G-Engineering in Hybrid Rotaxanes to Create AB and AB2 Electron Spin Systems: EPR Spectroscopic Studies of Weak Interactions between Dissimilar Electron Spin Qubits

Article abstract of DOI:10.1002/anie.201504487

Hybrid [2]rotaxanes and pseudorotaxanes are reported where the magnetic interaction between dissimilar spins is controlled to create AB and AB₂ electron spin systems, allowing independent control of weakly interacting S= 1/2 centers.

Full text of DOI:10.1002/anie.201504487

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International Edition: DOI: 10.1002/anie.201504487
German Edition: DOI: 10.1002/ange.201504487
EPR Spectroscopy
g-Engineering in Hybrid Rotaxanes To Create AB and AB2 Electron
Spin Systems: EPR Spectroscopic Studies of Weak Interactions
between Dissimilar Electron Spin Qubits
Antonio Fernandez, Eufemio Moreno Pineda, Christopher A. Muryn, Stephen Sproules,
Fabrizio Moro, Grigore A. Timco, Eric J. L. McInnes, and Richard E. P. Winpenny*
Abstract: Hybrid [2]rotaxanes and pseudorotaxanes are
reported where the magnetic interaction between dissimilar
spins is controlled to create AB and AB2 electron spin systems,
PyCH2NHCH2CH2Ph, that features a pyridyl group as
a stopper on one end and a benzyl group as stopper at the
other end, to make the [2]rotaxane [PyCH2NH2CH2CH2Ph]-
[Cr7Ni(m-F)8(O2CtBu)16] 1 in 32% yield (see the Supporting
Information).
allowing independent control of weakly interacting S = 1=
2
centers.
The stoichiometric reaction of
1 with [Cu(hfac)2]
S
everal groups have proposed the idea that molecules could
(Hhfac = 1,1,1,6,6,6-hexafluoroacetylacetone) yields another
be used as electron spin qubits.[1–6] Molecular qubits can be
designed such that phase memory times (Tm) approach other
solid-state electron spin technologies,[7] and have the advant-
age that they can be functionalized by synthetic-chemistry
methods. Proposed molecular spin qubits include organic
radicals,[2] simple coordination complexes,[7] high-spin[1] and
low-spin clusters,[3–5] and 4f ions.[6] One challenge is to bring
together ensembles of such qubits, and particularly to bring
together qubits with different electronic g-factors, so called
g-engineering,[2,6] which would allow the qubits to be
addressed individually and controllably within a complex
molecule. Takui and co-workers have done this using elegant
organic chemistry, and have reported the operation of the
CNOT gate using such an approach.[2] Herein we show how
similar g-engineering can be achieved using coordination
chemistry of 3d metal cages.
[2]rotaxane
{[Cu(hfac)2][PyCH2NH2CH2CH2Ph][Cr7Ni(m-
F)8(O2CtBu)16]} 2. X-ray crystallography[11] of 2 confirms
that [Cu(hfac)2] has bound to the pyridyl of the rotaxane
thread (Figure 1a,b and Figure S1 in the Supporting Infor-
mation).
The heterometallic ring in 2 is unchanged from that in
rotaxane 1, containing eight metals in an octagon, bridged by
fluoride and pivalate ligands (Figure 1b). The ammonium
group of the thread hydrogen bonds to the fluorides within
the metal octagon. The pyridyl group from the thread binds to
copper, occupying the apical site of a square-based pyramid.
We have been studying heterometallic {Cr7M} rings for
their fascinating spin physics.[8] Where M is Ni, antiferro-
magnetic exchange coupling gives a well-isolated S = 1=
2
ground state; pulsed electron paramagnetic resonance
(EPR) spectroscopy shows these have sufficiently long
phase memory times to use as qubits.[9] The chemical robust-
ness and versatility of these units allow their incorporation in
hybrid [2]rotaxanes.[10] Herein we use
a
thread,
[*] Dr. A. Fernandez, Dr. E. Moreno Pineda,[+] Dr. C. A. Muryn,
Dr. S. Sproules,[++] Dr. F. Moro,[+++] Dr. G. A. Timco,
Prof. E. J. L. McInnes, Prof. R. E. P. Winpenny
School of Chemistry, The University of Manchester
Oxford Road, Manchester M13 9PL (UK)
E-mail: Richard.winpenny@manchester.ac.uk
[+] Current address: Institute of Nanotechnology
Karlsruhe Institute of Technology
76344 Eggenstein-Leopoldshafen (Germany)
++] Current address: WestCHEM, School of Chemistry
University of Glasgow, Glasgow G12 8QQ (UK)
+++] Current address: School of Physics and Astronomy
The University of Nottingham
Figure 1. Crystal structure of 2 (ball-and-stick model) viewed a) side-
on, and b) perpendicular to the {Cr7Ni} plane. c) Arrow representation
of the gz-component of the CuII and {Cr7Ni} fragments. The dotted
lines are Cu···M vectors for opposite M sites on the {Cr7Ni} ring and
[
[
À
À
the average trans M Cu M angle is shown. Atom colors: Cr=green,
Ni=purple, Cu=dark blue, F=yellow, O=red, C=gray, N=pale
blue. H atoms and tBu groups of pivalate ligands have been omitted
for clarity. C and N atoms of the thread are drawn larger to highlight
this structural feature.
