Lanthanide cryptate monometallic coordination complexes

Article abstract of DOI:10.1039/d0dt02448a

We report the synthesis, characterisation and magnetic properties of six novel neutral lanthanide cryptate coordination complexes. Reaction of 2,6-diformyl-4-methylphenol, tris(2-aminoethyl)amine and Ln(OTf)3·9H2O in the ratio 3?:?2?:?1, respectively, and in the presence of base affords the isolation of the six complexes LnL·4H2O (Ln = Tb (1), Dy (2), Ho (3), Er (4), Tm (5) and Yb (6)), with H3L being the cryptand N[(CH2)2NCH-R-CHN-(CH2)2]3N (R = m-C6H2OH-2-Me-5). Powder X-ray diffraction confirms that the six complexes are isostructural. The crystal structure of 6 reveals that the Ln(iii) centre is heptacoordinated, in a geometry close to a monocapped distorted octahedron and lies on a pseudo (non-crystallographically imposed) C3 axis. This coordination sphere is similar to the one found in the previously studied Ln(trensal) complexes (H3trensal = 2,2′,2′′-tris(salicylideneimino)triethylamine). The static and dynamic magnetic properties of these complexes were investigated by SQUID magnetometry. Crystal field parameters were determined for all complexes by modelling of the direct current magnetic susceptibility and variable-temperature-variable-field magnetisation data. As for Ln(trensal), only complexes containing the Kramers ions Dy, Er and Yb displayed out-of-phase susceptibility signals in SQUID measurements in an applied magnetic field. Investigation of the dynamic susceptibility of the Yb complex revealed that the magnetic relaxation is governed by a direct process at low temperatures and a Raman process at higher temperatures, similar to Yb(trensal). This journal is

Full text of DOI:10.1039/d0dt02448a

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DOI: 10.1039/D0DT02448A
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Lanthanide cryptate monometallic coordination complexes
Christian D. Bucha, Dmitri Mitcova and Stergios Piligkos *a
Received 00th January 20xx,
Accepted 00th January 20xx
We report the synthesis, characterisation and magnetic properties of six novel neutral lanthanide cryptate coordination
complexes. Reaction of 2,6-diformyl-4-methylphenol, tris(2-aminoethyl)amine and Ln(OTf)39H2O in the ratio 3:2:1,
respectively, and in the presence of base affords the isolation of the six complexes LnL4H2O (Ln = Tb (1), Dy (2), Ho (3), Er
(4), Tm (5) and Yb (6)), with H3L being the cryptand N[(CH2)2N=CH-R-CH=N-(CH2)2]3N (R = m-C6H2OH-2-Me-5). Powder X-ray
diffraction confirms that the six complexes are isostructural. The crystal structure of 6 reveals that the Ln(III) centre is
heptacoordinated, in a geometry close to a monocapped distorted octahedron and lies on a pseudo (non-
crystallographically imposed) C3 axis. This coordination sphere is similar to the one found in the previously studied
Ln(trensal) complexes (H3trensal = 2,2’,2’’-tris(salicylideneimino)triethylamine). The static and dynamic magnetic
properties of these complexes were investigated by SQUID magnetometry. Crystal field parameters were determined for
all complexes by modelling of the direct current magnetic susceptibility and variable-temperature-variable-field
magnetisation data. As for Ln(trensal), only complexes containing the Kramers ions Dy, Er and Yb displayed out-of-phase
susceptibility signals in SQUID measurements in an applied magnetic field. Investigation of the dynamic susceptibility of
the Yb complex revealed that the magnetic relaxation is governed by a direct process at low temperatures and a Raman
process at higher temperatures, similar to Yb(trensal).
DOI: 10.1039/x0xx00000x
exploited by Balestro et al. to implement Grover’s quantum
algorithm.46 A key criterion for surface deposition is the
stability of the molecules both during deposition and on the
surface. Metal cryptates are known to be kinetically and
Introduction
Lanthanide (Ln) coordination complexes are a very interesting
class of molecular magnetic materials because of the plethora
of quantum phenomena that they display both at the
macroscopic and single molecule levels. Almost two decades
ago, Ishikawa et al. discovered that Ln(III) phthalocyanine
double decker complexes1-4 displayed single-molecule magnet
(SMM) behaviour.5, 6 Such mononuclear Ln-based coordination
complexes displaying SMM behaviour were termed Single Ion
Magnets (SIMs).7 In the following years new Ln complexes
offered improved blocking temperatures8-10 over the
previously developed transition-metal-based SMMs.11-13
Recently, blocking temperatures of dysprocenium SIMs have
reached the liquid nitrogen regime.14-16
thermodynamically stable,47 making them an interesting class
of compounds for potential surface deposition.
