Ligand-Field Energy Splitting in Lanthanide-Based Single-Molecule Magnets by NMR Spectroscopy

Article abstract of DOI:10.1021/acs.inorgchem.7b02704

A method for the experimental determination of ligand-field (LF) energy splitting in mononuclear lanthanide complexes, based purely on variable-temperature NMR spectroscopy, was developed. The application of this method in an isostructural series of anion

Full text of DOI:10.1021/acs.inorgchem.7b02704

Article
pubs.acs.org/IC
Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
Ligand-Field Energy Splitting in Lanthanide-Based Single-Molecule
Magnets by NMR Spectroscopy
Markus Hiller,† Saskia Krieg,† Naoto Ishikawa,‡ and Markus Enders*,†
†Institute of Inorganic Chemistry, Heidelberg University, Im Neuenheimer Feld 270, 69120 Heidelberg, Germany
‡Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
S
* Supporting Information
ABSTRACT: A method for the experimental determination of
ligand-field (LF) energy splitting in mononuclear lanthanide
complexes, based purely on variable-temperature NMR spectrosco-
py, was developed. The application of this method in an isostructural
series of anionic lanthanide bis(cyclooctatetraenide) double-decker
compounds bearing large rigid substituents is demonstrated. Using
the three-nuclei plot approach devised by Reilley, the isostructurality
of the compound series and the identical orientation of the magnetic
main axis of all Ln3+ ions in the series Tb3+ to Tm3+ are
2
demonstrated. Measurement of the H NMR spectra of partially
deuterated analogues of the complexes permitted determination of
the axial magnetic susceptibility anisotropies χax for all five ions in
the temperature range from 185 to 335 K. For this purpose, analysis
of the hyperfine shifts was combined with structural models derived from density functional theory calculations. In a final step,
the temperature dependence of the χax values was used for determination of the three axial LF parameters, adapting a method
employed previously for phthalocyanine-based systems. The temperature dependence dictated by the LF parameters determined
by this NMR-based approach is compared to the results of recently published ab initio calculations of the system, indicating
reasonable agreement of both methods. For all ions except Dy3+, the NMR method determines the same mJ ground state as the
calculations and the order and energies of the excited states match well. However, the sign of the magnetic anisotropy of the
dysprosium complex in the temperature range evaluated here is not correctly predicted by the published calculations but can be
described accurately by the NMR approach. This shows that our experimental method for determination of the LF parameters is
an ideal complementation to other theoretical and experimental methods.
for many axial SMMs. Ishikawa et al. combined paramagnetic
NMR shifts and SQUID magnetization data in order to obtain
LF parameters in phthalocyaninide (Pc)-based double- and
triple-decker compounds.16,17 This allowed for the prediction
and validation of the SMM behavior for Pc2Tb, which had the
highest anisotropy barrier to date18 and is one of the most
studied SMM systems. In the last years, NMR has been applied
in a growing number of studies for the investigation of SMMs
and related compounds.19−26 In this work, a purely NMR-based
method for determination of the LF parameters in cyclo-
octatetraenide-based lanthanide double-decker complexes is
described. This class of SMMs was first introduced by Long,
Murugesu, and co-workers.27−30 The methodology presented
here is based on the fact that each of the 2J + 1 substates is
connected to a magnetic anisotropy. The energetic splitting of
this mJ manifold by the LF leads to an overall, temperature-
dependent anisotropy of the magnetic susceptibility. This
resulting axial anisotropy χax can be determined quickly and
reliably by NMR measurements. The advantage of a solution
INTRODUCTION
■
The rational design of coordination compounds with single or a
few lanthanide centers has led to a dramatic increase of the
anisotropy barriers of single-molecule magnets (SMMs).1−8
The current record in the blocking temperature is 60 K in an
axially coordinated dysprosium compound.2,3 The main point
of control for a further increase of the magnetic anisotropy
barrier in SMMs with single lanthanide centers is the ligand
field (LF), which causes energy splitting of the 2J + 1 levels in
the spin−orbit-coupled J ground state. The LF can be described
quantitatively by the LF parameters, and their theoretical and
experimental determination is a prerequisite for a thorough
understanding of the relationship between the ligand environ-
ment and SMM behavior.9 Consequently, methods for a fast
and reliable determination of the LF parameters are very
important for SMM research.10,11 Usually, this is achieved by an
investigation of luminescence12−14 or torque magnetometry
measurements.15 However, up to 27 LF parameters may
contribute to the energy splitting, and therefore their
experimental determination is often hampered by over-
parametrization. The situation is simplified if the ligand
environment leads to a higher symmetry, which is the case
Received: October 24, 2017
© XXXX American Chemical Society
A
DOI: 10.1021/acs.inorgchem.7b02704
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method for LF parameter determination is the fact that the
magnetic molecules are well separated from each other and
hence intermolecular interactions do not hamper analysis.
