Spectral Addressability in a Modular Two Qubit System

Article abstract of DOI:10.1021/jacs.1c02417

The combination of structural precision and reproducibility of synthetic chemistry is perfectly suited for the creation of chemical qubits, the core units of a quantum information science (QIS) system. By exploiting the atomistic control inherent to synthetic chemistry, we address a fundamental question of how the spin-spin distance between two qubits impacts electronic spin coherence. To achieve this goal, we designed a series of molecules featuring two spectrally distinct qubits, an early transition metal, Ti3+, and a late transition metal, Cu2+ with increasing separation between the two metals. Crucially, we also synthesized the monometallic congeners to serve as controls. The spectral separation between the two metals enables us to probe each metal individually in the bimetallic species and compare it with the monometallic control samples. Across a range of 1.2-2.5 nm, we find that electron spins have a negligible effect on coherence times, a finding we attribute to the distinct resonance frequencies. Coherence times are governed, instead, by the distance to nuclear spins on the other qubit's ligand framework. This finding offers guidance for the design of spectrally addressable molecular qubits.

Full text of DOI:10.1021/jacs.1c02417

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Spectral Addressability in a Modular Two Qubit System
Stephen von Kugelgen, Matthew D. Krzyaniak, Mingqiang Gu, Danilo Puggioni,* James M. Rondinelli,*
Michael R. Wasielewski,* and Danna E. Freedman*
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ABSTRACT: The combination of structural precision and
reproducibility of synthetic chemistry is perfectly suited for the
creation of chemical qubits, the core units of a quantum information
science (QIS) system. By exploiting the atomistic control inherent
to synthetic chemistry, we address a fundamental question of how
the spin−spin distance between two qubits impacts electronic spin
coherence. To achieve this goal, we designed a series of molecules
featuring two spectrally distinct qubits, an early transition metal,
Ti3+, and a late transition metal, Cu2+ with increasing separation
between the two metals. Crucially, we also synthesized the
monometallic congeners to serve as controls. The spectral separation
between the two metals enables us to probe each metal individually
in the bimetallic species and compare it with the monometallic
control samples. Across a range of 1.2−2.5 nm, we find that electron spins have a negligible effect on coherence times, a finding we
attribute to the distinct resonance frequencies. Coherence times are governed, instead, by the distance to nuclear spins on the other
qubit’s ligand framework. This finding offers guidance for the design of spectrally addressable molecular qubits.
execute logic gates in spectrally addressable systems.17−20 To
INTRODUCTION
■
harness this approach for molecular electronic spin-based
We are living in the second quantum revolution, a time when
systems, the critical first steps are synthesizing frequency
our newfound ability to harness quantum properties is
addressable systems and unraveling their coherence properties.
transforming disciplines ranging from computation to
Herein, we describe the design, synthesis, and electron
communication.1−3 Each of these subfields of quantum
paramagnetic resonance (EPR) spectroscopic investigation of a
information science (QIS) is built around a fundamental unit
series of spectrally addressable, transition metal-based, two
of information, the quantum bit or qubit. Chemical synthesis
spin qubit systems featuring Ti3+ centers spatially separated
uniquely enables atomically precise design and fabrication of
from Cu2+ centers. The series CuTPP−[CC−(p−C6H4)]n‑1
−
qubits.4 Transition metal complexes confer significant
tunability for modulating electronic structure, bringing new
insight for the creation of novel spin-based qubits.5,6
Progressing from single qubit systems to multiqubit systems
is an essential step toward realizing QIS applications such as
logic gates in computing and entanglement enhanced
sensing.7−9
To construct multiqubit systems, we imbued molecular
systems with spectral addressability by designing the energy
levels of their quantum states so each individual qubit can each