University Park, NG7 2RD, Nottingham (UK)
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/anie.201504487.
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Figure 2. Experimental Q-band (ca. 34 GHz) EPR spectra and simulations for a) 2, b) 3, and c) 5 in a 1:1 solution of toluene/CH2Cl2 at 5 K.
Simulation parameters: a) gxC;ry7;zNi =1.780, 1.765, 1.710; gxC;uy;z =2.065, 2.045, 2.325; AzCu =450 MHz; J=À0.032 cmÀ1; b) gxC;ry7;zNi =1.785, 1.775, 1.715;
gxC;uy;z =2.050, 2.020, 2.287; AzCu =450 MHz; J=À0.020 cmÀ1; and c) gxC;ry7;zNi =1.780, 1.775, 1.705; gxC;uy;z =2.060, 2.045, 2.322; ACz u =450 MHz;
J=À0.020 cmÀ1. d–f) Zeeman plots for H along the molecular z axis, with Q-band EPR transitions shown.
À
The distance between the centroid of the {Cr7Ni} ring and the
CuII center is 7.332(1) Š, whereas the average Cu···Cr/Ni
distance is 8.56 Š with the Cr···Cu vectors making an average
angle (q) of 318 to the {Cr7Ni} normal (which is parallel to the
the Cu N vector) is parallel to the normal of the {Cr7Ni} ring,
Cr7Ni
Cu
the g and gjj
axes correspond to the same molecular
jj
Cu
orientation of 2. The multiplet pattern on the g signal
jj
clearly shows two overlapping hyperfine quartets (63CuII,
À
Cu N vector, Figure 1c). The pivalate moieties in the ring are
65CuII, I = 3/2), thus the Jjj value is of the same order as the
Cu
jj
sterically demanding and there is little flexibility in the
molecule (Figure S1); therefore the crystal structure of 2 is
representative of the structure in solution.
A
value. Measurement of the doublet splittings of the g?
features then reveals that J? ꢀ Jjj, that is, the interaction is
essentially isotropic. To test this we simulated[14] the spectrum
with a simple isotropic exchange Hamiltonian:
The only through-bond pathway between the spin centers
of the {Cr7Ni} ring and the single CuII site involves hydrogen
bonds between fluorides and the protonated ammonium site
of the thread, therefore any magnetic interactions between
the two components are expected to be very weak. Never-
theless, clear evidence of such interactions is detected by
continuous wave (cw) EPR spectroscopy (Figure 2).
*
*
Cu
Cr7 Ni
7Ni
Cu
Cu
^
Cu
Cr7Ni
H ¼ mBS Á gCu Á B þ mBS
Á gCr Á B þ S Á ACu Á I À JS Á S
^
^
^
^
^
^
We initially fixed the g-values and CuII hyperfine inter-
action from model complexes, with J as the only free variable,
but then refined all parameters: better fits are found by
introducing a slight rhombicity in the g-value (Figure 2a).
This gives J = À0.032 cmÀ1; the relative transition intensities
within the exchange doublets are sensitive to the sign of the
J value.
At low temperature (5 K) only the S = 1= ground state of
2
{Cr7Ni} is populated substantially; this state is approximately
Cr7Ni
axially symmetric with gC?r Ni ꢀ 1.78 and gjj ꢀ 1.74 where the
7
“unique” axis is perpendicular to the {Cr7Ni} plane.[12] The
EPR spectrum of 2 at Q-band (34 GHz) and 5 K is very
The interaction is weak and antiferromagnetic, but it is
perhaps surprising it is seen at all as the only through-bond
pathway involves hydrogen bonds. As the interaction is
isotropic this implies that it cannot be dipolar (through space)
in origin. For comparison, we have calculated the dipolar
interaction (D) for 2. Avery crude treatment is to take {Cr7Ni}
as a spin localized at its centroid: this gives Dxx,yy =+ 0.004,
Dzz = À0.009 cmÀ1. This is too weak to explain the spectrum
and moreover such a model cannot, by definition, give an
isotropic interaction. A more rigorous treatment is to
calculate the full dipolar interaction matrix D for the nine-
spin system: the effective {Cr7Ni}···Cu interaction can be
calculated by the sum of the individual Cr···Cu and Ni···Cu
dipolar interactions weighted by the projection factors of the
simple with two sets of features, centered at the g-values
Cu
expected for {Cr7Ni} and for CuII (g?Cu ꢀ 2.05, g ꢀ 2.30) with
jj
resolution of copper hyperfine coupling (ACu) on the
Cu
jj
g
feature. Each of these g-features is split into a spectro-
scopic doublet; that is, the spectrum has the form of a simple
AB spin pattern, where the spin–spin coupling is much
smaller than the difference in Zeeman energy (the difference
in Zeeman energy is 0.17 cmÀ1 for a static field of 1.21 T and
g = 2.1 and 1.8). This scenario is familiar from NMR
spectroscopy, but examples of AB electron spin patterns
resolved by cw-EPR spectroscopy are rare.[2a,13]
The resolution of the spectrum is such that we can read the
parallel and perpendicular components of the interaction (J)
between the Cu and {Cr7Ni} sites directly from the spectrum.