Simultaneously, recent results show that the treatment of the
structure in solution requires careful consideration.31
ment in solution, which can be used to determine the magnetic
susceptibility anisotropies by an independent approach.42
RESULTS
■
A new series of lanthanide cyclooctatetraenide sandwich
complexes was synthesized by the reduction of tdnCOT and
subsequent reaction with anhydrous lanthanide trichlorides
(Scheme 1). This method was previously employed for similar
Depending on the ligand environment, different lanthanide
ions lead to easy-plane or easy-axis magnetization. The latter is
a prerequisite of the SMM behavior. Cyclic polydentate ligands
like derivatives of Pc or COT have been utilized extensively for
the synthesis of double-decker-type SMMs. In the case of
monoanionic compounds of the type [Ln(COT′)2]− (COT′ =
substituted cyclooctatetraenide), the Er3+ and Dy3+ compounds
exhibit slow relaxation of magnetization.28−30 In a recent study,
we demonstrated the application of two new ligand derivatives,
easily accessible by dimerization of dialkynes.25,32 The axial
magnetic susceptibility anisotropies (χax) of the lanthanide
complexes from Tb3+ to Tm3+ could be determined by a
simultaneous analysis of the NMR spectra of the series. The
analysis revealed, that, for the Dy3+, Er3+, and Tm3+ ions, χax is
positive; i.e., the magnetization along the magnetic main axis is
larger than that in the perpendicular direction, which is a
requirement for SMMs. While this observation is in agreement
with the observed magnetic behavior, it is in striking contrast to
the classic Bleaney approach, which predicts a different sign of
χax for Dy3+ and Tm3+.33 Several recent reports indicate that the
assumptions used by Bleaney, particularly the comparable
population of all mJ levels, are not satisfied in compounds with
large magnetic anisotropies typical for SMMs and related
systems.34,35
Scheme 1. Synthesis of the Li(MeCN)[Ln(tdnCOT)2]
a
Complex Series
a
The substituents are drawn schematically without regard for their
conformation. The blue numbers indicate the NMR signal assignment.
systems.25 The five trivalent lanthanide ions from Tb3+ to Tm3+
were investigated because these are characterized by large
magnetic moments and anisotropies. The corresponding Y3+
compound was chosen as a diamagnetic reference. The
complexes were obtained in yields ranging from 40 to 67% as
orange (Tb3+), brown (Tm3+) or yellow (Y3+, Dy3+, Ho3+, and
Er3+) powders and contained acetonitrile (MeCN), as
determined by elemental analysis and NMR spectroscopy.
The compounds are readily soluble in tetrahydrofuran (THF)
and, to a smaller extent, in MeCN. Because of their ionic
nature, the solubility in noncoordinating solvents including
dichloromethane is severely limited, despite the large
substituents.
NMR Spectroscopy. The NMR measurements were
carried out with THF as the solvent because it allows
measurement at lower temperatures in comparison to MeCN.
The 1H and 13C NMR spectra at room temperature (Figure 1)
consist of a maximum of five and six signals, respectively. This
agrees well with the expected high molecular symmetry (D2 or
S4). Assignment of the signals was achieved primarily on the
basis of their respective line widths, as described in detail in the
Supporting Information (SI).
Analysis of the NMR spectra was achieved according to a
methodology based on the three-nuclei plot introduced by
Reilley,43,44 which was used previously for the Li[Ln-
(odbCOT)2] and Li[Ln(hdcCOT)2] series.25 This method
assumes approximately identical structures for the entire series
of investigated compounds and was successfully applied in a
variety of systems.43,45,46 Two important consequences result
from this approximation. First, the propagation of the spin
density through the ligand can be assumed to be identical for all
compounds; i.e., the hyperfine coupling constant Ai/ℏ of a
particular nucleus i is independent of the investigated
lanthanide ion j and identical throughout the series. The
second important simplification of this approach is that the
geometric factor Gi of the investigated nucleus is independent
of the investigated lanthanide ion as well and constant within
the series. Gi depends on the metal−nucleus distance ri as well
as the polar angle θi with respect to the main magnetic axis. The
latter is assumed to be identical for all lanthanide ions,43,44
which is plausible for highly symmetric coordination environ-
ments such as in the system investigated here but not
necessarily in lower symmetry.26,47 Under the condition of
isostructurality, the hyperfine shifts of all nuclei in all complexes
The classification of the lanthanide ions as prolate (Er3+,
Tm3+, and Yb3+) and oblate (Tb3+, Dy3+ and Ho3+) groups,
depending on the asphericity of their respective ground states,
has been suggested as a guideline for the choice of a suitable
ligand environment.1,36 Within this framework, oblate ions
should be combined with axial LFs in order to enhance the
SMM properties, whereas for prolate ions, equatorial LFs
should be applied. The recently reported dysprosocenium
system2,3 exploits this approach with impressive results.
