Azide-Coordination in Homometallic Dinuclear Lanthanide(III) Complexes Containing Nonequivalent Lanthanide Metal Ions: Zero-Field SMM Behavior in the Dysprosium Analogue

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Azide-Coordination in Homometallic Dinuclear Lanthanide(III)

Complexes Containing Nonequivalent Lanthanide Metal Ions: Zero-

Field SMM Behavior in the Dysprosium Analogue

Pawan Kumar, Sourav Biswas, Abinash Swain, Joydev Acharya, Vierandra Kumar, Pankaj Kalita,

Jessica Flores Gonzalez, Olivier Cador, Fabrice Pointillart,* Gopalan Rajaraman,*

and Vadapalli Chandrasekhar *

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ABSTRACT: A series of homometallic dinuclear lanthanide complexes containing nonequivalent lanthanide metal centers

[Ln₂(LH₂)(LH)(CH₃OH)(N₃)]·xMeOH·yH₂O [1, Ln = Dy^III, x = 0, y = 2; 2, Ln = Tb^III, x = 1, y = 1] have been synthesized [LH₄

= 6-((bis(2-hydroxyethyl)amino)-N′-(2-hydroxybenzylidene)picolinohydrazide] and characterized. The dinuclear assembly contains

two diﬀerent types of nine-coordinated lanthanide centers, because the nonequivalent binding of the azide co-ligand as well as the

varying coordination of the deprotonated Schiﬀ base ligand. Detailed magnetic studies have been performed on the complexes 1 and

2. Complex 1 and its diluted analogue (1_5%) are zero-ﬁeld SMMs with eﬀective energy barriers (U_eff) of magnetization reversal equal

to 59(3) K and 66(3) K and relaxation times of τ₀= 10(4) × 10⁻⁶s and 10(4) × 10⁻⁸s, respectively. On the other hand, complex 2

shows a ﬁeld-induced SMM behavior. Combined ab initio and density functional theory calculations were performed to explain the

experimental ﬁndings and to unravel the nature of the magnetic anisotropy, exchange-coupled spectra, and magnetic exchange

interactions between the two lanthanide centers.

of these having a large ground-state single-ion magnetic

anisotropy, which results from a very high spin−orbit coupling.

In addition many lanthanide ions such as Dy^IIIand Tb^IIIhave a

reasonable ground state spin, because of the presence of a

suﬃcient number of unpaired electrons.³The investigations on

INTRODUCTION

■

Single-molecule magnets (SMMs) are discrete molecular

complexes comprising 3d/4d/5d/4f/5f metal ions or a

combination thereof, such as 3d/4f heterometallic complexes,

which can be magnetized upon application of a magnetic ﬁeld

and retain their magnetization below a certain temperature

(known as the blocking temperature, T_B).¹These systems

show slow relaxation of magnetization, which depends on an

energy barrier (U_eff) for the magnetization reversal.²For

molecules to display SMM behavior, there is a requirement of a

large ground spin state (S) and an Ising-type anisotropy.

Among the various types of complexes investigated, complexes

containing lanthanide metal ions are most promising, because

Received: January 26, 2021

Published: June 4, 2021

https://doi.org/10.1021/acs.inorgchem.1c00249

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Table 1. Crystal Data and Structure Reﬁnement Parameters of 1, 1_Y, and 2

1

1_Y

C₃₇H₄₃Y₂N₁₁O₉

963.64

2

formula

g/mol

C₃₇H₄₃Dy₂N₁₁O₉

1110.82

C₃₇H₄₃N₁₁O₉Tb₂

1139.69

crystal system

space group

a/Å

b/Å

c/Å

α (deg)

β (deg)

γ (deg)

V/Å³

monoclinic

C2/c

25.561(11)

16.456(11)

22.709(11)

90

90.605(2)

90

9552.4(9)

8

monoclinic

C2/c

25.494(7)

16.411(4)

22.618(6)

90

90.366(2)

90

9463.6(4)

8

monoclinic

C2/c

25.519(14)

16.432(14)

22.762(14)

90

90.779(10)

90

9544.6(11)

8

Z

ρ_c/g cm⁻³

μ/mm⁻¹

F(000)

1.545

3.162

4368.0

1.353

2.499

3936.0

1.586

3.003

4512.0

cryst size (mm³)

2θ range (deg)

limiting indices

0.24 × 0.15 × 0.13

4.628−56.518

−34 ≤ h ≤ 34

−21 ≤ k ≤ 21

−30 ≤ l ≤ 30

75597

0.11 × 0.1 × 0.08

5.28−57.92

−33 ≤ h ≤ 32

−16 ≤ k ≤ 22

−30 ≤ l ≤ 30

78591

0.24 × 0.16 × 0.012

5.662−56.616

−34 ≤ h ≤ 34

−21 ≤ k ≤ 21

−30 ≤ l ≤ 30

100713

reﬂns collected

ind reﬂns

11815 [R(int) = 0.0507]

100

full-matrix least-squares on F²

11815/0/547

1.029

R₁= 0.0218

wR₂= 0.0505

R₁= 0.0286

wR₂= 0.0532

2026262

11502 [R(int) = 0.0681]

100

full-matrix least-squares on F²

11502/12/545

1.033

R₁= 0.0495

wR₂= 0.1148

R₁= 0.0668

wR₂= 0.1197

2058082

11827 [R(int) = 0.0417]

100

full-matrix least-squares on F²

11827/12/545

1.060

R₁= 0.0227

wR₂= 0.0547

R₁= 0.0265

completeness to θ (%)

reﬁnement method

data/restraints/params

goodness-of-ﬁt on F²

Final R indices [I > 2θ(I)]

R indices (all data)

wR₂= 0.0562

2026261

CCDC no.

lanthanide complexes as SMMs began with Isikawa’s seminal

discovery of slow relaxation of magnetization in the sandwich

complex [Bu₄N][TbPc₂].⁴It was quickly realized that

lanthanide ions with their intrinsic unquenched orbital angular

momenta could contribute to magnetic anisotropy. In recent

years, a large number of lanthanide-based SMMs with very

high eﬀective energy barriers of magnetization above 1000 K⁵

and blocking temperatures up to 80 K⁶have been reported.

While the mononuclear Dy^IIIcomplexes yielded very attractive

blocking temperatures in recent years, the axial limit set by the

ligand ﬁeld has already been breached for mononuclear

complexes. Therefore, expanding the structural motif beyond

monomers is important.⁷Among these systems, dinuclear

complexes are of interest because these allow an understanding

of the interactions between the two lanthanide ions.⁸The

magnetic coupling between the lanthanide ions can generate an

exchange bias ﬁeld that could minimize the quantum tunneling

of the magnetization.⁹Among such dinuclear complexes, those

containing nonequivalent lanthanide ions are especially

sparse.^8a,10

in incorporating the azide ligand in the assembly of these

complexes in view of its demonstrated coordination motif

versatility in transition-metal complexes.¹³Although we

anticipated a bridging coordination action from the azide

ligand, as discussed below, we observe that this ligand binds in

a monodentate fashion as a terminal ligand. Accordingly,

herein, we report the synthesis, structural characterization and

magnetic studies of [Ln₂(LH₂)(LH)(CH₃OH)(N₃)]·xMeOH·

yH₂O [1, Ln = Dy^III, x = 0, y = 2; 2, Ln = Tb^III, x = 1, y = 1].

Although we have prepared the Gd(III) analogue (3), we were

unable to establish the bulk purity of this compound. However,

we were able to get single crystals in some quantity. We could

perform the structural study, which are presented in the

Supporting Information. Among these complexes, the Dy^III

analogue is a zero-ﬁeld SMM. Also, while the Dy^IIIanalogue

has been shown to have antiferromagnetic interaction between

the two Dy^IIIcenters, the Tb^IIIanalogue has been shown to

possess ferromagnetic interactions. These conclusions were

possible by a theoretical study of the Gd^IIIanalogue. The

diﬀerences between the Dy^IIIand Tb^IIIderivatives could be

correlated to small structural changes in these complexes. All of

these aspects are discussed herein through combined

experimental and ab initio theoretical calculations.