We, and others, have previously studied the Ln(trensal)
complexes (with H3trensal = 2,2’,2’’-tris(salicylideneimino)
triethylamine).40, 48-56 For this series of complexes crystal field
(CF) parameters have been determined for all members except
53, 54
for Ce(III), Gd(III) and Pm(III),40,
and the magnetic
properties have been investigated for the latter members of
the series.39, 40, 55, 56 Moreover, all complexes are isostructural
and crystallise in a trigonal crystal system, P3¯ or P3¯c1,48-52 with
the metal ion lying on a crystalographically imposed C3 axis.
This trigonal symmetry results in a reduction of the amount of
parameters needed to describe the CF splittings to only 9, with
respect to the 27 ones needed for the general low symmetry
case.
H3trensal can be transformed into the cryptand H3L (with L =
N[(CH2)2N=CH-R-CH=N-(CH2)2]3N and R = m-C6H2OH-2-Me-5,
Figure 1). Complexes of the type H3LLn(NO3)3 are known.57, 58
They have been found to be kinetically stable59 and have, thus,
been investigated as MRI contrast agents.60 However, the
neutral complexes LnL are, besides a Gd complex,61 unknown.
SMMs and SIMs have been proposed for applications in
Quantum Information Processing (QIP).17-39 In particular, we
have recently demonstrated that Yb(trensal),40 is an excellent
electronic qubit39 and that it also acts as a prototypical
coupled
electron-qubit-nuclear-qudit
where
intrinsic
implementation of quantum error corrections is possible.41
Integration of SMMs and SIMs in QIP devices requires
controlled surface deposition of the complexes.42 Read-out of
surface-deposited SIMs has been performed both on
ensembles43 and at the single molecule level.44, 45 In recent
ground-breaking work, the four-level nuclear spin of Tb(III) was
The neutral LnL complexes, display
a
coordination
environment similar to Ln(trensal). We report herein, the
synthesis, characterisation and magnetic properties of six
novel Ln cryptates, of the type LnL with Ln = Tb (1), Dy (2), Ho
(3), Er (4), Tm (5), and Yb (6). We compare their
a. Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-
2100 Copenhagen, Denmark
* Corresponding author: piligkos@chem.ku.dk.
Electronic Supplementary Information (ESI) available: Experimental details and
additional data for all the characterizations and analyses presented in the main
text. See DOI: 10.1039/x0xx00000x
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triflate salts were prepared as described in literaVtiuewreA.r6ti4cleTOonlainne
aqueous suspension of the Ln DoOxI:id10e.103c9o/Dn0cDeTn0t2ra44te8dA
trifluoromethanesulfonic (triflic) acid was added. The
suspension was refluxed overnight and the triflate salts were
isolated by evaporation. For the preparation of Tb(OTf)39H2O
aqueous H2O2 was added to the aqueous suspension of the
oxide (Tb4O7) before refluxing was commenced. The water
content of the final Ln(OTf)3xH2O was determined by EDTA
titration using xylenol orange as indicator.
Synthesis of 2,6-diformyl-p-cresol (DFMP)
Figure 1. H3trensal (left) and its cryptand version H3L(right).
DFMP was synthesized according to a modification of a
published procedure.65 To a mixture of p-cresol (51.5 g; 0.48
mol) and acetic acid (500 ml) hexamethylenetetramine (280 g;
2.0 mol) and paraformaldehyde (300 g; 10 mol) were added.
The suspension was then stirred while at 70-90 °C for 2 hours.
The solution was then cooled to room temperature before
concentrated sulphuric acid (50 ml) was added slowly to the
yellow suspension. Upon complete addition of sulphuric acid
the reaction mixture was refluxed for 30 min and then poured
into 4 L of ice water affording the product as a yellow
precipitate. The precipitate was isolated and washed with
water. It was then recrystallized from toluene (400 ml) yielding
white needles which were washed with heptane and pentane.
Yield: 16.89 g (21 %). Anal. Calcd. for C9H8O3: C, 65.85; H, 4.91.
Found: C, 65.79; H, 4.97. 1H NMR (500 MHz, CDCl3, Figure S10)
δ= 11.45 (s, 1 H), 10.21 (s, 2 H), 7.77 (s, 2H) and 2.39 (s, 3H).
13C NMR (125.74 MHz, CDCl3, Figure S11) δ= 192.53, 161.94,
138.15, 129.67, 123.04 and 20.24. IR νC=O : 1679 cm-1 (Figure
S1).
structure, CF and dynamic magnetic properties to those of the
corresponding Ln(trensal) complexes.