be manipulated with different microwave frequencies.10−13 We
achieved this by selecting a pair of elements featuring
significantly different g-factors, a property that determines
the frequency at which a transition will appear. Notably, this is
straightforward with transition metal complexes since g-factors
are dictated by elemental identity and ligand fields.14,15 This
approach mimics the nuclear magnetic resonance (NMR)
approach of addressing individual spins with specific
frequencies, albeit with electronic rather than nuclear spins.16
As such, there is a deep literature of technical approaches to
CO2TiCp2 (n = 1, 2, 3; 1, 2, 3) features well-defined metal−
metal distances and synthetic access to the monometallic
analogues (i.e., Cu2+ and Ti3+-only) CuTPP−[CC−(p−
C6H4)]n‑1−CO2CH3 (n = 1, 2, 3; 1a, 2a, 3a) and NiTPP−
[CC−(p−C6H4)]n‑1−CO2TiCp2 (n = 1, 2, 3; 1b, 2b, 3b),
respectively (Chart 1). Through deliberate design of g-
anisotropy in 1−3, the spectrally well-resolved Cu2+ and Ti3+
features not only enable precise mapping of the electron−
electron interactions and independent interrogation of their
spin dynamics but also control of both spin centers under the
same applied magnetic field. This independent spin manipu-
lation enables quantum state tomography to probe the impact
Received: March 3, 2021
Published: May 20, 2021
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© 2021 American Chemical Society
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3a. Hydrolysis of the ester followed by metalation with
[Cp2TiCl]2 gave the bimetallic complexes 1, 2 and 3. We
accessed the Ti-only derivatives 1b, 2b, and 3b analogously
after protection of the porphyrin site with Ni(acac)2. Solid-
state metal−metal distances of 11.631(2), 18.534(2), and
25.18(1) Å are enforced by the ligand framework in 1b, 2, and
3 (Figure 1a) as determined by single-crystal X-ray
crystallography.
Chart 1. Modular Transition Metal-Based Molecular Qubits
of a neighboring qubit on the fidelity of single qubit gate
operations and provides essential insights for the design of
molecular multiqubit systems.
RESULTS AND DISCUSSION
■
To enable a detailed study of coherence properties and
operational fidelity in molecular multiqubit systems, we
designed a two-qubit system to meet three criteria: two S =
1/2 metal centers that are simultaneously and separately
addressable within the bandwidth of a standard microwave
resonator (e.g., several hundred MHz to a GHz for an
overcoupled Bruker split-ring resonator), embedded in a ligand
framework that enforces a specific orientation of their g-
tensors, and connected by a rigid but modular linker to enable
deterministic tuning of the qubit−qubit distance.
To achieve spectral addressability, we needed to design small
differences in g-factors and manage electron−nuclear hyperfine
interactions. Many lanthanide complexes and multinuclear
clusters exhibit large deviations from the free electron g factor
of ∼2, necessitating large microwave bandwidths to address
their wide operating frequency ranges. With our widely
available experimental setup of a pulse X-band spectrometer,
we achieve reasonable (<50 ns) π pulses within the 200 MHz
bandwidth, corresponding to an accessible difference in g-
factor of ∼0.1 at 0.34 T and 9.5 GHz. Ti3+ and Cu2+ satisfy this
addressability criterion, as their respective positions at the
beginning and end of the transition series lead to deviations
from g = 2 (<2 for Ti3+ and >2 for Cu2+).21
Next, judicious ligand design is key to enforcing rigid
intermetallic distances and well-defined intramolecular ori-
entations of the two metal fragments. Thus, when selecting the
component transition metal fragments, we prioritized systems
where the g-tensor aligns with specific molecular axes amenable
to functionalization. The g-tensor of Cu2+ porphyrins is
typically aligned with the local 4-fold symmetry axis and the
vectors bisecting the Cu−N bonds pointing at the meso
carbons.22 In titanocene complexes of κ2 carboxylates the Ti3+
gz axis parallels the Ti−Ccarboxyl vector, with the gx along the
TiO2 plane.23 Combining these transition metal fragments,
attachment of the Ti3+ carboxylate to the meso-aryl groups of
the porphyrin guarantees alignment of the Ti gz axis with a
Cu2+ gx/y axis along the intermetal vector.
Finally, we chose an oligo-(p-phenyleneethynylene) spacer
as a rigid but modular linkage between the metal centers.