As a result of the fact that the local z axis at the Cu site (along
CrIII and NiII local spins onto the S = 1= ground state of the
2
{Cr7Ni} ring (see the Supporting Information).[16] We used spin
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projection factors determined from solid-state 53Cr NMR
spectroscopic studies on (Me2NH2)[Cr7NiF8(O2CtBu)16].[17]
The full calculated dipolar matrix is given in the Supporting
Information. The leading term of the dipolar matrix (orien-
tated along the gjj direction) is Dzz = À0.0034 cmÀ1, that is, an
order of magnitude smaller than the experimentally measured
coupling. Including this D matrix makes no significant
difference to the calculated EPR spectrum. Thus, the
ring···Cu couplings are not a result of dipolar interactions.
The pathway for the isotropic exchange interaction remains
unclear but must be through bond. Interestingly, the value
found here falls within the range predicted by Coffman and
Buettnerꢀs[15] empirical limit function for long-range super-
exchange interactions. In the cases they discuss there are
always more obvious through bond pathways.
This result led us to explore closely related but more
complex heterospin systems. First, [Cu(NO3)2(Me2CO)]-
{[PyCH2NH2CH2CH2Et][Cr7Ni(m-F)8(O2CtBu)16]}2 3 was syn-
thesized, which contains two pseudo[2]rotaxanes bound to
a single CuII site (Figure 3a). The thread in 3 differs from that
in 1 and 2, with an ethyl group at one end rather than a benzyl,
which could in principle allow dethreading in solution.
However, this process is not detected, as demonstrated from
the form of its EPR spectrum. The CuII site has the two
pyridyl rings from the pseudorotaxanes trans to each other,
with two nitrates and an acetone coordinated in the plane.
The nitrates are chelating with one long (2.6 Š) and one short
[{PyCH2NH2(CH2)5}2][Cr7Ni(m-F)8(O2CtBu)16]2] 4.[18] Coordi-
nation of a [Cu(hfac)2] unit to each end of 4 then gives the
system [Cu(hfac)2(H2O)]2[{PyCH2NH2(CH2)5}2][Cr7Ni(m-F)8-
(O2CtBu)16]2] 5 (Figure 3b). The copper coordination geom-
etry is now six-coordinate with two hfac ligands and a water
molecule, with the water molecule coordinated cis to the
À
pyridyl ring. The Cu O/N distances are surprisingly regular
À
À
(Cu N 2.21, Cu O 2.126–2.162 Š). Thus it is unclear where
the unique CuII axis is located. The relationship between the
{Cr7Ni} rings and CuII ions in both 3 and 5 are similar to that in
2, because in each case the ring is formed around the
ammonium site of R-NH2CH2CH2-pyridyl where the pyridyl
binds to the CuII center (3: {Cr7Ni} centroid···Cu 7.34 and
7.07 Š, average Cr···Cu 8.44 Š, average q = 318; 5: {Cr7Ni}
centroid···Cu 7.34 Š;, average Cr···Cu 8.54 Š, average q =
318). Unlike in 2 and 3, there is flexibility in 5 (Figure S3)
because of the C5 chain at the center of the [3]rotaxane.
For both 3 and 5 the Q-band EPR spectra of frozen
solutions at 5 K again show weak coupling. For 3 an AB2 spin
system pattern is obtained, with the resonance signals
attributable to the {Cr7Ni} ring (the B spin) split into a doublet,
whereas the resonances for the Cu center (the A spin) are
split into 1:2:1 triplets (Figure 2b). The spectrum of 4 is very
similar to that of 1, that is, that of an isolated {Cr7Ni} ring,
where any {Cr7Ni}···{Cr7Ni} interaction within the [3]rotaxane
is very weak and not detectable by cw-EPR. This may be
connected to the flexibility of the thread resulting from the
saturated C5 chain at the center. The spectrum of 5 is very
similar to that of 2 with a weak {Cr7Ni}···Cu interaction; the
spin structure (as regards cw-EPR) is therefore two very
weakly or non-interacting AB spin pairs (Figure 2c). Simu-
lations of 3 and 5 both give J = À0.020 cmÀ1 (Figure 2b,c).
