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Title: An introduction to pulsed ESR: technical considerations.


1
An Introduction to Electron Spin Resonance
(ESR). Part 2. Pulse methods and distance
measurements.
Boris Dzikovski, ACERT, Cornell University
  • An introduction to pulsed ESR technical
    considerations.
  • Important instrumentation differences between
    pulsed and cw ESR.
  • Introduction to typical pulse ESR experiments
    COSY, SECSY, ELDOR, DQC
  • Examples of pulsed ESR experiments on biological
    systems.
  • Peaceful coexistence/symbiotic relations between
    pulse and CW ESR.
  • ENDOR ESR detected NMR.
  • Summary

An introduction to Electron Spin Resonance (ESR),
Nov 1st 2006
2
What is special about ESR, in particular
spin-label ESR? (e.g. compared to NMR) ESR is
much more sensitive per spin (than NMR). In time
domain experiments ESRs time-scale is
nanoseconds (NMRs is milliseconds). The
spin-label spectrum is simple, and can focus on a
limited number of spins. ESR spectra change
dramatically as the tumbling motion of the probe
slows, thereby providing great sensitivity to
local fluidity. In NMR nearly complete
averaging occurs, so only residual rotational
effects are observed by T1 and T2. Multi-frequenc
y ESR permits one to take fast-snapshots using
very high-frequencies and slow-snapshots using
lower frequencies to help unravel the complex
dynamics of bio-systems. Pulsed ESR methods
enable one to distinguish homogeneous broadening
reporting on dynamics vs. inhomogeneous
broadening reporting on local structure.
An introduction to Electron Spin Resonance (ESR),
Nov 1st 2006
3
Why pulse ESR? And why CW ESR still survives?
Look back at the Bloch equations in the rotating
frame
In an ideal pulse experiment we either irradiate
spins (apply B1) or record the signal, hence, in
the recording phase we do not care about B1
4
  • PULSE vs. CW
  • ? In Fourier Transfer Spectroscopy one records
    signal when B1 is zero. For CW one sees frequency
    modulation noise of the carrier. We also do not
    care about field modulation Hard pulses B1gt
    spectral range
  • If one uses Hard Pulses, the pulse excitation
    can be used for all spins at once. For narrow
    lines a CW spectrometer measures baseline most of
    the time such a waste of time A FT
    spectrometer measures signal all the time.
    However, FT requires a broader band spectrometer.
    And the noise goes as a square root of the
    bandwidth

VS.
5
  • Sensitivity issue one rotates all spins into the
    X-Y plane and detects total magnetization. In CW
    one usually rotates only a small fraction of the
    possible magnetization into X-Y plane, to avoid
    saturation effects.
  • However the dead-time problem in pulsed ESR.
    Dead time is finite time when the spectrometer
    relaxes to zero-power levels. It is not an issue
    in solution NMR, but a problem in solid state NMR
    and EPR.
  • Pulse ESR can isolate interactions and detect
    correlations that are not observable by CW
    methods. The additional information about weakly
    coupled spins and relaxation properties of the
    spin system that can be obtained by manipulating
    the spins with sequences of MW pulses explains
    the efforts put into the development of new pulse
    methods.
  • Time resolution (response time) of 10 ns is
    much better than in CW ESR

6
FT ESR has clear advantage vs CW If spectral
width lt 100 MHz (35 G) line width lt 3 MHz (1
G) Typical systems organic radicals in
solution exchange narrowed lines or conduction
electrons proton-free single crystals
disordered solids only IF
high local symmetry (cubic, tetrahedral)
pathological cases (fullerenes, Mn2 central
lines)
virtually no hyperfine couplings (silica glass)
7
A short review of basic pulse experiments (ESR
and/or NMR)
  • Free Induction Decay (FID)
  • much of NMR and occasionally in ESR. In the
    90-FID pulse sequence,
  • net magnetization is rotated down into the X'Y'
    plane with a 90o pulse.