We have been involved in the design of polydentate ligands

for assembling various types of lanthanide complexes whose

nuclearity varied from 1 to 21.¹¹In these eﬀorts, we found,

similar to some other groups, that aroylhydrazone-based Schiﬀ

base ligands are particularly eﬃcient in the construction of

lanthanide complexes.¹²We have synthesized a pyridine-based

Schiﬀ base ligand (LH₄) and utilized it for preparing

lanthanide complexes. Furthermore, we were also interested

EXPERIMENTAL SECTION

■

Solvents and other general reagents used in this work were puriﬁed

according to standard procedures.¹⁴Pyridine-2,6-dicarboxylic acid,

sodium borohydride, sodium azide, DyCl₃·6H₂O, TbCl₃·6H₂O, YCl₃·

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6H₂O, and GdCl₃·6H₂O were obtained from Sigma−Aldrich

Chemical Co. and were used as received. Diethanolamine, hydrazine

hydrate (80%), PBr₃, and sodium sulfate (anhydrous) were obtained

from SD. Fine Chemicals, Mumbai, India. Methyl-6-(hydroxymethyl)

picolinate,¹⁵methyl 6-(bromomethyl)picolinate,¹⁵methyl-6-((bis(2-

hydroxyethyl)amine)methyl)picolinate,^11dand 6-((bis(2-

hydroxyethyl)amino)methyl)picolinohydrazide (A₅),^11dwere pre-

pared according to literature procedure.

doublets and 195 quartet roots were taken into consideration in the

RASSI-SO step, as established earlier by us and others.²⁵The basis

sets are of ANO-RCC···8s7p4d3f2g1h TZVP level for the para-

magnetic center Ln^IIIand Lu^III, ANO-RCC···8s7p4d3f2g1h TZV

quality for O and N atoms, since they are coordinating to the metal

ion and ANO-RCC···3s2p/ANO-RCC···2s DZV level for the rest of

the atoms. The relativistic eﬀect was taken care of by taking DKH

Hamiltonian. In order to save disk space, Cholesky decomposition has

been incorporated for our calculations.^23aSpin−orbit coupling was

taken into account through the RASSI-SO module using the CASSCF

functions as input states. From the SINGLE-ANISO computation, the

g tensor for the ground state and excited state, magnetic susceptibility,

crystal ﬁeld parameter and orientation of main magnetic axes have

been obtained.²⁶Lines model was employed to calculate the exchange

interaction between two Ln^IIIsites using POLY-ANISO program.²⁷

The experimentally obtained susceptibility values were simulated with

the POLY_ANISO module/program to get the exchange interaction

between the two Ln^IIIcenters for both 1 and 2.

The exchange values obtained through this method was further

veriﬁed by density functional calculations using the Gaussian 09

program employing the DFT broken symmetry approach.²⁸For this

approach, we have used the B3LYP hybrid functional, with Cundari−

Stevens (CS) relativistic eﬀective core potential for Gd atom and TZV

level of basis set for the rest of the atoms.²⁹Quadratic convergence

method was followed to the most stable wave function. Since the Dy^III

and Tb^IIIion are highly anisotropic paramagnetic systems, to reduce

the complexity in using DFT methods, we have replaced the Dy^IIIand

Tb^IIIion in the corresponding X-ray structure with Gd^IIIion and

computed the Js using the DFT method and rescaled the J values

later, using appropriate spin to get the exchange values.³⁰By this

approach, the diﬀerence in structural parameters, however small, can

be captured in the estimation of J values. Also, this being an

independent method oﬀers the possibility to cross-verify results

obtained using the Lines model wherein the experimental

susceptibility data is ﬁt to the ab initio computed parameters to

extract the J values. The exchange values for Dy^III/Tb^IIIhas been

calculated by multiplying 5/7 and 6/7 with the exchange values

obtained from DFT using Gd^IIIion. For the Gd(III) analogue, the

exchange values were estimated by the use of broken symmetry

calculation using ORCA 4.2 package. For this, TZVP level was used

for Gd, and for the rest of the atoms, def2-SVP has been used.

Synthesis. Compounds A₁−A₅(Scheme S1 in the Supporting

Information) were prepared according to literature procedures.^11d,15

6 - ( ( B i s ( 2 - h y d r o x y e t h y l ) a m i n o ) m e t h y l ) -N ′ - ( 2 -

hydroxybenzylidene)picolinohydrazide (LH₄). Salicylaldehyde

(A₆) (0.19g, 1.6 mmol) was added to a solution of 6-((bis(2-

hydroxyethyl)amino)methyl)picolinohydrazide (A₅) (0.406 g, 0.0016

mol) in ethanol with stirring. The reaction mixture was reﬂuxed for 6

h, cooled, and the solvent reduced in vacuo. The concentrated

solution was kept in a refrigerator aﬀording a white precipitate which

was washed with diethyl ether and dried. This was shown to be 6-

((bis(2-hydroxyethyl)amino)methyl)-N′-(2-hydroxybenzylidene)-

picolinohydrazide (LH₄) (0.305, 76%). Anal. Calcd For C₁₈H₂₂N₄O₄

(358.40): C, 60.32; H, 6.19; N, 15.63. Found: C, 60.58; H, 5.99; N,

15.52. Mp: 164 °C.

Instrumentation. Melting points were measured using a JSGW

melting point apparatus and are uncorrected. IR spectra were

recorded as KBr pellets on a Bruker Vector 22 FT IR

spectrophotometer operating at 400−4000 cm⁻¹. Elemental analyses

of the compounds were obtained from Thermoquest CE instruments

CHNS-O, EA/110 model. ESI-MS spectra were recorded on a

Micromass Quattro II triple quadrupole mass spectrometer. ¹H NMR

spectra were recorded in CDCl₃and DMSO-d⁶solutions on a JEOL

JNM Lambda 400 model spectrometer operating at 500.0 MHz,

Chemical shifts are reported in parts per million (ppm) and are

referenced with respect to internal tetramethylsilane (¹H). A powder

X-ray diﬀraction (XRD) study was done on 1 and 2 with a Bruker D8

Avance powder XRD diﬀractometer. The samples for study were

prepared by ﬁnely grinding the crystals of 1 and 2 to powder form.

X-ray Crystallography. Single-crystal data for the complexes

were collected on a Bruker SMART CCD diﬀractometer (Mo Kα

radiation, λ = 0.71073 Å). The program SMART¹⁶was used for

collecting frames of data, indexing reﬂections, and determining lattice

parameters, SAINT for integration of the intensity of reﬂections and

scaling, SADABS¹⁷for absorption correction, and SHELXTL¹⁸for

space group and structure determination and least-squares reﬁne-

ments on F². On the other hand, XRD data for complex 1_Ywas

collected at low temperature (120 K) by using Rigaku diﬀractometer

with graphite-monochromated Mo Kα radiation, λ = 0.71073 Å. Data

integration and reduction were processed with CrysAlisPro

software.¹⁹An empirical absorption correction was applied to the

collected reﬂections with SCALE3 ABSPACK integrated with

CrysAlisPro. The crystal structures were solved and reﬁned by full-

matrix least-squares methods against F²by using the program

SHELXL-2014,²⁰using Olex-2²¹software. All the non-hydrogen

atoms were reﬁned with anisotropic displacement parameters.

Hydrogen positions were ﬁxed at calculated positions and reﬁned

isotropically. The crystallographic ﬁgures have been generated using

Diamond 3.1e software.²²In addition, some disorderd solvent

molecules was present in complexes 1 and 2. We could not assign

all the solvent molecules properly due to the disorder and weak

residual Q peaks. So the Olex-2 mask program was utilized to discard

the disordered solvents molecules which give an electron density of

∼18 and 26, corresponding to the presence of two water molecules in

1 and one methanol molecule and one water molecule in 2,

respectively. The possible masked electron counts and void volumes

has been included in the corresponding CIFs.

