Giant spin-phonon bottleneck effects in evaporable vanadyl-based molecules with long spin coherence

Article abstract of DOI:10.1039/c6dt02559e

Vanadium(iv) complexes have recently shown record quantum spin coherence times that in several circumstances are limited by spin-lattice relaxation. The role of the environment and vibronic properties in the low temperature dynamics is here investigated by a comparative study of the magnetization dynamics as a function of crystallite size and the steric hindrance of the β-diketonate ligands in VO(acac)₂ (1), VO(dpm)₂ (2) and VO(dbm)₂ (3) evaporable complexes (acac^- = acetylacetonate, dpm^- = dipivaloylmethanate, and dbm^- = dibenzoylmethanate). A pronounced crystallite size dependence of the relaxation time is observed at unusually high temperatures (up to 40 K), which is associated with a giant spin-phonon bottleneck effect. We model this behaviour by an ad hoc force field approach derived from density functional theory calculations, which evidences a correlation of the intensity of the phenomenon with ligand dimensions and the unit cell size.

Full text of DOI:10.1039/c6dt02559e

View Article Online
View Journal
Dalton
Transactions
Accepted Manuscript
This article can be cited before page numbers have been issued, to do this please use: L. Tesi, A. Lunghi,
M. Atzori, E. Lucaccini, L. Sorace, F. Totti and R. Sessoli, Dalton Trans., 2016, DOI: 10.1039/C6DT02559E.
This is an Accepted Manuscript, which has been through the
Royal Society of Chemistry peer review process and has been
accepted for publication.
Accepted Manuscripts are published online shortly after
acceptance, before technical editing, formatting and proof reading.
Using this free service, authors can make their results available
to the community, in citable form, before we publish the edited
article. We will replace this Accepted Manuscript with the edited
and formatted Advance Article as soon as it is available.
You can find more information about Accepted Manuscripts in the
Information for Authors.
Please note that technical editing may introduce minor changes
to the text and/or graphics, which may alter content. The journal’s
standard Terms & Conditions and the Ethical guidelines still
apply. In no event shall the Royal Society of Chemistry be held
responsible for any errors or omissions in this Accepted Manuscript
or any consequences arising from the use of any information it
contains.
www.rsc.org/dalton

Page 1 of 10
Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
View Article Online
DOI: 10.1039/C6DT02559E
Journal Name
ARTICLE
Giant spin-phonon bottleneck effects in evaporable vanadyl-
based molecules with long spin coherence
Received 00th January 20xx,
Accepted 00th January 20xx
a
a,b
a
a
a
a
a,
L. Tesi, A. Lunghi, M. Atzori, E. Lucaccini, L. Sorace, F. Totti, and R. Sessoli *
DOI: 10.1039/x0xx00000x
Vanadium(IV) complexes have recently shown record quantum spin coherence times that in
several circumstances are limited by spin-lattice relaxation. The role of the environment and vibronic
properties in the low temperature dynamics is here investigated by a comparative study of the
www.rsc.org/
magnetization dynamics as a function of crystallites size and steric hindrance of the
-diketonate
-
ligands in VO(acac) ), VO(dpm) ) and VO(dbm) ) evaporable complexes (acac =
2
(
1
2
(
2
2
(
3
-
-
acetylacetonate, dpm = dipivaloylmethanate, and dbm = dibenzoylmethanate). A pronounced
crystallites size dependence of the relaxation time is observed at unusually high temperatures (up to
4
0 K) which is associated to a giant spin-phonon bottleneck effect. We model this behaviour by an
ad-hoc force field approach derived from density functional theory calculations, which evidences a
correlation of the intensity of the phenomenon with ligand dimensions and unit cell size.
processed to obtain ordered nanostructures, which is a
1
0
Introduction
Magnetic molecules characterized by a large spin and easy axis
magnetic anisotropy have been the focus of significant interest
prerequisite if a real device is to be developed, and synthetic
chemistry techniques allow in principle to tune the interaction
to couple two or more qubits.
1
6, 17
On the other hand, their
1
spin coherence time (i.e. the lifetime of any quantum
superposition of states), is, in general, significantly shorter
than that observed for other qubits candidates based on
since two decades. The interest in their properties is dual:
from one side, their long relaxation time of the magnetization
makes them appealing to build miniaturized memory units,
while, from a fundamental point of view, they are studied as
model systems to investigate quantum effects in the
magnetization dynamics. Molecular magnets are nowadays
investigated also at single molecule level mainly depositing
electronic
semiconductors.
spins,
such
as
defects
in
inorganic
1
8, 19
However, remarkably long quantum
coherence times have been recently achieved in molecular
systems by a rational design of the nuclear spin environment.
14
2
, 3
4
Freedman et al. reported on a value of the phase memory
time T (a lower estimation of T ), for a vanadium(IV) complex
dissolved in CS of ca. 0.7 ms at 10 K. Furthermore, dilution in
crystalline matrices provided detectable quantum coherence
-14 at room temperature in [(Ph) P] [Cu(mnt) (mnt
and, more recently, for the
them on surfaces or inside nanojunctions to realize single
5
, 6
m
2
molecule spintronics devices. More recently another class of
magnetic molecules, characterized by a small (S=1/2) and
essentially isotropic spin state gained much attention thanks
to their relatively long spin-spin or spin coherence time, T .
2
The latter is one of the key features if a system has to be used
2
7
4
2
2
]
=
8
maleonitriledithiolate)
processable VOPc (Pc = phthalocyanine) complex, where Rab9i
oscillations were also observed at room temperature.
Although the optimization of quantum coherence times is
fundamental to perform coherent quantum logic operations,
another step toward the integration of these molecular
systems in real devices is their controlled deposition on solid
surfaces and the investigation of their quantum coherence in
the hybrid architecture. In this respect, still very little is known
about the role that unusual environment, such as that of an
isolated molecule on a surface, can have on spin lattice
as a quantum bits, or qubits, i.e. the fundamental unit of a
1
5
quantum computer.
Though many different physical
realizations of qubits are available, magnetic molecules
present some advantages. First, the electronic spin is the most
intuitive and simple choice to reproduce the sought-after
15
quantum behaviour of qubits . Moreover, molecules can be
a.
Dipartimento di Chimica “Ugo Schiff” e INSTM, Università degli Studi di Firenze,
Via della Lastruccia 3, I50019 Sesto Fiorentino (Firenze), Italy
School of Physics, CRANN and AMBER Trinity College Dublin 2, Ireland.
b.
1 2
relaxation time, T , as well as on T . Indeed, a recent report
Electronic Supplementary Information (ESI) available: X-ray powder diffraction
data, EPR spectra and analysis, AC susceptibility data, and details on the Force highlighted the environment role played by a substrate made
Field and DFT calculations. See DOI: 10.1039/x0xx00000x
of a thin layer of MgO deposited on Ag on the magnetic
This journal is © The Royal Society of Chemistry 20xx
J. Name., 2013, 00, 1-3 | 1
Please do not adjust margins

Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
Page 2 of 10
ARTICLE
Journal Name
bistability of a Ho atom, which reaches a very long relaxation phenomenon with ligand dimensions and unit cell size has
View Article Online
DOI: 10.1039/C6DT02559E
2
0
time for the magnetization, 1500 s at 10 K.
been evidenced.
We have recently shown that the combination of
alternating current (AC) susceptometry and pulsed electron
paramagnetic resonance (EPR) spectroscopy can help to
identify molecular systems with long-lived coherence at high
temperature, where the coherence time is limited by the spin-
Results and discussion
Synthesis and crystal structures description
9
10
lattice relaxation. In our previous studies, we observed
1
,
2
and
procedure already reported in the literature. The reaction
between an aqueous solution of VOSO ·xH O and the β-
diketonate ligand (1:2 molar ratio) partially deprotonated with
Na CO in EtOH/H O (1:1) solution affords the desired
products in good yields. Polycrystalline samples of compounds
were characterized through powder X-ray diffraction
PXRD) analyses by comparing the experimental patterns with
those calculated from the atomic coordinates of the reported
3 were prepared according to a general synthetic
-
relatively long T
m
for frozen solutions of VO(dpm)
2
(dpm =
29
dipivaloylmethanate), 2
s at 80 K, and an anomalous
4
2
coefficient for the direct mechanism of spin-lattice relaxation
at low temperatures. The latter behaviour was attributed to
the spin-phonon bottleneck effect, a phenomenon due to the
lack of an efficient exchange between spins and the thermal
bath mediated by low-frequency phonons, with the resulting
2
3
2
1-3
(
2
1
slowing down of the relaxation process. This environmental
effect, that depends on the crystallites size and on the
concentration of paramagnetic ions, is particularly relevant for
S=1/2 systems at low temperature, when the relaxation occurs
through the direct process, which involves low energy
30-32
single crystal X-ray structures.
The good agreement
between experimental and simulated patterns (see ESI, Figures
S1-S3) demonstrates the phase purity of the investigated
samples.
2
2-25
26-28
resonant phonons.
On the contrary few observations
on spin-phonon bottleneck effects were reported for
molecules with spin higher than 1/2, e.g. Single Molecule
Magnets (SMMs), because multi-phonon processes like the
Orbach mechanism, which involves higher energy phonons,
1
dominate.
The interaction of the magnetic systems with the
environment presents several crucial aspects which involves
structural, electronic, and vibrational properties. In this
framework, the spin-phonon bottleneck effect in molecular
systems is an intriguing issue that can evidence the key role of
the environment on the magnetic relaxation and consequently
also on the quantum coherence time. Indeed, it is clear that a
deeper understanding of this effect and its control by tiny
chemical modifications could in principle allow a further
enhancement of the quantum coherence time.
To evaluate the spin-phonon bottleneck effect in potential
molecular spin qubits, we have performed an experimental
investigation of the spin dynamics of the magnetization for
three crystalline vanadyl
-diketonate complexes, namely
-
VO(acac) ), VO(dpm) (2) and VO(dbm) (3)( acac =
2
(
1
2
2
-
-
acetylacetonate, dpm = dipivaloylmethanate, and dbm =
dibenzoylmethanate), which feature the same vanadyl ion and
ligand moiety with substituents of different steric hindrance.
The spin dynamics of compounds 1-3 have been investigated
by AC susceptometry on macro and microcrystalline samples
over a wide range of temperatures and static magnetic fields.
A giant spin-phonon bottleneck effect, detectable up to 40 K,
with relaxation times of the magnetization, τ, spanning two
orders of magnitude depending on the crystallite sizes, has
been observed. Theoretical modelling has been used to get
insights on the origin of this effect. For that purpose, an ad-hoc
force field for the three systems has been derived from density
functional theory (DFT) calculations and exploited to
rationalize lattice properties such as phonon dispersion curves
and vibrational density of states (DOS) for the three
complexes. A strong correlation of the intensity of the
Figure 1. Molecular structures of 1 (a), 2 (b), and 3 (c), with principal atoms labelling
scheme and coordination geometry of the V ions highlighted.
IV
2
| J. Name., 2012, 00, 1-3
This journal is © The Royal Society of Chemistry 20xx
Please do not adjust margins

Page 3 of 10
Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
Journal Name
ARTICLE
2
+
All investigated compounds show a vanadyl ion VO
coordinated by two chelating bidentate
The coordination geometry around the penta-coordinated V
metal centre is a distorted square pyramid with the metal ion for all the compounds in zero static magnetic field; on
slightly above the basal plane (0.545(1) Å ( ), 0.573(1) Å ( ), application of a moderate static magnetic field (20 mT) a
.559(1) Å ( )) (Figure 1).The V=O bond distances are 1.585(1) maximum in the χ''( ) plot is observed accompanied by a
Å, 1.574(1) Å, and 1.578(1) Å for and , respectively, concomitant decrease of the real part, χ' (Figure S7-S9). The
whereas the average V O bond lengths are 1.969(2) Å for
.964(2) Å for , and 1.946(2) Å for . The V=O double bond, dependence of χ'', thus allowing to extrapolate the values of
being ca. 0.4 Å shorter than the V O single bonds, induces a the relaxation time, , the width of the relaxation time
strong axial distortion of the ligand field acting on the d- distribution, , and the difference between isothermal and
- χ as a function of temperature and

m) (1c). The dimensions of the crystallites were qualitatively
View Article Online
DOI: 10.1039/C6DT02559E

-diketonate ligands. estimated by X-ray microtomography (Figure S6). As expected,
IV
the imaginary component of magnetic susceptibility, χ'', is zero
1
2
0
3