?/2 RF pulse
By using the Bloch equations
signal
The complex signal which is proportional to
My-iMx as called an FID and is described as
Pulse
T1 process
Relaxation
T2 process
8
FID from 1mM TEMPO in decane
One-shot S/N
In phase receiver response
Quadrature receiver response
Receiver on
9
FID for T1 measurements
t
Two ?/2 pulses
Pulse sequence
FID
FID amplitude
One measures the FID amplitude of the second
pulse as a function of the time between pulses,
the signal intensity is proportional to
In practice, it is more convenient to measure T1
from a ? - ?/2 pulse sequence called Inversion
Recovery Pulse Sequence
?
We measure FID stepping t.
?/2
t
FID amplitude ?
10
Can we measure T2 from FID?
It is not so simple as it seems. What we see as
T2 is actually the dephasing time T2, a
combination of the real T2 relaxation and the
relaxation due to inhomogeneous field on the
sample and hence a variety of Larmor frequencies
experienced by spins (T2)-1 T2-1
(T2(inhomogenious))-1
2. Spin echo
?/2
?
t
t
Pulse sequence
Second pulse
Refocusing
11
A brief history of spin echoes, with cartoons!
The first nuclear spin echo observed by E. Hahn
in 1950.
(a-c) the "race-track" echo, (d-f) the "pancake"
echo
The first electron spin echo reported by R.
Blume in 1958.
From the website of Zürich pulse ESR group
12
Spin Echo ?-irradiated quartz
?/2-? sequence
Spin echo
In phase receiver response
Quadrature receiver response
13
T2 is usually determined by measuring the decay
of the two-pulse echo as a function of the pulse
interval t when the spread due to inhomogeneity
is refocused along the Y-axis Mx(2t)0
My(2t)
We do not reverse true relaxation
The Carr-Purcell-Meiboom-Gill (CPMG) sequence is
derived from the Hahn spin echo and equipped
with a "built-in" procedure to self-correct pulse
accuracy error
  • If the first inversion pulse applied is shorter
  • (e.g. 1750) than a 1800 pulse, a systematic
  • error is introduced in the measurement.
  • The echo will form above the XY plane.
  • To correct that error, instead of sampling the
    echo immediately, a third ? delay is introduced,
    during which, the magnetization evolve slightly
    above the XY plane

If the second inversion pulse, also shorter than
1800 (1750), is applied, as the magnetization is
already above the plane, this shorter inversion
pulse will put the magnetization exactly in the
XY plane. At the end of the last ? delay, the
echo will form exactly in the XY plane self
correcting the pulse error!
14
Stimulated (three-pulse) echo
The equilibrium Z-magnetization is transferred to
transverse magnetization by the first ?/2 pulse
During free evolution of length ?, the
magnetization dephases The second ?/2 pulse
rotates the magnetization vectors into the XZ
plane During time T, the transverse
magnetization decays At time tT ?, the third
?/2 pulse transfers the Z-magnetization pattern
again to transverse magnetization, which forms an
echo at time t T 2? along the Y-axis. The
dotted curve represents the locus of the
magnetization vector tips, the open arrow is the
stimulated echo
15
Fourier-Transform ESR, Basic pulse sequences in
2D ESR
COSY
SECSY
2D FT ELDOR
preparation
mixing
detection
Corresponds to 2D-NOESY in NMR
16
Relationship between spectral coverage and B1
?e 2.84MHz/Gauss
5G
5G of B1 implies a ?/2 pulse length of
approximately 18ns.
17
Populations and coherences
Ensemble of isolated spins S1/2. A single spin
is in a general superposition state
, which means
The expectation value of an operator Q
Which is
,a quadratic product of C? and C?
then
If
The approach becomes useful if many independent
spins involved. The ensemble average instead of
becomes
Operator
Is known as density operator
18
Take a look at the matrix of the density operator
The diagonal elements are called populations of
states ? and ?
The off-diagonal elements are called coherences
A coherence between two energy eigenstates ?r?
and ?s? defined as
In high magnetic field, the two energy
eigenstates have well-defined values of the
angular momentum in the magnetic field direction
The order prs of coherence is defined as prs
Mr-Ms
The populations and coherences may be identified
as the coefficients of the shift and projection
operators in the expression of density operator
19
Physical interpretation of the populations
Since their sum is always equal to one, only the
difference has physical significance
and indicates net longitudinal spin
polarization (in the direction of the field)
Physical interpretation of the coherences (which
are complex numbers) Coherence requires (1) the
existence of spins with transverse polarization
(superposition state) (2) the transverse
polarization must be partially aligned
-the phase of the (-1)-quantum coherence ??? is
the same as transverse magnetization with
respect to the x-axis -the amplitude is the net
transverse polarization. What about 1
coherence? Forget about it!
See Malcolm Levitt. Spin Dynamics
20
The density operator allows the state of the
entire spin-1/2 ensemble to be specified using
just four numbers. What are the numbers?
For one important point in time, thermal
equilibrium
  1. The coherences between the states are all zero
    ?rs(eq)0 for r?s
  2. The populations of the energy states obey the
    Boltzmann distribution

