Scaling Up Electronic Spin Qubits into a Three-Dimensional Metal-Organic Framework

Article abstract of DOI:10.1021/jacs.8b06733

Practical implementation of highly coherent molecular spin qubits for challenging technological applications, such as quantum information processing or quantum sensing, requires precise organization of electronic qubit molecular components into extended frameworks. Realization of spatial control over qubit-qubit distances can be achieved by coordination chemistry approaches through an appropriate choice of the molecular building blocks. However, translating single qubit molecular building units into extended arrays does not guarantee a priori retention of long quantum coherence and spin-lattice relaxation times due to the introduced modifications over qubit-qubit reciprocal distances and molecular crystal lattice phonon structure. In this work, we report the preparation of a three-dimensional (3D) metal-organic framework (MOF) based on vanadyl qubits, [VO(TCPP-Zn₂-bpy)] (TCPP = tetracarboxylphenylporphyrinate; bpy = 4,4′-bipyridyl) (1), and the investigation of how such structural modifications influence qubits' performances. This has been done through a multitechnique approach where the structure and properties of a representative molecular building block of formula [VO(TPP)] (TPP = tetraphenylporphyrinate) (2) have been compared with those of the 3D MOF 1. Pulsed electron paramagnetic resonance measurements on magnetically diluted samples in titanyl isostructural analogues revealed that coherence times are retained almost unchanged for 1 with respect to 2 up to room temperature, while the temperature dependence of the spin-lattice relaxation time revealed insights into the role of low-energy vibrations, detected through terahertz spectroscopy, on the spin dynamics.

Full text of DOI:10.1021/jacs.8b06733

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Article
Scaling up Electronic Spin Qubits into a
Three-Dimensional Metal-Organic Framework
Tsutomu Yamabayashi, Matteo Atzori, Lorenzo Tesi, Goulven Cosquer, Fabio
Santanni, Marie-Emmanuelle Boulon, Elena Morra, Stefano Benci, Renato
Torre, Mario Chiesa, Lorenzo Sorace, Roberta Sessoli, and Masahiro Yamashita
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b06733 • Publication Date (Web): 26 Aug 2018
Downloaded from http://pubs.acs.org on August 26, 2018
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Scaling up Electronic Spin Qubits into a ThreeꢀDimensional
MetalꢀOrganic Framework
†
‡
‡
†
‡
§
Tsutomu Yamabayashi, Matteo Atzori, Lorenzo Tesi, Goulven Cosquer, Fabio Santanni,
‡
§
||
||,⸸
MarieꢀEmmanuelle Boulon, Elena Morra, Stefano Benci, Renato Torre, Mario Chiesa,
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Lorenzo Sorace, Roberta Sessoli * and Masahiro Yamashita†,∇,◊,*
‡
‡,#,
†
Department of Chemistry, Graduate School of Science, Tohoku University, 6ꢀ3
Aramaki AzaꢀAoba, Aobaꢀku, 980ꢀ8578 Sendai, Japan.
‡
Dipartimento di Chimica “Ugo Schiff” & INSTM RU, Università degli Studi di
Firenze, Via della Lastruccia 3, I50019 Sesto Fiorentino (Firenze), Italy.
§
Dipartimento di Chimica e NIS Centre, Università di Torino, Via P. Giuria 7, I10125
Torino, Italy.
ǁ
European Laboratory for NonꢀLinear Spectroscopy, Università degli Studi di Firenze,
Via Nello Carrara 1, I50019 Sesto Fiorentino (Firenze), Italy.
⸸
Dipartimento di Fisica ed Astronomia, Università degli Studi di Firenze, Via G.
Sansone 1, I50019 Sesto Fiorentino (Firenze), Italy.
#
ICCOMꢀCNR, Research Area Firenze, Via Madonna del Piano 10, I50019 Sesto
Fiorentino (Firenze), Italy.
∇
◊
WPI, Advanced Institute for Materials Research, Tohoku University, 2ꢀ1ꢀ1 Katahira,
AobaꢀKu, Sendai 980ꢀ8577, Japan.
School of Materials Science and Engineering, Nankai University, Tianjin 300350,
China.
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ABSTRACT: Practical implementation of highly coherent molecular spin qubits for
challenging technological applications, such as quantum information processing or quantum
sensing, requires precise organization of electronic qubit molecular components into extended
frameworks. Realization of spatial control over qubitꢀqubit distances can be achieved by
coordination chemistry approaches through an appropriate choice of the molecular building
blocks. However, translating single qubit molecular building units into extended arrays does
not guarantee a priori retention of long quantum coherence and spinꢀlattice relaxation times
due to the introduced modifications over qubitꢀqubit reciprocal distances and molecular
crystal lattice phonons structure. In this work, we report the preparation of a threeꢀ
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dimensional (3D) metalꢀorganic framework (MOF) based on vanadyl qubits, [VO(TCPPꢀZn ꢀ
bpy)] (TCPP = tetracarboxylꢀphenylporphyrinate; bpy = 4,4’ꢀbipyridyl) (1), and the
investigation of how such structural modifications influence qubits performances. This has
been done through a multitechnique approach where the structure and properties of a
representative molecular building block of formula [VO(TPP)] (TPP
=
tetraphenylporphyrinate) (2) have been compared with those of the 3D MOF 1. Pulsed
electron paramagnetic resonance measurements on magnetically diluted samples in titanyl
isostructural analogues revealed that coherence times are retained almost unchanged for 1
with respect to 2 up to room temperature, while the temperature dependence of the spinꢀlattice
relaxation time revealed insights on the role of low energy vibrations, detected through
terahertz (THz) spectroscopy, on the spin dynamics.
INTRODUCTION
Quantum bits, or qubits, represent the elementary units for the realization of quantum
1
2–4
computers as well as the active units of potential quantum sensors. For both applications,
the quantum superposition of state that characterizes qubits physical realizations is exploited
for specific purposes. In quantum computation, a highly coherent superposition state allows
for the retention of the quantum information on the qubits for a time longer than that required
to perform a quantum operation (quantum gate), whereas in quantum sensing a loss of
coherent superposition is used to probe the presence of environmental perturbations.
Nowadays, finding suitable, robust, and scalable systems as potential qubits represents one of
the main challenges in chemistry, physics and materials science for the development of these
technological applications.
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Many physical systems, such as photon, trapped ions, quantum dots, and coherent
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9–11
coupled systems of superconducting qubits with nitrogenꢀvacancy centers in diamond
are
investigated as qubits candidates, each of them showing both merits and demerits. Among
these qubits realizations, moleculeꢀbased spin qubits have been investigated only recently and
have shown remarkable advantages, such as the capacity of facile addressing via pulsed
12
electron paramagnetic resonance (EPR) techniques ꢀ although not yet at the single qubit
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level ꢀ a high processability through surface deposition, and a high degree of chemical
14,15
tunability.
These features are crucial for their practical development and are not easily
satisfied for other classes of potential qubits, such as, for example, electronic defects in
9
–11
extended inorganic solids.
relatively short lifetime of the quantum superposition states compared to other potential
systems. This loss of information is related to the spinꢀspin relaxation time T , that is usually
estimated by measuring the phase memory time T , which is a lower limit of T . Interactions
On the other hand, molecular spin qubits often suffer from a
2
m
2
with the environment contribute to the collapse of the already fragile superposition state of
electronic spins in a process known as decoherence. In this respect, intense investigations
aimed at increasing molecular qubits performance through chemical design have been
16–22
reported in recent years.
Another feature that places moleculeꢀbased spin qubits in a noteworthy position with
respect to electronic defects in extended inorganic solids is the potential spatial control over
qubitꢀqubit distances achievable through coordination chemistry approaches. Indeed,
extended coordination polymers, or metalꢀorganic frameworks (MOFs), with specific
structural features such as overall dimensionality (bidimensional, 2D, or tridimensional, 3D),
type of structural backbone (cubic, hexagonal), and controlled internal surface area, can be
prepared at will through a wise selection of the molecular building blocks and wellꢀdeveloped
23–25
coordination chemistry strategies.