Experimental
Materials and methods
CHN elemental analyses were performed on a FLASHEA 1112
instrument at The Microanalytical Laboratory at The
Department of Chemistry, University of Copenhagen. Infrared
spectroscopy was performed on an Agilent Technologies Cary
1
630 FTIR. H and 13C NMR spectra were recorded on a Bruker
1
500 MHz instrument with a cryoprobe. For H and 13C NMR
calibration was done against solvent signals from the
deuterated solvent. Powder X-ray diffraction (PXRD) data were
obtained with a BRUKER D8 ADVANCE powder diffractometer
using a Co Kα radiation (λ = 1.7902 Å) source. Mass
spectrometry was performed on a Bruker Solarix XR 7T
ESI/MALDI FT-ICR MS at The Department of Chemistry,
University of Copenhagen. Direct current (d.c.) and alternating
current (a.c.) magnetic susceptibility measurements were
Caution: DFMP colours the skin extremely yellow on the
slightest contact.
carried out on
magnetometer. All χT data were corrected for diamagnetism
of the sample and n-hexadecane following Pascal’s constants.
a
Quantum-Design MPMS-XL SQUID
TbL4H2O (1) DFMP (0.58 g; 3.5 mmol) and Tb(OTf)39H2O (0.91
g; 1.2 mmol) were dissolved in hot MeCN (100 ml). To this, a
solution of tris(2-aminoethyl)amine (tren) (0.35 g; 2.4 mmol) in
MeOH (25 ml) was added dropwise over the course of 0.5 h.
The resulting orange solution was reduced to approximately
100 ml by boiling and then Et3N (0.6 ml, 4 mmol) was added
quickly and the solution was immediately taken off the heat.
Left for slow evaporation at room temperature, crystals
formed within a week. These were washed with EtOH and
diethyl ether.
Crystallography
Single-crystal X-ray diffraction was performed on a single
crystal of
6 at 120 K using a BRUKER D8 VENTURE
diffractometer equipped with a Mo Kα high-brilliance IµS S3
radiation source (λ = 0.71073 Å), a PHOTON 100 CMOS
detector, and an Oxford Cryosystems cooling system. The
setup was controlled with the APEX2 software package. The
structure collected was solved using SHELXT (Intrinsic Phasing)
and refined using SHELXL (Least Squares).62 To visualize the
crystallographic data during the refinement, the OLEX2
program package was used.63 All atoms besides hydrogens
were refined anisotropically. Hydrogen atoms were placed at
calculated positions using the “Add H” command in OLEX2.
Yield: 0.35 g (32 %). Anal. Calcd. for C39H53N8O7Tb: C, 51.77; H,
5.90; N, 12.38. Found: C, 51.80; H, 6.03; N, 12.08. MALDI mass
spectrum: 833.29 m/z [TbLH]+ (Figure S12). IR νC=N : 1618 cm-1
(Figure S2).
DyL4H2O (2) Synthesised similarly to 1. DFMP (0.57 g; 3.5
mmol), Dy(OTf)39H2O (0.90 g; 1.16 mmol), tren (0.34 g; 2.3
mmol), and Et3N (0.6 ml, 4 mmol).
Yield: 0.51 g (48 %). Anal. Calcd. for C39H53N8O7Dy: C, 51.57; H,
5.88; N, 12.34. Found: C, 51.99; H, 5.82; N, 12.13. MALDI mass
spectrum: 838.30 m/z [DyLH]+ (Figure S13). IR νC=N : 1618 cm-1
(Figure S3).
Synthetic procedures
During the syntheses no attempts were made to exclude
moisture or oxygen. All chemicals and solvents were
purchased from commercial sources and used as received. Ln
2 | J. Name., 2012, 00, 1-3
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Table 1. Crystallographic data for 6
HoL4H2O (3) Synthesised similarly to 1. DFMP (0.59 g; 3.6
mmol), Ho(OTf)39H2O (0.92 g; 1.2 mmol), tren (0.35 g; 2.4
mmol), and Et3N (0.6 ml, 4 mmol).
Yield: 0.73 g (67 %). Anal. Calcd. for C39H53N8O7Ho: C, 51.43; H,
5.76; N, 12.30. Found: C, 51.39; H, 5.72; N, 12.08. MALDI mass
spectrum:839.30 m/z [HoLH]+ (Figure S14). IR νC=N : 1618 cm-1
(Figure S4).