However, this simple and useful tool must be applied with
care because the ground state, and thus the classification as
oblate/prolate, is subject to the influence of the LF. This is
demonstrated by the Dy(COT)2− system because it represents
the combination of a typical oblate ion and an equatorial LF.
This peculiarity can be explained by computational inves-
tigations of the system,37,38 which showed that the lowest-lying
mJ substate is the | 9/2⟩ doublet, exhibiting a slightly prolate
shape.
For closer insight into the electronic structure of the ions
from experimental data, it is necessary to determine the
temperature dependence of the χax values. In this work, the
ligand (6Z,14Z)-5,8,13,16-tetrahydrocycloocta[1,2-b:5,6-b′]-
dinaphthalene (tdnCOT) was prepared32,39 and used for the
synthesis of new lanthanide double-decker complexes. tdnCOT
offers the advantage of increased distance between the NMR-
active nuclei and paramagnetic ion. Consequently, the line
widths of the NMR signals of the double-decker complexes are
smaller, allowing signal detection at lower temperatures.
2
Additionally, the straightforward introduction of H nuclei is
possible, further decreasing the signal line widths due to the
smaller gyromagnetic ratio.40,41 Finally, the quadrupole mo-
2
ment of H introduces the opportunity for the detection of
residual quadrupolar couplings (RQCs) due to partial align-
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1
−
Figure 1. H (left) and 13C{1H} (right) NMR spectra (14.1 T, 295 K, THF-d8) of the individual ions in the Ln(tdnCOT)2 series. The ions are
ordered with increasing χax values, resulting in monotonic shifts of the individual signals along the series. The Dy3+ ion is omitted for clarity because
it exhibits very small shifts. Signals marked with asterisks refer to decomposition products.
of a series can be expressed by eq 1 if only axial anisotropy of
j
the magnetic susceptibility χax is present.
i
μB
A
1
12π
i,j
j
δHF
=
⟨Sz⟩j +
Giχax
3kTγi
ℏ
(1)
In eq 1, the first product corresponds to the Fermi contact
term, with μB representing the Bohr magneton, k the
Boltzmann constant, T the absolute temperature, and γi the
gyromagnetic ratio of the nucleus under consideration. The
quantity ⟨Sz⟩j is the average reduced spin polarization, which
was taken from the literature.43−46 The second product is the
pseudocontact shift.
The approximations discussed above are easily verified by a
so-called three-nuclei plot by plotting a property Yi (Figure 2)
calculated from the observed hyperfine shifts and the literature
values of ⟨Sz⟩j. The data points for the individual nuclei
positions show a linear dependence, which confirms both the
assignment of the signals and the validity of the three-nuclei
approach for this complex series. In addition, it is demonstrated
clearly that the main magnetic axes are identical for all
lanthanide ions and that no relevant rhombic components of
the magnetic susceptibility anisotropy are present. The slopes
of the linear functions indicated in Figure 2 correspond to the
ratio of the geometric factors of the individual nuclei with
respect to the H3i position (cf. Figure 3) serving as a reference.
If no structural information (i.e., geometric factors Gi) is
available, the NMR spectra can be investigated using relative
geometric factors and susceptibility anisotropies, as demon-
strated successfully in a previous study.25 Because the values of
both Gi and χaxj in eq 1 are unknown in this case, the geometric
factor is fixed to unity for one arbitrarily chosen nucleus (here
H3i; see Figure 3). Through fitting of the observed hyperfine
shifts, the relative geometric factors G′i = Gi/Gref are obtained
for the remaining nuclei. The ratio of the geometrical and
relative geometric factors is identical for any two nuclei. This
Figure 2. Three-nuclei plot of all detectable signals in the
−
Ln(tdnCOT)2 series at 295 K. The Er3+ ion and the H3i position
were chosen as references. Consequently, the data points representing
the H3i position are arranged horizontally, while the values for the
remaining nuclei are displayed in the vertical direction. The values Y
i
are calculated as YEr,Ln = δHF,Lni⟨Sz⟩Er/⟨Sz⟩Ln − δHF,Eri. Lines represent
the best linear fits through the origin.
method is described in more detail in the SI and is particularly
beneficial if the solution-averaged structure cannot be
represented by a single structure due to flexibility, as in the
present case.