The crystal data, the cell parameters and ccdc information for all

the complexes are summarized in Table 1 and Table S1 in the

Supporting Information.

Magnetic Measurements. The dc magnetic susceptibility

measurements were performed on solid polycrystalline samples with

a Quantum Design MPMS-XL SQUID magnetometer between 2 and

300 K in applied magnetic ﬁeld of 200 Oe for temperatures between 2

and 20 K, 2 kOe between 20 K and 80 K, and 10 kOe at >80 K. The

sample was immobilized in a pellet made with Teﬂon tape. These

measurements were all corrected for the diamagnetic contribution as

calculated with Pascal’s constants. The ac magnetic susceptibility

measurements were performed on Quantum Design MPMS-XL

SQUID magnetometer in the frequency range of 1−1000 Hz.

Computational Details. The ab initio calculations have been

performed using MOLCAS 8.2 software package using CASSCF/

RASSI-SO/SINGLE_ANISO module.²³For POLY_ANISO simu-

lations, the inputs were taken from the SINGLE_ANISO results.²⁴In

the CASSCF step for Dy^IIIcomplex, nine electrons in seven 4f active

orbitals and for Tb^IIIcomplex eight electrons in seven 4f orbitals were

taken into consideration. For 1 21 sextets and for 2 7 septets, 140

¹H NMR (400 MHz, DMSO-d₆) 12.12 (s,1H,NH), 11.36

(s,1H,Ph-OH), 8.86 (s,1H,CH), 8.04 (m,2H,Py-H), δ = 7.84-

(d,1H,Py-H), 7.52 (d,1H,Ph-H), 7.32 (t,1H,Ph-H), 6.94 (m,2H,Ph-

H), 4.47 (br,2H,OH) 3.95 (s,2H,CH₂), 3.50 (t,4H,CH₂), 2.65

(t,4H,CH₂), IR (KBr) cm⁻¹: 3498 (br), 3443 (br), 3176 (br), 2955

(s), 2880 (br), 2804 (s), 1675 (s), 1622 (s), 1594 (w), 1536 (s), 1491

(w), 1474 (w), 1449 (s), 1398 (w), 1380 (s), 1371 (w), 1273 (s),

1244 (w), 1222 (w), 1169 (w), 1154 (s), 1045 (s), 971 (s), 898 (s),

780 (w), 737 (s), 698 (w), 678 (s), 566 (w), 518 (s). ESI-MS m/z,

ion: 359.1701, (C₁₈H₂₃N₄O₄)⁺.

General Synthetic Procedure for the Preparation of the

Complexes 1 and 2. To a stirred solution of LH₄(0.040 g, 0.11

mmol), in methanol (30 mL), LnCl₃·6H₂O (0.11 mmol) was added

to give a yellow-colored solution, which was allowed to stir for 10 min

at room temperature. Then, NaN₃(0.010 g, 0.15 mmol) was added,

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Scheme 1. LH₄Showing Unsymmetrical Coordination Pockets, Various Conformations Based on Base-Assisted Reversible

Keto-Enol Tautomerization and Coordination Modes

followed by the addition of triethylamine (0.046 mL, 0.33 mmol).

The reaction mixture was allowed to stir for 6−8 h at room

temperature. The reaction mixture was ﬁltered and stripped oﬀ its

solvent in vacuo aﬀording a semisolid yellow residue, which was

dissolved in methanol containing a few drops of chloroform. Suitable

crystals for XRD were obtained by slow evaporation of the solvents

within a week. A similar synthetic method was employed for the

preparation of the yttrium analogue, the diluted analogue of complex

1 (1_5%). Speciﬁc details of each reaction and the characterization data

of the complexes are given below.

[Dy₂(LH₂)(LH)(CH₃OH)(N₃)]·2H₂O (1). Quantities: LH₄(0.040 g,

0.11 mmol), DyCl₃·6H₂O (0.041 g, 0.11 mmol), NaN₃(0.010 g, 0.15

mmol), Et₃N (0.046 mL, 0.33 mmol). Yield: 0.046 g, 74.07% (based

on the Dy^IIIsalt). Mp: > 250 °C (d). IR (KBr) cm⁻¹: 3373 (br), 2963

(br), 2848 (br), 2053.37(s), 2036(s), 1609 (s), 1571 (w), 1554 (s),

1536 (s), 1474 (s), 1442 (w), 1429, 1356 (s), 1263 (w), 1220 (w),

1198 (s), 1149 (s), 1080 (s), 1015 (s), 1010 (w), 883 (s), 850 (s),

796 (w), 759 (s), 709 (w), 691 (s), 595 (s), 532 (s). Anal. Calcd For

C₃₈H₄₇Dy₂N₁₁O₁₀(1142.86): C, 38.75; H, 4.13; N, 13.43 Found: C,

39.05; H, 4.55; N, 13.91. ESI-MS m/z, ion: 518.5698,

(C₃₆H₄₀Dy₂N₈O₈)²⁺.

[Y₂(LH₂)(LH)(CH₃OH)(N₃)]·2H₂O (1_Y). Quantities: LH₄(0.040 g,

0.11 mmol), YCl₃·6H₂O (0.0338 g, 0.11 mmol), NaN₃(0.010 g, 0.15

mmol), Et₃N (0.046 mL, 0.33 mmol). Yield: 0.041 g, 73.74% IR

(KBr) cm⁻¹: 3342 (br), 2036.35 (s), 1610.78 (s), 1571 (w), 1556.33

(s), 1475 (s), 1357.42 (s), 1199 (s), 1079 (s), 851 (s), 760 (s). Anal.

Calcd For C₃₇H₄₇Y₂N₁₁O₁₁(999.15): C, 44.76; H, 4.74; N, 15.41

Found: C, 45.17; H, 4.95; N, 15.89.

5% Diluted Analogue of 1 (1_5%). Quantities: LH₄(0.040 g, 0.11

mmol), DyCl₃·6H₂O (0.0021 g, 0.005 mmol), YCl₃·6H₂O (0.0321 g,

0.105 mmol), NaN₃(0.010 g, 0.15 mmol), Et₃N (0.046 mL, 0.33

mmol). IR (KBr) cm⁻¹: 3341 (br), 2854 (br), 2036.29(s),1610 (s),

1571 (w), 1536 (s), 1474 (s), 1444 (w), 1357 (s), 1263 (w), 1198

(s), 1149 (s), 1078 (s), 1015 (s), 851 (s), 759 (s).

1474 (s), 1442 (w), 1359 (s), 1262 (w), 1221 (w), 1198 (s), 1129

(w), 1078 (s), 1015 (s), 904 (w), 884 (w), 850 (s), 816 (w), 776 (w),

759 (s), 711 (w), 691 (w), 630 (w), 595 (w), 535 (s). Anal. Calcd

For C₃₈H₄₉Tb₂N₁₁O₁₁(1153.73): C, 39.56; H, 4.28; N, 13.35

Found: C, 39.97; H, 4.73; N, 13.89. ESI-MS m/z, ion: 515.0687,

(C₃₆H₄₀Tb₂N₈O₈)²⁺.

RESULTS AND DISCUSSION

■

Synthetic Aspects. Polyfunctional ligands have been used

with a great deal of eﬃcacy to assemble various complexes

containing lanthanide ions. Among such multidentate ligands

aroylhydrazone-based Schiﬀ base ligands are particularly

versatile, because of several features, including their ﬂexibility

involving C−C bond rotation and the potential of utilizing

either the enolate or the keto forms of the ligand to bind to the

metal ion.^11d,f,31Harnessing these features, previously we have

assembled dinuclear lanthanide complexes (Scheme S2 in the

Supporting Information).^11d

Motivated by the above results, we have designed and

synthesized 6-((bis(2-hydroxyethyl)amino)-N′-(2-

hydroxybenzylidene)picolinohydrazide (LH₄). The latter was

prepared by following a ﬁve-step synthetic protocol (see

Scheme S1 in the Supporting Information).