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DOI: 10.1039/D0DT02448A
6
Formula
Formula weight
Temperature/K
Crystal system
C39H51N8O7Yb
916.91
120
monoclinic
Space group
C2/c
a/Å
b/Å
c/Å
α/°
β/°
γ/°
V/Å3
13.2414(13)
22.0413(19)
27.359(3)
90
90.219(4)
90
7985.0(13)
8
1.525
2.401
3736.0
0.057 × 0.093 × 0.186
0.71073
ErL4H2O (4) DFMP (0.16 g; 0.97 mmol) was dissolved in a
mixture of CHCl3 (30 ml) and MeCN (10 ml). To this was added
a solution of Er(OTf)39H2O (0.25 g; 0.32 mmol) in MeCN (5 ml)
and the resulting solution was heated until hot. Then, tren
(0.096 g; 0.66 mmol) in MeOH (10 ml) was added dropwise for
10 min. The resulting orange solution was then reduced to
approximately 30 ml by boiling for 0.5 h. After volume
reduction, Et3N (0.3 ml, 2 mmol) was added and the solution
was left to evaporate at room temperature. Within a week, a
crystalline precipitate had formed. This was isolated and
washed with EtOH and diethyl ether.
Z
ρcalcg/cm3
μ/mm-1
F(000)
Crystal size/mm3
λ (MoKα)
Yield: 0.23 g (79 %). Anal. Calcd. for C39H53N8O7Er: C, 51.30; H,
5.85; N, 12.27. Found: C, 51.83; H, 5.67; N, 12.06. MALDI mass
spectrum: 841.30 m/z [ErLH]+ (Figure S15). IR νC=N : 1618 cm-1
(Figure S5).
2Θ range for data collection/°
Reflections collected
Independent reflections
Data/restraints/parameters
Goodness-of-fit on F2
R1, wR2 [I>=2σ (I)]
R1, wR2 (all data)
Residual electron density / e Å-3
4.656 to 60.066
126779
11676 [Rint = 0.0506, Rsigma = 0.0262]
11676/0/534
1.149
0.0315, 0.0578
0.0438, 0.0610
0.99/-1.01
TmL4H2O (5) Synthesised similarly to 4. DFMP (0.33 g; 2.0
mmol) in CHCl3 (60 ml), Tm(OTf)39H2O (0.55 g; 0.71 mmol),
tren (0.21 g; 1.4 mmol) in MeOH (25 ml) and Et3N (0.6 ml, 4
mmol).
Yield: 0.35 g (58 %). Anal. Calcd. for C39H53N8O7Tm: C, 51.20; H,
5.84; N, 12.25. Found: C, 51.43; H, 5.40; N, 11.94. MALDI mass
spectrum: 843.30 m/z [TmLH]+ (Figure S16). IR νC=N : 1619 cm-1
(Figure S6).
packing of 1-6, which is confirmed by elemental analysis and
the crystal structure discussed vide infra. PXRD (Figures S8 and
S9) confirms the phase purity of 1-6 and that 1-5 are
isostructural to 6.
To ensure the phase purity of the microcrystalline powders
two different solvents were used for the syntheses; MeCN was
used for 1-3, while MeCN/CHCl3 was used for 4-6. 4-6 can be
synthesised using the procedure of 1-3, however, this leads to
a different crystal phase (details are given in pages S53-S56 of
the Supporting Information). Attempts to prepare 1 and 2
from the MeCN/CHCl3 mixture were unsuccessful, while 3
could be isolated but in lower yield.
YbL4H2O (6) Synthesised similarly to 4. DFMP (0.17 g; 1.0
mmol) in CHCl3 (30 ml), Yb(OTf) 9H2O (0.27 g; 0.35 mmol),
3
tren (0.10 g; 0.70 mmol) in MeOH (10 ml), Et3N (0.3 ml, 2
mmol).
Yield: 0.19 g (60 %). Anal. Calcd. for C39H53N8O7Yb: C, 50.97; H,
5.81; N, 12.19. Found: C, 51.02; H, 5.41; N, 11.99. MALDI mass
spectrum: 848.31 m/z [YbLH]+ (Figure S17). IR νC=N : 1619 cm-1
(Figure S7).
Attempts to synthesise complexes with larger Ln ions such as
Pr(III) and Gd(III) were unsuccessful with the two synthetic
protocols employed, even using much larger concentrations of
all materials. This might be related to the larger size of the
earlier Ln ions which leads to solvent, e.g. H2O, coordinating to
the Ln ion and thereby increasing the solubility of the
complexes. The ligand is large enough to encompass the early
Ln ions, as H3LLn(NO3)3 with all Ln(III) ions are known.58
Results and discussion
Synthesis and characterization
The complexes were prepared as yellow microcrystalline
powders through a Schiff base reaction involving DFMP and
tren in the presence of Ln(OTf)39H2O and base. Mass
spectrometry (Figures S12-S17) confirms the presence of the
complexes with the dominant peaks corresponding to the
[LnLH]+ ion and its isotope distribution pattern. In addition, all
complexes display a strong IR band at 1618-1619 cm-1
corresponding to the formation of imines, but no IR band in
the carbonyl region (1780-1650 cm-1) confirming the complete
closure of the cage (Figures S2-S7). Broad IR bands between
3500-3000 cm-1 suggest the presence of water in the crystal
Crystal structure
Crystals of 6 suitable for single-crystal X-ray diffraction were
obtained through slow evaporation of the mother liquor. For
the remaining complexes (1-5), crystals of suitable size could
not be obtained.