1
,
2
3
1

1
,
Debye model has been used to reproduce the frequency
1
2
3



orbitals of the metal ion; this, together with the out of plane adiabatic susceptibility, χ
position of the metal atom, results in the dxy orbital lying applied field.
lowest and being singly occupied. The large energy difference
T
S
between the magnetic orbital and the unoccupied ones make
these S = 1/2 systems ideal candidates as molecular spin
33
qubits.
The substituents on the common
moiety have a steric hindrance that increase in the order
. Accordingly, the unit cell parameters increase in the same
order, although they are further increased by the higher
symmetry of the space groups of 3. Indeed, even if all
compounds crystallize with only one crystallographically
independent molecule in the asymmetric unit, crystallizes in
the triclinic centrosymmetric space group P-1 (Z=2), whereas
and crystallize in the P2 and Pbca monoclinic space groups

-diketonate ligand
1
< 2
<
3
1
2
3
1
with Z = 2 and Z = 8, respectively. Such crystallographic
differences have important implications on the theoretical
calculations of the lattice properties (vide infra).
The very similar coordination environment along the series
is reflected in practically identical frozen solution EPR spectra
Figure 2. Magnetization relaxation time for samples 1a, 1b, 1c as a function of the
static magnetic field at T = 10 K, reported as a log-log plot. Solid lines are best fit curves
(
Figure S4), which show the typical features of an anisotropic
5
1
doublet interacting with an I = 7/2 nuclear spin ( V, n. ab. obtained by using eq. (1) with the parameters reported in Table 1.
3
4
9
9.75%). The spectra have been simulated on the basis of the
Spin Hamiltonian
, providing almost identical It is evident from Figure 2 that the three morphologically
parameters for the three derivatives (Table S1) indicating only different samples show very different absolute values of the
negligible differences in the electronic structure of the relaxation time , which is ca. one order of magnitude higher
complexes. The obtained parameters are in the range for 1a with respect to 1c at T = 10 K and B up to 1 T.
B
H =  BgS + IAS

2+
35, 36
previously reported for VO
and are characterized, as expected, by partially rhombic
tensors. Larger deviations from the free electron values for
and larger hyperfine coupling are observed along the z the temperature, being as high as two orders of magnitude at

-diketonate-type derivatives
Remarkably the sample dependence of
and to 1-2 T but almost disappears at the highest investigated field
of 9 T. On the other hand, it increases dramatically on lowering
 remains constant up
g
A
g
3
6
direction, which is directed along the V=O bond. The T = 5 K and B = 0.2 T (Figure 3a).
corresponding field/energy levels obtained for field applied The field dependence of the relaxation time follows for all
along z and along x axis are reported in Figure S5.
three samples a behaviour observed for other vanadyl-based
9, 10
compounds
, which can be simulated using equation (1),
37, 38
Magnetization dynamics
derived from the Brons-van Vleck model.
The investigation of the spin-phonon bottleneck effect was
based on the comparison of AC susceptibility data measured
for several samples of 1-3 made up of crystallites of different
ꢀ
ꢀ
+ 푒퐵2
+ 푓퐵2
휏−1 = 푐퐵 + 푑
4
(1)
sizes. We began our investigation by measuring AC magnetic The first term accounts for the field dependence of the direct
susceptibility as a function of the applied static magnetic field mechanism of relaxation between two states split by the
(
Figure 2) and temperature (Figure 3a) on three polycrystalline Zeeman energy, while the second term takes into account
samples of with different crystallite dimensions (d): several mechanisms of mixing between the levels depending
macroscopic crystals as obtained from crystallization (d ca. 1-5 on inter and intramolecular interactions. The best-fit
mm) (1a), moderately crushed crystals (d ca. 500 m) (1b), and parameters are reported in Table 1.
1

well crushed and pressed microcrystalline powders (d ca. 10
This journal is © The Royal Society of Chemistry 20xx
J. Name., 2013, 00, 1-3 | 3
Please do not adjust margins

Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
Page 4 of 10
ARTICLE
The observed differences between 1a
Journal Name
Having established that the observed differences in are
,
1b and 1c could be

View Article Online
in principle due to a non-statistical random orientation of the due to the different crystallite sizes in thDeOI:th10r.e10e3s9a/Cm6pDlTe0s25a5n9dE
crystals, especially for non-crushed crystallites, as in sample then to spin-phonon bottleneck effects, the reduced
1a: the anisotropic Spin Hamiltonian parameters might indeed differences observed at higher field values (Figure 2) can be
result in different relaxation times for field applied along easily explained. Indeed, the splitting of the S=1/2 doublet
different directions. To test this hypothesis, a 5.4 mg single increases with the field and phonons of higher frequency are
crystal of
1 was investigated, following the same protocol used involved in the resonant mechanism of relaxation, thus
for polycrystalline samples, by applying the static and AC reducing the efficiency of the spin-phonon bottleneck effect.
magnetic fields parallel and perpendicular to the V=O bond.
The triclinic space group of this derivative further assures that
-
4
-4
-1
-2
-2
all molecules in the crystal structure have the same orientation
of the and tensors, thus providing the same energy pattern
Sample
c ∙ 10 (T
d (ms )
e (T )
f (T )
-
1
g
A
ms )
for all the molecules in a given applied field. The results,
reported in ESI, Figure S10, revealed no significant differences
between the two orientations, clearly demonstrating the key
role of the crystallites dimensions in determining the spin
dynamics. Indeed, these results evidence that the strong
anisotropy in the hyperfine interaction does not play a role in
the investigated field and temperature range, despite that
both energy and composition of the eigenstates are strongly
affected by the orientation of the field (Figure S5). The reason
is that at the investigated temperatures all the 16 states of the
hyperfine split doublet are essentially equi-populated:
temperatures below 100 mK will be necessary to evidence
1a
4.8 ± 0.2
6.0 ± 0.2
6.3 ± 0.1
0.5 ± 0.2
1.9 ± 0.1
4.0 ± 0.3
11 ± 3
6.1 ± 0.6
4.2 ± 0.3
248 ± 163
72 ± 10
56 ± 6
1
b
1
c
Table 1. Best-fit parameters of the model (eq. 1) used to reproduce the field
dependence of the magnetization relaxation rate  for 1a, 1b and 1c.
-1
A pronounced dependence of  for 1 on crystallites size is also
evident by analysing its temperature dependence (Figure 3a).
These differences become more evident on lowering the
temperature, but are still present at the highest investigated
temperature, 42 K. The slopes in the log-log plot of
 for the
three samples and their trends are quite different: they tend
to the same value at high temperature, but from ca. 20 K to
lower temperature, the slope for 1b and 1c decreases, while
for 1a increases. This behaviour can be qualitatively
interpreted as due to two different regimes: a low
temperature one, where direct process dominates, and a
higher temperature one, where a Raman-like process drives
the relaxation. According to this interpretation, we obtained
the slope coefficients under and above 20 K for 1a 1b and 1c
by two distinct linear fits (Table 2) of the thermal dependence
of
3
9
nuclear spin effects on the dynamics of the magnetization.
4
0
,