Because of the relatively rigid substituents, only one dynamic
process appears likely, corresponding to the interchange of the
two possible arrangements of the cyclohexadiene motifs (C2,
C3, and C4 positions). This “flapping” of the benzene moieties
can be represented by two molecular conformations, where all
four substituents point inward (all-endo conformation) or
outward (all-exo conformation). Naturally, three further
combinations are possible. However, the above extreme cases
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−
Figure 3. DFT-optimized structures (B3LYP, Def2TZVP/6-311g, and GD3) of Y(tdnCOT)2 in the all-endo (left) and all-exo (right)
1
conformations. The labeling of the H nuclei, as was used for the NMR assignment, is included.
are the limitations for the geometric factors, and thus these two
possibilities were explored by density functional theory (DFT)
optimization (B3LYP and Def2TZVP/6-311g), the results of
which are displayed in Figure 3. Depending on the method
used, either the all-exo (calculations without dispersion
correction) or the all-endo (calculations with dispersion
correction) conformer is slightly favored energetically. This
result is in accordance with the NMR data, which show that
each of the four benzene groups can adopt an endo or exo
orientation in solution (see below).
A comparison of the relative geometric factors (listed in
Table S9) obtained from the fitting of the hyperfine shifts to eq
1 shows that neither the all-endo nor the all-exo conformation
gives good agreement. However, if a ratio of all-endo/all-exo of
approximately 1:1 is assumed, excellent agreement is observed
(Figure 4). This suggests that at ambient temperature, on
average, two of the four benzene cores point inward and
outward, respectively, and that the reorientation is fast on the
NMR time scale. Note that, for calculation of the relative
geometric factors, the vector connecting the C8 centroids was
Figure 4. Comparison of the experimentally derived relative geometric
factors (horizontal) with the values obtained from the DFT-optimized
structures (black and red) and the solution average (green). The gray
line represents perfect agreement. Note that the position of the H1
(COT-H) nucleus is poorly represented in all three models.
presumed to represent the magnetic main axis. The excellent
agreement depicted in Figure 4 and the three-nuclei plot in
−
Figure 2 demonstrate clearly that, in the Ln(tdnCOT)2
system, this assumption is justified. However, in systems with
lower symmetry, the magnetic axis system does not necessarily
coincide with molecular symmetry elements. Analysis of the
Table 1. Magnetic Susceptibility Anisotropies at 295 K
Obtained by the Fitting Procedure and from the RQC
Splitting
a
2
temperature dependence of the H NMR spectra shows that
χax (×10−31 m3)
the relative geometric factors derived from the three-nuclei
plots change approximately linearly with the temperature (see
Figure S17). This behavior was successfully described by a
temperature-dependent ratio of the two conformers (Table
S15). On the basis of the determined mixture of both
conformations at the different temperatures and the geometric
factors calculated from the model geometries, the relative
geometric factors of all nuclei were calculated. With these
relative geometric factors describing the solution average, the
magnetic susceptibility anisotropies summarized in Table 1
were obtained.
Ln3+
fit
RQC
Tb3+
Dy3+
Ho3+
Er3+
−8.30 2.03
0.711 0.098
−1.58 0.27
6.48 0.91
−8.58 0.37
1.00 0.09
−1.30 0.10
6.56 0.30
10.46 0.44
Tm3+
10.48 1.19
a
The signs of the latter were chosen in order to agree with the first set.
The given uncertainties for the values from the fit are standard
deviations due to the use of geometric factors of different positions.