6 crystallizes in the monoclinic space group C2/c (Table 1) with
the whole molecule contained in the asymmetric unit (Figure
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J. Name., 2013, 00, 1-3 | 3
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2a). The ligand forms a two compartment cryptand where the
Yb(III) ion occupies one compartment with the other one left
empty. No residual electron density is found in the second
compartment confirming that the Yb(III) ion is not disordered
over the two compartments. The Yb(III) ion is
heptacoordinated by three phenoxide groups, three imines
and one tertiary amine, in a geometry best described as a
monocapped distorted octahedron (Figure 2b). A pseudo (non-
crystallographically imposed) C3 axis passes through the Yb(III)
ion and the two tertiary amines in each end of the ligand
(Figure 2c). The threefold rotation symmetry around Yb(III) is
close to ideal with only small differences in the bond lengths
around it and with angles between the imines and phenoxide
groups being close to 60° (Table 2). This coordination
environment resembles the one found in the Ln(trensal)
complexes, where the Ln ion is coordinated by the same
chemical groups and lying on a crystallographically imposed C3
axis.52 Comparing 6 to Yb(trensal) (Table 2), very similar bond
lengths between Yb(III) and the imines and phenoxide groups
are found. However, the distance to the tertiary amine (N1) is
much shorter in 6. A similar shortening of the bond to the
tertiary amine was observed for the Ln(trenovan) series with
H3trenovan = tris(((3-methoxysalicylidene)amino)ethyl)amine.
There the bond to N1 is 2.55 Å for Tm(trenovan) (a crystal
structure for Yb(trenovan) has not been determined).66 The
shorter bond length to N1 results in an increase of the bond
angles N1-Yb-Nimine (N2, N3, N4) and N1-Yb-Ophenoxide (O1, O2,
O3), as compared to Yb(trensal) (Table 2). Overall the
coordination environment around Yb(III) in 6 remains very
close to the one found in Yb(trensal).
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DOI: 10.1039/D0DT02448A
Figure 2. Crystal structure of 6. a) View from the side of the complex showing the three
hydrogen bonded water molecules outside the empty cavity. b) The distorted
monocapped octahedral coordination environment around Yb(III) c) View along the
pseudo three-fold axis. Additional water molecules and hydrogen atoms have been
omitted for clarity. Thermal ellipsoids are set to 50 % probability. Colour scheme Yb:
green, N: blue, O: red, C: grey, H: white.
Besides the complex, five water molecules are also found in
the asymmetric unit. Three of these water molecules are
hydrogen bonding to the uncoordinated imines in the second
compartment of the complex (Figure 2a). Two of the three
hydrogen bonded waters, lie on a two-fold axis and form
hydrogen bonds to a neighbouring complex, meaning that only
four crystal waters are present per complex. Although the
empty cavity of the complex contains four potential hydrogen
bond acceptors (three imines and one tertiary amine) and is
surrounded by five water molecules, surprisingly, there is no
solvent found in the cavity, as confirmed by lack of residual
electron density inside the cavity. In crystal structures of
protonated versions of the complex, the cavity is found both
with60 and without57 a water molecule inside it.
Static magnetic properties and crystal field analysis
D.c. magnetic susceptibility measurements were performed on
polycrystalline samples of 1-6 in the temperature, T, range 2-
270 K and under an applied magnetic field, B, of 1000 Oe. In
Figure 3, the susceptibility data are plotted as the χT product,
where χ = M/B, with χ the molar magnetic susceptibility and M
the magnetisation. At 270 K the χT product is 11.25, 12.91,
12.85, 10.84, 6.03, and 1.87 cm3 K mol-1 for 1-6, respectively.