Define Boltzmann factor B
hence
High temperature approximation
Thermal equilibrium density operator the
starting point for subsequent calculations
21
Effect of MW pulses on populations and coherences
Strong ?/2 pulse
Spin density operator before the pulse
After the pulse
(?/2)x
The pulse (1)equalizes the populations (2)
Converts the population difference into coherences
Strong ? pulse
(?)x
The pulse exchange the populations of the two
states, generating an inverted population
distribution
X,Y and Z are cyclic permutable in this
relation..
Sandwich relation for angular momentum operators
22
Spin ½ Rotation Operators
The operator for a rotation about the x-axis
through the angle ? is given by
23
Larger spin systems
A general quantum state of the spin ½ pair
The total angular momentum defined as follows
The four Zeeman product states are eigenstates
of the total z- angular momentum operator
Maa1
Mab0
Mba0
Mbb-1
Density operator
24
2S1xS2z 2S1yS2z 2S1zS2x 2S1zS2y
2S1zS2z
2S1xS2x 2S1yS2x 2S1yS2y 2S1xS2y
For coupled spin systems instead of rotating
single angular momentum operators, one must
rotate their products
25
Two spin system (hints on how to handle)
?/2 pulse
Thermal equilibrium
Individual spin states
give coherences as direct products
Action of the ?/2 pulse on multiple-quantum cohere
nces
Multiple QC transformed into single
26
It can help to think of pulse experiments in
terms of coherence-transfer pathway diagrams
  • An electronic spin transition
  • is labeled by the p index,
  • which can have values -1, 0, or 1.
  • If two spins are coupled, the
  • p index can take on larger (gt1) or smaller (lt-1)
    values, as in DQC where products of transition
    operators may be excited.
  • The different coherences are combined in various
    ways to display SECSY, COSY, and ELDOR
    experiments. The ways always start at p0 and
    come to p-1
  • Solid pathways report on inhomogeneous, dotted
    pathways on homogeneous broadening.

COSY
Sc-
Sc
SECSY
Sc-
Sc
ELDOR/EXCSY
preparation
mixing
detection
Sc-
Sc
27
Other ways of thinking about the pulse spectrum
  • Sometimes, the dotted coherence path is called
    the FID-like path and the
  • solid coherence path is called the echo-like
    path.
  • The echo-like path tends to re-focus the
    coherence and reduce the inhomogeneous
  • broadening of the resonance line.
  • The FID-like path does not have this refocusing
    character (no transfer of coherence
  • from plus to minus or vice versa).
  • In order to separate out a particular coherence
    we generally use a phase-cycling
  • procedure which consists of repeating the
    experiment with pulses applied along
  • different axes in the rotating frame of the spin
    system.
  • By taking suitable combinations of the spectra
    produced by these pulse sequences,
  • we can selectively enhance those terms of the
    spin Hamiltonian in which we are
  • interested.

A pulse applied along the x-axis
becomes
A pulse applied along the y-axis
If the appropriate phase shift is applied to the
pulse
28
From presentation by G. Jeschke
29
Sc- signal has lower inhomogeneous broadening...
than the Sc signal
30
One dimensional pulse experiment
Fourier Transform spectrum
Time domain spectrum
31
Example of a two dimensional Fourier Transform
Spectrum
Easy answer (specific goal) simulate and fit
2D-FT-ESR spectra
16-PC in pure DPPC vescicles
Time domain representation
Frequency domain representation
General goal 2D methods capabilities to study
biological systems
32
True Fourier Transform Spectroscopy...
2D-ELDOR of 1mM TEMPONE in water/glycerol
The active sample volume was about 500 nl.
... in aqueous samples at room temperature at
95GHz!
33
Spin-labeled Gramicidin A in Oriented Membrane
(DPPC)
B0 n
  • Slow motional nitroxyl spectrum at 7oC.
  • Orientation selection at 95 GHz (3.2 mm)
  • gz parallel to membrane normal (z-ordered)