.
Sample\Temperature
< 20 K
4.2
> 20 K
3.4
1a
1b
1.9
2.7
1c
1.5
2.4
Table 2. Slopes of the temperature dependence of  in the log-log plot for 1a, 1b, and
-
n
1
c, given as the n parameter of   T .
The results reported in Table 2 are unusual because the direct
mechanism, which is dominant at low temperature, should
depend linearly on temperature, while deviations from this
behaviour are observed for all samples, especially for 1a
.
-
3
Above 20 K the Raman-like mechanism dominates and a T
dependence on temperature, typical of vanadyl-based
9, 10, 41, 42
systems
, is observed.
To describe the paramagnetic relaxation in presence of the
23
spin-phonon bottleneck effect Stoneham derived, from
thermodynamic bases, an equation to take into account the
contributions involved in the relaxation (equation 2),
independently from the mechanisms of the relaxation process:
Figure 3. Temperature dependence of the magnetization relaxation time for 1a, 1b and
c (a) and for 2a, 2c and 3a, 3c (b), at B = 0.2 T.
1
4
| J. Name., 2012, 00, 1-3
This journal is © The Royal Society of Chemistry 20xx
Please do not adjust margins

Page 5 of 10
Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
Journal Name
ARTICLE
the three investigated complexes, we also report in Figure 4
View Article Online
푐푆
휏 = 휏푆퐿 + ( ) 휏퐿ꢁ
푐퐿
DO
I:
10
.
10
39
/C
6
D
roT0sc
2
55
9E
(2)
the ratio between the relaxation time

o
f
t
he
m
a
c
opic
crystallites ( ) and that of the crushed crystallites (
a
c). Indeed,
where
휏
is the spin-bath relaxation time, actually the one according to eq. (2), in the macroscopic crystallites the effect
measured by AC susceptibility, 휏푆퐿 is the spin-lattice relaxation should be maximum, whereas it should be negligible in the
time, 푐푆 is the specific heat of the spin system, 푐퐿 the lattice other one. This approach allows to highlight a clear trend for
specific heat, and 휏퐿ꢁthe lattice-bath relaxation time. Equation the three compounds: the smaller the mass of the molecule,
(
2) suggests that, if 휏퐿ꢁ is high enough, a variation of the the higher is the temperature at which size effects become
magnetic ions concentration (equal to a change in c /c
) or on visible. We further note that while and show a constant
the crystallite size (equal to a change of 휏퐿ꢁ) results in a increase of this ratio on lowering the temperature, reaches a
modification of the observed relaxation time.
plateau around 5 K. This is probably due to the different
The rate-determining step for the phonon-bath exchange morphology of the crystals: and form almost isometric
process could involve the transfer of energy in space (spatial crystals, while forms thin plates, thus hampering to reach the
1
3
S
L
2
1
3
2
bottleneck) or in frequency (spectral bottleneck). Stoneham infinite size regime for this compound.
observed that when spatial bottleneck dominates then
휏 → 휏퐿ꢁ ⋅ 푇− and 휏퐿ꢁ ∝ 푑, where d is the size of the
2
-
n
crystallites. The exponent n=2 in   T , originated by the
specific heat ratio in eq. (2), is indeed the most commonly
found in S = 1/2 systems affected by the spin-phonon
2
4
III
bottleneck, including the pseudo-spin S=1/2 of an Yb
2
2
complex. However, van Vleck suggested that, taking into
account the finite life time of phonons, 휏퐿ꢁ could also depend
on temperature and an exponent up to n = 6 can be
2
1
expected. The latter seems the case of 1a, which, thanks to
the rapid divergence at low temperature, reaches remarkable
large values of , e.g. 400 ms at 5 K, and shows butterfly-like
magnetic hysteresis around 2 K (Figure S11). This occurs at a
much higher temperature than previously observed in other
2
5
vanadium(IV) containing systems.
To confirm that our observation can be associated to a
poorly efficient energy transfer to the thermal bath and not to
changes induced by the mechanical stress on the crystallites,
we have investigated the magnetization dynamics of 1a
covered by activated carbon (1a’). This is expected to favour
the thermal exchange between the helium gas (acting as the
Figure 4. Ratio of the spin-lattice relaxation time between macroscopic crystallites
crystals) and crushed crystallites (powders) for 1, 2 and 3 as a function of the
(
bath) and the crystallites, resulting in a faster relaxation temperature at B = 0.2 T.
process. The extracted spin-lattice relaxation times, (Figure
S12) evidence a small but significant reduction of
that this effect is more pronounced at low temperature. These surprisingly proved a neat and remarkable relation between
results confirm that the heat exchange between the the dynamic magnetic properties of vanadyl -diketonate and
crystallites and the bath plays a key role in determining the their organic ligands moieties, suggesting a strong correlation
relaxation time.
between the spin relaxation and vibrational degrees of

for 1a’, and
We can conclude that this experimental investigation

Finally, to evaluate the contribution of the crystal and the freedom.
molecular structures on spin-phonon bottleneck, we analysed
Theoretical calculations
measured only for macroscopic crystallites as obtained from In order to provide a microscopic link between the observed
crystallization (d ca. 1 mm) (2a and 3a) and for the same experimental behaviour for the relaxation time in and
crystallites subsequently crushed in microcrystalline powders and their structural features, lattice dynamics simulations
d ca. 10
m) (2c and 3c), in the same field and temperature were performed for all of them.
range of . The data for the real, χ’, and the imaginary, χ’’,
The phonon dispersion curves for 1-3, reported in Figure 5,
component of the susceptibility for and
are reported in the have been calculated along the arbitrary path X(0.5,0,0)-
supporting information (Figure S13-S16). Figure 3b shows the
(0,0,0)-Y(0,0.5,0)- (0,0,0)-Z(0,0,0.5), where the coordinates
temperature dependence of the extrapolated relaxation times are expressed in the reciprocal lattice basis units. They show
the magnetization dynamics of
2 and 3. AC susceptibility was
1,
2
3
(