These values are lower than the expected Curie constants (CLn)
of the free ions: Tb(III) (S = 3, L = 3, 7F6, g = 3/2, CTb = 11.82 cm3
K mol-1); Dy(III) (S = 5/2, L = 5, 6H15/2, g = 4/3, CDy = 14.17 cm3 K
mol-1); Ho(III) (S = 2, L = 6, 5I8, g = 5/4, CHo = 14.07 cm3 K mol-1);
Table 2. Selected bond lengths (Å) and angles (degrees) in 6 and Yb(trensal)
Compound
Yb-N1
6
Yb(trensal)40
2.70458(13)
2.43050(8)
2. 43050(8)
2. 43050(8)
2.16575(8)
2. 16575(8)
2. 16575(8)
66.5808(17)
66.5808(17)
66.5808(17)
122.0565(19)
122.0565(19)
122.0565(19)
60.00
2.567(2)
2.420(2)
2.426(2)
2.426(2)
2.152(2)
2.158(2)
2.166(2)
69.92(7)
70.06(7)
70.31(7)
127.58(7)
128.72(7)
127.20(7)
59.34(5)
60.33(5)
60.33(5)
60.23(6)
60.38(6)
59.39(6)
Yb-N2
Yb-N3
Yb-N4
Yb-O1
Yb-O2
Yb-O3
N1-Yb-N2
N1-Yb-N3
N1-Yb-N4
N1-Yb-O1
N1-Yb-O2
N1-Yb-O3
N2-N3-N4
N3-N4-N2
N4-N2-N3
O1-O2-O3
O2-O3-O1
O3-O1-O2
4
Er(III) (S = 3/2, L = 6, F15/2, g = 6/5, CEr = 11.48 cm3 K mol-1);
3
Tm(III) (S = 1, L = 5, H6, g = 7/6, CTm = 7.15 cm3 K mol-1); and
Yb(III) (S = 1/2, L = 3, 2F7/2, g = 8/7, CYb = 2.57 cm3 K mol-1). This
points towards large ligand field splittings of the ground
multiplets with respect to the thermal energy at room
temperature. Upon cooling the χT products of 1-5 decrease
steadily until around 50 K, before decreasing rapidly down to 2
K, where they reach their lowest values of 1.52, 5.62, 4.32,
5.29, and 0.33 cm3 K mol-1, respectively. In contrast the χT
product of 6 decreases almost monotonically over the whole
60.00
60.00
60.00
temperature range, reaching its lowest value of 0.91 cm3
K
60.00
mol-1 at 2 K. The decrease of the χT product on lowering the
temperature is due to thermal depopulation of the mJ
sublevels of the ground spectroscopic term multiplet
60.00
4 | J. Name., 2012, 00, 1-3
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퐻퐶퐹 = 퐵02푂02 + 퐵04푂40 + 퐵4+3푂4+3 + 퐵60푂60 + 퐵6± 3푂6± 3 + 퐵6± 6푂6± 6
View Article Online
14
12
10
8
DOI: 10.1039/D0DT02448A
For the modelling of the experimental data, we used as initial
values the parameters determined for the corresponding
Ln(trensal) complexes.40, 53, 54 These are given in Table S1 of the
Supporting Information section where we also briefly explain
(page 32 of the SI) the procedure of transforming the
numerical values of these parameters from their original
definition in the Wybourne formalism,53, 54 to the ones within
the Stevens operator formalism, used in this work. To avoid
overparameterisation, the data were first modelled using only
diagonal parameters (q = 0), with all other CF parameters fixed
to zero. This model turned out to be too simple as it failed to
simultaneously reproduce the VTVB and χT measurements
(Figure S24-S35 and Table S2 for the corresponding best-fit CF
parameters). Subsequently, the off-diagonal CF parameters
were set to the values of the corresponding Ln(trensal)
complexes. Again, to avoid overparameterisation, the off-
diagonal parameters were only included in the model as
constant parameters. With only 3 out of 8 parameters set as fit
Tb
exp,
exp,
exp,
sim,
sim,
sim,
CTb
CHo
CTm
;
Dy
Er
exp,
exp,
exp,
sim,
sim,
sim,
CDy
CEr
CYb
Ho
Tm
;
;
Yb
6

4
2
0
0
50
100
150
200
250
Temperature / K
Figure 3. Temperature dependence of the χT product for polycrystalline samples of 1-6.
Circles (experiment), lines (best fit to the magnetic susceptibility data and variable-
temperature-variable-field measurements as described in the text), and dashed lines
(Curie constants).
퐵0, 퐵0
퐵0
parameters, namely
4 and 6, excellent simultaneous fits
2
Furthermore,
variable-temperature-variable-field
(VTVB)
measurements of 1-6 were performed in the temperature
range 2-10 K with applied fields of 500, 5000, 10000, 20000,
30000, 40000, and 50000 Oe (Figures S18-S23). The reduced
magnetisation curves of the VTVB measurements are only
superimposed for 6, suggesting that low lying excited states
are close in energy to the ground energy level, for the
remaining complexes.
