
Selected NMR properties of some
elements
Physical Methods – Magnetic Resonance
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
Physical Methods – Magnetic Resonance
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.
Opposite effects may be observed for transition metals (ligand effects).
Physical Methods – Magnetic Resonance
Effect of Charge, Substituents
and Oxidation State
Physical Methods – Magnetic Resonance
The effect of coordination on the
chemical shift of a transition metal
Remember
1. The paramagnetic shielding contribution sp ~ 1/E
2. paramagnetic currents AUGMENT the magnetic field (sp is
negative, hence a DESHIELDING parameter!)
 / ppm
E / cm-1
Co(PF3)3-
-4200
-
Co(CN)63-
0
26300
Co(NH3)63+
6940
23210
Co(en)33+
7010
21400
Co(NO2)63-
7350
20670
Co(acac)3
12300
16900
E
|sp|* 
Typically, shifts follow the spectrochemical series: strong field
ligands give small or negative chemical shifts whilst halogens
give larger chemical shifts.
Chemical Exchange
Physical Methods – Magnetic Resonance
Remember:
k
 ( A  B )
2
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
Physical Methods – Magnetic Resonance
17O
spectrum of Co4(CO)12
The 31P spectrum of PF4N(Me)2
Physical Methods – Magnetic Resonance
All 19F equivalent at high Temperature
Fa
Fe P
Fa
N(Me)2
Fe
I(31P) = (19F) = 1/2
19F
e
and 19Fea not equivalent at low Temperature
Physical Methods – Magnetic Resonance
13C{H}
spectrum of [(CH3)3C 6Li]4
Recall: multiplets
2nI + 1
I(6Li) = 1
x
Jav = (5.4 Hz 3 + 0)/4
= 4.1 Hz
J(13C-6Li) = 5.4 Hz
n=4
n=3
Physical Methods – Magnetic Resonance
NMR Acronyms
Nuclear
Overhauser
Spectroscopy
Correlated
Spectroscopy
Electron Nuclear
Double
Resonance
Magic Angle
Spinning
Physical Methods – Magnetic Resonance
Methods
Continuous wave
E
h
B
B
Spin Lattice Relaxation and The
Inversion-Recovery Experiment
Physical Methods – Magnetic Resonance

t
t1
t2
/2
/2
/2
t3
/2
t4
/2
Physical Methods – Magnetic Resonance
Inversion Recovery Method
t1
z
t2
z
y
y
x
/2
x
t3
t4
z
z
y
x
y
x
NMR Signal
I(t)
M z ( t )  M 0 ( 1  2e
t

T1
)
Spin Spin Relaxation and the
Spin Echo Experiment
Physical Methods – Magnetic Resonance
/2 t  t echo
z
z
=
y
x
z
xf
x
=
y
y
x
y
y
x
t
t
x
m
t
s
m
s
y

y
f x
Physical Methods – Magnetic Resonance
What is the effect of relaxation on
the echo amplitude?
Spin spin
Relaxation
random magnetic fields destroy phase
coherence and are not refocused by  pulse
NMR Echo of each signal:
I ( 2t )  I ( 0 )e

2t
T2
Physical Methods – Magnetic Resonance
Echo Trains
The Method of Spin Decoupling
Physical Methods – Magnetic Resonance
FACT: Spin–Spin 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.
RESULT: decoupled spectra are less crowded and have
much higher sensitivity as all available NMR intensity
concentrated into single line (and Nuclear Overhauser).
The Origin of the Spin Decoupling Effect
Physical Methods – Magnetic Resonance
I(X) = I(A) = 1/2
A
A
X( )
J
X
irrad at X
X
X( )
A( )
A( )
Notation: A{X}
A
Irradiation of X at its
resonance frequency
induces rapid transitions
from X( ) to X( ) and vice
versa. A “sees” a single,
averaged field.