D
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2
The possibility of introducing H nuclei in a straightforward
manner permits detection of the corresponding 2H NMR
signals within the entire liquidity range of the solvent (THF),
thus allowing determination of the susceptibility anisotropies at
significantly lower temperatures than was possible for the
previously investigated series.25 Additionally, the quadrupole
moment of 2H gives a second, independent approach for
larger line widths are observed, leading to an observable
splitting only for the respective signals of D5. Notably, the
narrowest signal (D6) reveals no splitting in any of the
complexes, indicating that the orientation of the corresponding
C−D bond leads to an angle close to 54°, minimizing the
absolute value of the 3 cos2 α − 1 expression (eq 2). From the
size of the splitting of D5, observable for all ions at 14.1 T (295
K), a second set of χax values was obtained (see Table 1). For
this purpose, an angle α of 90 3° was used for the calculation
with eq 2, in agreement with the DFT-optimized structures of
both conformations. The angles for the remaining positions
depend on the conformation and are summarized in Table S12.
The magnetic anisotropy values obtained from analysis of the
hyperfine shifts (eq 1) and from the RQC data agree well.
j
determination of the χax values. The large magnetic
anisotropies of the molecules lead to a partial alignment in
the magnetic field of the NMR spectrometer; i.e., they orient
partially in such a way that the largest susceptibility tensor
component is aligned with the magnetic field direction. As a
result, the signals of nuclei with I > 1/2 may show RQC and are
split into 2I lines, which may, however, be obscured by the line
widths of the signals. The size of the observable RQC can be
described by eq 2,47,48 wherein B0 represents the magnetic flux
density, μ0 the vacuum permeability, and e2qQ/h the nuclear
quadrupole coupling constant. A value of 186 kHz for the C−D
quadrupolar coupling constant has been used in this work for
the aromatic D5 position;49 for the methylene group, no precise
literature value is available. Presumably, the value is between
those reported for CD2Cl2 (160 kHz) and cyclohexane-d12 (174
kHz).50 Furthermore, RQCs are dependent on the angle α,
which is measured between the main magnetic axis and electric
field gradient surrounding the quadrupolar nucleus, which is
defined by the C−D bond vector. Because of the connectivity
of the employed ligand, in both conformers (all-endo and all-
exo), the main magnetic axis of the compounds (assumed to
coincide with the vector connecting the C8 centroids) and the
C5−D5 bond are perpendicular, resulting in an angle α of 90°.
Consequently, the RQC splitting of D5 is independent of the
flexibility of this molecule and ideal for an additional
determination of χax. In eq 2, χax represents the anisotropy of
the entire molecule, including contributions from the
diamagnetic ligands. However, the latter lies in the range of
0.5 Hz for deuterobenzene (same magnetic field as that used in
this study)51 and is therefore negligible compared to the
anisotropy resulting from the lanthanide center. It should be
noted that the sign of the anisotropy cannot be determined
directly from the splitting.
2
The temperature dependence of the H NMR signals could
be measured over the entire liquidity range of the solvent THF
and is represented for the Tb3+ ion in Figure 6. Using the
2
(e2qQ /h)B0
|ΔνQ | =
(3 cos2 α − 1)χax
20μ0kT
(2)
The effects of the RQC splitting can be observed best in the
2H NMR spectrum of the Tb3+ analogue, displayed in Figure 5.
As expected, the splitting is largest for D5 (310 Hz).
Additionally, splittings are observed for the D3o (116 Hz)
and D3i resonances (not fully resolved). For the remaining ions,
Figure 6. Variable-temperature 2H NMR spectra (61.4 MHz, THF) of
−
Tb(tdnCOT)2 with expansion of the D5 signal, showing the RQC
splitting.
chemical shifts of four nuclei positions (D3i, D3o, D5, and D6,
identical with the designation in Figure 3) in the complexes of
the five ions Tb3+−Tm3+ at eight different temperatures
permitted determination of the temperature dependence of
j
the magnetic susceptibility anisotropies χax , as depicted in
Figure 7. Details of the procedure are provided in the SI.
Figure 7 shows the variation of the susceptibility anisotropies
with temperature, which strongly depends on the lanthanide
ion. For Tb3+ and Ho3+ in the entire temperature range easy-
Figure 5. 2H NMR spectrum (14.1 T, 295 K, THF) of
Tb(tdnCOT)2 .