These rod-like polymers are very stiff, exhibiting solution-state
persistence lengths in excess of 100 Å.24 We harnessed a
modular synthetic approach, coupling oligo(p-phenyleneethy-
nylene) carboxylate linkers with 5-(4-iodophenyl)-10,15,20-
triphenylporphyrin. Metalation with Cu(OAc)2·H2O under
standard conditions25 gave the Cu-only complexes 1a, 2a, and
Figure 1. (a) Single-crystal X-ray structures of bimetallic complexes
1b (top), 2 (center), and 3 (bottom). The g-tensor alignments to the
molecular frame are depicted adjacent to the metal centers. Color
coding: C (gray), N (blue), O (red), Cu, Ni (copper), Ti (silver).
Hydrogen atoms, solvent molecules, and phenyl ring disorder are
omitted for clarity. (b) CW EPR spectra (solid lines) of 1 (pink), 2
(blue), and 3 (green) obtained at 9.529 GHz in 1:1 CS2: toluene-d8
glass at 77 K. Simulations from best fit parameters are shown in black.
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Electron Paramagnetic Resonance Spectroscopy. We
performed continuous-wave (CW) EPR spectroscopy on these
compounds to understand the electronic interactions between
qubits and to determine whether their electronic structures
were perturbed by the linker. The CW EPR spectrum of 2a
was best fit with an axial g-tensor with values in the range
typical for Cu2+ porphyrins of gz = 2.189 and gx ≈ gy = 2.046,
while 2b was best fit with a rhombic g-tensor with gx = 2.002, gy
= 1.953, and gz = 1.984, closely matching the reported values
for other Cp2TiO2CR derivatives.26 The CW EPR spectra of
bimetallic compounds 1−3 are shown in Figure 1b. When we
compared them to the monometallic analogues, 2a and 2b, we
observe spectral differences we attribute to intramolecular
electron−electron dipolar and exchange couplings (see
Supporting Information, Figure S1). To account for these
interactions, we fit these spectra using a Hamiltonian for a
static magnetic field B (eq 1) that includes the Cu2+ g-tensor
gCu and hyperfine tensor ACu, the Ti3+ g-tensor gTi and
hyperfine tensor ATi and the electron−electron interaction
matrix J.
Information, Table S1 for full parameters) and the simulated
spectra shown in Figure 1b. The small values of J we observed
are consistent with theoretical calculations of the spin density
in the appended Ti3+ fragments, which have approximately
80% of the spin residing on Ti (Table S2) and virtually no
delocalization onto the bridge (Figure S1).
Next, we performed pulse EPR spectroscopy to interrogate
the impact of the Cu2+-Ti3+ electronic interaction on their spin
dynamics. Our initial studies focused on the spin−lattice
relaxation time, T1, which describes the time for a qubit to
relax to its thermal ground state. For QIS applications, T1
comprises the spin’s initialization speed and maximum
operation time. In systems with multiple spin centers, a
faster-relaxing spin can facilitate the transfer of spin excitation
energy to the environment and dictate the dynamics of the
other spin centers.29 The T1 of a system of multiple qubits
depends on which population is relaxing, and here, we
selectively characterize this time scale for states centered at
either Cu2+ or Ti3+. Despite their disparate structures, these
pulse EPR saturation recovery measurements (Figure 2a,b)
show the Ti3+ and Cu2+ centers in 1−3 exhibit similar T1
values (Figure 2c). The larger spin−orbit coupling of Cu2+
compared to Ti3+ (829 cm−1 vs 153 cm−1)30 likely enhances
relaxation mechanisms, thereby slightly shortening its T1. In
cases where there is a fast relaxing qubit and a slow relaxing
qubit, the spin flips of the fast relaxing one are a major source
of magnetic noise.31 But when two off-resonant spin centers
exhibit similar values of T1, the impact of their interactions on
their coherence properties remains unknown.