This bottomꢀup approach can play a key role for
quantum computation in increasing the scalability of the system by controlling the number of
interconnected qubits within an extended network. This is equally relevant for quantum
sensing, since extended porous networks allow analytes to diffuse selectively inside the voids
4
,26–28
of the solid and to be precisely detected by the qubit sensor units.
The above mentioned bottomꢀup approach has been employed for the preparation of
II
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2
D nanosheets embedding Cu ꢀtetracarboxylꢀphenylporphyrinate units, and a porous 3D
II
network obtained linking Co ꢀtetracarboxylꢀphenylporphyrinate complexes through
3
0
II
II
[Zr (OH) ] units. For both materials the coherence times of the corresponding Cu and Co ꢀ
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based electronic spin qubits have been investigated. In the latter, the strong hyperfineꢀ
coupling induces a mixing of M
S
and M
I
levels of the S = 1/2 and I = 7/2 electronic and
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nuclear spin values of Co . This generates an avoided level crossing at low magnetic fields (<
.3 T), whose related EPR transitions frequencies are characterized by a weak magnetic field
dependence, i.e. f/ B = 0. Such a condition is typically observed for isolated atoms and can
0
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ꢀ
be used for the realization of a certain class of atomic clocks, thus these transitions assume the
name of clock transitions. Such transitions are particularly insensitive to the magnetic noise,
leading to enhanced coherence. However, it is exactly the low sensitivity to magnetic noise
that makes them not ideal for quantum sensors applications, as also pointed out by the authors
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of the study.
It should be also considered that room temperature coherence is highly desirable for
sensing purposes. In this temperature regime, spinꢀlattice relaxation is a limiting factor.
Indeed, both local and extended vibrational modes (phonons) can be significantly modified
passing from isolated molecules that weakly interact in the crystal structure, mainly through
nonꢀcovalent interactions, to extended molecular networks, where the units are covalently
22,31–33
linked. This can induce relevant modification on the spin dynamics.
For the design of molecular spin qubit with viable coherence times,
oxidovanadium(IV) complexes constitute one of the most promising choice thanks to the
weak orbital contribution to the magnetism and an inefficient spinꢀphonon coupling
16,34
interaction, which provides long spinꢀlattice relaxation even at room temperature.
characterization of the spinꢀlattice relaxation time, T
The
1
, is then crucial in the design of highly
performing molecular spin qubits since this process provides an upper limit for the coherence
13
time. Moreover, the investigation of spinꢀlattice and coherence times of vanadylꢀbased
potential qubits embedded into a 3D crystalline material has not been reported yet.
Motivated by the need to acquire additional insights on the role of the crystal lattice
properties in determining electronic spin qubits performance, here we report the preparation
2
of a porous vanadylꢀbased 3D MOF of formula [VO(TCPPꢀZn ꢀbpy)] (1) (TCPP =
tetracarboxylꢀphenylporphyrinate; bpy = 4,4’ꢀbipyridyl). The spinꢀlattice relaxation times of 1
were studied by alternate current (AC) susceptibility measurements, and the coherence times
2
of an isostructural magnetically diluted sample [VO0.05TiO0.95(TCPPꢀZn ꢀbpy)] (1’) were
investigated through pulsedꢀEPR spectroscopy. The results have been compared to those
obtained on a representative mononuclear molecular building block (0D) of formula
[
VO(TPP)] (TPP = tetraphenylporphyrinate) (2) and its isostructural magnetically diluted
sample [VO0.02TiO0.98(TCPP)] (2’). The analysis of the temperature dependence of the spinꢀ
lattice relaxation time, which plays a crucial role in determining the coherence at room
temperature for the two materials, is discussed considering the different structural and
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spectroscopic features in the terahertz regime shown by the 3D network and the 0D
mononuclear analogue.
RESULTS
Design & Synthesis. Metalated tetraphenylporphyrins have been largely employed as
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molecular building blocks for the preparation of regular 3D heteroꢀ and homoꢀmetallic
30,35,36
MOFs.
Unlike other metalloligands, their planar and symmetric structure is ideal to both
accommodate a large variety of metal ions inside the porphyrinate macrocycle, or to prepare
crystal structures with wellꢀdefined topologies. In particular, it has been shown that
combination of metalated tetracarboxylꢀphenylporphyrinates with bare divalent metal ions
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such as Zn or Cu , and a pillarꢀlike molecular ligand such as bpy, allows preparation of
porphyrinate paddleꢀwheel frameworks for which the 3D stacking is controlled by the
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coordination geometry of the porphyrin metal center (Figure 1).
Figure 1. Schematic representation of the twoꢀstep selfꢀassembling process responsible for the
formation of the 3D MOFs 1 and 1’. Color codes: green: vanadium, orange: zinc, red: oxygen, light
blue: nitrogen, gray: carbon. Hydrogen atoms are omitted for graphical clarity.
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As an example, tetracoordinated ions such as Mn and Fe ions easily allow further axial
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coordination with the Nꢀdonating pillar ligand, while Pt and Ni prefer to maintain the
square planar coordination geometry of the porphyrin macrocycle; in the latter case, further
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axial coordination is limited to the bridged Cu and Zn ions within the paddleꢀwheel motif.
The case of oxidovanadium(IV) is expected to be peculiar because further coordination with
IV
the pillarꢀlike ligand is in this case hampered by the preformed bond between V and the
oxido ligand, which results in an overall modification of the coordination geometry of the
metal center to a square pyramidal one.
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Within this general scheme, the reaction between preformed vanadylꢀ and/or titanylꢀ
2+
tetracarboxylꢀphenylporphyrinates with Zn and bpy has been performed to obtain the 3D
structure reported in Figure 1c.
The synthesis of the vanadyl tetracarboxylꢀphenylporphyrinate [VO(TCPP)] building
block has been achieved by following a reported procedure that has been adapted to the
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oxidovanadium(IV) ion. It consists in the reaction between the vanadyl precursor
−
[
VO(acac) ] (acac = acetylacetonate) and the tetrakis(4ꢀcarboxyphenyl)porphyrin ligand with
2
carboxyl groups protected by ester functionalities,
2
H TMeCPP (tetrakis(4ꢀ
methoxycarbonylphenyl)porphyrin), in PhOH at reflux temperature (Scheme 1a).
Scheme 1. Reaction schemes for the synthesis of vanadyl and titanyl tetraphenylporphyrin derivatives
(
M = V, Ti; x = 1, 2).
Subsequent deprotection of the ester groups through basic hydrolysis provides the
VO(TCPP)] molecular building block (Scheme 1b). The same reaction conditions have been
[
used to prepare the 0D reference compound [VO(TPP)] (2) as well as the titanyl diamagnetic
analogues [TiO(TCPP)] and [TiO(TPP)] (3) (Scheme 1). It should be highlighted that
metalation of the tetracarboxylꢀphenylporphyrin with the oxidovanadium(IV) moiety is easily
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accomplished within ca. 6 hours of reaction, whereas metalation with the oxidotitanium(IV)
ion appears to be more difficult, requiring longer reaction times (ca. 36 hours) and a larger
excess of the titanyl precursor [TiO(acac) ] . This chemical inertness is reflected by the lack
2
2
of titanyl porphyrinates reported so far in the literature with respect to other transition metal
ion derivatives, including the vanadyl analogues.
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Selfꢀassembly of vanadyl tetracarboxylꢀphenylporphyrinate building blocks, Zn and
bpy in DMF at 80 °C followed by slow cooling to room temperature provides airꢀstable red
cubic single crystals of compound 1 suitable for Xꢀray diffraction analysis. The magnetically
diluted sample 1’ was prepared by following the same synthetic procedure developed for the
preparation of 1 by reacting a mixture of [VO(TCPP)] and [TiO(TCPP)] in 5:95 molar ratios
2
+
with Zn and bpy. Instead, the magnetically diluted samples 2’ and 2’’ were prepared by
recrystallization of [VO(TPP)] and [TiO(TPP)] in 2:98 and 30:70 molar ratios, respectively.