−
E
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Figure 7. Temperature dependence of the magnetic susceptibility
−
Figure 8. Hysteresis measured for a powdered sample of Li(MeCN)-
[Er(tdnCOT)2] at 2 K (average scan rate: 7 Oe·s−1). The inset shows
that the loop is closed at zero field, which was previously observed in
related systems and attributed to a magnetic avalanche effect.29,30
anisotropies for the individual ions in Ln(tdnCOT)2 . The values for
the Ho3+ analogues are enlarged in the inset.
plane anisotropy is observed, while the remaining ions are easy-
axis systems. However, the Tb3+, Dy3+, and Er3+ ions show
variations that resemble hyperbolas, while the Tm3+ ion follows
a rather linear dependence. Finally, the curve of the Ho3+ ion is
consistent with the presence of an inflection point, and upon
further lowering of the temperature, the anisotropy is indicated
to decrease, which is, at first glance, a rather unexpected
behavior. However, it can be explained by the mJ level splitting
described below. The small value of χax for the Dy3+ ion is
rather unexpected considering the reported SMM behavior of
such systems.27,28,52 However, computational analyses37
determined the lowest Kramers doublet to be composed
mainly of the mJ = | 9/2⟩ states, which possess smaller intrinsic
anisotropies compared to the Ising ground states mJ = | 15/2⟩
and mJ = |6⟩ for the Er3+ and Tm3+ ions, respectively. The LF
parameters determined here confirm these results; however, the
mJ = | 11/2⟩ state is determined as the ground state for Dy3+
(see below).
related to the LF parameters Aqk⟨rk⟩, as described by eq 4,
wherein the Stevens coefficients kjk are encountered.
Bkq = kJkAkq⟨rk⟩
(4)
In order to minimize the number of required parameters, a
linear dependence of the values of Aqk⟨rk⟩ on the atomic number
was imposed.16,17,55 In this way, only 6 instead of 15 parameters
are required for the five ions Tb3+−Tm3+.
From a given set of LF parameters Bqk, the relative energies Ei
of the different wave functions and their Boltzmann
occupancies pi can be readily obtained. The magnetic
susceptibility in the magnetic z direction can be computed
subsequently using the Van Vleck equation (5), with
corresponding expressions for the x and y directions of the
orthogonal system.56
2
μ0μB g 2
⎡
⎢
⎣
J
⎢
SQUID Magnetic Measurements. For a powdered sample
of the Er3+ compound, a magnetic hysteresis loop could be
measured at 2 K, which is closed at zero field. This behavior
and the saturation magnetization are similar to those of related
systems.29,30 For neither the Dy3+ nor Tm3+ complex, hysteresis
was observed under identical measurement conditions (Figure
8). This is in agreement with data for a related Dy3+
derivative.28 Very recent results of Murugesu et al. confirm
the SMM behavior of the Tm3+ ion in the COT2 environ-
ment.53
̂
̂
i
χz =
∑ p ⟨φ|J |φ⟩⟨φ|J |φ⟩ − 2kT
i
i
i
z
z
i
kT
i
⎤
⎥
̂
̂
z
⟨φ|J |φ⟩⟨φ|J |φ⟩
i
j
j
i
z
∑
⎥
⎦
Ei − Ej
j≠i
(5)
The values pi are the Boltzmann occupancies of the different
wave functions φi; the values Ei represent their relative energies.
Using eq 6, the magnetic susceptibility anisotropies χax for
the different ions can be obtained, allowing a comparison with
experimentally derived values.
−
Determination of the LF Parameters. The Ln(COT)2
sandwich system represents a particularly suitable system for
determination of the LF parameters if a D8h-symmetric
environment of the lanthanide ions is assumed. In this case,
the LF Hamiltonian acting on the 2J + 1 mJ states of the J
manifold of the lanthanide ion only contains three axial terms,
as described by eq 3. The associated spin operator matrices
only possess nonzero elements along the diagonal. Thus, the
wave functions correspond to the pure mJ states of the free
ions; i.e., there is no mixing of these states.
1
2
χax = χz − (χx + χy)
(6)
The LF parameter optimization was carried out by
minimization of the root-mean-square deviations of these
values at different temperatures, using the Simplex algorithm.57
The fitting procedure was implemented in the software GNU
Octave 4.258 (see the SI for the scripts used). In this way, the LF
parameters given in Table 2 were obtained, and the splitting of
the mJ sublevels of the individual ions have been computed, as
shown in Figure 9.