B2 of same order as 2JAX
X should be sufficiently far
away from A
The Method of Spin Decoupling
i) irrad
Fluorine Spectrum I(19F) = 1/2
Physical Methods – Magnetic Resonance
ii) irrad
Fa
Fe A
Fa
i) irrad
X
X
i) irrad
I(A) = I(X) = 0
ii) irrad
i)
Fe{Fa}
ii)
Fa{Fe}
Physical Methods – Magnetic Resonance
31P(CH
31P(CH CH O)
3
2
3
I(31P)=1/2
3CH2O)3
irrad
31P(CH CH O)
3
2
3
irrad
31P(CH CH O)
3
2
3
Physical Methods – Magnetic Resonance
Recall: Exercise
B = 1.41T
Electron:
1H:
Nlower
Nupper 
g B B
 1
 0.904
kT
N lower
B
 1
 0.999855
N  upper
kT
Can we
transfer this
polarisation?
The Nuclear Overhauser Effect
1) Enhancement of Sensitivity
Physical Methods – Magnetic Resonance
ie, the heteronuclear (13C – H) Nuclear Overhauser Effect
(1H)  26.75 107 rad T-1 s-1
(13C) = 6.72 107 rad T-1 s-1
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.
The origin of the Nuclear
Overhauser Effect
Result: saturated proton transitions,
13C population difference increased
3-fold
1
Irradiate proton resonances
2
ysical Methods – Magnetic Resonance
0
13C
H
sat
1
4
3
H
1
2
4
sat
13C
5
Boltzmann
3
Protons saturated
4
Cross Relaxation
Takes spins from top to bottom
level, competition with 13C
relaxation (restoring Boltzmann
in 13C population)
The maximum attainable
enhancement (the fractional increase in
Physical Methods – Magnetic Resonance
intensity)
max  1/2 I/S
where I is the saturated spin and S is the observed spin.
•Maximum effect occurs when there is no “leakage” as a
result of relaxation mechanisms other than the dipoledipole interaction (a through space interaction!).
•For homonuclear systems, maximum enhancement is 50%.
•Remember that 15N and 29Si have negative .
Selective Nuclear Overhauser
enhancements
Physical Methods – Magnetic Resonance
irrad
 
Difference Spectrum

Integration



29SiH(Ph)
Physical Methods – Magnetic Resonance
Si   5.31 107 rad T-1s-1
H  26.75 107 rad T-1s-1
29Si{1H}
Proton Decoupled
Coupled
3
Magnitude: 1+max  1+1/2 I/S
~ -1.5
Physical Methods – Magnetic Resonance
Principles of 2-Dimensional NMR
Father of 2D NMR: Jeener, Belgium
Main Developers: RR Ernst
(Switzerland),
R Freeman (UK, Oxford)
Physical Methods – Magnetic Resonance
What we know from FT NMR
/2
FT
Physical Methods – Magnetic Resonance
2D NMR is a domain of FT and pulsed
spectroscopy
Physical Methods – Magnetic Resonance
Principles of 2-Dimensional NMR
The time-intervals of 2D NMR
Physical Methods – Magnetic Resonance
A 2-Dimensional Experiment
evolution
t1
evolution
t1
evolution
t1
Series of onedimensional
NMR spectra
must be
recorded
Physical Methods – Magnetic Resonance
Amplitude Modulation
t1
t1
Phase Modulation
Physical Methods – Magnetic Resonance
Fourier transformation of FID signal, S(t1, t2)
must be performed to obtain 2D spectrum
as function of two frequency variables S(F1, F2)
Larmor precession active during
t2, hence F2 contains chemical
shift
Spin-spin coupling was
active during t1, hence F1
contains coupling constant
What happens during the pulse
sequences?
/2x
t1
/2x
t2
Pulse Sequence
z
/2x
t1
z
x
/2x
y
y
y
x
z
x
?
What happens during the second /2x
Pulse?
