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resolved in solid-state c.w. EPR spectra can be separated and
precisely measured with appropriate pulse sequences3 . The
most popular techniques are concerned with determining hfi
with nuclear spins near the paramagnetic center and with measuring
distances between such centers. The possibility to add
additional rf pulses, driving nuclear spin transitions, opened
the way to apply ENDOR for a larger group of samples than with
c.w. techniques. By now pulsed ENDOR has superseded c. w.
ENDOR almost completely. This aspect is described in more
detail in section D.
At present, commercial pulsed EPR spectrometers are available
working at 3.5, 9, 35 and 94 GHz. Excitation pulse lengths, defi ned
by a π / 2 pulse are of the order of 10 ns (at 9 GHz) to about
30 ns (at 3.5, 35, and 94 GHz). The corresponding excitation
bandwidth is still somewhat limited (30 MHz and 10 MHz, respectively),
but suffi cient to investigate a wide class of paramagnetic
centers in solid matrices by echo experiments. In particular,
dynamical processes can be probed by measuring relaxation
times as function of temperature, limited only by the dead time
of the spectrometer of approximately 50 ns.
Many pulsed EPR experiments can be understood on the basis
of concepts that are familiar from pulsed NMR spectroscopy.
The most important exception are electron spin echo envelope
modulation (ESEEM) experiments that rely on the excitation
of formally forbidden transitions in which both the electron
and nuclear spin magnetic quantum numbers change by unity.
Such experiments are explained in more detail in Box 4. Using
these techniques the NMR spectra of paramagnetic substances
can be determined. In three-pulse ESEEM the fi rst two pulses
generate nuclear coherence that evolves during a variable interpulse
delay T between the second and third pulse. The third
pulse reconverts the nuclear coherence to observable electron
coherence and simultaneously creates a stimulated echo. The
spectrum is obtained by Fourier transformation of time traces
that are acquired by measuring echo intensity as a function of
delay T.
The most informative type of ESEEM spectroscopy is two-dimensional
hyperfi ne sublevel correlation spectroscopy (HYSCORE) 13 ,
which is an extension of three-pulse ESEEM. In this experiment
the variable delay T is separated by a mw π pulse into two variable
delays t1 and t2. The π pulse inverts the electron spin and
thus the hyperfi ne fi eld at the nucleus. As a result, the nuclear
frequencies corresponding to the electron spin α and β manifolds
are correlated with each other. A plot of the spectrum
separates the nuclear Zeeman interaction (shift along the diagonal),
the hfi (splitting along the antidiagonal), and the nuclear
quadrupole interaction (splitting along the diagonal). For powder
samples or frozen solutions each hyperfi ne coupling is represented
by a ridge that is roughly parallel to the antidiagonal.
The level mixing by anisotropic hyperfi ne interaction leads to
small orientation-dependent frequency shifts, so that the ridges
are somewhat curved. By analyzing the curvature the anisotropic
and isotropic contributions to the hfi can be separated14 .
At present a restriction of the applicability of this very powerful
method is given by the fi nite excitation width, thus allowing for
the investigation of rather small hfi only. Extension to larger hfi
would require going to higher fi elds to match nuclear Zeeman
interaction to the larger hfi and achieving shorter mw pulse
lengths. In order to show the principle of HYSCORE, a particularly
simple spectrum is displayed in Fig. 4. In this example, all
peaks originate
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FIG. 4: HYSCORE spectrum of Single Wall Carbon Nanotubes. The signals
originate from 13 C in natural abundance as can be concluded from
the frequency value, at which the anti-diagonal connecting the off-diagonal
ridge crosses the 2D diagonal. The HYSCORE spectrum was taken at B0=346
mT, corresponding to ν( 13 C)— 3.705 MHz.
from weakly coupled 13 C nuclei, as can be deduced from the
symmetry point of the spectrum.
The conceptually most simple way of separating the interaction
between two sets of electron spins from other interactions relies
on the use of two mw frequencies to excite them individually.
Details of the experiment are explained in BOX 5. In essence, the
local fi eld at the observer spins A created by a specifi c group of
distant spins B is sensed by measuring the change of the resonance
frequency that is induced by selectively inverting these B spins.
The resulting shift of the resonance frequency of the A spin, is
given by the dipole-dipole coupling between A and B spins. This
frequency shift is observed as a modulation of the echo signal
as a function of the position of the pump pulse in the sequence
(Fig. 5A) 15,16 . For a well defined distance r the oscillation
frequency is proportional to r –3 with a proportionality constant
that can be computed from fi rst principles. Exact distance measurements
are thus possible without calibration. Even in case
of disordered structures the observed time dependence can be
directly converted into a distance distribution using appropriate
transformations 4,17,18 .
As an example, the separation of two biradicals in a mixture by
four-pulse DEER 19 and subsequent Tikhonov regularization is
shown in Fig. 5B—D. For the shorter biradical 1 with an end-to-end
distance of about 2.8 nm, an asymmetric distance distribution
is observed as is expected from backbone dynamics of
such biradicals 20 . For the longer biradical 2 with an end-to-end
distance of about 3.6 nm, this asymmetry is unresolved for this
data set, because the observation time is limited to about 2.9 μs.
This specifl c form of “two color“ pulsed EPR is now usually referred
to as Double Electron Electron Resonance (DEER) and has
gained major attention from biologists, because site-directed
mutagenesis allows to place spin labels at specifi c sites in proteins,
whose distance can subsequently be determined by this
technique 21,22 .
Various research groups established pulsed EPR at much higher
frequencies of currently up to 360 GHz. Because of limited power
available from phase coherent sources in this frequency
range, pulse duration is of the order of several hundred ns, much
longer than record setting values like 1 ns seen at 95 GHz 23 .
Still the possibility to perform multi-pulse experiments, mostly
in combination with additional rf pulses, opens the way for the
study of complicated spin systems.
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