The difference in the nominal concentration of paramagnetic species between the two lower
concentrated materials has been designed to achieve similar spin concentrations in view of the
presence of large voids for the 3D compound 1 with respect to the 0D compound 2 (vide
infra).
Crystal Structures. Compound 1 crystallizes in the tetragonal P4 space group with one
2+
anionic complex, two Zn ions and one bpy molecule in the unit cell, the asymmetric unit
being one fourth of the molecule. The peripheral carboxyl substituents of the porphyrin
2
+
macrocycle (Figure 1a) interact with Zn to form 2D layers where the porphyrin units are
connected in a fourꢀfolded symmetry through [Zn (COO) ] subunits (Figure 1b), similarly to
]. The pillarꢀlike ligands bpy then allow
connection between the 2D layers to form a 3D MOF by further axial coordination between
2
4
29
2 2 2
what recently reported for [Cu(TCPP)ꢀZn (H O)
pairs of [Zn
2
(COO)
4
] subunits (Figure 1c). The obtained structure has 3D channels with a
2
pore dimension of 1.66
×
1.38 nm along the
a
and
b
axes. The percentage of void volume in
3
3
the structure of 1 was estimated to be ca. 74 % (2842 Å ) and 72.8 % (2795 Å ) of the total
3
volume (3838 Å ) considering H and N as probe gases, respectively (kinetic radii, H ,
r =
2
2
2
38
1.40 Å; N
2
, r = 1.82 Å).
2
+
The coordination geometry of the Zn ions, which templates the formation of the
2
+
overall crystal structure, consists in a square pyramid where pairs of Zn ions are bridged in a
ꢁꢀtype binding mode by four carboxylate ligands. The resulting equatorial plane around each
2
+
Zn ion is thus formed by four oxygen donor atoms, while the axial position of the square
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pyramid is completed by the nitrogen donor of a bpy ligand, which bridges pairs of Zn ions
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Figure 2. Molecular structures of compounds 1 (a) and 3 (b) with coordination geometry of the metal
ions highlighted. Color codes: green: vanadium, orange: zinc, silver: titanium, red: oxygen, light blue:
nitrogen, gray: carbon. Hydrogen atoms and disordered fragments are omitted for graphical clarity.
4−
The molecular structure of the anionic complex [VO(TCPP)] shows a vanadium(IV)
ion in a square pyramidal coordination geometry with the metal ion slightly above the basal
plane (ca. 0.59 Å) formed by the four nitrogen donor atoms of the porphyrin macrocycle
(
Figure 2a). The V=O moiety is sitting on the fourꢀfold symmetry axis and is disordered on
two positions, symmetric with respect to the macrocycle ring, with 50:50 occupancy factors,
leading to a nonꢀpolar crystal structure. The V−O and V−N distances, 1.60 Å and 2.09 Å
respectively, are in agreement with what is usually encountered for similar vanadyl
complexes. The planes of the phenyl substituents are 90° tilted with respect to the plane of the
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porphyrin macrocycle, in agreement with what observed for analogous MOFs based on
isostructural building blocks (Figure 2a). This leads to an overall crystal structure of
tetragonal symmetry where all vanadyl moieties are oriented along the
V···V shortest distances in the crystal structure of 1 correspond to the unit cell distances, i.e.
3.9 Å along the axis and 16.6 Å in the ab plane. Finally, it should be noted that the
c axis (Figure S1). The
1
c
1
1
1
1
1
1
1
1
1
1
2
2
2
2
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2
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pyridine rings of the bpy ligand appear disordered in two 90°ꢀtilted orientations, with the
orientation of the two independent rings 45°ꢀtilted with respect to each other.
Single crystals suitable for Xꢀray diffraction analysis of compounds 2 and 3 were
2 2
obtained by slow evaporation of CH Cl solutions. Both compounds crystallize in the
tetragonal I4 space group with two neutral complexes in the unit cell; even in this case the
asymmetric unit is one fourth of the molecule. Due to the better quality of the collected
diffraction data and the isostructurality between the two compounds, here we report only the
data related to the [TiO(TPP)] compound 3.
The crystal structure of 3 consists of neutral titanyl tetraphenylporphyrinate complexes
with all Ti=O units lying on the fourfold symmetry
c axis (Figure S2). The shortest M···M
distance is 10.9 Å and involves metal complexes of adjacent layers. No significant
intermolecular contacts involving the phenyl rings are present. The molecular structure of the
IV
complex is reported in Figure 2b. The coordination geometry around the Ti ion is a square
pyramid with a Ti−O distance of 1.58 Å and Ti−N distances of 2.11 Å. As already observed
for 1, the metalꢀoxido cationic moiety is disordered along the tetragonal axis on two positions
with equal occupancy factors, with the metal center lying 0.58 Å from the basal plane of the
porphyrin macrocycle.
Powder Xꢀray diffraction (PXRD) patterns were recorded on polycrystalline samples
of all investigated systems, both pure compounds and crystalline dispersions, to ascertain their
structural phase homogeneity. This is clearly evidenced by the good agreement between
experimental and simulated patterns (Figures S3−S4).
Magnetization dynamics. AC susceptibility measurements were performed on
microcrystalline samples of compounds 1, 2 and the crystalline dispersion 2’’ to investigate
their magnetization dynamics. The choice to study the dilution 2’’ is due to the pronounced
difference in the spin concentration between 1 and 2. Indeed, the spin concentration for 1 is
−3
−3
0
.26 spin nm , whereas for 2 it is 1.1 spin nm . 2’’ provides a spin concentration of 0.34
−3
spin nm , which is closer to that of 1, and thus associated to a comparable dipolar internal
magnetic field.
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As commonly observed for S = ½ molecular spin qubit systems, the thermal variation
of the complex magnetic susceptibility in zero static magnetic field reveals no outꢀofꢀphase
component of the susceptibility (χ'') in the whole investigated temperature range. When a
small static magnetic field (> 40 mT) is applied, slow magnetic relaxation is observed for all
samples with appearance of a peak in the outꢀofꢀphase component of the susceptibility and a
0
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3,34
concomitant decrease of the inꢀphase part (
χ
') (Figures S5ꢀS17).
The relaxation time, τ,
which is representative of the spinꢀlattice relaxation, was obtained by simultaneously fitting
the real and imaginary components of the magnetic susceptibility with the generalized Debye
39
model (see Supporting Information). The extracted values of
under a static magnetic field B = 1.0 T scanning the temperature, are reported in Figure 3a in a
log( ) vs log(T) plot.
τ for 1, 2 and 2’’ obtained
τ
Figure 3. Temperature (a) and magnetic field (b) dependence of
τ extracted from AC susceptibility
measurements for microcrystalline samples of compounds 1, 2 and 2’’ under an applied static
magnetic field of 1.0 T (a) and in the 0.0−8.5 T range at 5.0 K (b). Solid lines are the bestꢀfit of the
models (see text).
The absolute values of the spinꢀlattice relaxation times are comparable for 1 and 2’’ in
a wide temperature region, whereas those of 2 are lower, thus following the trend of the spin
concentrations. The temperature dependence of
τ shows a qualitatively similar behavior for
the three compounds in the entire T range. At the lowest temperatures, between 4 and 10 K,
the spinꢀlattice relaxation time shows a T−2 dependence, which suggests the presence of an
40,41
important spinꢀphonon bottleneck effect.
This phenomenon affects the direct spinꢀlattice
relaxation mechanism in magnetically concentrated samples and is particularly relevant in
4
2
vanadylꢀbased molecules. Figure 3a shows that in the 10−30 K range, an unexpected
remarkably weak temperature dependence of is observed, with an exponent significantly
τ
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lower than the unity expected for a pure direct mechanism relaxation process. For T > 30 K,
τ
of both compounds exhibits a faster decrease with increasing temperature.