0
0
4
0
0
0
0
̂
̂
̂
̂
HLF = B2 O2 + B4 O + B6 O6
(3)
q
̂
The matrix elements of the spin equivalent operators Ok (eq
3) are tabulated in the literature.54 The associated values Bkq are
The energy splitting determined by NMR spectroscopy was
then compared with the two sets of values derived from
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Table 2. LF Parameters (cm−1) for the Individual Ions in Ln(tdnCOT)2− As Obtained by Fitting of the χax Values Determined
2
by Temperature-Dependent H NMR Measurements
Tb3+
Dy3+
Ho3+
Er3+
Tm3+
A02⟨r2⟩
A04⟨r4⟩
A06⟨r6⟩
−643 39
−651 26
79 7.1
−571 62
−582 40
65 11
−499 85
−513 54
51 14
−427 108
−444 68
37 17
−355 131
−375 82
23 21
for the Dy3+ ion: the mJ = | 11/2⟩ state is determined as the
ground state by our method, while the mJ = | 9/2⟩ state results
from ab initio calculations. This deviation is reflected in the
value of χax, which is negative according to the computations
mentioned above but experimentally observed to be positive. In
contrast to the computational approach, the mJ splitting derived
by our method explains the sign and magnitude of χax for all
investigated ions adequately (see Figure S20). Particularly, the
irregular temperature dependence of the Ho3+ ion is
reproduced well. At a temperature of ca. 107 K, a zero
transition of χax is calculated. A similar transition is calculated
for Dy3+ at ca. 437 K (cf. Figure S21).
SUMMARY
■
A new series of lanthanide cyclooctatetraenide sandwich
compounds was synthesized that was used for detailed NMR
analysis. A dynamic process leads to two different orientations
of the substituents, which both contribute to the average NMR
signals in solution. The introduction of 2H nuclei permitted the
detection of signals over a large temperature range, thus
allowing determination of the axial magnetic susceptibility
anisotropies χax for the five ions Tb3+−Tm3+ in the COT
sandwich environment. Tb3+ and Ho3+ exhibit easy-plane
behavior in the investigated temperature range, while Dy3+,
Er3+, and Tm3+ are easy-axis systems, in agreement with our
previous analysis. The Ho3+ ion shows a remarkable depend-
ence of χax on the temperature, which clearly deviated from
T−2-type behavior. Using the data obtained from the NMR
analysis of all synthesized compounds, the LF parameters of the
system could be determined. The results of this approach show
good agreement with those of ab initio calculations of the
system. The electronic structure of the Tm3+ ion exhibits the
required characteristics for a SMM system as well. In particular,
the separation between the lowest and first excited-state
doublet is very large with approximately 500 cm−1.
Figure 9. Relative energies of the different mJ sublevels for the
individual lanthanide ions in the Ln(tdnCOT)2 series as obtained
from the fitted LF parameters.
−
computational methods. A comprehensive theoretical study of
the entire lanthanide series was reported by Gendron et al.38
while Ungur et al.37 only employed calculations for the Dy3+
and Er3+ ions. In general, the results from computational studies
show a smaller overall LF splitting than those obtained by the
method presented herein. Apart from the Dy3+ ion, the same
ground state is found by the computational and our NMR-
based approaches. The overall appearance of the energetic
splitting of the mJ manifolds agrees well, as demonstrated for
the Er3+ ion in Figure 10. However, a notable difference occurs
EXPERIMENTAL SECTION
■
General Procedures. All reactions were carried out using standard
Schlenk or glovebox techniques. Anhydrous solvents were obtained
from a MBraun SPS-800 solvent purification system. Anhydrous
MeCN was purchased from Sigma-Aldrich, checked for moisture by
Karl Fischer titration, and used without further purification.
Deuterated THF for NMR spectroscopy was dried by stirring with
potassium benzophenone and distilled. Celite was heated for at least 4
h to 140 °C under high vacuum to remove traces of moisture. NMR
spectra were recorded on a Bruker AVANCE II NMR spectrometer
(9.4 T and 400 MHz for 1H; 61.4 MHz for 2H) or a Bruker AVANCE
1
III NMR spectrometer (14.1 T and 600 MHz for H; 92.1 MHz for
2H; 150 MHz for 13C). The temperature-controlling unit was
calibrated using a standard substance (ethylene glycol in dimethyl
sulfoxide or methanol).59 Spectra were referenced using the residual
solvent resonance reported at 1.72 ppm (1H and H) and 25.31 ppm
2
(13C).60 Elemental analyses were carried out at the Microanalytical
Laboratory of Heidelberg University using a Vario MICRO cube
(Elementar). The ligand tdnCOT was synthesized according to
literature methods.32,39 The partially deuterated equivalent was
prepared using the same synthetic route starting from deuterated
Figure 10. Detailed splitting of the mJ sublevels for the Er3+ ion in
−
Er(tdnCOT)2 as obtained from the fitted LF parameters (black) in
comparison with values obtained from ab initio calculations (red).
