Angewandte
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Chemie
approximately perpendicular to the thread. While the thread
plane. The third pulse, after variable time t, converts this
refocusing transverse magnetization into longitudinal mag-
netization. The system is then allowed to evolve freely for
À
is rather rigid, the N C linkage between the TEMPO group
and the adjacent phenyl ring places the O-atom off the thread
axis; free rotation about this bond would produce a circle with
a radius of approximately 2.59 ꢀ. The distance between the
radical and the ring is too great for any interaction to be
observed by magnetometry or by CW EPR spectroscopy (see
Figure S2).
r
a time Ton the order of the longitudinal relaxation time T1 of
the ring (Figure 3). During this time T, the ring spin will flip
1
r
spontaneously with a probability of = {1Àexp(ÀT/T1 )}.[11]
A
2
final refocusing p/2 and p pulse series is used to obtain
a refocused virtual echo (RVE). The time between the 3rd
and 4th pulses (T) is held constant and both pulse positions
are incremented at constant rate. The echo intensity is
detected as a function of t (Figure 3). If the ring spin flips
during the evolution time T, the resonance frequency of the
nitroxide shifts by the interaction frequency, thus modulating
the final echo amplitude. The interval time T used was
The field-swept echo-detected (FSED) EPR spectrum of
1 at Q-band and 5 K shows two well-separated transitions:
a sharp resonance split by 14N-hyperfine centered at ca. g =
2.007 for the TEMPO radical and a much broader and axial
resonance for the {Cr7Ni} ring centered at ca. g = 1.779
(Figure 2); these values are typical for the two spins.[14,15]
r
4000 ns, which is around four times T1 under these conditions
(Figure S5). Measurement at Q-band suppresses electron spin
echo envelope modulation effects under these conditions
(Figure S6).
Removing a background function of the form exp(Àkt)
where k = 1.8 ꢁ 105 nsÀ1 gives the experimental form factor
that displays a modulation depth of 0.287 (Figure 4a, raw data
is given in Figure S7). Fourier transform gives the frequency–
space spectrum which contains two peaks; the separation of
these two peaks is a direct measure of 2D, D being the
magnetic interaction which is around 8 MHz (Figure 4b).
Fitting the data with DeerAnalysis[17] using a point dipole
model based on two localized S = 1= species is wholly
2
inadequate due to the spin density distribution in the
Figure 2. 33.823 GHz FSED spectra at 5 K on a frozen toluene
solution.
ground state of the {Cr7Ni} ring.[18,19]
To go beyond this limitation we have simulated the data
using an in-house code SSD (“Spatial Spin Density”), which
calculates the form factor directly using a spatially distributed
dipolar model[20] considering the perturbation from the
flipping spin of the ring during the time interval T. The spin
RIDME benefits from the two spins having different
longitudinal (spin-lattice) relaxation times, T1: in 1 the nitro-
xide has a very long T1n (0.2 s at 10 K[16]) and the {Cr7Ni} ring
has a comparatively short T1 (ca. 1 ms at 5 K[2a]). The spin
projection coefficients for the S = 1= ground state of {Cr7Ni}
r
2
echo of the more slowly relaxing spin is measured and the
modulation of this echo caused by the spontaneous flipping of
the more rapidly relaxing spin allows the spin···spin inter-
action to be quantified. The RIDME sequence requires
pulsed EPR resonances to be measured only at the resonant
frequency of the slowly relaxing spin which makes it useful for
heterospin systems. RIDME is also less orientation selective
than DEER and therefore can benefit from more intense
signals and spectral simplicity.
were obtained using the “Irreducible Tensor Operator” (ITO)
technique with the PHI[21] program. This includes the full
microscopic Hamiltonian,[15] and reproduces the spin distri-
bution measured by NMR spectroscopy.[19] Using the struc-
ture and including random rotations of the TEMPO and ring
about the thread (Figure 4c), we directly fit the RIDME form
factor by introducing the standard deviation for a Gaussian
distribution of the ring–nitroxide distance, s.
While this one-parameter model can give a good fit to the
data (Figure S8), a significantly better fit (Figures 4a and b) is
obtained when allowing for an isotropic exchange parameter
(J =+ 0.15 MHz) or a small change in the average ring–
nitroxide distance (ca. À0.1 ꢀ). Both of these models give
excellent simulations of the data, revealing that the dipolar
interactions perpendicular and parallel to the thread axis are
The five-pulse RIDME[12a] sequence was used at Q-band
(ca. 34 GHz) at 5 K (Figure 3). This sequence is dead-time-
free and uses only one frequency centered on the observer
spin (the nitroxide, Figure 2). First, a Carr–Purcell Method A
sequence (p/2ÀtÀp) tips and re-focuses the spins in the xy
D
perp = 9(2) MHz (0.0003 cmÀ1) and
D
para = À18(3) MHz
(0.0006 cmÀ1), respectively. In previous work where we
looked at the interaction between a ring and a single CuII
center[8] an exchange interaction of around 0.02 cmÀ1 was
observed and was unambiguously not dipolar; in this case the
exchange parameter is much weaker, ca. 0.000005 cmÀ1.
This magnetic interaction would give a gate time of 125 ns,
which falls in the correct range to implement a two-qubit gate
with 1.[3] Unfortunately, while RIDME is very good at
Figure 3. 5-pulse RIDME sequence. The p/2 and p pulses had dura-
tions of 20 and 40 ns, respectively, separated by t=140 ns. The
positions of the third and fourth pulses were incremented by 4 ns. The
experiment was carried out at the nitroxide absorption peak at Q-band.
2
ꢀ 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2017, 56, 1 – 5
These are not the final page numbers!
Boulon, Marie-Emmanuelle