To have a better understanding of the relaxation mechanisms involved in such
compounds, the magnetization dynamics was also studied as a function of the static magnetic
field in a wide magnetic field range (0.0−8.5 T) at different temperatures (5.0 K, 7.5 K and
10.0 K) for each compound (Figures S9−S17). The relaxation times extracted with the
generalized Debye model at 5.0 K are shown in Figure 3b, while the data obtained at all
investigated temperatures are reported in Figures S18−S20. All compounds show the expected
1
1
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2
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0
nonꢀmonotonous behavior of the relaxation time, with an increase of
τ at low field, a plateau
at intermediate fields, and then a decrease at high fields. In the low field region, up to 1.0 T,
spinꢀspin and spinꢀnuclei interactions, which promote spin relaxation by breaking the timeꢀ
4
4,45
reversal symmetry of the Kramers doublet,
magnetic field, resulting in a rapid growth of
the strong field dependence of the direct mechanism causes the rapid decrease of
are suppressed by the increasing of the
. Instead, in the high field region, beyond 3.0 T,
. Indeed,
states, the larger is the number of phonons
τ
τ
the larger is the Zeeman splitting of the two M
s
matching this energy difference.
The absolute values of the relaxation times of 1 and 2’’, as well as the magnetic field
dependence, are again comparable, whereas 2 shows lower values of , in agreement with its
τ
temperature dependence (Figure 3a). A striking feature in the magnetic field dependence of
the relaxation times is the dip shown by all compounds at 2.0 T. This feature is particularly
pronounced for 2 (Figure S21) and less pronounced for 2’’, suggesting that the presence of
this dip might be related to the spinꢀphonon bottleneck effect. However, the reason why an
acceleration of the relaxation rate at 2.0 T is observed, is, at the moment, unclear. To check if
an anomalous temperature dependence of
τ is also present at this field value, AC
susceptibility data for compound 2 were recorded also at 2.0 T, showing a very similar
behavior (Figure S22).
The magnetic field dependence of
τ for 1 is reproduced by the Brons − van Vleck
4
5,46
model
with a slight modification (eq. 1):
1
+ ꢅꢆꢇ
+ ꢈꢆꢇ
(1)
ꢀꢁꢂ
ꢉ + ꢊꢆꢋ
= ꢃ ꢄ
1
1
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The first term is related to the lowꢀfield region where
τ
increases due to the suppression of the
internal fields, whereas the second term accounts for the direct relaxation mechanism. In the
standard Brons – van Vleck model, the direct contribution to the spinꢀlattice relaxation rate in
−
1
4
Kramers systems depends on the field as
τ
∝ cB . This has indeed been confirmed by
13,16,22,32,34,42
previous studies on vanadiumꢀbased molecular spin qubits.
However, in this case
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0
τ
shows a weaker magnetic field dependence, and the bestꢀfits of the experimental data
obtained for 1 assuming different integer values of m (Figures S23−S25 and Table S1) clearly
favor a cubic field dependence. This points to a nonꢀconventional direct relaxation
mechanism, in agreement with the observed anomalous weak temperature dependence of τ.
3
2
The extended Bronsꢀvan Vleck model has been used to properly reproduce the data
obtained for 2’’:
+ ꢅꢆꢇ
1 + ꢅꢆꢇ
1 + ℎꢆꢇ
ꢀꢁꢂ = ꢃ ꢄ11
ꢇꢉ + ꢌ ꢄ
ꢉ + ꢊꢆꢋ
(2)
+ ꢈꢆ
In this case, a second term accounting for the suppression of the internal fields due to the
increase of the magnetic field is introduced. The use of the extended law is justified in Figure
S26, where the data of 2’’ are fitted with both models, while Table S1 contains the bestꢀfit
parameters for the three different temperatures. Finally, it should be highlighted that the
modelling of the magnetic field dependence of the spinꢀlattice relaxation time for 2 is not
feasible because the distortions observed between 2.0 and 7.0 T do not allow for reasonable
fits with both standard and extended Brons − van Vleck models.
Continuous Wave and Pulsed Electron Paramagnetic Resonance Spectroscopy. While
AC susceptometry provides useful information about spinꢀlattice relaxation as a function of
the applied static magnetic field in concentrated samples, pulsed EPR spectroscopy allows to
determine both spinꢀlattice and spin coherence relaxation times for magnetically diluted
systems in a wide temperature range.
Continuous wave (CW) and echoꢀdetected fieldꢀswept (EDFS) EPR spectra of the
diluted compounds 1’ and 2’ recorded at T = 10 K and T = 50 K, respectively, are reported in
Figure 4 together with their simulations.
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Figure 4. Experimental and simulated CW and EDFS EPR spectra for 1’ (a) and 2’ (b) at Xꢀband
frequency (9.7 GHz). Spectral simulations corresponding to the spin Hamiltonian parameters reported
in Table 1 are shown in red. The asterisk and the arrow on the CW EPR spectrum of 2’ evidence the
presence of unavoidable paramagnetic impurities that have been included in the simulation (see text
and Supporting Information for further details).
Both compounds show similar spectra that are characterized by the eightꢀfold hyperfine
IV
structure due to the coupling between the S = 1/2 electronic spin of V and the I = 7/2 nuclear
51
spin of its most abundant isotope ( V, abundance 99.76%). The signals are further split by
the anisotropic components of the hyperfine coupling in perpendicular and parallel directions.
4
7
Spectral simulations were then performed using the following spin Hamiltonian
ꢏ
ꢓ
ꢓ
ꢕ
(3)
ꢍ = ꢎ ꢐ ꢑ ꢐ ꢒ + ꢔ ꢒ ꢐ ꢖ ꢐ ꢗ
to evaluate the anisotropy of the g factor as well as of the hyperfine coupling constant A. The
experimental spectra can be satisfactorily reproduced assuming an axial model (i.e. x = y ≠ z)
for both compounds, in agreement with the tetragonal site symmetry of the molecular
systems. The bestꢀfit parameters are reported in Table 1.
Table 1. Bestꢀfit parameters extracted from simulation of the experimental spectra of 1’ and 2’.
Compound
g
x
g
y
g
z
|A
x
| (MHz)
|A
y
|(MHz)
z
|A |(MHz)
1
’
’
1.9865(1)
1.9865(1)
1.9865(1)
1.9865(1)
1.963(1)
1.963(1)
168(2)
169(2)
168(2)
169(2)
477(2)
480(2)
2
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The parameters reported in Table 1 agree with those expected for vanadyl
48,49
porphyrinate derivatives
and correspond to a ground state with the unpaired electron in a
dxy orbital. It is evident that the EPR spectrum of 2’ also shows some weak features (< 4% of
the total signal and indicated in Figure 4b) which cannot be attributed to vanadyl species. On
the basis of the best simulation parameters (Figure S27 and Table S2) these were attributed to
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III
radical monoanionic ligand and a residual Ti species.
Hyperfine Sublevel Correlation (HYSCORE) experiments have been performed on the
two compounds to detect and determine the hyperfine interactions due to the ligand nitrogen
atoms of the porphyrin ring and nearby hydrogens. The spectra of 1’ and 2’ (Figures
S28−S29) are practically superimposable and typical for vanadyl porphyrin and
4
9
14
phthalocyanine molecular systems. Spectra simulation (Figure S30) provided N hyperfine
and quadrupole splitting parameters that well compare with previously reported data on
similar coordination environments (Table S3).
The intense spinꢀecho detected EPR spectrum let us anticipate that quantum
coherence could be measured for both compounds. Moreover, the spin Hamiltonian
parameters obtained through the simulation of the CW spectrum provide good simulations of
the EDFS spectra as well, hence indicating that the entire paramagnetic components are
experiencing the detected coherence.