The ligand LH₄contains seven coordination sites, which can

be partitioned into two unsymmetrical pockets: a tridentate

pocket consisting of a phenolic oxygen, an imine N, and

hydrazine O (2O,1N), and the other is pentadentate,

̀

consisting of a pyridine N, a common hydrazone oxygen and

a diethanolamine motif (2N, 3O). The observed coordination

behavior would be dependent also on the extent of

deprotonation and can be summarized in the following way.

If double deprotonation occurs the ligand would exist in the

enol form, [LH₂]²⁻. On the other hand, if triple deprotonation

were to occur, where one arm of diethanolammine is

deprotonated, [LH]³⁻(enol form) would result. In fact, in

[Tb₂(LH₂)(LH)(CH₃OH)(N₃)]·H₂O·MeOH (2). Quantities: LH₄(0.040

g, 0.11 mmol), TbCl₃·6H₂O (0.041 g, 0.11 mmol), NaN₃(0.01 g,

0.15 mmol), Et₃N (0.046 mL, 0.33 mmol). Yield: 0.035 g, 55.2%

(based on the Tb^IIIsalt). Mp: > 250 °C (d). IR (KBr) cm⁻¹: 3342

(br), 2960 (br), 2909 (br), 2036 (s), 1610 (s), 1554 (w), 1536 (w),

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Scheme 2. Synthesis of Ln₂Complexes 1−2

Figure 1. (a) Molecular structure of 1, (b) side view of 1, and (c) top view of 1. Thermal ellipsoids at 50% probability level are shown (selected

hydrogen atoms and the solvent molecules have been omitted for the sake of clarity). [Color codes: N = blue; O = red; C = gray; Dy = dark green,

and H = black.]

the formation of the dinuclear complexes discussed herein,

both [LH₂]²⁻and [LH]³⁻are involved (Scheme 1).

In order to check the phase purity of the complexes, powder

XRD measurement for complexes was done and found that the

sequence and pattern of the peaks are in reasonable agreement

with the simulated data obtained from single-crystal data (see

Figures S1 and S2 in the Supporting Information).

We have performed ESI-MS studies to check the structural

integrity of these complexes in solution. These studies reveal

peaks at m/z = 518.5698 and 515.0687 for 1, 2 respectively,

corresponding to the species [Dy₂(LH₂)(LH)H]²⁺,

[Tb₂(LH₂)(LH)H]²⁺. This indicates that these complexes

remain partially intact in solution. The ESI-MS spectra of

complexes are given in the Supporting Information (see

Figures S3 and S4 in the Supporting Information).

In addition to using the ligand LH₄, we have used sodium

azide as the co-ligand with the intention of exploring the

coordination capability of the azide ion. We anticipated a

bridging coordination role for the azide ligand. However, as

described below, because of the competing bridging coordi-

nation of the enolate form the ligand, the azide takes up a

terminal position. Thus, the reaction of LH₄, LnCl₃·6H₂O and

sodium azide in the presence of triethylamine in a molar ratio

of 1:1:1:3 aﬀorded dinuclear complexes, [Ln₂(LH₂)(LH)-

(CH₃OH)(N₃)]·xMeOH·yH₂O [1, Ln = Dy^III, x = 0, y = 2; 2,

Ln = Tb^III, x = 0, y = 2] (see Scheme 2).

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Table 2. Selected Bond Distances and Bond Angles of 1

Bond Distances around Dy1

Bond Distances around Dy2

Bond Angles around Dy

bond angle value (°)

bond pair

distance (Å)

bond pair

distance (Å)

Dy(1)−O(7)

Dy(1)−O(8)

Dy(1)−O(3)

Dy(1)−O(9)

Dy(1)−O(2)

Dy(1)−O(1)

Dy(1)−N(11)

Dy(1)−N(10)

Dy(1)−N(4)

2.557(17)

2.312(17)

2.359(17)

2.526(19)

2.234(17)

2.492(19)

2.628(2)

2.525(2)

2.512(2)

Dy(2)−O(7)

Dy(2)−O(3)

Dy(2)−O(5)

Dy(2)−O(4)

Dy(2)−O(6)

Dy(2)−N(6)

Dy(2)−N(8)

Dy(2)−N(7)

Dy(2)−N(1)

2.341(17)

2.516(17)

2.376(19)

2.404(18)

2.217(18)

2.487(2)

2.516(2)

2.636(2)

2.544(2)

Dy(1)−O(3)−Dy(2)

Dy(1)−O(7)−Dy(2)

115.80(7)

114.87(7)

Figure 2. (a) Quadrilateral Dy₂O₂core of 1; (b) core structure of 1. The outer backbone of the ligands are omitted for the sake of clarity.

Figure 3. Spherical capped square antiprism coordination geometry around (a) Dy1 and (b) Dy2.

X-ray Crystallography. Suitable single crystals of the

complexes 1−2 were obtained by slow evaporation of their

solutions in methanol/chloroform mixture (1:1) within a week.

Single-crystal XRD study reveals that the complexes 1−2 are

isostructural and charge neutral. These crystallize in a

monoclinic system (C2/c with Z = 8). Since 1 and 2 are

isostructural, we describe the molecular structure of 1 as a

representative example. A perspective view of 1 is given in

Figure 1 and that of complex 2 is given in the Supporting

Information (see Figure S5 in the Supporting Information).

Selected bond lengths and bond angles of 1 are given in Table

2, while those of 2 are given in Table S2 in the Supporting

Information.

The molecular structure of 1 consists of two Dy^IIIions, a

dianionic ligand [LH₂]²⁻, a trianionic ligand [LH]³⁻, an azide

anion, and a neutral methanol giving an overall neutral

dinuclear assembly. Interestingly, the two lanthanide ions

present in the assembly are nonequivalent as described below.

The [LH₂]²⁻and [LH]³⁻ligands encapsulate the two Dy^III

ions in a “head-to-tail” manner utilizing their two coordination

pockets, a tridentate P1 (O, 2N) and a pentadentate P2 (3O,

2N) unit to generate the dimeric [Dy₂(LH₂)(LH)]⁺motif

(Figure 1 and Scheme 1). Note that, in the formation of 1, the

ligand has exclusively utilized the enol form to generate the

Dy₂O₂core. The enolate oxygen atoms (O3 and O7) of the

ligand bridge the two metal centers aﬀording a quadrilateral

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four-membered Dy₂O₂core as deduced from the bond

distances, Dy1−O3 = 2.359 Å, Dy1−O7 = 2.557 Å, Dy2−

O3 = 2.516 Å, and Dy2−O7 = 2.341 Å. (See Figure 2). The

Dy···Dy distance and the two Dy−O−Dy angles in the central

Dy₂O₂cores are found to be 4.131 Å and 115.80(7)°, and

114.87(7)°, respectively. Because of the bridging coordination

of the enolate form of the ligand, we believe that the azide

ligand is forced to function as a terminal ligand to one of the

lanthanide centers. On the other lanthanide center, the ninth

coordination is provided by a neutral methanol. Overall, the

dinuclear assembly contains two types of nine-coordinated

Dy^IIIcenters: Dy1 (coordination environment, 3N, 6O) and

Dy2 (coordination environment, 4N, 5O).

In order to ascertain if other mono anions such as chloride

would similarly bind in a monodentate fashion, we performed

the reaction using DyCl₃·6H₂O as the starting material but in

the absence of the additional azide ligand. Under these

conditions, however, we were not able to isolate any pure

crystalline products.