The lifetime of a coherent superposition state of a qubit is
parametrized by the phase memory time, Tm. In systems of
multiple qubits, each coherence has a characteristic Tm, so we
examined the Tm of single quantum coherences created at
either the Cu2+ or Ti3+ center. Since Tm encompasses the
intrinsic dephasing time, T2, as well as extrinsic factors, this is
fundamentally a measurement of the interaction between the
spin and its environment. Magnetic noise from nuclear spins
and neighboring electron spins are two key sources of
decoherence, or collapse of the superposition state. To
quantify Tm, we performed Hahn-echo experiments at variable
temperatures (Figure 2a, right). Fitting the decay of the echo
intensity (Figure 2d) with a stretched exponential I(2τ)= A
exp[-(2τ/Tm)β]to obtain the coherence time Tm and stretch
factor, β, reflecting the echo decay curve shape.
To suppress extrinsic contributions to decoherence, we
sought a matrix with few nuclear spins. Although 1−3 are
soluble in nuclear spin-free CS2, aggregation during freezing
precluded its use as a pure solvent. However, toluene and CS2
form a homogeneous glass below 92 K,32 and a 1:1 mixture of
toluene-d8:CS2 has only 15% of the nuclear magnetic moment
of pure toluene. Above 40 K, Tm in this system is limited by
classical methyl rotation, but the increased mass of the CD3
group relative to CH3 suppresses low-temperature methyl
tunneling.33 We observe Tm values as high as 29 μs for the
Cu2+ center of 3 at 5 K, which compares favorably to the
several μs Tm observed in other copper porphyrins.34,35 The
corresponding 9 μs Tm values at the Ti3+ are in close
agreement with ∼10 μs Tm exhibited by other titanocene-based
qubit candidates.36 A comparison of their Hahn-echo behavior
to the monometallic references 2a and 2b reveals that Tm is not
limited by the presence of the second qubit nor correlated with
the Cu−Ti separation (Figure 2).
Cu
Cu
Ti
Ti
Cu Ti
Cu,N
Ti
Ti
Cu
Ti
H = μBBgCu
S
+ S A I
+ μBBg S + S A I + S JS
̂
̂
̂
̂
̂
̂
̂
̂
(1)
J = J + d + D
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D
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0
dz −d
xx
xy xz
J 0 0
0 J 0
0 0 J
y
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−d
dy −dx
0
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=
+
+
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The matrix J can be decomposed (eq 2) into an isotropic
term J representing isotropic components of the exchange and
through-space dipolar coupling, an antisymmetric term d
encompassing the antisymmetric exchange interaction, and an
anisotropic term described by the traceless matrix D containing
the anisotropic dipolar coupling and anisotropic exchange
arising from g-anisotropy.27 Since the Cu2+ and Ti3+ g-tensors
are aligned to both the intermetallic axis and each other, the
off-diagonal elements of D are zero. Due to their C2v symmetry,
antisymmetric exchange (term d) is also zero for these
complexes.28 This reduces the number of free parameters in J
to three (eq 3). Fitting the experimental spectra yielded
coupling parameters tabulated in Table 1 (see Supporting
Table 1. Electron-Electron Coupling Terms for 1, 2, and 3
c
rCu−Ti (nm) J (MHz) Dxx (MHz) Dyy (MHz) Dzz (MHz)
a
1
1.16
1.85
2.52
+19
−36
−40
−11
−10
−4
−32
−31
−6
−8
−3
+68
+71
+17
+18
+7
b
b
b
calc.
+2.5
+0.1
+0.5
−0.2
+0.2
a
d
2
calc.
a
d
3
calc.
−4
−3
+7
a
b
Fit from CW-EPR spectra. Calculated through-space dipolar
coupling with the point dipole approximation and anisotropic g
factors. Negative ferromagnetic, positive antiferromagnetic. Below
c
d
error of the fit.
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Figure 2. (a) Pulse sequence and Bloch sphere representation of pulse EPR experiments measuring T1 and Tm.41 (b) Representative saturation-
recovery curve, with the formula for its relationship to T1 (inset). (c) Temperature dependence of T1 for 1−3, 2a, 2b in toluene. (d) Representative
Hahn-echo decay curve (3, Ti3+ transition, 5 K, CS2: toluene-d8), with the formula for its relationship to Tm (inset). (e) Temperature dependence
of Tm in toluene (open symbols) and CS2: toluene-d8 (solid symbols) 1 (pink), 2 (blue), 3 (green), 2a (orange), and 2b (gray). Circles represent
data observed at Cu2+ EPR transitions and triangles at Ti3+.