Inversion recovery experiments on 1’ and 2’ were performed in the 5.0−290 K
temperature range at Xꢀband frequency to investigate the temperature dependence of the spinꢀ
lattice relaxation time T
transition M = −1/2 → +1/2. The resulting saturation recovery traces were fitted with a
stretchedꢀexponential equation
1
at the resonant magnetic field corresponding to the hyperfine
I
ꢤ
ꢟꢠ
ꢡꢢ
ꢢ
ꢝꢁꢞ
ꢣ
ꢥ
(4)
ꢘ = ꢘ + ꢚ ꢅꢛꢜ
ꢙ
ꢂ
and the extracted T values (Tables S4−S5) as a function of T are reported in Figure 5.
1
1
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1 m
Figure 5. Temperature dependence of T and T for 1’ and 2’ (see legend) from pulsed EPR inversion
recovery experiments at Xꢀband frequency. Solid lines are the bestꢀfits considering local vibrational
modes according to eq. (7). Shortꢀdashed lines represent a guide for the eyes. Error bars are within the
size of the symbols.
1
The temperature dependence of T for the magnetically diluted samples 1’ and 2’ shows an
increase of the slope on rising the temperature, which is characteristic of the crossover from a
dominating direct process of relaxation at low temperature to a Raman mechanism at high
1
temperatures. T values of 1’ at low temperature are ca. one order of magnitude lower than
that of 2’ despite the similar spin concentration of the two compounds. As the temperature
increases, the spinꢀlattice relaxation time for 2’ starts to decrease more abruptly above 30 K,
whereas 1’ shows such a behavior only at higher temperature and with a weaker temperature
dependence. Consequently, the curves for the two compounds intersect around 60 K, and at
room temperature T for 1’ reaches a value of ca. 1 ꢁs vs 0.6 ꢁs observed for 2.
1
Different analytical functions are commonly used to reproduce the temperature
50
dependence of T1. Here, the experimental data are well reproduced (Figure S31) by the
phenomenological relation
ꢦꢂꢁꢂ = ꢧꢨꢩꢪꢦ + ꢧ
ꢫ
ꢦꢮ
(5)
ꢬꢭꢋ
where, unlike to previous reports, the exponent x of the temperature dependence of the direct
4
3
process is left free to vary from the unitary value which is expected for the direct process.
The bestꢀfit values for the direct process are x = 0.54(6) and x = 0.3(3) for 1’ and 2’, thus
1
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deviating significantly from unity. On the other hand, the Raman process exponents, n =
2.5(1) and 3.4(1) for 1’ and 2’ respectively, are within the usual range observed for vanadyl
13,16,34,51
complexes (n ca. 3).
It is worth noting that replacement of the second term of eq. (5)
with the Debye transport integral function (equation S3) does not significantly improve the
overall fitting of data for 1 and worsen that for 2 (Figure S31 and Table S6).
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To investigate the quantum coherence in detail and to determine the phase memory
time, T
m
, for 1’ and 2’ as a function of the temperature, echo decay experiments were also
values, which limit the T values especially at high temperatures, are
performed. Because T
1
m
sufficiently long for both compounds in the whole investigated temperature range, echo decay
traces were detected up to room temperature for both 1’ and 2’. The decay traces were fitted
using the stretchedꢀexponential equation
ꢤꢰ
ꢇꢟ
ꢡ
ꢰ
ꢝꢁꢯ ꢠꢱ
ꢥ
(
6)
ꢘ = ꢘ + ꢚ ꢅꢛꢜ
ꢙ
ꢋ
50
as usually done for transition metal systems, where I indicates the echo intensity, 2
delay between the initial pulse and the echo detection and is the stretch factor. The
temperature dependences of T for 1’ and 2’ are reported in Figure 5.
p
τ is the
β
m
m
The thermal variation of T
behavior in the 5.0−100 K range for 1’ (ca. 0.5 ꢁs) and in the 5.0−60 K range for 2’ (ca. 1.0
s), with relative values that follow the corresponding T ones. These values are comparable
m
for 1’ and 2’ shows an almost temperature independent
ꢁ
1
to those recently reported for a 2D network formulated as [Cu(TCPP)ꢀZn
2 2 2
(H O) ] and the
relative mononuclear building block [Cu(TPP)] measured in a frozen solution, although
2
9
coherence times data are only available up to 90 K. At 150 K, T
for 1’ and 2’ (ca. 0.4 ꢁs) and decreases to reach the lowest values at room temperature (ca.
0.14 ꢁs). It is interesting to note that a crossover between the T values of 1’ and 2’ occurs in
much the same way as observed for T at slightly lower temperatures.
m
assumes the same value
m
1
To prove that the observed coherence times for 1 and 2’ allow to perform coherent
spin manipulations, i.e. to place the spins in any arbitrary superposition of states, nutation
experiments were performed at different microwave powers. Remarkably, Rabi oscillations
were clearly observed with the expected linear dependence of the Rabi frequency,
R
ꢂ , as a
function of the microwave attenuation for both 1’ (Figure 6) and 2’ (Figure S32).
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Figure 6. (a) Rabi oscillations recorded for 1’ at 5 K for different microwave attenuations (Xꢀband).
(
b) Fourier Transform of the Rabi oscillations. (c) Linear dependence of the Rabi frequency (
R
ꢂ ) as a
function of the relative intensity of the oscillating field B
1
.
−1
THz Vibrational Spectroscopy. Terahertz spectra, corresponding to the 10−110 cm range,
were recorded by timeꢀdomain transmission spectroscopy (THzꢀTD) on polycrystalline
samples of 1 and 2 dispersed in polyethylene pellets.
A striking difference between the isolated [VO(TPP)] units of 2 and the extended
−1
structures of 1 is observed. Indeed, 2 shows a wellꢀdefined absorption band at ca. 67 cm ,
which is absent in 1 (Figure 7).
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−
1
Figure 7. Vibrational spectra in the 0.6−3.0 THz range (20−100 cm ) of compounds 1 and 2 recorded
at 295 K. The arrow indicates the frequency of the absorption. Inset shows the temperature
dependence (20−295 K range) of the absorption spectra of 2.
Assignment of the low energy absorption of 2 is not straightforward because
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porphyrinate complexes show metalꢀligand vibrations that are often mixed with porphyrin
5
2–54
ring deformations.
Moreover, previous theoretical studies on simpler vanadylꢀbased
potential molecular qubits showed that in the THz frequency range a strong admixing
3
2
between local and collective degrees of freedom is also present.
The temperature dependence of the spectra of 2 (inset in Figure 7) shows a
pronounced narrowing and shift to higher frequency of the absorption peak on lowering the
temperature. According to the idea that structure stiffening at low temperature is expected to
increase the vibration energy of collective modes, we can deduce that a significant
contribution of collective vibrations to the nature of this mode is present. This is also in
agreement with the lack of this mode in the covalent lattice of 1, as well as its similar
frequency in the titanyl derivative 3 (Figure S33).
DISCUSSION
Our investigation proves the successful inclusion of paramagnetic vanadyl units in a
well structurally characterized MOF, which is, to the best of our knowledge, unprecedented
though not unexpected. More relevant is the preservation of spin coherence at room
temperature, with comparable coherence times for the MOF and the mononuclear unit. This is
a remarkable result because it allows to apply pulsed EPR techniques, which are known to
provide more detailed information on the nature and the adsorption mode of guest molecules
5
5,56
than CW techniques.
The origin of this appealing behavior can be rationalized thanks to the comparative
study that we have performed. First of all, it is important to stress that the electronic structure
of the vanadyl unit is practically identical in the MOF and in the isolated molecule. This is
clearly demonstrated by the very minor modifications of the Spin Hamiltonian parameters,
reported in Table 1, as well as of the hyperfine coupling values with neighboring nuclei
detected by HYSCORE and listed in Table S3. It is also interesting to note that some
characteristic features of the spin dynamics are preserved on increasing the material
dimensionality, such as the field dependence of the magnetization relaxation time that shows
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a wide plateau extended up to several Tesla as reported in Figure 3b. This behavior, typical of
IV
the V ion and much more pronounced than in analogous S = 1/2 systems based, for example,
II 29
on Cu , allows highꢀfield/highꢀfrequency applications without significant acceleration of the
spin dynamics.