As alluded above, 1 contains two diﬀerent types of Dy^III

centers. While both the Dy1 and Dy2 are nine-coordinated,

they are nonequivalent, because they are surrounded by

slightly diﬀerent coordination environments. Dy1 is bound by

the deprotonated arm of the diethanolamine of ligand [LH]³⁻

with the ninth coordination provided by neutral methanol,

while Dy2 is bound by the neutral diethanolamine arm of

[LH₂]²⁻with the ninth coordination provided by the azide

ligand. The ligand in this assembly binds in two ways: one as

[LH₂]²⁻and the other as [LH]³⁻. In the latter, one of the

diethanolamine arm is deprotonated. The bond lengths found

in the deprotoated arm (−CH₂−CH₂−O (O8) are consistent

with literature precedents.^11fSHAPE analysis reveals that the

coordination geometry around Dy1 and Dy2 (and other

analogues) can be described as spherical capped square

antiprism (see Figure 3, as well as Table S4 in the Supporting

Information).³²

●

Figure 4. Thermal dependence of the χ_MT product for ( ) 1 and

(

△

) 2. Red and blue lines correspond to the best simulated curves

from POLY_ANISO program implemented in MOLCAS 8.2 package

for complex 1 and 2. M vs H plot at 2 K is ﬁtted and given in the inset.

reach the value of 20.68 cm³K mol⁻¹at 8 K and ﬁnally slightly

increases at very low temperature (20.88 cm³K mol⁻¹at 2 K).

For both compounds 1 and 2, the decrease can be mainly

attributed to the depopulation of the ligand-ﬁeld levels, while

the change of slope at a lower temperature than 25 K could be

due to the existence of weak magnetic interactions.

The ﬁeld dependence of the magnetization has been

measured for diﬀerent temperatures from 2 K to 5 K. At 2

K, these show a classic behavior with values of 10.54 Nβ and

9.26 Nβ, respectively, for two Dy^IIIions with the presence of a

magnetically anisotropic ground state and two Tb^IIIions (inset

of Figure 4). Furthermore, the absence of a superposition in

the diﬀerent M vs H curves for each system (Figure S9 in the

Supporting Information), elucidates the presence of signiﬁcant

magnetic anisotropy for 1 and 2, as well as the possibility of

low-lying excites states in the systems.

Dynamic Magnetic Properties. ac measurements have been

performed for 1 and 2. At zero dc magnetic ﬁeld 1 displays a

frequency dependence of the magnetic susceptibility in the

temperature range of 2−15 K in the window 1−1000 Hz

frequency of the oscillating ﬁeld (see Figure 5a, as well as

Figure S10 in the Supporting Information). The relaxation

time (τ) has been extracted with an extended Debye model³⁵

(see Figure S11 and Table S6 in the Supporting Information).

The Argand plot conﬁrms that the observed slow magnetic

relaxation corresponds to the entire sample (Figure S12 in the

Supporting Information). The corresponding thermal variation

of the log(τ) is depicted in Figure 5d and clearly shows a linear

dependence (Orbach process) in the temperature range of 7−

11 K, while a deviation from the linearity is observed down to

6 K, because of the presence of under-barrier processes such as

Raman and quantum tunnelling of the magnetization (QTM).

It is well-known that the latter can be canceled by applying a

dc magnetic ﬁeld.^36a,bThus, the ﬁeld dependence of the

magnetic susceptibility at 2 K (Figure S13 in the Supporting

Information) shows an optimal behavior at a selected dc

magnetic ﬁeld value of 800 Oe (Figure 5b, as well as Table S7

in the Supporting Information). At 2 K and zero applied dc

ﬁeld, χ_M′′ vs ν curve passes through a maximum at 5 Hz, which

The Dy−O bond lengths fall in a range (2.217−2.557 Å).

The Dy−O_methanol(2.492 Å) bond length is slightly longer than

those observed previously^31,33The deprotonated Dy−

O_{diethanolamine}(O8) (2.312 Å) bond length is slightly longer

than that observed in the literature, but smaller than the bond

length involving the neutral diethanolamine arm.^11fAll the

Dy−N bond lengths fall in a very narrow range, 2.487−2.636

Å, consistent with values found in the literature.³¹The bond

angles, Dy1−O3−Dy2 and Dy1−O7−Dy2 are 115.80° and

117.86°, respectively (Figure 2 and Table 2).

The crystal structure of 1 reveals the presence of

intramolecular and intermolecular hydrogen bonds leading to

the formation of a 1D polymeric chain (see Figures S7 and S8

in the Supporting Information).

Magnetic Studies. Static Magnetic Properties. dc

magnetic properties of the two complexes 1 and 2 were

determined by measuring the thermal dependence of the molar

magnetic susceptibility (χ_M) from 2 K to 300 K (Figure 4).

The room-temperature values of the χ_MT product are 27.90

cm³K mol⁻¹and 22.42 cm³K mol⁻¹, close to the expected

values of 28.34 cm³K mol⁻¹and 23.64 cm³K mol⁻¹,

respectively, for two isolated Dy^IIIions (⁶H_15/2and g_J= 4/3)

and Tb^III(⁷F₆and g_J= 3/2).³⁴On cooling, χ_MT of 1

monotonously decreases down to 25 K, temperature for which

a plateau is almost observed, and then decreases progressively

reaching a minimum of 23.60 cm³K mol⁻¹at 2 K. The χ_MT of

2 remains almost constant down to 75 K, then decreases to

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Figure 6. (a) Out-of-phase component of the ac magnetic

susceptibility data for 1_5%in zero ﬁeld in the temperature range of

2−15 K. (b) Out-of-phase component of the ac magnetic

susceptibility data for 1_5%at 2 K from 0 to 3000 Oe. (c) Out-of-

phase component of the ac magnetic susceptibility data for 1 in 800

Oe in the temperature range of 2−15 K. (d) Thermal dependence of

Figure 5. (a) Out-of-phase component of the ac magnetic

susceptibility data for 1 in zero ﬁeld in the temperature range of

2−15 K. (b) Field dependence of the magnetic relaxation time at 2 K

in the ﬁeld range of 0−3000 Oe with the full red line is the best-ﬁtted

curves (see text), while the dashed lines are the Orbach/Raman

(brown), QTM (blue), and Direct (orange) contributions. (c) Out-

of-phase component of the ac magnetic susceptibility data for 1 in 800

Oe in the temperature range of 2−15 K. (d) Thermal dependence of

●

the magnetic relaxation time for 1 in ( ) zero ﬁeld in the 2−11 K

○

temperature range and ( ) 800 Oe applied magnetic ﬁeld in the 2−

10 K temperature range. Full lines are the best-ﬁtted curves (see text),

while the dashed lines represent the Orbach (green), Raman (purple),

and QTM (blue) contributions.

●

the magnetic relaxation time for 1 at ( ) zero ﬁeld in the 2−11 K

○

temperature range and ( ) 800 Oe applied magnetic ﬁeld in the 2−

10 K temperature range. Full lines are the best-ﬁtted curves (see text)

while the dashed lines are the Orbach (green), Raman (purple), and

QTM (blue) contributions.