1
2
3



, evidencing that, as observed for
significant dependence of on the crystallite size.
To directly compare the effect of the crystallite size on
and thus the relative importance of the bottleneck effect in acoustic phonons are expected to be populated. Furthermore,
1
, also
2
and
3
exhibit a optical modes lying at extremely low energy. This hints to a
possible important role of these modes in the lattice dynamics


,
even in the low temperature regime, where usually only
This journal is © The Royal Society of Chemistry 20xx
J. Name., 2013, 00, 1-3 | 5
Please do not adjust margins

Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
Page 6 of 10
ARTICLE
Journal Name
the mixing between the latter and the low lying optical modes delocalized vibrations, involving, for instance, local molecular
View Article Online
DOI: 10.1039/C6DT02559E
rotations and internal torsions. This feature is also highlighted
is present for all compounds.
The most striking difference between the three by the vibrational density of states (DOS), reported in the right
compounds is the increased number of bands in the low hand side of Figure 5. Indeed, the smallest density of states is
energy region of the vibrational spectra, passing from
This effect is due to the increasing size of their unit cells, which is computed for
in turn makes possible the formation of more low-energy
1
to
3
.
computed for
1
while a much higher phonon density of states
.An intermediate result is computed for 2.
3
Figure 5. Dispersion curves for 1, 2 and 3 (left) and normalized vibrational DOS (right).
A similar trend is also observed for the temperatures at which high lattice specific heat. When the latter condition does not
the three systems access to non-zero density of states: the apply, the crystal non-equilibrium features, such as the
lowest and the highest were found for
3
and
1
, respectively.
phonon life-time, become relevant also for the spin dynamics.
Along the same progression of the unit cell dimensions It should also be noted that 휏푖푞 itself would in principle
vide supra), it is also possible to observe the reduction of the contribute to reduce the lattice thermal conductivity.
(
acoustic bands slope. This is in agreement with the However, its effects in this respect are expected to become
dependence of this property with the inverse square root of notable only at high temperatures, where the anharmonic
the mass of the unit cell. Indeed, proceeding from
1 to 3, the phonon-phonon scattering processes take place. The specific
slope of the acoustic branch, which correlates to the speed of heat of a given mode, with energy ℏ흎풊풒, vanishes at 0 K and
sound in the crystal, decreases and an increased efficiency in starts increasing with T according to:.
promoting relaxation is thus expected.
2
ℏ휔푖푞
ℏ휔푖푞
As already discussed, the spin-phonon bottleneck effect is
related to the inefficiency of the crystal lattice to dissipate the
phonons created during the spin relaxation process. Therefore,
the possibility to observe deviation of the spin dynamics as a
side effect of the spin-phonon bottleneck is directly related to
the conductivity of the material where the spin is embedded
in. According to the heat conductivity (k) formula obtained
from the Boltzmann transport equation (BTE), equation(3),
each phonon (iq) in the system contributes to this property
with three factors: its life-time 휏푖푞, its group velocity v and its
2
(4)
퐶푣푖푞 = 푘 ꢃ
ꢅ 푐표푠푒푐ℎ ꢃ
ꢄ푘 푇
ꢅ
ꢁ
ꢄ푘 푇
ꢁ
ꢁ
According to eq. (3) and eq.(4), the higher the phonon density
of states near or below a certain k T, the higher would be the
value of C and k at that temperature and, therefore, the lower
would be the chance to observe the spin-phonon bottleneck.
For what concerns the three samples under study, is
expected to show a spin-phonon bottleneck effect up to higher
temperatures with respect to and , due to the dramatic
drop in the amount of accessible phonons at frequencies lower
B
v
4
3
1
2
3
v
specific heat C :
-
1
than 30 cm (40 K), corresponding to the highest temperature
at which the spin-phonon bottleneck has been observed for
this compound. The same argument holds for the comparison
훼
훽
푘훼훽 = ∑ 퐶푣푖푞ꢂ ꢂ 휏
(3)
푖푞 푖푞 푖푞
푖푞
between
2 and 3, where the latter would be expected to show
At low temperature, the k limiting factor is expected to be the a spin-phonon bottleneck to a lesser extent, as it indeed does.
lacking of heat carriers (phonons) and this feature is accounted The presented analysis is, of course, mainly based on simple
by the specific heat. This assumption is also in agreement with statistic considerations since it does not take into account the
the Stoneham model (equation 2), where the ratio of the spin coupling of the vibrational and the spin degrees of freedom,
and lattice specific heats gauges the effects on
 by the but only a larger or minor density of states accessible at low
phonons relaxation time, suppressing them completely for
6
| J. Name., 2012, 00, 1-3
This journal is © The Royal Society of Chemistry 20xx
Please do not adjust margins

Page 7 of 10
Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
Journal Name
ARTICLE
temperature. A preliminary attempt to face this problem was equipped with a linear detector. The scans were collected
View Article Online
4
4
DOI: 10.1039/C6DT02559E
reported by Moreno et al.
α
within the range 540° (2θ) using CuK radiation ( = 1.540 Å).
The simulated patterns were generated from the atomic
coordinates of the single crystal structure solutions using the
46
Mercury
http://www.ccdc.cam.ac.uk/mercury/) using a FWHM (full
width at half maximum) of 0.15 and a 2 step of 0.025.
CSD
3.3
program
(copyright
CCDC,
Conclusions