gy
gz
gx
B0 ? n
34
Spin-labeled Gramicidin A in Oriented Membrane
2D-ELDOR (echo-like component) at 7Co
T 50 ns
Slow motional regime - coverage 350 MHz
Az1
Az 0
Note the pulse is not hard
Az-1
gy
T 200 ns
gx
Az1
Az 0
gy
Az-1
B0 n
35
What the different experiments measure
COSY The COSY experiment measures the transfer
of coherence from one ESR allowed transition to
another. Its time scale is usually limited
to t1 t2 lt T2 SECSY The SECSY experiment is
a spin echo implementation of the COSY idea.
Instead of the FID detected after a COSY
experiment, the echo spectrum is recorded.
SECSY measures the variation of the phase memory
time across the ESR spectrum since the second
pulse refocuses hyperfine and resonance
offsets. ELDOR By including a mixing time in
this three pulse sequence and transferring cohere
nces to the z axis, this experiment is sensitive
to processes that occur on the T1 time scale
which is usually longer than the T2 time
scale accessible to COSY. Spectra are usually
displayed in SECSY format. DQC This experiment
measures distances between dipolar coupled
electron spins.
36
2D-ELDOR, A POWERFUL TOOL FOR STUDYING MEMBRANE
DYNAMICS OVER LARGE TEMPERATURE AND COMPOSITION
RANGES
  • The phase diagram is determined based on
  • 1) spectroscopic evidence
  • 2) dynamic parameters
  • 3) recovered absorption spectra.

Ld
Lo
gel
  • The new DPPC/Chol phase diagram determined by
    2D-ELDOR is, in general, consistent with what was
    studied using a combination of different
    methods, including DSC, NMR, and fluorescence
    techniques.

Tm
( Vist, Biochemistry 29 (1990) 451 Sankaram,
PNAS 88 (1991) 8686 )
37
Introduction to DQC
  • Higher order coherences can be created and
    manipulated in systems of coupled electron spins.
  • Double-quantum coherence (DQC) between two
    electron spins coupled by their dipole-dipole
    interaction is of particular interest.
  • This provides the tool ? separating weak dipolar
    couplings from stronger interactions ? accurate
    measurements of distances over a broad range.
  • Site-directed nitroxide spin labeling DQC ESR
  • ?
  • structure determination and the study of
    functions
  • of a broad class of biomolecules such as proteins
    and RNA.

38
DQC ESR
The system two interacting spins a and b
Coherences single-quantum in-phase,
I? single-quantum antiphase, A? double
quantum, DQ?
  • All these coherences can be manipulated by
    pulses and be refocused.
  • Refocusing of DQ? is particularly useful ?
    singles out the part of the signal
  • that evolves solely due to spin coupling.

39
DQC ESR
  • Antiphase coherences, which can be converted to
    DQC, can be prepared by
  • the effect of coupling terms in
    Spin-Hamiltonian.
  • The simplest case is the evolution caused by the
    secular part of dipolar
  • coupling
  • Manipulating with SQCs I?, A?, and DQC, DQ? in
    various ways led to several pulse sequences for
    distance measurements.
  • In DQC, signals unrelated to dipolar coupling are
    suppressed by phase-cycling
  • Let us consider the 6-pulse DQC sequence, which
    we use the most often.

40
The 6-pulse DQC Sequence
Signal is recorded vs. t?? tp - t2 tm ? tp
t2 and tDQ both fixed
The coherence pathways for the 6-pulse DQC
sequence
p
?????
41
Biological Applications of DQC ESR
  • DQC ESR is well-suited for measuring distances
    over a broad range.
  • 17 GHz DQC ESR has been applied to measure
    distances
  • from 14 Å (small rigid biradicals)
  • to 70 Å (RNAs),
  • with the likelihood of both limits being
    improved.
  • large distances can be measured in spin-labeled
    proteins,
  • using just small
    amounts.