Since these two processes are ﬁeld-independent (eq 2), they

can be considered constant for both relaxation times at 0 and

i

Δ y

−1

τ⁻¹= CTⁿ+ τ₀⁻¹exp −

+

τ

j

z

j

T1

ß

is shifted to 1 Hz upon applying a 800 Oe magnetic ﬁeld

(Figure 5c, as well as Figure S14 in the Supporting

Information), because of the removal of the QTM

contribution.

kT

k

{

´ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖ≠ÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÖÆ

Raman

QTM

Orbach

The relaxation time (τ) has been extracted with the

extended Debye model (Table S7 in the Supporting

Information) and the corresponding relaxation time of the

magnetization in the temperature range of 2−11 K are given in

Figure 5d, corresponding again to a general behavior of the

sample as seen in the Argand plot (Figure S15 in the

Supporting Information). As for 1 in zero ﬁeld, the linear

region depicted in the temperature dependence of the

magnetic relaxation time has deviated at the lower temper-

atures, which is a sign of a remaining contribution of under

energy barrier processes. At the optimal ﬁeld of 800 Oe, the

involvement of a signiﬁcant Direct process or remaining QTM

can be discarded. To support this aﬃrmation, the τ vs H curve

was ﬁtted with the eq 1 for the 0−2000 Oe ﬁeld range (Figure

6b).^36c,d

800 Oe. Indeed, the thermal variation of the relaxation time is

simultaneously ﬁtted for 1 in zero ﬁeld and 800 Oe with

Orbach (Δ and τ₀) and Raman (C and n) shared parameters

while QTM (τ_TI) appears only at 0 Oe. The best-ﬁtted curves

are represented in Figure 5d with Δ = 59(3) K, τ₀= 10(4) ×

10⁻⁶s, C = 1.2(2) K⁻ⁿs⁻¹, n = 2.3(1) and τ_TI= 0.032(2) s.

Importantly, τ_TIﬁtted from thermal variation matches the zero

ﬁeld limit of eq 1 (B₁⁻¹) obtained from ﬁeld variations. The

expected n value for Kramers ions should be 9,³⁷but it is well-

known that, for molecular systems,³⁸the presence of both

acoustic and optical phonons could lead to lower values,

between 2 and 7.³⁹A search in the literature reveals that Dy-

based dimers show a most common coordination number of

8,^8,10and more recently the tendency tries to go to low

coordination systems.^8hHowever, very few unsymmetric Dy-

based dimers have been reported.^{8a,10d,e,40a,g}The properties

found in such complexes are consistent with the results found

in this work. These results are summarized in Table

3.^{8a,10d,e,40a,g}If one considers a similar coordination geometry,

viz., the spherical capped square antiprism geometry, examples

with ﬁeld-induced relaxation are known.⁴¹In the present

instance, however, we have observed zero-ﬁeld SMM behavior.

The molecular structure of 1 highlighted two Dy^IIIions in

diﬀerent coordination sphere, i.e., N3O6 and N4O5,

respectively, for the Dy1 and Dy2 surroundings. One could

expect two distinct magnetic behaviors while it was observed

that both Dy^IIIcenters are involved in the magnetic relaxation

at the same frequency for a given temperature. The previous

B₁

τ⁻¹

=

+ 2B₃H^m+ B₄

1 + B₂H²

(1)

where the three terms correspond respectively to the QTM,

Direct, and ﬁeld-independent magnetic relaxation processes

(Raman and Orbach). The best ﬁt was obtained for B₁= 31.25

s⁻¹; B₂= 3.795(10) × 10⁻⁵Oe⁻²; B₃= 1.95(4) × 10⁻¹³s⁻¹K⁻¹

Oe⁻⁴; and B₄= 2.38(4) s⁻¹leading to τ⁻¹(QTM) = 1.23 s⁻¹

(blue contribution on Figure 5b), τ⁻¹(Direct) = 0.16 s⁻¹

(orange contribution on Figure 5b) and τ⁻¹(Raman +

Orbach) = 2.38 s⁻¹(brown contribution on Figure 5b). Thus,

the thermal variation of the magnetic relaxation times could be

ﬁtted using a combination of Orbach and Raman processes.

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Table 3. Some Representative Examples of Dinuclear Dysprosium Complexes with Unsymmertrical Coordination

Environment

local geometries around Ln^III

compound

centers

magnetic properties

ref

[Dy₂ovph₂Cl₂(MeOH)₃]3 MeCN, H₂ovph = pyridine-2-carboxylic

acid [(2-hydroxy-3-methoxyphenyl)methylene] hydrazide)

hula hoop-like geometry

(center 1) and pentagonal

bypyramidal (center 2)

SMM

8a

U_eff= 150 K, τ₀= 2.3 × 10⁻¹⁰

U_eff= 198 K, τ₀= 7.3 × 10⁻⁹

s

[hqH2][Dy₂(hq)₄(NO₃)₃] MeOH 8-hydroxyquinoline (hqH)

bicapped trigonal prism

geometry

ﬁeld-induced SMM

10d

10e

U_eff= 41 cm ⁻¹, τ₀= 1.4 × 10⁻⁶

s

[(μ-mbpymNO)-{(tmh)3Dy}2] (tmh = 2,2,6,6-tetramethyl-3,5-

heptanedionate mbpymNO = bipyrimidine-N-oxide

triangular dodecahedron and

square-antiprismatic

SMM

U

_eff= 54.7 K, τ₀= 1.7(3) × 10⁻⁹; and U_eff

= 47.8 K, τ₀= 1.5(4) × 10⁻⁹

s

[[Dy(Cy₃PO)₂- (μ -Br)(Br)₂]₂2C₇H₈(Cy₃PO =

distorted octahedral

SMM

40a

40b

40c

40d

U_eff= 684.1 K, τ₀= 3.84 × 10⁻¹²

s

tricyclohexylphosphine oxide))

[[Dy(Cy₃PO)₂-(μ -I)(I)₂]₂4C₇H₈(Cy₃PO = tricyclohexylphosphine

oxide))

SMM

U_eff= 1290 K, τ₀= 1.26 × 10⁻¹²

s

[Dy₂(Hhmb)₃(NCS)₃]·2MeOH·py (H2hmb = N′-(2-hydroxy-3-

monocapped distorted square

antiprismatic geometry

ﬁeld-induced SMM

U_eff= 2.4 K, τ₀= 0.16 s

methoxybenzylidene)- benzhydrazide)

[Dy₂(L1)₂(acac)₂(H₂O)]·2CH₂Cl₂L₁= N,N-bis(salicylidene)-o-

phenylenediamine

distorted square antiprism and SMM

capped trigonal prism

U_eff= 36 K, τ₀= 4.2 × 10⁻⁷

U_eff= 80 K, τ₀= 8.3 × 10⁻⁸

s

[ Dy₂(L1)₂(DBM)₂(H₂O)]·2CH₂Cl₂L₁= N,N-bis(salicylidene)-o-

distorted square antiprism and SMM

40e

40f

U_eff= 31.4 K, τ₀= 6.6 × 10⁻⁷

U_eff= 59.6 K, τ₀= 7.3 × 10⁻⁸

s

phenylenediamine, DBM = dibenzoylmethane

capped trigonal prism

[Dy₂L₂(HL)(NO₃)(EtOH)]·0.5C₂H₅OH (LH₂= 5-chloro-2-(((2-

hydroxy-3-methoxybenzyl)imino)methyl) phenol)

triangular dodecahedron and

square antiprism

SMM

U_eff= 69.19 K, τ₀= 9.5 × 10⁻⁶

U_eff= 45.73 K, τ₀= 4.6 × 10⁻⁶

s

(HNEt₃)[Dy₂(MQ)₄(NO₃)₃]·EtOH·H₂O (HMQ = 2-methyl-8-

hydroxyquinoline)

square antiprism and spherical slow relaxation of magnetization

tricapped trigonal prism

40g

[Dy₂(LH₂)(LH)(CH₃OH)(N₃)]·2H₂O

capped square antiprismatic

geometry

SMM

U_eff= 59(3) K, τ₀= 10(4) × 10⁻⁶

this work

s

published dissymmetrical Dy^IIIdinuclear SMMs displayed

either single^40a,bor multiple^40d,grelaxation contributions.