In understanding these data, we considered various sources
of decoherence. Two key sources are spectral diffusion, which
arises from nuclear spin flips in the environment, and
instantaneous diffusion, which causes decoherence in the
Hahn echo sequence when the refocusing pulse coincidentally
causes nearby on-resonant electron spin flips (Figure 3a).
Spectral diffusion is an intrinsic property, whereas instanta-
neous diffusion can be viewed as a measurement artifact that
can be corrected (Figure 3b). To deconvolute these two
processes in 1−3, we examined their coherence times as a
function of the refocusing pulse turning angle, θ, by varying the
applied microwave power. The plots of 1/Tm vs sin2(θ/2)
(Figure 3c) exhibit the linear relationship characteristic of
instantaneous diffusion. The slope of this plot is dependent on
several experimental factors, most notable being its proportion-
ality to concentration. Despite consistent solution concen-
trations, differences in solubility and association kinetics
between compounds during freezing can result in different
final concentrations of molecules that remain well-dispersed in
the solvent instead of being sequestered in off-resonant
aggregates.
To control for differences in aggregation, extrapolation to
infinitely small θ gives an estimate of the “true” Tm with only
contributions from spectral diffusion comparable with Tm that
would arise from a single-molecule experiment (Figure 3d).
Crucially, this analysis reveals a monotonic dependence on
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matrix is in the 4−10 Å range (the so-called “spin diffusion
barrier”).37−40 In 2b, the porphyrin is diamagnetic, and so all
1
of its H nuclei contribute maximally to decoherence through
spin flip-flops. Installation of a Cu2+ center paramagnetically
shifts these 1H nuclei off-resonance and reduces their
contribution to decoherence, leading to a longer Tm at the
Ti3+ center in 2. This does not perfectly suppress their impact,
and therefore, we observe moving the porphyrin closer
increases decoherence in 1 while moving it further attenuates
their influence in 3. The extrapolated Tm values of the Ti3+
centers increase from 24 μs in Ti-only complex 2b to 40 μs in
3. In contrast, the Cu2+ porphyrins, which themselves host the
1
majority of the decohering H spins, are minimally impacted
by the Ti3+ center. Indeed, the substitution of the methyl ester
(3 1H spins) for the titanocene fragment (10 1H spins) causes
only a small decrease in extrapolated Tm from 2a to 2.
With a complete picture of the coherence properties of this
series of bimetallic qubits, we progressed to more complex
operations such as quantum gates. Rabi oscillations (Figure 4a)
establish that both the Cu2+ and Ti3+ centers can be placed in
any arbitrary superposition state, but these measurements do
not quantify the fidelity of these manipulations, i.e., the
accuracy of the information encoded into the superposition.
Quantum state tomography measures how close the result of
an operation on our qubit is to the desired outcome. For a two-
qubit gate operation, both qubits must operate under the same
external magnetic field. By design, at a constant field of 340
mT the Cu2+ gx/gy and Ti3+ resonances in 1−3 are addressable
with 48 ns π-pulses within the bandwidth of our EPR
resonator. Selecting the appropriate microwave frequency
enables us to address transitions which are purely Cu2+ or
purely Ti3+ under the same applied field and with the same
microwave pulse lengths, which controls for field- and
bandwidth-dependent effects. Operating on a thermally
initialized state, we executed a suite of qubit operations to
encode information in the superposition, denoted by the
intended position on the Bloch sphere. By projecting the
components of the magnetization onto the x−y plane, we
measure the elements of the full density matrix (Figure 4b,c).42
A comparison of the measured elements to the theoretical
product of our operation gives the “true” fidelity F1 of these
quantum states by eq 4
F(ρ , ρ ) = [Tr
ρ ρ2 ρ ]2
1 1
1
1
2
(4)
where ρ1 is the theoretical density matrix produced by an ideal
gate and ρ2 is the experimental density matrix.43 The resulting
values of F1 for several single-qubit operations are tabulated in
Figure 4d.