42
Example spin labeled Gramicidin A (GASL)
Interspin distance
ndipolar, MHz,
43
ALIGNED MEMBRANE
n
There is no averaging over all orientations of
the membrane normal relative to B0. BUT a tilt
of the interspin vector will manifest itself as
partial averaging.
Dipolar pulse spectroscopy offers a good
opportunity to determine the orientation of
interspin vectors and, hence, whole embedded
molecules in the in the membrane
44
Equilibrium of gramicidin conformations in the
membrane by dipolar pulse ESR
In a mismatching membrane gramicidin does
not form channels, but exists in some non-channel
conformation which could be either double helical
or monomeric. The non-channel form(s) tend to
aggregate.
Dipolar signal from aggregates due to many
distances possible is poorly resolved, weak, and
often beyond detection this complicates
identification of particular form. Solution of
the problem We use double-labeled Gramicidin
with an addition of 201 by unlabeled GA, making
the interspin distance a fingerprint of a
distinct conformation.
Double helical dimer (DHD)
20.0Å
DPPC
DLPC
Monomer
31.1Å
45
CheA, X-Ray Structure of CheA?289 construct
The details of the structure of WT CheA are not
known, however the structure of its subdomains
and that of CheW has been solved by X-ray
crystallography and NMR. Pulsed ESR
dipolar spectroscopy (PDS) has been applied to
establish how CheW binds to CheA?289, for which
the X-ray structure was determined.
Site-directed Spin-labelling (SDSL) PDS requires
one to introduce nitroxide reporter groups, which
in our case was MTSSL that forms a covalent bond
with cysteine, introduced by site-directed
mutagenesis.
P4
P5
P3
Cysteine residue labeling by MTS
(methanethiosulfonate) reagent and the
corresponding side-chain, R1, introduced into the
protein.
?289 of CheA from T. maritima
46
Spin-labeling Sites and the Distances
A number of single and double cysteine mutants
of CheA or ?289 CheA were engineered for pulsed
ESR study. CheA complexes with labeled or
unlabeled CheW in various combinations have been
used.
Histidine Kinase, CheA is a dimer and binds two
CheW. Thus, there are four electron spins. This
is a complication, which was overcame by
carefully selecting spin-labeling sites such that
the distances of interest were significantly
shorter than the rest, thereby making their
measurement straightforward.
72
Average Intra-Protein Spin Distances
15
80
?289 CheA
CheW
Intra-domain and inter-domain distances, Å.
Mutated site 15 72 80 553 568 579 646
15 2729(a) 18.2 37 54.5 61 43.7
72 X 24.530(a) 27 49 46 32.5
80 X X 26 47 54.5 39.5
553 X X X 23.5 34.5 32
568 X X X X 32.5 35.5
579 X X X X X 28
646 X X X X X X
Mutated Residues
CheA?289 N553C, E646C, S579C, D568C
CheW S15,S80,S72
47
Triangulation
A cartoon depicting the triangulation grid of
sparse large distance constraints from ESR for
CheA P5 domain (blue) and CheW (red). Small
spheres represent volumes occupied by the
nitroxide groups. The increase in the number of
constraints (which are fairly accurate distances)
will tend to reduce the uncertainty in the
position of the backbone.
Quick Solution Metric Matrix Distance Geometry
D is the matrix of distances dik between
nitroxides i an k
xjk ?k½ wjk
gij Skx,y,z xik xjk Skx,y,z wikwjk?k
Metric matrix, g is constructed from D
(w eigenvector of gij ? eigenvalue of
gij)
gij ½ (di02dj02-dij2)
Any atom as origin(0)
Thus (x, y, z) coordinates of all atom found.
48
4-pulse DEER, another pulse method for measuring
interspin dostances
The echo intensity is recorded as a function of
t. In the absence of dipolar interaction, a pulse
at frequency 2 has no impact on echo intensity at
frequency 1. Dipolar interaction causes
oscillation in echo intensity with a period that
is characteristic of the interspin distance.
Excitation at spectral position ?2
Excitation at spectral position ?1
M. Pannier, S. Veit, G. Jeschke, and H. W.
Speiss, J. Magn. Reson. 142, 331 (2000).
From presentation by Sandra Eaton, ACERT 8/7/04)
49
Why CW ESR is still alive? CW NMR died many years
ago
  • Simpler recording, simpler interpretation and
    simulation.
  • Higher sensitivity in many cases
  • Most pulse ESR experiments need low measuring
    temperatures imposed by the short T2 relaxation
    time, especially for transition metal ions. On
    the contrary, CW EPR spectra can be recorded at
    room temperature for a large number of spin
    systems, including radicals and transition metal
    ions

Pulse and CW ESR are not rivals but rather
complementary methods.
50
Distance measurement by ESR numbers and orders
of magnitude
r is in cm
r is in Å, g assumed 2
The CW lineshape at the rigid limit is a
convolution of the no broadening spectrum with
Pake
The Fourier transform of the convolution of F and
P is equal to the product of the Fourier
transforms of F and P
51
Resolved Splittings of CW Spectra
Consistent with a distance of 7.5Å
  • Analysis by computer simulation of lineshapes
  • For shorter distances may need to include
    exchange as well as dipolar interaction
  • In favorable cases may be able to define the
    relative orientations of the interspin vector and
    hyperfine axes for two labels.
  • Usually assumes that relative orientations of
    magnetic axes for two centers are well defined
  • Analysis of data at two microwave frequencies may
    be required to obtain definitive results.