/2x Pulse
Pulse does not affect x-component!
z
z
y
x
y
x
Physical Methods – Magnetic Resonance
Pulse
Sequence:
z
/2x
/2x
t1
z
z
x
x
t2
/2x
z
?
y
y
y
x
t1
/2x
x
y
=
t2
y
y
x
x
Physical Methods – Magnetic Resonance
A Simple 2D NMR Spectrum results
F2
F1
W
W
Correlated Spectroscopy (COSY)
Physical Methods – Magnetic Resonance
Pulse Sequence
Aim : To discover spin-spin
couplings in a molecule.
Answer: Which resonance
belongs to which nucleus?
/2x
t1
/2x
t2
1
1
J ( A, X ) A2 :  A  J ( A, X )
2
2
1
1
X 1 :  X + J ( A, X ) X 2 :  X  J ( A , X )
2
2
A1 :  A +
Schematic COSY spectrum
of an AX system
Physical Methods – Magnetic Resonance
Use of COSY to assign 11B NMR of B10H14.
Physical Methods – Magnetic Resonance
(no couplings via H-bridges)
22
4
2
3=4
1=2
5=6=7=8
9=10
a
d
b
c
a: 2B coupled to all kinds of B
= 3,4
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
2D-Nuclear Overhauser Spectroscopy
I
WI
D
S
WS
/2
/2xx
/2/2
x x /2x
t1t1
tmtm
tt22
Physical Methods – Magnetic Resonance
And the resulting spectrum
I
WI
D
S
WS
Cross Peaks tell us about interacting spins.
Physical Methods – Magnetic Resonance
2D NOESY vs 1D NMR
69 amino acids, M = 7688
Physical Methods – Magnetic Resonance
2 D NOESY – Why?
Advantages wrt 1D 1H{1H} NOE:
•Simplification of crowded spectra
•No need for selective excitation of individual
resonances
•Higher efficiency
NMR in Solids
Physical Methods – Magnetic Resonance
Problems:
•Through Space dipolar coupling not averaged out
Distance dependent – information on spin
(broadened spectra)
separations!
•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)
Often broad, structureless resonance
Temperature dependence of line
width
Physical Methods – Magnetic Resonance
Proton resonance line
Solid complex adduct
Physical Methods – Magnetic Resonance
The Dipolar Coupling-Through
Space Coupling
N
S
S
repulsion
N
N
S
N
attraction
Every nucleus with non-zero I, has a magnetic dipole I
z
Bz
Bx
q

r
y
x
0 
Bx 
3 sin q cos q
3
4 r
By  0
0 
2
Bz 
(
3
cos
q 1 )
3
4 r
Anisotropic quantity
S
In a single crystal, this is simple:
Physical Methods – Magnetic Resonance
Recall:
A
D
X
( 3 cos2 q 1 )  0,ie,q  54.7
KAX: splitting in spectrum of X caused by dipolar coupling to A
Physical Methods – Magnetic Resonance
Magic Angle Spinning
0 
2
Bz 
(3 cos q  1)
3
4 r
=0
for q  54.7o
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 ± BAz where BAz is the dipolar field generated
by A on X.
But what about a powder?
Physical Methods – Magnetic Resonance
Every molecule AX has a unique q but different molecules
have different q. We need a trick.
54.7o
54.7o
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).
How fast can you spin?
- Or the relevance of the
spinning speed.
Physical Methods – Magnetic Resonance
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.
(Ph)331PO
sper
spar
Physical Methods – Magnetic Resonance
static
1.9kHz
Typical spectrum of a system
with axial chemical shift
anisotropy.
At low spinning rates,
observation of side bands (info
about principal components of
shielding tensor).
3.8kHz
At high spinning rate we see a
single resonance at isotropic
chemical shift.
siso
Physical Methods – Magnetic Resonance
CP-MAS 15N spectrum of
(NH4)NO3 CPMAS
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.
Physical Methods – Magnetic Resonance
2Ca(CH3CO2)2.H2O
Electron Paramagnetic
Resonance (EPR)
=
Electron Spin
Resonance (ESR)
Modulation Depth
Physical Methods – Magnetic Resonance
10 Gauss
1
0.95
0.9
0.85
0
0.5
1
Time / µs
1.5
Physical Methods – Magnetic Resonance
ENDOR at 275 GHz
(Schmidt et al 2005).