The magnetic properties of the diluted 1_5%analogue were

studied in order to obtain a greater information on the slow

relaxation mechanism in such Dy₂SMM, especially to

understand the eﬀects of magnetic interactions within the

dynamic magnetic properties in the dimer. The ﬁeld

dependence of the magnetization at 2 K (Figure S16 in the

Supporting Information) shows a classic behavior with a value

of 0.614 Nβ at 5 T, conﬁrming a magnetic dilution of ∼6%.

sample (Argand in Figure S15). Again, the thermal variation of

the relaxation time is simultaneously ﬁtted for zero ﬁeld and

800 Oe ﬁeld with Orbach parameters (Δ and τ₀), injected from

the linear ﬁt at high temperature region (from 8 K to 12 K) of

the in-ﬁeld relaxation curve (Figure 6d), and Raman (C and n)

shared parameters, while QTM (τ_TI) appears only at 0 Oe. The

best ﬁtted curves are represented on Figure 6d with Δ = 66(1)

K, τ₀= 7.3(8) × 10⁻⁷s, C = 9(3) × 10⁻⁴K⁻ⁿs⁻¹, n = 5.9(2),

and τ_TI= 1.10(6) × 10⁻³s.

Figure 7 depicts the four thermal dependence of the

relaxation times for 1 and 1_5%. Indeed, at zero applied ﬁeld, the

suppression of the magnetic interactions between magnetic

centers by magnetic dilution leads to an increase of the fast

relaxation QTM process. However, under an applied magnetic

ﬁeld, the magnetization of the diluted sample relaxed slower

than the magnetization of 1 (Figure 7) because of the decrease

of the Raman contribution (T < 6 K) for 1_5%, compared to 1.

Such diminution of the Raman contribution might be

attributed to the diamagnetic dilution which reduces the

interactions with the matrix. Such trend in the magnetic

1_5%display an SMM behavior at zero applied ﬁeld (see Figure

6, as well as Figures S17 and S18 in the Supporting

Information), which is shifted to the higher frequencies (158

Hz), compared to 1 (5 Hz) at 2 K. Such shift is in agreement

with a faster magnetic relaxation time when the magnetic

interactions are canceled by magnetic dilution.

As previously, the extended Debye model was used in order

to extract the temperature dependence of the relaxation

mechanism (see Tables S8 and S9 in the Supporting

Information), corresponding to a general behavior of the

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nature of the terminal coordination environment. For complex

1, the low lying 8 KDs are lying in the range of 176.3−820.8

cm⁻¹for the Dy1 center, where methanol is coordinated,

whereas for the Dy2 center, the ground to highest excited state

lays in the range of 117.6−536.0 cm⁻¹(Table S12 in the

Supporting Information), where terminal azide coordination is

present. Although the splitting of 8 KDs is up to the range of

820.8 and 536.0 cm⁻¹, the relaxation is occurring at the ﬁrst

excited state, because of the displacement of the anisotropic

axis at the excited state, compared to the ground state. The

large diﬀerence for the two Dy centers is due to the diﬀerence

in the crystal ﬁeld eﬀect provided by the two diﬀerent terminal

ligands and their inﬂuence on the geometry.⁴³The MeOH

terminal coordination provides stronger axial CF, compared to

azide coordination. The required crystal ﬁeld Hamiltonian is

described as H_CF= ∑_k,qB^q_kO_k^q, where B^q_kis the crystal-ﬁeld

parameter and O^q_kis Steven’s operator (Table S14 in the

Supporting Information).⁴⁴The axial parameter B^q_k(where k =

0 and q = 2) is comparatively larger for the Dy1 ion (−8.98),

compared to the Dy2 site (−2.35). This is in agreement with

our computed low lying energy splitting for the lowest eight

doublets. To further understand the diﬀerence between

electronic eﬀects induced by the MeOH versus azide and

geometric eﬀects caused by the same, we performed additional

calculations on model systems 1a and 1b. Here, model 1a

represents a structure where both Dy1 and Dy2 are

coordinated to the methanol while model 1b represents a

structure where both the Dy^IIIcenters are coordinated to an

azide group. The energy splitting obtained for both the models

1a (for 1a-Dy1, 185.4−829.8 cm⁻¹; for 1a-Dy2, 137.5−630.9

cm⁻¹) and 1b (for 1b-Dy1, 178.5−823.5 cm⁻¹; for 1b-Dy2,

131.5 to 675 cm⁻¹) are similar to the original structures (see

Table S12). This unequivocally reveals that the geometric

eﬀects due to the substitution play a prominent role in

dictating the anisotropy and not the individual MeOH versus

azide electronic eﬀects. The analysis of Loprop charges also

arrives at the same conclusion. Since the diﬀerences lie in the

geometry, we looked at the SHAPE analysis, and this reveals

that Dy1 has a CShM value of 1.432, while Dy2 has a value of

0.905, with respect to ideal nine-coordinated Muﬃne (MFF-9)

geometry. Thus, stronger deviation from MFF-9 in Dy1 yields

larger anisotropy, compared to Dy2.

Furthermore, to understand the magnetic relaxation

contributed by the single Dy^IIIcenter, we have looked into

the nature of the ground state for both the Dy^IIIcenters. The

ground state for Dy1 is of pure m_J= 15/2 in nature, whereas

for Dy2, a strong mixing of m_J= 15/2 with other excited

states is noticed. The U_calvalues obtained for both the centers

is 176.3 and 117.6 cm⁻¹respectively. The calculated energy

barrier for magnetic relaxations is overestimated, compared to

the experimental U_effvalue. This suggests that the exchange

interaction present between the Dy^III···Dy^IIIcenter/other

under-barrier process/QTM eﬀects alters the barrier height

for magnetization reversal; hence, we looked at the exchange-

coupled state of {Dy2} dimer. Although the nature of

anisotropy at the ground level is Ising in nature (Table 4)

for both Dy1 and Dy2 centers, the angle of deviation of the

ground state axis (Figure 8) signiﬁcantly deviates at the ﬁrst

excited state for Dy2 (∼7° vs ∼49°). The combination angle of

deviation of the anisotropic axis and the contribution of higher

excited state wave functions lead to diﬀerent magnetic

relaxations oﬀered by Dy2.

Figure 7. Thermal variation of the relaxation time for 1 at H = 0 Oe

(full black spots) and H = 800 Oe (open black circles) and 1_5%at H =

0 Oe (full gray spots) and H = 800 Oe (open gray circles). Full red

and black lines are the best-ﬁtted curves (see text) for 1 and 1_5%

,

respectively.

relaxation time can be reinforced by the behavior of the

hysteresis loop of the magnetization of both compounds at 2

K. In which, once an applied magnetic ﬁeld and the QTM is

released, the hysteresis loop for 1_5%opens, in opposition to 1,

which remains closed (see Figure S21 in the Supporting

Information).

At zero applied magnetic ﬁeld, 2 was not displaying any out-

of-phase component of the susceptibility at 2 K in the

frequency window of the oscillating ﬁeld (Figure S22 in the

Supporting Information) (1−1000 Hz). Indeed, 2 involves

non-Kramers Tb^IIIions, which require a highly axial symmetric

ligand ﬁeld to possess a bistable ground state and prevent

eﬃcient QTM.⁴²In order to cancel the possible QTM, the

magnetic susceptibility has been measured under various

applied magnetic ﬁeld (Figure S23 in the Supporting

Information). As soon as a dc ﬁeld is applied, an out-of-

phase contribution appears at 30 Hz which grows with the

increase of the applied magnetic ﬁeld. The 2800 Oe value is

selected as the optimal applied magnetic ﬁeld. At such ﬁeld, the

magnetic susceptibility displays a frequency dependence

between 2 and 6 K (Figure S23), which is an indication of

the slow magnetic relaxation for 2. The thermal dependence of

the relaxation time has been plotted by selecting, by hand, the

maxima of the out-of-phase signal at each temperature (see

Figure S24 in the Supporting Information). Considering the

weak thermal dependence of the relaxation time and the 2800

Oe applied magnetic ﬁeld value, one might suggest that the

most probable magnetic relaxation occurs via a direct process

(τ⁻¹= AH⁴T).