Although the relationship between the {Cr7Ni} and
CuII fragments are similar in each case, minor changes in
the spin coupling are justified because of the differing
coordination geometry at the CuII center. In 2 the “unique”
(z) axis of the CuII ion (defining the orientation of the dx2Ày2
magnetic orbital) is unambiguously parallel to the
À
À
(1.95 Š) Cu O distance each. The two Cu N and the two
À
short Cu O(nitrate) distances define a square plane (N-Cu-N
and O-Cu-O 168 and 1758, respectively) with the acetone in
À
an axial position (Cu O 2.41 Š). Thus the best description of
the CuII geometry seems to be again square pyramidal, but
now with the axial orientation perpendicular to the {Cr7Ni}
planes. As with 2, the steric requirements of the pivalate
ligands lead to the structure of 3 being rigid in solution
(Figure S2).
Second, to increase the complexity further, a [3]rotaxane
was made about an axle with a pyridyl at each end:
À
{Cr7Ni}···Cu axis (or equivalently the Cu N direction). In 3,
this axis is orthogonal to {Cr7Ni}···Cu; the situation in 5 is
ambiguous.
The weak coupling regime of AB spin systems allows the
spins to be addressed individually. This is the basis of the g-
engineering approach of Takui and co-workers to construct
a CNOT gate with dissimilar organic radicals,[2] and towards
Lloyd’s proposal of periodic (ABC)n arrays using inequiva-
lently orientated metal ions in helicates.[19] The heterospin
structure of 2, and its dimerization into a more complex array
in 5, shows how such arrays can be achieved exploiting the
facile coupling between molecules enabled by coordination
and supramolecular-chemistry approaches.
An important question is whether such complex systems
can be constructed without deleterious effects on the spin
coherence properties of the components. To test this we
measured the phase memory times (Tm) for 2 and 5 by pulsed
EPR at the X-band using a standard Hahn echo sequence
[p/2-t-p-t-echo].
Figure 3. Side-view crystal structure (ball-and-stick model) of
a) pseudo[2]rotaxanes 3 and b) [3]rotaxane 5. Atom colors: Cr=green,
Ni=purple, Cu=dark blue, F=yellow, O=red, C=gray, N=pale
blue. H atoms and tBu groups of pivalate ligands have been omitted
for clarity.
Static magnetic-field positions were chosen that selec-
tively pumped EPR transitions on the {Cr7Ni} ring and on the
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CuII site (409 and 310 mT, respectively, for 2; Figure S4). The
Tm value for the {Cr7Ni} component is circa 600 ns at 5 K in
both 2 and 5 (Figure S5). This is in the 400–700 ns range
(depending on the nature of the R substituent) found for
isolated [R2NH2][Cr7Ni(m-F)8(O2CtBu)16] at 5 K.[9] Tm times
for the CuII resonance are larger, at 1.0 ms for both 2 and 5,
and of the same order as found for related isolated CuII
complexes, for example, [Cu(hfac)2(4,4’-Me2-bipy)] has Tm =
3 ms at 5 K.[20] Thus, the phase memory times are not
significantly decreased as a result of the interspin interaction.
This bodes well for performing spin manipulation experi-
ments in supramolecular arrays of molecular nanomagnets.
The next steps require tuning the interaction strengths and
Zeeman frequencies such that the components can be
addressed individually within the resonator bandwidths
available with current pulsed microwave technologies. The
interaction strength will be controllable through supramolec-
ular chemistry. The difference in Zeeman frequency could be
achieved, for example, with spin clusters of marginally
different g-values[21] or with homospin clusters exploiting
non-parallel orientations and g-anisotropy.[22]
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The Cambridge Crystallographic Data Centre. Crystallographic
Acknowledgements
data for
2 was collected on a Bruker Prospector CCD
diffractometer with CuKa radiation (l = 1.5418 Š). Crystallo-
graphic data for 3 was collected on an Agilent SuperNova CCD
diffractometer with MoKa radiation (l = 0.71073 Š) and was
solved using SHELX; b) G. M. Sheldrick, Acta Crystallogr. Sect.
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This work was supported by the EPSRC (UK, EP/L018470/1),
the National EPR Facility, and the European Commission
(Marie Curie Intra-European Fellowship to A.F. (300402)).
E.M.P. thanks the Panamanian agency SENACYT-IFARHU
for funding. We also thank the EPSRC (UK) for funding an
X-ray diffractometer (grant number EP/K039547/1).
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Keywords: EPR spectroscopy · heterometallic complexes ·
magnetic properties · quantum computing · rotaxanes
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Received: May 18, 2015
Published online: July 24, 2015
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