The substantially lower F1 for the composite-pulse
Hadamard gate (H)44 compared to other single-pulse
operations can be attributed to pulse inhomogeneities, a
major source of error that reduces measured fidelities.45
Precise calibration of each turning pulse or implementation of
broad-band pulses to limit spectral diffusion could ameliorate
these issues in the future. The present measurements represent
what is possible with the most widely available technology and
therefore serve as an important baseline for future experiments
in our laboratory and others. Despite these limitations, we can
control for instrumental sources of error and intrinsic
decoherence by comparing the observed density matrices in
1−3 to the real states produced in 2a or 2b instead of an ideal
quantum state (eq 5).
Figure 3. (a) Tm measurement sequence with schematic illustrating
how the flip of a nearby spin during the refocusing pulse leads to
instantaneous diffusion and (b) its elimination using low pulse turning
angle, θ. (c) Decoherence rate (1/Tm) vs pulse turning angle θ for 1
(pink), 2 (blue), 3 (green), 2a (orange), and 2b (gray) in
CS2:toluene-d8 at 10 K. Data were collected at the Cu (circles) and
Ti3+ (triangles) spectral maxima corresponding to the Cu2+ gx/y
transition and the Ti3+ gz transition. (d) Instantaneous diffusion-free
Tm from extrapolation to infinitely small turning angle.
Cu2+-Ti3+ distance, reflecting the impact of the nuclear spins of
the other qubit. In S = 1/2 systems, the region where nuclei are
paramagnetically shifted off-resonance with those of the bulk
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Figure 4. (a) Nutation experiments demonstrating Rabi oscillations for all complexes. (b) Pulse sequence and Bloch sphere representation of
quantum state tomography experiment measuring ⟨Sx⟩, ⟨Sy⟩ (top) and the measurement of ⟨Sz⟩ (bottom). (c) Select experimental density matrices
showing the agreement between ideal (black outline) and measured (colored fill) real matrix elements measured for 2 Cu. (d) Experimental “ideal”
and “dyad” fidelities from quantum state tomography at 340 mT. The Cu2+ gx/gy transition is addressed at 9.7006 GHz and the Ti3+ gy transition at
9.3168 GHz.
2
large enough that inhomogeneities in the phase shift due to
F (ρ2a,b, ρ1−3) = [Tr
ρ
2a,b ρ
ρ2a,b ]
2
1−3
(5)
selection of a range of molecular orientations leads to apparent
dephasing of the spin echo as it acquires an average phase shift
of much more than 2π. However, the qubit−qubit dipolar
coupling for 3 corresponds to a period close to τ at the
orientation addressed, so that the acquired phase shift is less
than 2π and is not averaged out by poor orientation selection.
This phase shift more strongly impacts fidelity than random
dephasing, reducing F2 in 3. Orientation of 3 to narrow the
distribution of dipolar couplings could deliberately leverage
this phase evolution. Since Tm is more than an order of
magnitude longer than the required evolution times for a π
phase shift (0.1−0.4 μs) this could enable entangling these
bimetallic qubit dyads through two-qubit quantum logic
operations like the CNOT gate.46,47 These results highlight
how quantum tomography, a relatively simple single-frequency
measurement, can generate insights into spin−spin interactions
without more complex multifrequency pulse EPR techniques.
This comparison between the monometallic and bimetallic
complexes enables the calculation of a new metric, the dyad
fidelity F2, which corrects for these experimental limitations.
These F2 values reveal (Figure 4d, right) the influence of the
second qubit on the measured quantum state of the first.
Comparison of 1 and 2 reveals that the single qubit operations
in these qubit dyads are not substantially impacted by the
second qubit, reflected in their F2 values near unity. Curiously,
the fidelities for the longest complexes, 3, are lower, which
cannot be due to simple decoherence since the Tm of 1−3 and
2a/2b are nearly identical in toluene. The decreased F2
indicates the intramolecular qubit−qubit interaction in 3
perturbs the measured density matrix. In the two-pulse
measurement of ⟨Sx⟩, ⟨Sy⟩, the π pulse refocuses any dipolar
interaction between Cu2+ and Ti3+. However, our measure-
ment of ⟨Sz⟩ requires a third free precession, during which time
the qubits can acquire a phase shift due to the dipolar field of
their partner. In 1 and 2, the qubit−qubit dipolar coupling is
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CONCLUSION
ASSOCIATED CONTENT
■
■
sı
Molecular synthesis enables the creation of designer quantum
systems, each tailor-made for a specific application in QIS.