Another common feature between the MOF and isolated molecule is the very weak
temperature dependence of the spinꢀlattice relaxation time in the temperature range 10−30 K,
where magnetic relaxation is dominated by the direct mechanism and a linear dependence
with temperature is expected. Such a behavior was also observed, though not highlighted, for
1
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4
a vanadylꢀphthalocyaninate complex. As data for the latter were collected on less
concentrated samples with respect to those investigated here, we can safely exclude that an
intermolecular processes of relaxation is responsible for such a phenomenon. This leads us to
associate this peculiarity to the macrocyclic coordination mode, although a rational for it is
still lacking.
In contrast to this remarkable similarity, 1 and 2 differ significantly in their low energy
−1
vibrational spectrum. The first IR active vibrational mode, occurring at 67 cm for 2, exceeds
−1
our accessible range (110 cm ) in 1. This originates remarkable differences in the
1
temperature dependence of T above 30 K. Local vibration modes have already been
considered as sources of magnetic relaxation, but the support of optical investigations is
57,58
uncommon.
We have therefore reproduced the temperature dependence of the spinꢀlattice
5
0
dynamics through the already proposed phenomenological model
expꢵħꢶ⁄ꢚ ꢦꢷ
ꢦꢂꢁꢂ = ꢧꢨꢩꢪꢦ + ꢧ
ꢫ
ꢕ
(7)
ꢲꢳꢴ
ꢇ
ꢵ
expꢵħꢶ⁄ꢚ ꢦꢷ − 1ꢷ
ꢕ
where ω is the frequency of the vibrational mode and adir and aloc are coupling coefficients as
1
in equation (5). The T data of 1 are successfully simulated (Figure 5) with x = 0.64 and ω =
−1
1
84(2) cm , thus suggesting that the first active mode is present at a frequency higher than
our accessible spectral range. Data simulation of 2 were performed by fixing the frequency of
−1
the vibration mode to 67 cm , accordingly to spectral findings. The whole temperature range
−1
is well reproduced including a second mode at higher frequency, 303(35) cm , to the model.
This is not surprising because an increasing number of active vibrational modes is expected to
be present at higher frequencies. Notably, similar unusually low x exponents of the direct
process are obtained independently of the model used to simulate the data (see Table S6),
confirming the robustness of the analysis.
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CONCLUSIONS
In conclusion, we have successfully synthesized a 3D porous network embedding vanadyl
spin units that retains spin coherence up to room temperature. This is a remarkable result for
coherent magnetic sensing of potentially adsorbed species. Engineering of MOF structures
with embedded vanadyl moieties acting as quantum spin sensors towards specific analytes
seems indeed quite straightforward.
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Our multitechnique investigation has also provided precious hints for a better
understanding of the spin dynamics in molecular systems. In contrast to what could be
intuitively expected, the inclusion of [VO(TPP)] units in an extended network does not affect
−n
the low temperature regime. The n < 1 exponent in the T ∝ T law seems rather typical of the
1
rigidity of the tetraphenylꢀporphyrin coordination environment. On the contrary, linking the
vanadyl units in the 3D network has pronounced effects on the infrared active low energy
1
vibrational modes. This reflects on the temperature dependence of T in the intermediate
temperature regime. The observed behavior is of paramount importance for quantum sensing
as it warrants that spin coherence is not limited at room temperature by a rapid spinꢀlattice
magnetic relaxation.
It also emerges from this study that the optimization of metalꢀorganic frameworks
performance through chemical design requires a deeper understanding of the role of
intramolecular and intermolecular vibration in the spin dynamics. The first steps we can
envisage in this direction is obtaining high quality IR spectra on a continuous range to detect
the lowest vibrational mode of 1. Recording also Raman spectra in the THz regime is also
important as it will allow to exclude the presence of relevant low energy vibrational modes
that might have remained undetected in the IR absorption spectra. The disorder in V=O
orientation in fact symmetrizes the otherwise acentric crystal structures of 1 and 2.
Theoretical analysis of the vibrational modes and their coupling to the spin system would also
add significant information, although they are expected to be particularly challenging for 1.
IV
Finally, the results presented here highlight the potentiality of V molecular units as highly
coherent spin qubits units for quantum sensing applications despite a complex and nuclear
spinꢀactive rich crystal structure. This opens the doors for further studies focused on the spin
coherence measurements in the presence of guest solvents inside the MOFs cavities, to probe
its potential use as a moleculeꢀbased quantum sensor.
2
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EXPERIMENTAL SECTION
General Remarks. All chemicals were purchased and used without further purification
except for the tetrakis(4ꢀmethoxycarbonylphenyl)porphyrin (H TMeCPP), the precursor of
tetrakis(4ꢀcarboxyphenyl)porphyrin (H TCPP), that was synthesized according to a
1
1
1
1
1
1
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2
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previously reported study.
Synthesis of [VO(TCPP)]·MeOH·2H
2
2 2
O. H TMeCPP (1.00 g, 1.18 mmol) and [VO(acac) ]
(0.31 g, 1.18 mmol) were reacted at 180 °C in 5 mL of PhOH for 6 h. After that, the solvent
was removed under vacuum and the resulting solid of [VO(TMeCPP)] was washed with
EtOH and dried under vacuum. (Yield: 83%). [VO(TMeCPP)] (1.00 g, 1.10 mmol) was
stirred in a mixture of THF (25 mL) and MeOH (25 mL). To this solution, a solution of KOH
(
2.65 g, 47.2 mmol) in H O (25 mL) was added. The mixture was refluxed for 12 h. After
2
refluxing, THF and MeOH were removed under reduced pressure through rotary evaporation.
Additional water was added to the solution, then the solution was acidified with 1 M HCl
until no further precipitation occurred. The solid was collected by filtration, washed with
water and dried in vacuum. Needleꢀshape crystals of [VO(TCPP)]·MeOH·2H
obtained by slow evaporation (one week) of a MeOH solution of the crude [VO(TCPP)].
Yield: 95%. Elemental anal. calcd for C49 12V: C, 63.71; H, 3.93; N, 6.07; found: C,
4.04; H, 3.89; N, 6.11. FTꢀIR (ῡmax/cm , KBr pellet): 3445m, 1696vs, 1606s, 1510vw,
404m, 1276m, 1100w, 1005m, 803m.
2
O were
36 4
H N O
1
−
6
1
Synthesis of [TiO(TCPP)]·H
modified procedure with respect that of [VO(TCPP)]. H
TiO(acac) (97 mg, 0.37 mmol) were reacted at 180 °C in 5 mL of PhOH for 63 h. After
2
O. [TiO(TCPP)] was synthesized by following a slightly
2
TMeCPP (260 mg, 0.31 mmol) and
[
2 2
]
that, PhOH was removed under vacuum. The resulting solid was dissolved into a mixture of
THF (15 mL) and MeOH (15 mL). To this solution, a solution of KOH (0.7 g, 12.4 mmol) in
2
H O (15 mL) was added. The mixture was refluxed for 12 h. After refluxing, THF and MeOH
were removed under reduced pressure through rotary evaporation. Additional water was
added to the solution, then the solution was acidified with 1 M HCl until no further
precipitation occurred. The solid was collected by filtration, washed with water and dried in
30 4
vacuum. Yield: 45 %. Elemental anal. calcd for C48H N O10Ti: C, 66.22; H, 3.47; N, 6.44;
2
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−
found: C, 66.79; H, 3.66; N, 7.03. FTꢀIR (ῡmax/cm , KBr pellet): 2953m, 1692vs, 1603s,
1
563vw, 1488vw, 1406w, 1248m, 1106w, 1004s,941w, 798w.