2
4
6
10-3

The magnetic susceptibility and VTVB measurements of 1-6
were modelled by using Hamiltonian (1).
퐻 = 푔jµB퐽퐵 +
퐵푞푘푂푞푘
(1)
∑
10-4
푘, ― 푘 ≤ 푞 ≤ 푘
2
2.5
3
3.5
4
푔
where the first term describes the Zeeman interaction,
is
j
T / K
퐽
the Landé g factor, µB is the Bohr magneton, is the total
10-2
퐵
angular momentum operator of the ground multiplet and is
the magnetic field. The second term describes the CF potential
퐵푘푞
using the Stevens formalism67 with parameters
and
푂푞
operators 푘, where k = 2, 4 or 6 and q = -k, -k + 1, ..., k - 1, k.
The χT product and the VTVB magnetisation data, for each of
1-6, were simultaneously fitted to Hamiltonian (1) by
numerical diagonalisation of the Hamiltonian matrix and by
use of the Simplex algorithm.68 In the general case of Ln ions in
low symmetry environments, 27 parameters are needed to
describe the CF. In the case of 1-6, the complexes crystallise
without any symmetry elements passing through or lying on
top of the Ln centres, meaning that these are
crystallographically of low symmetry. However, a pseudo C3
axis passes through the Ln centres as described in the
crystallography section. Thus, in this assumed approximate C3
symmetry the number of nonzero CF parameters reduces to 9.
However, by choosing an appropriate orientation of the
퐵4―3
10-3

6
Fit
Direct
Raman
10-4
2
3
4
T / K
Figure 4. Top: Relaxation times of the complexes 2, 4 and 6 plotted as a function of
temperature. Bottom: Relaxation times of 6 as a function of temperature together with
the best fit using a direct and Raman process.
coordinate system the
parameter vanishes. Thus, for
trigonal symmetry the CF can be described in terms of Stevens
operators67 as:
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Journal Name
are obtained for the χT (Figure 3) and VTVB measurements function of temperature (Figure 4, top). For both 2 and 4 the
View Article Online
DOI: 10.1039/D0DT02448A
(Figures S18-S23). This suggests that the CF around the Ln ion relaxation of the complexes quickly becomes faster than what
is very similar in magnitude and symmetry to the one found in can be measured on our instrument and, thus, only a very
Ln(trensal), which justifies our approximation to assume limited amount of relaxation times could be extracted Tables
trigonal symmetry for the modelling of the experimental data. S11 and S12), preventing a detailed analysis of the relaxation
Comparing these best-fit CF parameters (Table S3) with the mechanisms. In contrast, 6 relaxes slower (Figure 4, bottom)
ones of the Ln(trensal) complexes (Table S1), very similar and relaxation times up to 4 K could be obtained (Table S13).
values are generally found, further indicating that the CF is Plotting the relaxation times in an Arrhenius-type plot, a linear
affected minimally by the closure of the H3trensal ligand. The regime is found only at high temperatures. This indicates that
energy spectra of the ground term of 1-6, as well as these of the magnetisation dynamics of 6 is not solely determined by
the corresponding Ln(trensal) complexes, are given in Figures an Orbach process. Such an Orbach process would be
S36 and S37, respectively, and Table S4. From these energy characterised by an energy barrier of 16 K (Figure S49),
spectra can be seen that the general structure of the energy extracted from this high temperature regime. However, the
spectrum for 1-6, is very similar to the one of the curvature of the low temperature regime indicates that
corresponding Ln(trensal) complexes. The eigenvector instead of an Orbach process, the relaxation is rather governed
composition of the ground multiplets for 1-6, are given in by direct and Raman processes.71 This is in line with the
Tables S5-S10, from where one can see that the eigenvectors Ln(trensal) complexes for which the Orbach process has been
are not pure mj states but are linear combinations of these, found to be insignificant.40, 55
obeying the assumed trigonal symmetry.
We numerically fitted the relaxation times determined for 6 to
direct and Raman processes (equation 2).
Dynamic magnetic properties
휏―1 = 퐶푇푛 + 퐷푇
Where τ is the relaxation time, C is the Raman coefficient, T is
the temperature, n is the Raman exponent and D is the
coefficient for the direct process.