52
Human Carbonic Anhydrase II(examples from
presentation by Sandra Eaton, ACERT 8/7/04)
Selected distances in HCA II 67-206 121-206 67-12
1 59-174
53
Half-Field Transitions
Dipolar interaction between two spins shifts the
triplet state ms ? 1 energy levels relative to
the ms 0 level, and causes the normally
forbidden transition probability between the ms
-1 and ms 1 levels to become non-zero. This
transition occurs at half the magnetic field
required for the allowed transitions (at constant
microwave frequency), and hence is called the
half-field transition.
R is interspin distance in Å ? is MW frequency GHz
54
Fourier Convolution/Deconvolution
  • Assume random distribution of relative
    orientations or interspin vector and hyperfine
    axes.
  • Fourier convolve spectrum of singly-labeled
    sample with broadening function to match spectrum
    of doubly-labeled samples
  • OR
  • Divide Fourier transform of doubly-labeled
    spectrum by Fourier transform of singly-labeled
    spectrum to obtain broadening function
  • Calculate the interspin distance from the
    "average" broadening.

M. D. Rabenstein and Y.-K. Shin, Proc. Natl.
Acad. Sci (US) 92, 8329 (1995). H.-J. Steinhoff
et al., Biophys J. 73, 3287 (1997).
55
Fourier Deconvolution
Doubly-labeled
Sum of singly-labeled
After subtraction
Note that the baseline for the deconvoluted
function is close to zero for the subtracted
spectrum.
r 8 9 Å
56
Simulation and Fourier Deconvolution
First integral
r 16 18 Å
57
DEER measurement of distance between spin labels
in carbonic anhydrase
r 18 Å (70) 24 Å 30)
r 20 1.8 Å
58
Distances (Å) Between Spin Labels on Carbonic
Anhydrase Determined from EPR Spectra
Doubly spin-labeled variant Distance between b-carbonsa Half-field transition Fourier Deconvo-lution Lineshape Simulation DEER
HCAII67-121 8.8 7 7-8 -
HCAII59-174 5.4 8 8.5-9 9-10 -
HCAII121-206 10.9 - 16-18 17-19b 18 (70) 24 (30)
HCAII67-206 17.9 - 17-20 20 ? 1.8
aDistance between b-carbons of native amino acids
at the sites where substitution with cysteine
was performed, calculated from the X-ray crystal
structure, cAssuming 100 doubly-labeled protein.
Persson et al., Biophys. J. 80, 2886 (2001).
59
Electron-nuclear double resonance (ENDOR)
The observation of the nuclear spin spectrum is
realized by the simultaneous irradiation of an
electron spin transition and a nuclear spin
transition, a technique named Electron-Nuclear
Double Resonance (ENDOR). The dramatic resolution
enhancement achieved by ENDOR results to a large
extent from the fact that two resonance
conditions have to be fulfilled simultaneously
one for the electron spin transition (EPR) and
one for the nuclear spin transition (NMR).
One stays in ESR resonance (MW) keeping ESR lines
saturated and sweeps rf field ESR-detected NMR
ESR signal vs rf field At the NMR resonance an
increase in relaxation lifts saturation and
produces ESR signal ENDOR is much more sensitive
than NMR (NB splitting and population difference
in ESR and NMR)
BRUKER reference
60
ENDOR resolution enhancement
The double resonance technique can highly
simplify a spectrum since every additional
nucleus with spin I multiplies the number of
lines by (2I1) . But only adds two lines to the
ENDOR spectrum
Too bad a Huge number of hyperfine lines in ESR
Even worse the hf structure is totally unresolved
Nice and clean ENDOR spectra!
BRUKER reference
61
Useful references for cw and pulse ESR
Wertz and Bolton. Electron paramagnetic
resonance. Carrington and MacLachlan. Magnetic
resonance in chemistry. Slichter (Good general
background on NMR and ESR) Principles of
magnetic resonance, 3rd Ed. Schweiger and
Jeschke (pulse ESR/EPR) Principles of pulse
electron paramagnetic resonance Berliner (Ed.)
(Biological applications of resonance techniques
gt20vv.) Biological Magnetic Resonance, Spin
Labeling (vv. 1, 2, 8), Distance
measurements (v. 19) Poole (Experimental
methods, mostly cw) Electron spin resonance A
comprehensive treatise on experimental techniques
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