Synthesis of [VO(TCPPꢀZn
Zn(NO ·6H O (35 mg, 116 ꢁmol) and 4,4’ꢀbipyridyl (18.1 mg, 116 ꢁmol) were dissolved in
mL of DMF, and the solution placed in a glass capped vial. The solution was heated in oven
2 2
ꢀbpy)]·4DMF·4H O (1). [VO(TCPP)] (50 mg, 58 ꢁmol),
3
)
2
2
0
1
2
3
4
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at 80 °C for 24 h. After cooling, purple cubicꢀshape singleꢀcrystals were obtained. They were
collected by filtration and washed with DMF and MeOH. Yield: 65 %. Elemental anal. calcd
for C70
H
68
N
10
O
17VZn
2
: C, 55.93; H, 4.56; N, 9.32; found: C, 56.11; H, 5.06; N, 9.48. FTꢀIR
(ῡmax/cm , KBr pellet): 3340w, 1630vs, 1548m, 1403vs, 1335w, 1204vw, 1180vw, 1069vw,
007s,806m, 779m, 713w.
1
−
1
Synthesis of VO0.05TiO0.95(TCPPꢀZn
2
ꢀbpy)] (1’). [VO(TCPP)] (2.0 mg 2.34 ꢁmol) and
[TiO(TCPP)] (64.5 mg 75.66 ꢁmol) were mixed in 6 mL of DMF by using ultrasonication for
3
0 min. To the solution, Zn(NO ) ·6H O (46.4 mg, 156 ꢁmol) and 4,4’ꢀbipyridyl (29.2 mg,
3
2
2
1
87.2 ꢁmol) were added and placed in a glass capped vial. The solution was heated in oven at
80 °C for 24 h, and after cooling, purple cubic crystals of 1’ were obtained. They were
collected by filtration and washed with DMF and MeOH. Yield: 57 %. Inductive coupled
plasma atomic emission spectrometry (ICPꢀAES) was used to determine the effective
IV
IV
concentration of V :Ti . This was found to be 4.94:95.06.
Synthesis of [VO(TPP)] (2). H TPP (0.25 g, 0.40 mmol) and [VO(acac) ] (0.133 g, 0.50
2
2
mmol) were reacted at 180 °C in 6 mL of PhOH for 9 h. After that, the solvent was removed
under vacuum and the residual solid was solubilized in CH Cl . A small portion of MeOH
was added to the CH Cl solution, inducing precipitation of 2 as a redꢀpurple microcrystalline
2
2
2
2
powder. The precipitate was washed several times with MeOH, then with Et
2
2
O and air dried.
solution, which
Yield: 70 %. Compound 2 was recrystallized by slow evaporation of a CH Cl
2
gives purple shiny crystals suitable for Xꢀray analysis. Elemental anal. calcd for C H N OV:
44
28
4
1
−
C, 77.76; H, 4.15; N, 8.24; found: C, 76.72; H, 4.36; N, 7.79. FTꢀIR (ῡmax/cm , KBr pellet):
3
1
130vw, 3111vw, 3024vw, 1831vw, 1595m, 1506w, 1487m, 1439m, 1337m, 1204m, 1175s,
157m, 1070s, 1005vs, 835w, 806s, 750s, 725m, 702s, 661m, 527w, 453m.
Synthesis of [TiO(TPP)] (3). H
mmol) were reacted at 180 °C in 12 mL of PhOH for 3 days. After that, the solvent was
removed under vacuum and the residual solid was solubilized in CH Cl . A small portion of
2 2 2
TPP (0.50 g, 0.81 mmol) and [TiO(acac) ] (0.260 g, 0.50
2
2
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MeOH was added to the CH
2 2
Cl solution, inducing precipitation of 3 as a redꢀpurple
microcrystalline solid. The precipitate was washed several times with MeOH, then with Et
2
O
and air dried. Yield: 74 %. Compound 3 was recrystallized by slow evaporation of a CH Cl2
2
solution, which gives purple shiny crystals suitable for Xꢀray analysis. Elemental anal. calcd
for C44
H
28
N
4
OTi: C, 78.11; H, 4.17; N, 8.28; found: C, 77.54; H, 4.41; N, 7.79. FTꢀIR
1
1
1
1
1
1
1
1
1
1
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2
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0
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2
3
4
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8
9
0
1
−
(ῡmax/cm , KBr pellet): 3130vw, 3111vw, 3024vw, 1831vw, 1595m, 1506w, 1483m, 1439m,
1
6
335m, 1200m, 1175s, 1069s, 1157m, 1009vs, 979s, 966s, 835w, 806s, 748s, 723m, 702s,
60m, 525w, 438m.
Synthesis of [VO0.02TiO0.98(TPP)] (2’). 2 (2.5 mg, 0.0037 mmol) and 3 (97.5 mg, 0.144
mmol) were dissolved in 50 mL of CH Cl . The solution was filtrated and 5 mL of MeOH
were added, then the solvent was slowly evaporated under reduced pressure. 2’ precipitates as
a redꢀpurple microcrystalline solid, that was washed with MeOH, then Et O and air dried.
2
2
2
Yield: quantitative. Xꢀray fluorescence (XRF) analysis was used to estimate the effective
IV
percentage of doping of V by comparing the intensity of the XRF intensity of vanadium K
α
emission of compound 2’ to a calibration curve obtained by mixing weighted amounts of the
pure compounds (2 and 3) in the 1−20% concentration range. This was found to be 2(1)% of
2
+
2+
VO and 98(1)% of TiO .
Synthesis of [VO0.30TiO0.70(TPP)] (2’’). Compound 2’’ has been prepared according to the
method described above for 2’ by recrystallization of a mixture of 2 (30.0 mg, 0.044 mmol)
and 3 (70.0 mg, 0.103 mmol) in 75 mL of CH
2
2
Cl . Yield: quantitative. Magnetic
IV
measurements were used to estimate the effective percentage of V doping. This was found
2
+
to be in agreement with the nominal content of VO paramagnetic species (30(2)%).
Characterization. C, H, N analyses were performed with a CHNꢀS Flash E1112
Thermofinnigan analyzer. FTꢀIR spectra were performed on KBr pellets and collected with a
Shimadzuꢀ8400S spectrophotometer. Xꢀray fluorescence analyses were performed with a WDꢀ
XRF Rigaku PrimusII spectrophotometer. Inductive coupled plasma atomic emission
spectrometry (ICPꢀAES) was performed at Research and Analytical Centre for Giant
Molecules, Graduate school of Science, Tohoku University, Japan on a SHIMADZU ICPEꢀ
3
9000 spectrometer with 5 % HNO aqueous solution.
Single Xꢀray Crystallography. Single crystal Xꢀray diffraction measurements for compound
were performed on a ADSC Quantum210 installed in the Pohang Accelerator laboratory
1
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PLSꢀII beamlines. The synchrotron radiation was monochromated by using a double crystal
monochromator (λ = 0.8000 Å). Single crystal Xꢀray diffraction measurements for 3 were
performed on an Oxford Xcalibur PX Ultra ꢀ Onyx CCD diffractometer, using an Enhance
Ultra Xꢀray graphiteꢀmonochromated CuKα (λ = 1.540 Å) radiation. The structures were
59
2
solved by direct methods (SHELXL) and refined on F with fullꢀmatrix least squares
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0
60
(SHELXL), using the WinGX software package. All nonꢀH atoms were refined with
anisotropic displacement parameters. Graphical material was prepared using Mercury CSD
3
8
3
.9. A summary of the crystallographic data and the structure refinement for compounds 1
and 3 is reported in Table 2.
Table 2. Summary of Xꢀray crystallographic data for 1 and 3.