Leveraging g-anisotropy in systems of multiple chemical qubits
can be a powerful tool to create frequency addressable systems.
Here, we facilitate interrogation and deconvolution of the
intermolecular and intramolecular influences on qubit
coherence and measure the fidelity of quantum state
preparations. We find that the electron spins in these qubit
pairs do not contribute significantly to decoherence of their
partner due to their different resonance frequencies. Chemical
qubits have the intrinsic benefit of scalable, repeatable
fabrication, and our findings reinforce that spectral separation
of these qubits is a powerful strategy for qubit control
scalability through frequency multiplexing. Critically, this
strategy also mitigates decoherence in these larger multiqubit
systems by suppressing energy conserving mutual spin-flips
both between qubits and between environmental spins. This
work lays the foundation for bottom-up integration of multiple
qubits with distinct functions into custom quantum systems,
such as pairs of anisotropic quantum sensors for mapping
vector fields in 3D or multifunctional arrays featuring unique
quantum elements designed for initialization, sensing, storage,
and readout.
* Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/jacs.1c02417.
Full experimental details and synthetic procedures, EPR
spectroscopic data, X-ray crystallographic data, MALDI-
TOF mass spectra, and NMR spectra (PDF)
Accession Codes
CCDC 2063308, 2063311, and 2063319 contain the
supplementary crystallographic data for this paper. These
data can be obtained free of charge via www.ccdc.cam.ac.uk/
data_request/cif, or by emailing data_request@ccdc.cam.ac.
uk, or by contacting The Cambridge Crystallographic Data
Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44
1223 336033.
AUTHOR INFORMATION
■
Corresponding Authors
Danilo Puggioni − Department of Materials Science and
Engineering, Northwestern University, Evanston, Illinois
60208, United States; orcid.org/0000-0002-2128-4191;
Email: danilo.puggioni@northwestern.edu
James M. Rondinelli − Department of Materials Science and
Engineering, Northwestern University, Evanston, Illinois
60208, United States; orcid.org/0000-0003-0508-2175;
Email: jrondinelli@northwestern.edu
Michael R. Wasielewski − Department of Chemistry and The
Institute for Sustainability and Energy at Northwestern,
Northwestern University, Evanston, Illinois 60208, United
States; orcid.org/0000-0003-2920-5440; Email: m-
wasielewski@northwestern.edu
Danna E. Freedman − Department of Chemistry,
Northwestern University, Evanston, Illinois 60208, United
States; Department of Chemistry, Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139, United
States; orcid.org/0000-0002-2579-8835;
Email: danna.freedman@northwestern.edu, danna@
mit.edu
EXPERIMENTAL SECTION
■
See the Supporting Information for detailed methods, synthetic
procedures, and characterization data.
Sample Preparation. All EPR samples were prepared in dry,
deoxygenated solvents in an N2 glovebox. Sample solutions were
loaded in 4 mm OD Wilmad quartz EPR tubes, capped with rubber
septa, removed from the glovebox, attached to a Schlenk line by a
needle, and frozen in liquid N2 under positive pressure of N2. The
tubes were then evacuated to <50 mTorr and flame-sealed with a
hydrogen−oxygen torch. Samples of all compounds in toluene, CS2,
or their mixtures prepared in this way are stable for months stored in
the dark at ambient temperature as determined by EPR and NMR
spectroscopies.