The HIPER project
“Bringing the NMR
paradigm to ESR”
Graham Smith et al.
Möbius & coworkers 360GHz
EPR is developing fast…
…because its APPLICATIONS
so demand
Physical Methods – Magnetic Resonance
E R samples
Paramagnetic
Most substances do not contain paramagnetic species
and are hence EPR silent
Advantage
1) Easier to interpret
2) Introduction of “Spin Spies”
Disadvantage
Fewer accessible systems
a)
b)
O
S
N
O
S
N
O
O
H2N
+ Protein-SH
S
S
N
O
Protein
OH
Applications of EPR
Physical Methods – Magnetic Resonance
Study of Electron Transfer Processes
Applications of EPR
Study of N@C60 (and others)
Physical Methods – Magnetic Resonance
Quantum Computing
Phase transition temp: 260K
4S
3/2
(14N) = 1
FT-EPR
K.P. Dinse
Local Structure
Physical Methods – Magnetic Resonance
ENDOR/ESEEM in proteins
Applications of EPR
Physical Methods – Magnetic Resonance
Long range structure
Use of Spin Labels
Light Harvesting complexes
Energy Splittings and Selection Rule
ES= +mSgeBB0
Physical Methods – Magnetic Resonance
cf.
EI = - mIhB0
mS=±1 -eh = geB
(nucleus)
1H
200
– frequency/MHz
400
mS = +1/2
B0/T
10
20
mS = -1/2
Q
X
W
100
300
ESR frequency/GHz
The g-value
Physical Methods – Magnetic Resonance
The g-value is a unique property of the molecule as a whole and
independent of any electron – nuclear hyperfine interactions.
E = mSgeBB0
ge  2.00232
In case the electron
is the only source of
magnetism in the
sample
E = mSgBB0
SO coupling (SO constant l)
leads to derivation of g from that
of free electron
nl
g  
Ees  Egs
When unpaired electron couples to
1) Empty orbital (e.g., d1), g<ge
2) Occupied orbital (e.g., d9), g>ge
Physical Methods – Magnetic Resonance
h
 (GHz)
g
 0.07145
B B
B(T )
•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
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.
Isotropic Coupling between an electron
and a nuclear spin 1/2
Physical Methods – Magnetic Resonance
S in field
Hyperfine Coupling
I in field
S I
aiso/4
aiso/4
wI
SI
wS
wS
wS
wI
SI
w(mS , mI )  mSwS + mI wI + mS mI aiso
mS  1, mI  0
aiso/4
SI
aiso/4
|aiso|
wS
More than one nucleus
Physical Methods – Magnetic Resonance
1 spin ½ nucleus
SI
SI
Sb
Sb
2 spin ½ nuclei
SI1I2
SI1I2
SI1I2
SI1I2
SI1I2
SI1I2
SI1I2
SI1I2
w(mI )  wS + mI aiso
3 spin ½ nuclei
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
SI1I2I3
Allowed Transitions for N nuclei
with spins Ik
Physical Methods – Magnetic Resonance
N nuclei couple to S
Total Number of states:
N
2 (2 I k + 1)
k
Total number of allowed transitions
N
ne   (2 I k + 1)
k
Frequencies of allowed transitions
w(mI )  wS + mI aiso
The EPR signal is typically in
the first derivative form
Physical Methods – Magnetic Resonance
Employ modulation technique
Physical Methods – Magnetic Resonance
EPR of a Simple Isotropic Ccentred radical
1mT
e
Physical Methods – Magnetic Resonance
Another isotropic system in
solution: BH3 .
EPR spectrum of [BH3●]— in
solution. The stick diagram
marks the resonances for the
11B(I=3/2) and the three
protons. The remaining weak
resonances are due to the
radicals containing 10B(I=3).