In the last couple of years, the investigation of spin dynamics
of simple molecules by AC susceptometry has allowed to
identify in the vanadyl unit one of the most promising
candidates for a potential application as molecular based
Electron paramagnetic resonance (EPR) analysis
X-Band EPR spectra were recorded on a Bruker Elexsys E500
9
, 10, 33
spectrometer equipped with a SHQ cavity (
temperature (50 K) needed to freeze the measured solutions
1 mM, 2:3 toluene: CH Cl ) was obtained using an Oxford
 = 9.392 GHz). Low
quantum bits.
However, the present study points out
that these slow relaxing systems exhibit a giant spin-phonon
bottleneck and the relaxation times can vary over several
order of magnitudes depending on the crystallites size. This
evidences the need to carry out comparison of relaxation
times obtained by different samples with special care. In
particular, it is of absolute importance to separate effects
coming from the electronic structure and those related to the
exchange of energy with the thermal bath.
(
2
2
Instruments ESR900 continuous flow helium cryostat.
Magnetic measurements
Alternate current (AC) susceptibility measurements were
performed in the temperature range 1.8–40 K with applied
magnetic fields up to 8.8 T on polycrystalline samples of
compounds
Measurement System (PPMS) equipped with
susceptometer operating in the 10 Hz 10 kHz frequency range
1
-
3, by using a Quantum Design Physical Property
The investigation of a series of compounds exhibiting the
same electronic properties but different peripheral group on
the ligands has evidenced the key role played by the phonon
spectrum on the magnetization dynamics, highlighting that
smaller molecules exhibit a more pronounced spin-phonon
bottleneck effect and in general a slower relaxation due to a
higher velocity of acoustic phonons, as estimated from a
combination of DFT and molecular dynamics approaches.
Interestingly, similar comparative studies performed in frozen
a
AC

and a Quantum Design Magnetic Property Measurement
System (MPMS) equipped with a Superconducting Quantum
Interference Device (SQUID) AC susceptometer operating in the
0
.1 Hz
pressure (ca. 10 Torr) for all measurements. All samples were
measured wrapped in teflon. The well crushed ( ) samples
1 kHz frequency range at the same gas exchange
c
1
4
were also pressed in a pellet. Susceptibility and magnetic data
were corrected for the sample holder previously measured
using the same conditions and for the diamagnetic
contributions as deduced by using Pascal’s constant tables
solution have not highlighted any significant trend.
Though the concentrated samples investigated here are
not expected to exhibit long coherence time, the possibility to
evaporate them on surfaces makes this family of complexes
extremely appealing to further investigate the spin dynamics,
once these molecules are deposited on a substrate. Indeed the
latter can influence not only electronic but also vibrational
degrees of freedom of the molecular system, as evidenced in
this work. The reduced efficiency of energy exchange from the
spin system to the thermal bath could actually contribute to
47
(Figure S7-S16).
Force Field parametrization
Force field parameters for the three molecules have been
4
8
derived following the procedure outlined by Ryde and
49
exploiting the software Hess2FF. This approach requires the
calculation of the hessian matrix for the three isolated
molecules in order to map their eigenvalues and eigenvectors
on the chosen intra-molecular force field energy
representation. In this work, the energy has been chose
2
0
enhance the magnetic bistability, as observed for Ho atoms
4
5
2
or TbPc SMMs on MgO thin films, which constitute a very
rigid lattice. In these experiments, performed in ultra-high
vacuum conditions, the thermalisation of the spin systems
occurs, in fact, through the substrate, whose rational choice
could be an additional tool to control the molecular spin
dynamics.
5
0
according to the GAFF recipe, except for the choice of
completely screening the non-bonded 1-4 interactions (they
have been set to zero) in order to minimize the known
4
8
shortcoming of the parametrization method.
In this
framework, all the parameters related to internal degrees of
freedom have been optimized and no use of the GAFF library
has been made for the intra-molecular interactions. On the
other hand, the non-bonded part of the force filed, composed
by vdW and coulomb interactions, has been set up with the
original GAFF's Lennard Jones parameters and with RESP
charges. The assessment of the FF quality has been made on
the basis of its ability to reproduce structural features of both
isolated molecules and their crystalline cells. While the
isolated DFT calculations used as basis for the FF mapping offer
a straightforward way to rationalize the quality of the mapping
Experimental
General remarks
Acetylacetone (acac), dipivaloylmethane (dpm) and
dibenzoylmethane (dbm) were purchased from Sigma-Aldrich.
Powder X-Ray crystallography
Wide-Angle Powder X-ray Diffraction (PXRD) patterns on
polycrystalline samples were recorded on a Bruker New D8
Advance DAVINCI diffractometer in a θ - θ configuration
This journal is © The Royal Society of Chemistry 20xx
J. Name., 2013, 00, 1-3 | 7
Please do not adjust margins

Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
Page 8 of 10
ARTICLE
Journal Name
itself, another set of ab initio reference calculations for the where m are the masses of the atoms in the k\k' cVeielwl iAnrtsicidleeOntlhinee
periodic crystals must be provided. This second reference has considered supercell and q represenDtsOI: a10.1v0e3c9t/oCr6DTin025t5h9eE
been produced through the optimization of the unit cells for
1
,
reciprocal primitive lattice. Finally, r(k)-r(k') represents the
2
and with a periodic boundary condition based DFT distance between the primitive cell k and the considered cell k'
3
software (pDFT). A good overall agreement has been obtained in the supercell.
between FF, DFT, pDFT and experimental parameters. The The vibrational density of states (DOS) is defined as
details of these tests are listed and further discussed in the ESI.
1
All aforementioned optimization, hessian and RESP charges
calculations on the isolated molecules have been carried out
퐷푂ꢕꢇ휔ꢉ = 푁 ꢒ훼푞 훿ꢇ휔 ꢓ 휔훼푞
ꢉ
(7)
ꢖ
51
with the software Gaussian09 at the DFT level of theory. All
the elements have been described with a 6-31G* basis set and
where N
q
is the number of q-points in the reciprocal space and
ωαq is the α eigenvalue obtained through diagonalization of
the dynamical matrix D(q).
The DOS have been obtained integrating the Brillouin zone
with a 8x8x8 regular mesh of points in the crystals reciprocal
5
2
the PBE functional. pDFT calculations have been executed on
5
3
the molecules unit cell with the CP2K software , employing
the PBE functional with the DZVP-MOLOPT basis set and a
plane waves cut-off of 500 Ry, for all the elements. In all DFT
simulation protocols Grimme's D3 vdW correction scheme has
-
1
space. A normalized Gaussian broadening, with σ of 5 cm , has
also been applied to all frequencies.
5
4
been employed .
Lattice dynamics
Acknowledgements
Crystal properties calculations have been carried out with an
home-made software for the lattice dynamics part and with
lammps molecular dynamics package for what concerns Dr. S. Ciattini (CRIST, Univ. of Florence) is acknowledged for
crystal cells optimization and force calculations. Forces have assistance in microtomography experiments and Dr. M.
55
been calculated employing Ewald summations on the Perfetti for useful discussion. We acknowledge the financial
8
support of European Research Council (ERC) through AdG
MolNanoMaS (267746), Italian MIUR through the project
Futuro in Ricerca 2012 (RBFR12RPD1), and Fondazione Ente
Cassa di Risparmio di Firenze.
reciprocal space with an accuracy of 1.0x10 for the long-range
part of both electrostatic and dispersion interactions.
The dynamical matrices of the three molecules supercells have
been computed by force fields through lammps. The supercell
of
two molecules each), while the supercell of
larger amount of molecules contained, has been modelled as
x2x2 times the primitive cell (eight molecules). The three
1
and
2
has been chosen as 3x3x3 times the primitive cell
(
3
, due to the
Notes and references
2
supercells have been optimized with lammps through a
thermal annealing procedure with a final optimization at 0 K of
both atomic positions and cell parameters. The optimized
supercells have then be used to evaluate lattice properties by
perturbation theory. The real space dynamical matrix
elements are defined as
1
.
D. Gatteschi, R. Sessoli and J. Villain, Molecular
nanomagnets, Oxford University Press, Oxford, UK, 2006.
2
3
1
4
.
.
J. Dreiser, J. Phys. Condens. Matter, 2015, 27, 183203.
A. Cornia and M. Mannini, Structure and Bonding, 2014,
56
50, 1-38.
M. L. Perrin, E. Burzurí and H. S. J. van der Zant, Chem.
.
ꢊ
Soc. Rev., 2015, 44, 902-919.
5. M. Urdampilleta, S. Klyatskaya, J. P. Cleuziou, M. Ruben
and W. Wernsdorfer, Nat. Mater., 2011, 10, 502-506.
E. Burzurí, Y. Yamamoto, M. Warnock, X. Zhong, K. Park,
A. Cornia and H. S. J. van der Zant, Nano Lett., 2014, 14, 3191-
휕 퐸
′
푓 ꢇ푘ꢈ, 푘 푗ꢉ =
(5)
ꢆ푡
휕푥ꢋꢌꢍ휕푥ꢋꢎꢏꢐ
6
.
The indexes k and k' run over the cells inside the supercell, i
and j run over the atoms inside the specific cell while s and t
run over the three cartesian spatial coordinates.
calculation of fst(ki, k'j) has been done by numerical
differentiation, displacing each atoms in the primitive cell by
3
7
196.
.
The
A. Ardavan, O. Rival, J. J. L. Morton, S. J. Blundell, A. M.
Tyryshkin, G. A. Timco and R. E. P. Winpenny, Phys. Rev. Lett.,
007, 98, 057201.
8. K. Bader, D. Dengler, S. Lenz, B. Endeward, S.-D. Jiang, P.
Neugebauer and J. van Slageren, Nat. Commun., 2014, , 5304.
9. M. Atzori, L. Tesi, E. Morra, M. Chiesa, L. Sorace and R.
Sessoli, J. Am. Chem. Soc., 2016, 138, 2154-2157.
0. L. Tesi, E. Lucaccini, I. Cimatti, M. Perfetti, M. Mannini,
M. Atzori, E. Morra, M. Chiesa, A. Caneschi, L. Sorace and R.
Sessoli, Chem. Sci., 2016, , 2074-2083.
1. M. Warner, S. Din, I. S. Tupitsyn, G. W. Morley, A. M.
2
+
/-0.01 Å along the three spatial directions. Convergence of
the results with respect to the differentiation step has been
checked. The real space force constants have then been used
to build the dynamical matrix
5
1
퐷ꢆ푡ꢇꢈ푗, ꢑꢉ =
1
′
′
7
ꢒ 푓 ꢇ푘ꢈ, 푘 푗ꢉexp[ꢈꢑ ⋅ ꢇ푟ꢇ푘 ꢉ ꢓ 푟ꢇ푘ꢉꢉ]
(6)
ꢔ′ ꢆ푡
√
푚
ꢌ
푚
ꢏ
1
Stoneham, J. A. Gardener, Z. Wu, A. J. Fisher, S. Heutz, C. W.
M. Kay and G. Aeppli, Nature, 2013, 503, 504-508.
8
| J. Name., 2012, 00, 1-3
This journal is © The Royal Society of Chemistry 20xx
Please do not adjust margins