Instrumentation. CW-EPR spectra were acquired in perpendic-
ular mode at 9.5287 GHz at 77 K on a Bruker EMXplus spectrometer
equipped with an ER-4116DM resonator fitted with a quartz finger
dewar. Pulse EPR experiments were conducted at X-band frequency
(9.3−9.8 GHz) on a Bruker Elexsys E580 EPR spectrometer equipped
with a split ring resonator (ER4118X-MS5) overcoupled to a Q < 200
and employing a 1 kW TWT amplifier (Applied Systems Engineer-
ing). Temperature was controlled between 5 and 80 K via an Oxford
Instruments CF935 helium flow cryostat and an Oxford Instruments
MercuryiTC temperature controller. Unless otherwise stated, micro-
wave power attenuation was adjusted to achieve a 32 ns (EDFS, T1,
and Tm measurements) or 48 ns (tomography) π pulse determined by
nutation experiments using a p1−π/2−τ−π−τ−echo sequence, taking
the pulse length at the first minimum to be the π pulse. EDFS, T1, and
Tm data were acquired in quadrature and phased in Matlab r2020a to
maximize the real component. Quantum state tomography was
performed at a center frequency of 9.44 GHz and resonator Q of 116
and employed a [gate]−τ−π−τ−echo sequence to measure ⟨Sx⟩ +
i⟨Sy⟩ and a [gate]−τ−π−τ−π/2−τ−echo sequence to measure ⟨Sz⟩. A
τ of 400 ns with a 4-step or 16-step CYCLOPS48 phase cycle were
used for all measurements; the [gate] was not phase cycled. The echo
data were phased using the + z (no operation) as reference and zero-
filled to 4K points before windowing (Hamming) and FFT. The zero-
frequency component approximately equals the desired magnet-
ization, whose sum of absolute values was normalized to 1. The
Authors
Stephen von Kugelgen − Department of Chemistry,
Northwestern University, Evanston, Illinois 60208, United
States; orcid.org/0000-0003-2547-3333
Matthew D. Krzyaniak − Department of Chemistry and The
Institute for Sustainability and Energy at Northwestern,
Northwestern University, Evanston, Illinois 60208, United
States; orcid.org/0000-0002-8761-7323
Mingqiang Gu − Department of Materials Science and
Engineering, Northwestern University, Evanston, Illinois
60208, United States
Complete contact information is available at:
https://pubs.acs.org/10.1021/jacs.1c02417
Author Contributions
All authors have given approval to the final version of the
manuscript.
Notes
Ä
É
Å
Å
Ñ
Ñ
Ñ
1 + ⟨S ⟩ ⟨S ⟩
Å
z
x
Å
Å
Å
Å
Ñ
Ñ
Ñ
Ñ
resulting density matrix is constructed by
The authors declare no competing financial interest.
⟨S ⟩
1 − ⟨S ⟩
y
z
Å
Ñ
Å
Ç
Ñ
Ö
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J. Am. Chem. Soc. 2021, 143, 8069−8077

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
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Winpenny, R. E. P.; McInnes, E. J. L. Close Encounters of the Weak
Kind: Investigations of Electron-Electron Interactions between
Dissimilar Spins in Hybrid Rotaxanes. J. Am. Chem. Soc. 2019, 141
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ACKNOWLEDGMENTS
■
We thank Dr. Lei Sun and Dr. Tijana Rajh for help with
preliminary EPR experiments, Mr. Saman Shafaie for high
resolution mass spectrometry, and Dr. Chung-Jui Yu for expert
assistance with data visualization. This work was supported by
the U.S. Department of Energy, Office of Science, Basic Energy
Sciences under award DE-SC0019356. S.v.K. also acknowl-
edges support from the Arnold and Mabel Beckman
Foundation through a Postdoctoral Fellowship in the
Chemical Sciences. This research used resources of the
National Energy Research Scientific Computing Center, a
DOE Office of Science User Facility supported by the Office of
Science of the U.S. Department of Energy under Contract No.
DE-AC02-05CH11231. Mass spectrometry, NMR spectrosco-
py, and X-ray crystallography made use of the IMSERC at
Northwestern University, which has received support from the
NSF (CHE-1048773), Soft and Hybrid Nanotechnology
Experimental (SHyNE) Resource (NSF ECCS-1542205), the
State of Illinois and International Institute for Nanotechnology
(IIN).
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