1
3
Empirical formula
Formula weight
Crystal size, mm
Crystal system
Space group
a, b Å
C H N O VZn
C H N OTi
5
8
32
6
9
2
44 28
4
1138.58
676.57
0.20 × 0.20 × 0.20
0.50 × 0.30 × 0.15
Tetragonal
I4
Tetragonal
P4
16.644(2)
13.3796(2)
9.7766(3)
90
c, Å
13.854(2)
α,β, γ deg.
90
3
V, Å
3837.9(9)
1
1750.15(7)
2
Z
T, K
100(2)
100(2)
3
ρ
ꢁ
θ
(calcd), Mg/m
0.493
1.284
ꢀ
1
, mm
range, deg.
0.391
2.385
0.81−50.00
1.074
5.61−72.51
1.037
GooF
R1
0
.0879
.2547
0.0503
wR2
0
0.1399
2
2 2
2 2 ½ ,
2
2
2
R1 = Σ||F |−|F ||/Σ|F |, wR2 = [Σ[w(F −F ) ]/Σ[w(F ) ]]
w = 1/[σ (F ) + (aP) + bP], where P =
o
c
o
o
c
o
o
2 2
max(F ,0) + 2F ]/3.
o c
[
Full crystallographic data for the solved structures have been deposited in the Cambridge
Crystallographic Data Centre with CCDC numbers 1847868 (1), and 1849460 (3).
Powder Xꢀray Crystallography. Powder Xꢀray diffraction (PXRD) measurements on 1 and
1’ were performed on crushed polycrystalline samples by using an AFCꢀ7R/ LW (Rigaku,
Akishima, Japan) operated at 50 kV and 300 mA at 293 K. The data were collected in the
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diffraction angle range of 3–60° in steps of 0.02° with an irradiation time of 2 s/step. To
prevent evaporation of the crystal solvent, the samples were loaded into a capillary (diameter:
0.8 mm, length: 80 mm, Hilgenderg, Malsfeld, Germany) with the mother liquor. WideꢀAngle
Powder XꢀRay Diffraction (PXRD) patterns on polycrystalline samples of 2, 2’, 3 were
recorded on a Bruker New D8 Advance DAVINCI diffractometer in a thetaꢀtheta configuration
equipped with a linear detector. The scans were collected within the range 5−40° (2θ) using
1
1
1
1
1
1
1
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CuK
α
radiation (
λ
= 1.540 Å). Simulated patterns were generated from the atomic coordinates
52
of the singleꢀcrystal structure solutions using the Mercury CSD 3.5 software (copyright
CCDC, http://www.ccdc.cam.ac.uk/mercury/) using a FWHM (full width at half maximum)
of 0.10 and a 2θ step of 0.025.
Magnetic Measurements. Magnetic susceptibility measurements were performed by using a
Quantum Design Physical Property Measurement System (PPMS). Alternate current
susceptibility measurements were performed in the frequency (ν) range 10–10000 Hz in the
temperature range 2.0−50 K by applying an oscillating field of 10 Oe and applied static
magnetic fields up to 8.5 T. Measurements were performed on randomly oriented powder
samples of 1 (37.12 mg), 2 (51.68 mg) and 2’’ (45.38 mg). Susceptibility data were corrected
for the sample holder previously measured using the same conditions and for the diamagnetic
6
1
contributions as deduced by using Pascal’s constant tables.
THz timeꢀdomain spectroscopy setꢀup. THz spectra were measured by timeꢀdomain
transmission spectroscopy using a tableꢀtop experimental setꢀup equipped with optical laser
pulses (Tꢀlight 780 nm fiber laser, MenloSystems) and lowꢀtemperature GaAs
photoconductive antennas. Low temperatures measurements are allowed by means of a
closedꢀcycle Helium cryostat in the temperature range from 20 to 300 K. The developed
acquisition procedure enables to achieve a signalꢀtoꢀnoise ratio higher than what is commonly
achieved in standard farꢀinfrared investigations. The accurate analysis of the data enables to
disentangle the signals from spurious contributions coming from multiple reflections. The
detailed description of the experimental setꢀup and the data analysis procedure is reported
62,63
elsewhere.
The spectra were measured in pellets of 13.2 mm diameter and thickness of
about 0.7 mm. These were made by pressing under a manual hydraulic press (~ 0.8 GPa) a
mixture of microcrystals and polyethylene powder (Merck).
Electron Paramagnetic Resonance. CW XꢀBand EPR spectra of all samples were recorded
on a Bruker Elexsys E500 spectrometer equipped with a SHQ cavity (ν ≅ 9.70 GHz). Low
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temperature measurements were obtained using an Oxford Instruments ESR900 continuous
flow helium cryostat and the temperature controlled by an Oxford Instrument ITC. Pulsed
EPR measurements were carried out with a Bruker Elexsys E580 at Xꢀband (ν ≅ 9.70 GHz)
equipped with a flexline dielectric ring ENDOR resonator (Bruker EN 4118XꢀMD4).
Temperatures between 4.5 and 250 K were obtained with an Oxford Instruments CF935
continuous flow helium cryostat. Echo detected field swept EPR spectra were recorded by
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using the Hahn Echo pulse sequence (π/2—
τ—π—τ—echo) with fixed interpulse delay time τ
=
200 ns, tπ/2 = 16 ns and t = 32 ns. Phase memory times were measured by the Hahn Echo
π
sequence upon increasing the interpulse delay
were tπ/2 = 40 ns and t = 80 ns. Spinꢀlattice relaxation times were measured using the standard
inversion recovery sequence (π—t —π/2— —π— —echo), with π/2 = 16 ns. The uncertainty
in T estimated from replicate measurements was 5%−10% depending upon the signalꢀtoꢀ
noise ratio at a given temperatureꢀfield combination. Nutation measurements were performed
with a nutation pulse (t ) of variable length followed by a Hahn echo sequence (t —t —π/2—
— π — —echo) with t >> T (i.e. t = 7 µs for 4 K and 2 ꢁs for room temperature
measurements). The interpulse delay
sequence was adjusted depending on the attenuation level of B
τ starting from τ = 98 ns. Typical pulse lengths
π
d
τ
τ
1
p
p
d
τ
τ
d
m
d
τ
was 200 ns and the pulse length of the detection
. Hyperfine Sublevel
were carried out with the pulse sequence
−π/2−τ −echo with the microwave pulse length tπ/2 = 16 ns and t = 16 ns.
and t were varied in steps of 8 ns starting from 96 ns to 2704 ns. Spectra
values (100 ns and 136 ns), which are specified in the figure captions where
1
64
Correlation (HYSCORE) experiments
π/2−τ−π/2−τ −π−τ
The time intervals t
with two
1
2
π
1
2
τ
recorded to avoid blind spot effects. An eightꢀstep phase cycle was used for eliminating
unwanted echoes. The time traces of the HYSCORE spectra were baseline corrected with a
thirdꢀorder polynomial, apodized with a Hamming window and zero filled. After twoꢀ
dimensional Fourier transformation, the absolute value spectra were calculated. The
HYSCORE frequencies were computed for a threeꢀspin system (S = 1/2, I = 1, I = 1) using
a
b
47
the endorfrq function, implemented in the Easyspin program.
ASSOCIATED CONTENT
Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at
DOI: XXXXX. Additional figures, PXRD patterns, magnetic susceptibility and HYSCORE
data, as mentioned in the text.
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AUTHOR INFORMATION
Corresponding Authors
Eꢀmail: roberta.sessoli@unifi.it
*
*Eꢀmail: yamasita.m@gmail.com
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Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
This work was performed with the financial support of the Italian MIUR through the project
PRIN 2015ꢀHYFSRT, Fondazione Ente Cassa di Risparmio di Firenze, European Project
SUMO (QuantERA call 2017), and the Photon Factory Program Advisory Committee
(Proposal No. 2016G040, beamline NW2A). European COST Action CA15128 MOLSPIN is
also acknowledged. M.Y. thanks the support by the 111 project (B18030) from China. We
thank Sandra and Gareth Eaton (University of Denver, Colorado, U.S.A.) for the stimulating
discussions.
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