Physical Methods – Magnetic Resonance
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)
*
But nothing is ever that simple…
Physical Methods – Magnetic Resonance
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)
Recall:
Description of physical quantities
•Isotropic:
•Directional:
•Interactions between vectorial quantities:
scalars
vectors
tensors
g is anisotropic and varies with
direction
Physical Methods – Magnetic Resonance
g 'x'x' g 'x' y ' g 'x'z '
g ' y 'x' g ' y ' y ' g ' y'z '
g 'z 'x' g 'z ' y ' g 'z 'z '
where
g 'ij  g ' ji
Isotropic g:
Anisotropy:
Asymmetry:
Diagonalise
g xxx
0
0
0
g yyy
0
0
0
g zzz
Principal values
giso  1 ( g xx + g yy + g zz )
3
g  g zz  giso
  ( g zz  g xx ) g
Physical Methods – Magnetic Resonance
For an arbitrary orientation of
a crystal in a magnetic field
In spherical coordinates:
g  ( g sin q cos 
2
xx
2
2
+ g sin q sin 
2
yy
2
2
+ g cos q )
2
zz
2
1/ 2
Physical Methods – Magnetic Resonance
And the resulting powder
spectrum for a rhombic g-tensor
Low spin Fe3+ in
cytochrome P450
Powder
spectrum
1st derivative
g xx
g yy
g zz
Often the g tensor has axial
symmetry
Physical Methods – Magnetic Resonance
Then:
And:
g║  g zz
g┴  g xx  g yy
g  ( g sin q + g cos q )
2
┴
2
2
║
2
1/ 2
Physical Methods – Magnetic Resonance
ESR spectrum of a simple d1
system
g║
g
┴
But things are not that easy…
Physical Methods – Magnetic Resonance
The hyperfine couplings can also be anisotropic (and
often are!)
A  Aiso + Adipolar
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
A Model Cu2+ system
Axial symmetry
Physical Methods – Magnetic Resonance
I(65Cu) = 3/2 d9, S=1/2
g║
g
┴
Li+(13CO2─)
I(13C) = ½, I(7Li) = 3/2
Physical Methods – Magnetic Resonance
12
C
A(13C)>>A(7Li): Spin density mainly on 13C
Transition Metal EPR
Physical Methods – Magnetic Resonance
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
Systems:
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)
Multiple Resonance Techniques
Physical Methods – Magnetic Resonance
EPR spectrum of the phenalenyl radical
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.
This is analogous to recognising
Physical Methods – Magnetic Resonance
…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.
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)
Physical Methods – Magnetic Resonance
Electron Nuclear Double Resonance
Isotropic Coupling between an electron
and a nuclear spin 1/2
Physical Methods – Magnetic Resonance
Recall:
S I
aiso/4
aiso/4
wI
SI
wS
wS
wS
wI
SI
aiso/4
SI
aiso/4
The ENDOR experiment (simplified)
NMR transition(3-4) at
1
wI  a
2
Physical Methods – Magnetic Resonance
Recall:
1
1
1
E4  + w s + w I  a
2
2
4
1
1
1
E3  + ws  w I + a
2
2
4
4 | S I 
3
|  S I 
Thermal EPR 1-3
Equil. saturated.
1 
1 
1 
1
1+ 
1+ 
1+ 
1
sat
1
1
1
E2   w s + w I + a
2
2
4
2
1
1
1
E1   ws  w I  a
2
2
4
1
| S I 
|  S I 
Physical Methods – Magnetic Resonance
Previous overhead
• Relative populations are given by Boltzmann at thermal
equilibrium (wI<<wS, hence populations of 1 & 2, 3 & 4 assumed
identical)
• Irradiate 1-3 transition (saturate at high power) – same
populations in 1&3 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
1&3
• 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 1&3 is again
achieved and EPR transition enhance – the second ENDOR
signal
• In practice, need to consider spin lattice relaxation processes
Physical Methods – Magnetic Resonance
Tetracene cations in sulphuric acid
EPR spectrum
ENDOR
Orientation Selection
Physical Methods – Magnetic Resonance
EPR
Hyperfine
couplings not
resolved
1H
ENDOR
Toluene Solvent
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.