(2)
A.c. susceptibility measurements were performed using an
oscillating magnetic field of 3.5 Oe in the frequency range 0.1-
1500 Hz. Without an applied static magnetic field none of the
complexes showed an out-of-phase a.c. signal, suggesting fast
This afforded C = 1.9(3) s-1 K-5.5, n = 5.5(1) and D = 109(3) s-1 K-1
(Figure 4, bottom). These values are close to the ones
determined for a polycrystalline sample of Yb(trensal) (C = 0.15
s-1 K-6.2, n = 6.2 and D = 258 s-1 K-1),40 suggesting that closing of
the Ln(trensal) complex to create the cryptate Ln(L), has a
minimal effect on the dynamic magnetic properties, since
these changes consist on modifications of the outer
coordination sphere of the Ln centres. The Raman exponent n
= 5.5 determined for 6 is notably lower than the expected
exponent n = 9 for a two-phonon Raman process in Kramers
ions.72 However, depending on the CF splittings the Raman
exponent can be closer to n = 5 in Kramers ions.73 In fact a
large variation for n has been found for Kramers ions,74 with
one Yb(III) complex having a Raman exponent n = 2.37.75
magnetic relaxation probably due to
a large quantum
tunnelling of the magnetisation (QTM), similar to what was
seen in the Ln(trensal) complexes.40, 55 This is not surprising as
퐵± 3 퐵± 3
퐵± 6
are
6
the off-diagonal Stevens’ parameters
,
and
4
6
nonzero in trigonal symmetry. Applying a static magnetic field
to quench the QTM allowed for detection of out-of-phase a.c.
signals for the Kramers ion complexes 2, 4 and 6 only (Figures
S39-S41, S43-S45 and S47-S48). Similarly, only the Kramers
ions of the Ln(trenovan) complexes displayed an out-of-phase
a.c. signal.66 The field dependence of the out-of-phase
component of the susceptibility was investigated at 2 K to
identify the optimal field where the slowest magnetic
relaxation is observed. This was found to be 750, 750 and 3000
Oe for 2, 4 and 6, respectively. For 2 and 4 two peaks were
observed in the out-of-phase susceptibility with one peak
being present in the high-frequency range at small static fields,
while the other peak emerged in the low-frequency range at
large static fields. The low frequency signals decreased rapidly
in intensity with temperature, and the corresponding
relaxation times showed minimal temperature dependence.
Such behaviour has been previously reported for Ln-based
Conclusion
Six novel isostructural Ln complexes based on the cryptand H3L
have been synthesised and characterised. The crystal structure
of 6 revealed that the Ln ion is hepta-coordinated in one of the
two cavities of the ligand, with a pseudo C3 axis passing
through the ligand and Ln ion. A.c. susceptibility
measurements only showed signals for the Kramers ion
complexes (2, 4 and 6) and only in an applied magnetic field,
suggesting a large amount of QTM. For 6 the relaxation was
SIMs and has been ascribed to dipolar intermolecular
69
interactions.66,
Verifying this hypothesis requires detailed
dilution in the diamagnetic host measurements, which are
outside the scope of the present study. The out-of-phase
signal of the a.c. susceptibility at 750 Oe for 2 and 4, and at
3000 Oe for 6 showed marked temperature dependence
(Figures S40, S44 and S48). To investigate the temperature
dependent relaxation dynamics of these complexes, the a.c.
data were fitted to the generalized Debye model using CC-FIT2
program.70 The extracted relaxation times are plotted as a
found to be governed by
a Raman process at high
temperatures and a direct process at low temperatures.
The coordination environment around Yb(III) in 6 was found to
be very similar to the coordination environment in Yb(trensal).
Modelling of the χT product and VTVB data revealed that the
CF is very similar between 1-6 and the corresponding
6 | J. Name., 2012, 00, 1-3
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Journal of the American Chemical Society, 1993, 115,
Ln(trensal) complexes. Moreover, the dynamic magnetic
properties of 6 and Yb(trensal) were also found to be similar,
with both governed by a combination of a Raman and direct
process. This suggests that transforming a SIM into its
corresponding cryptate may have minimal effect on the
magnetic properties. This is important as we have previously
shown that Yb(trensal) acts both as an electron qubit and also
as a prototypical electron qubit-nuclear qudit coupled system
where intrinsic quantum error corrections can be
implemented. The results presented herein could suggest that
these coherent magnetic properties are also conserved in the
corresponding cryptate complexes that can be used in surface
deposition protocols. This will be the subject of upcoming
investigations.
View Article Online
1804-1816.
DOI: 10.1039/D0DT02448A
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Conflicts of interest
There are no conflicts to declare.
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Acknowledgements
SP thanks the VILLUM FONDEN for research grant 13376.
Notes and references
‡ Crystallographic data (including structure factors) for 6 have
been deposited with the Cambridge Crystallographic Data
Centre (CCDC 2015576). Copies of the data can be obtained, free
of charge, on application to Cambridge Crystallographic Data
Centre, 12 Union Road, Cambridge CB2 1EZ, UK, (fax: +44-
(0)1223-336033 or email: deposit@ccdc.cam.ac.uk).
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