Equivalent representations of the remaining Ln3+ ions are provided in
the SI.
G
DOI: 10.1021/acs.inorgchem.7b02704
Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
xylene (99% D). A detailed description is given in the SI. SQUID
measurements were carried out in polycarbonate capsules (Quantum
Design, QDS-AGC3). The background measured for one of the
capsules was subtracted from the data. A Quantum Design MPMS XL
was used for the measurements. The solid material was powdered
(agate mortar) before transfer to the capsules. All fitting procedures
were carried out using the Solver function of Microsoft Excel 2016,
with the exception of the fitting of the LF parameters, which was
accomplished using GNU Octave 4.2. Origin 2017 was used for data
plotting.
Synthesis of Li(MeCN)[Ln(tdnCOT)2]. The ligand tdnCOT
(typically 100 mg, 324 μmol) was dissolved in THF (2 mL). Excess
lithium metal band (typically 10 mg) was then added, and the mixture
was stirred overnight at ambient temperature. The remaining metal
was mechanically removed from the yellow solution and weighed to
ensure the consumption of 2 equiv. Anhydrous lanthanide chloride
(0.5 equiv) was then added, and the mixture was allowed to stir
overnight at ambient temperature. All volatiles were removed under
reduced pressure, and the residue was dried under vacuum. Extraction
with 10:1 (v/v) toluene/MeCN (2 mL) gave a colored solution and a
colorless solid, which were separated by centrifugation. The super-
natant was filtered over a short pad of Celite, and all volatiles were
removed under reduced pressure to give a colored solid.
Elem anal. Calcd: C, 71.70; H, 5.25; N, 2.46. Found: C, 71.01; H,
5.60; N, 2.16.
ASSOCIATED CONTENT
■
S
* Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.inorg-
chem.7b02704.
Synthetic procedures, NMR spectroscopic data at
variable temperatures, details of the fitting of the NMR
data, DFT-optimized structures, and the script file used
for determination of the LF parameters (PDF)
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: markus.enders@uni-heidelberg.de. Tel: +49-6221-
546247. Fax: +49-6221-541616247.
ORCID
Naoto Ishikawa: 0000-0002-3490-4222
Markus Enders: 0000-0003-0415-1992
Notes
Li(MeCN)[Y(tdnCOT)2]. Yield: 51 mg, 68 μmol, 42%.
1H NMR (THF-d8, 295 K, 14.1 T): δ 7.39 (dd, 3JH−H = 5.1 and 3.7
Hz, 8 H, H5), 7.16 (dd, 3JH−H = 5.4 and 3.2 Hz, 8 H, H6), 5.28 (s, 8 H,
2
2
H1), 3.92 (d, JH−H = 14.9 Hz, 8 H, H3i), 3.86 (d, JH−H = 14.9 Hz, 8
The authors declare no competing financial interest.
H, H3o).
13C{1H} NMR (THF-d8, 295 K, 14.1 T): δ 143.4 (s, C4), 126.0 (s,
ACKNOWLEDGMENTS
■
C5), 125.0 (s, C6), 98.9 (d, JC−Y = 1.5 Hz, C2), 92.5 (d, JC−Y = 2.3
1
1
This work has been supported by the Fonds der Chemischen
Hz, C1), 47.3 (s, C3).
Industry with a Kekule
support by the state of Baden-Wurttemberg through bwHPC
́
scholarship. The authors acknowledge
Elem anal. Calcd: C, 79.68; H, 5.75; N, 1.86. Found: C, 80.14; H,
5.92; N, 1.31.
Li(MeCN)[Tb(tdnCOT)2]. Yield: 134 mg, 163 μmol, 67% (from
̈
and the German Research Foundation through Grant INST
150 mg of tdnCOT).
40/467-1 FUGG. We thank Dr. Marko Damjanovic
discussions and valuable suggestions.
́
for fruitful
1H NMR (THF-d8, 295 K, 14.1 T): δ 280.3 (s, H3i), 116.1 (s, H1),
95.3 (s, H5), 44.9 (s, H6), 29.1 (s, H3o).
13C{1H} NMR (THF-d8, 295 K, 14.1 T): δ 279.4 (s, C4), 244.6 (s,
C3), 232.5 (s, C5), 187.7 (s, C6), −597 (s, C1 or C2), −910 (s, C1 or
C2).
Elem anal. Calcd: C, 72.90; H, 5.26; N, 1.70. Found: C, 71.75; H,
5.06; N, 0.93.
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