Page 9 of 10
Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
Journal Name
2. C. J. Wedge, G. A. Timco, E. T. Spielberg, R. E. George, F.
ARTICLE
1
38. J. H. van Vleck, Phys. Rev., 1940, 57, 426-447V.iew Article Online
DOI: 10.1039/C6DT02559E
Tuna, S. Rigby, E. J. L. McInnes, R. E. P. Winpenny, S. J. Blundell
39. S. Gómez-Coca, A. Urtizberea, E. Cremades, P. J. Alonso,
and A. Ardavan, Phys. Rev. Lett., 2012, 108, 107204.
A. Camón, E. Ruiz and F. Luis, Nat. Commun., 2014, 5, 4300.
1
3. J. M. Zadrozny, J. Niklas, O. G. Poluektov and D. E.
Freedman, J. Am. Chem. Soc., 2014, 136, 15841-15844.
4. J. M. Zadrozny, J. Niklas, O. G. Poluektov and D. E.
Freedman, ACS Central Sci., 2015, , 488-492.
40. A. Abragam and B. Bleaney, Electron Paramagnetic
Resonance of Transition Ions, Dover, New York, 1986.
41. K. N. Shrivastava, Phys. St. Solidi B, 1983, 117, 437-458.
42. J.-L. Du, G. R. Eaton and S. S. Eaton, J. Magn. Reson. A,
1
1
1
5. M. A. Nielsen and I. L. Chuang, Quantum Computation
1
4
6
4
996, 119, 240-246.
3. A. J. H. McGaughey and M. Kaviany, Phys. Rev. B, 2004,
and Quantum Information, Cambridge University Press,
Cambridge, 2000.
9, 094303.
1
6. J. Ferrando-Soria, E. M. Pineda, A. Chiesa, A. Fernandez,
4. L. E. Moreno, N. Suaud and
A. G. Arino,
S. A. Magee, S. Carretta, P. Santini, I. J. Vitorica-Yrezabal, F.
Tuna, G. A. Timco, E. J. L. McInnes and R. E. P. Winpenny, Nat.
arXiv:1512.05690, 2015.
5. C. Wäckerlin, F. Donati, A. Singha, R. Baltic, S. Rusponi, K.
4
Commun., 2016,
7. K. Bader, M. Winkler and J. van Slageren, Chem.
Commun., 2016, 52, 3623-3626.
7, 11377.
Diller, F. Patthey, M. Pivetta, Y. Lan, S. Klyatskaya, M. Ruben,
H. Brune and J. Dreiser, Adv. Mater., 2016, 28, 5195–5199.
1
4
6. C. F. Macrae, P. R. Edgington, P. McCabe, E. Pidcock, G. P.
1
1
2
8. A. Morello, Nat. Mater., 2015, 14, 135-136.
9. A. Morello, Nanotechnology, 2015, 26, 502501.
0. F. Donati, S. Rusponi, S. Stepanow, C. Wäckerlin, A.
Shields, R. Taylor, M. Towler and J. van de Streek, J. Appl.
Crystallogr., 2006, 39, 453-457.
4
4
2
4
7. G. A. Bain and J. F. Berry, J. Chem. Educ., 2008, 85, 532.
8. L. H. Hu. and U. Ryde, J. Chem. Theory Comput., 2011,
452-2463.
Singha, L. Persichetti, R. Baltic, K. Diller, F. Patthey, E.
Fernandes, J. Dreiser, Ž. Šljivančanin, K. Kummer, C. Nistor, P.
Gambardella and H. Brune, Science, 2016, 352, 318-321.
2
2
Johannesen, M. A. Sørensen, B. E. Nielsen, M. Sigrist, H.
Mutka, S. Rols, J. Bendix and a. S. Piligkos, Inorg. Chem., 2015,
5
2
2
7
,
9. P. Rydberg, L. Olsen, P. -O. Norrby and U. Ryde, J. Chem.
, 1765-1773.
0. J. M. Wang, R. M. Wolf, J. W. Caldwell and P. A. Kollman,
J. Chem. Comput., 2004, 25, 1157-1174.
1. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria,
1. J. H. van Vleck, Phys. Rev., 1941, 59, 724-729.
2. K. S. Pedersen, J. Dreiser, H. Weihe, R. Sibille, H. V.
Theory Comput., 2007,
5
3
5
4, 7600-7606.
3. A. M. Stoneham, Proc. Phys. Soc., 1965, 86, 1163.
4. K. J. Standley and R. A. Vaughan, Electron Spin Relaxation
M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B.
Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.
P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L.
Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J.
Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai,
T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M.
Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov,
R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C.
Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam,
M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J.
Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin,
R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K.
Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J.
Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B.
Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian 09,
Revision E.01, 2009.
Phenomena in Solids, Plenum Press, New York, 1969.
5. I. Chiorescu, W. Wernsdorfer, A. Muller, H. Bogge and B.
Barbara, Phys. Rev. Lett., 2000, 84, 3454-3457.
6. K. Petukhov, S. Bahr, W. Wernsdorfer, A.-L. Barra, and V.
Mosser, Phys. Rev. B 2007, 75, 064408.
7. G. de Loubens, D. A. Garanin, C. C. Beedle, D. N.
Hendrickson and A. D. Kent, Europhys. Lett., 2008, 83, 37006.
8. O. Waldmann, R. Koch, S. Schromm, P. Müller, I. Bernt
and R. W. Saalfrank, Phys. Rev. Lett., 2002, 89, 246401.
9. D. M. Murphy, I. A. Fallis, R. D. Farley, R. J. Tucker, K. L.
Avery, D. J. Willock, PCCP, 2002, , 4937-4943.
0. E. Shuter, S. J. Rettig, C. Orvig, Acta Crystallogr., Sect. C:
Cryst. Struct. Commun. , 1995, 51, 12.
1. M. Mohamadi, S. Y. Ebrahimipour, M. Torkzadeh-Mahani,
S. Foro, A. Akbari, RSC Advances 2015, , 101063.
2. M. A. K. Ahmed, H. Fjellvåg, A. Kjekshus and B. Klewe, Z.
Anorg. Allg. Chem., 2004, 630, 2311-2318.
3. M. Atzori, E. Morra, L. Tesi, M. Chiesa, L. Sorace and R.
Sessoli, Submitted for pubblication.
2
2
2
2
2
4
3
3
5
5
2. A. Becke, J. Chem. Phys., 1993, 98, 5648-5652.
3. J. Hutter, M. Iannuzzi, F. Schiffmann and J.
5
3
VandeVondele, Wiley Interdisciplinary Reviews: Computat.
Mol. Sci., 2014, , 15-25.
4. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem.
Phys., 2010, 132, 154104.
4
3
5
3
5
3
4. S. Stoll and A. Schweiger, J. Magn. Reson., 2006, 178, 42-
5.
5. A. J. Fielding, D. B. Back, M. Engler, B. Baruah, D. C. Crans,
5
5
5. S. Plimpton, J. Comput. Phys., 1995, 117, 1-19.
6. S. Califano, V. Schettino and N. Neto, Lattice Dynamics of
Molecular Crystals, Springer, Berlin, 1981.
G. R. Eaton and S. S. Eaton, ACS Symp. Ser., 2007, 974, 364–
3
3
1
3
75.
6. J. P. Fackler, J. D. Levy and J. A. Smith, J. Am. Chem. Soc.,
972, 94, 2436-2445.
7. A. C. De Vroomen, E. E. Lijphart, D. Y. H. Prins, J. Marks
and N. J. Poulis, Physica, 1972, 61, 241-249.
This journal is © The Royal Society of Chemistry 20xx
J. Name., 2013, 00, 1-3 | 9
Please do not adjust margins

Ple aDs ea l dt oo nn To rt aa nd sj ua sc tt imo na sr gins
Page 10 of 10
ARTICLE
Journal Name
View Article Online
DOI: 10.1039/C6DT02559E
Table of Content entry
The smaller the ligand the slower is the low temperature
magnetization dynamics of crystals of vanadyl complexes
1
0 | J. Name., 2012, 00, 1-3
This journal is © The Royal Society of Chemistry 20xx
Please do not adjust margins