Ab Initio Calculations. To investigate and quantify the

nature of magnetic relaxations occurring at the individual

magnetic center and for the entire complex, detailed

multireference ab initio calculation has been performed for

complexes 1 and 2. The methodology employed here for the

calculation is given in computational details (see the

Experimental Section). First, the magnetic properties at the

individual magnetic center have been calculated using the X-

ray structures, wherein one of the Tb/Dy centers were

replaced by a diamagnetic Lu^IIIion. The calculations were

performed on the entire complexes without further modeling.

Mechanism of Magnetic Relaxation by Individual

Dy^III/Tb^IIIions. Single ion calculations at the individual Ln^III

center shows that the lowest-lying eight Kramer Doublets

(KDs) behave diﬀerently for both centers, depending on the

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Here, J_i= J_idip+ J_iexch; that is, J_iare the total magnetic

interaction Ln^III···Ln^III, this describes the interaction between

the neighboring metal centers.

Table 4. Ab Initio Estimated g-Values, along with the

Ground State Wave Function Estimated for 1 and Their

Respective Models

Lnⁱ−Lnⁱ⁺¹

wave function contributions to

̂

H = −(−J_dip

+ J

)s s

̃ ̃

Ln_iLn_i+1

complex

g_x

g_y

g_z

the ground state

exch

(4)

1-Dy1

1-Dy2

0.0106

0.0124

0.0171

0.0199

19.9194 0.99| 15/2⟩

19.7092 0.70| 15/2⟩ + 0.02| 13/2⟩

2

i

j

y

z

μ_B

Lnⁱ−Lnⁱ⁺¹

2

Ln

+ 0.20| 11/2⟩ + 0.04|

9/2⟩

j

z

J

=

g

dip

3

j

z

j R_Dy_i_−Dy_i+1

1a-Dy1

1a-Dy2

1b-Dy1 0.0097

1b-Dy2 0.0271

0.0083

0.0176

0.0132

0.0280

0.0162

0.0476

19.9226 0.99| 15/2⟩

19.7353 0.96| 15/2⟩⟩ + 0.03| 11/2⟩

19.9138 0.99| 15/2⟩

(5)

k

{

Lines model yields an excellent ﬁt with the experimental data,

and the extracted J values are given in Table 5. Note that the

exchange interaction between Dy^III···Dy^IIIis weakly antiferro-

magnetic in nature, whereas for complex 2, the interaction

between Tb^III···Tb^IIIis found to ferromagnetic in nature. The

mechanism of magnetization relaxation developed for the

dinuclear model is shown in Figure 10. The mechanism

computing using the POLY_ANISO routine yields a U_calvalue

of 69 cm⁻¹and this matches closely with experimental U_eff

value (41 cm⁻¹). It has been observed that there is a

discrepancy in the U_effvalue obtained by experiment and U_cal

value obtained from ab initio calculation for the exchange

coupled state. Recently, we have reported an alternate equation

to estimate the U_calvalues for dinuclear Dy^IIIsystems.⁴⁷The

equation is given as follows.

19.7406 0.96| 15/2⟩⟩ + 0.03| 11/2⟩

For complex 2, the energy spectrum for the lowest Ising

doublets is in the range of 0.3−535.5 cm⁻¹and 0.4−408.6

cm⁻¹, respectively, for Tb1 and Tb2 centers. Despite having

signiﬁcant ground-state anisotropy, the non-Kramer nature of

the Tb^IIIion leads to a signiﬁcant tunnel splitting and lack of

zero ﬁeld SMM behavior for complex 2. The tunnel splitting

was found to be 0.19 and 0.15 cm⁻¹for Tb1 and Tb2 centers,

respectively, as a result of diﬀerent crystal ﬁeld eﬀects (see

Table S13 in the Supporting Information). The ground-state

anisotropic axis was plotted for both complexes 1 and 2 in

Figure 9. The anisotropic axis for complex 1 lies parallel to

each other in the same plane, which agrees well with the earlier

reported Dy2 SMMs.^8a,hIn contrast, for complex 2, a

signiﬁcant tilt between the g_zz-axis is noticed.

Mechanism of Magnetic Relaxation of Exchange

Coupled State of 1 and 2. For the dinuclear-exchanged

coupled state, the magnetic relaxation dynamics diagram for

complex 1 is plotted in Figure 10, using POLY_ANISO

calculations.⁴⁵For complexes 1 and 2, both the dipolar and

exchange interactions were taken into account by using the

Lines model, with the Hamiltonian given in eq 3 below.⁴⁶

The Hamiltonian below is used to calculate the dipolar and

exchange interaction between the Ln^III···Ln^IIIcenters.

Ä

Å

U

cal1

U

=

cal eff

3

Å

(QTM or TA‐QTM) × 10

Å

Ç

É

Ñ

U

cal2

+

+ 15J

Ñ

(QTM or TA‐QTM) × 10³

Ñ

(6)

Ñ

Ö

Here, U_cal1and U_cal2represent the calculated energy barrier for

the Dy1 and Dy2 centers, respectively, QTM or TA-QTM

represents the value of transition propbabilities between

ground states or excited state (one level below where the

relaxation is happening). These values are taken from Figure 8,

as well as Table S12 in the Supporting Information. Using the

above formula, the U_{cal eff}is now estimated to be 59 cm⁻¹

(compare to 41 cm⁻¹experimental value). This value is

̂

H_ex= − JSS

∑

i i+1

i

(3)

i

Figure 8. SINGLE_ANISO calculated relaxation pathways for Dy1 and Dy2 for complex 1. The red line represents the QTM, blue line represents

TA, and the green line represents the Orbach/Raman processes. The dark blue (smaller) line indicates the KDs as a function of magnetic moments.

The number above these lines represents the transition probabilities from one m_Jlevel to the other m_Jlevel.

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Figure 9. Arrangement of ground state anisotropy axes for complexes 1 and 2.

improved by 10 cm⁻¹though a small discrepancy is still there,

in comparison to the experimental value.

The ferro-antiferro exchange obtained from complexes 1 and

2 is interesting and may be due to subtle structural factors, as

argued below. Also note that the Lines model employed to

extract these parameters is semiempirical and not fully ab initio

as generally claimed. The alteration in the J values, however

small, could be due to the very small structural distortions

present inherently in complexes 1 and 2, and we have earlier

established that a small change in bond length or bond angle

can lead to the switching of ferromagnetic to antiferromagnetic

behavior.^30,47Alternately, it could be purely dictated by the

diﬀerence in anisotropy between 1 and 2. To ascertain the

origin further, DFT calculations were performed on the X-ray

structure of 1 and 2 where the anisotropic ions are substituted

by the isotropic Gd^IIIions. These calculations clearly suggest

the J value is antiferromagnetic in 1 and ferromagnetic in 2.

Since the sign is neatly reproduced in the DFT calculations,

the nature of switch in the exchange clearly originates from

small structural changes.

Furthermore, we have also performed DFT calculations on

Gd^IIIanalog of complexes 1 and 2 ([Gd₂(LH₂)(LH)-

(CH₃OH)(N₃)]·2MeOH·H₂O (3), see attached CIF ﬁles

and Supplementary Information for further details) which

yields a ferromagnetic J = +0.1 cm⁻¹. Furthermore, we have

also performed DFT calculations on complex 3, and this yields

a ferromagnetic J = +0.1 cm⁻¹. The exchange values are

veriﬁed with broken symmetry calculations performed by

ORCA as well (+0.07 cm⁻¹). The spin density plots are given

in Figure 11, and the spin density of 6.95 on Gd^IIIatom

indicates spin delocalization. The mechanism of exchange

coupling was studied in detail by us previously in {Gd2} dimer

Figure 10. POLY_ANISO derived magnetic relaxation pathways for

complex 1. The red line represents the QTM, blue line represents TA,

and green line represents the Orbach/Raman processes. The black

line indicates the KDs as a function of magnetic moments. The

number above these lines represents the transition probabilities from

one m_Jlevel to the other m_Jlevel.

Table 5. Ab Initio and DFT Computed Exchange Values for

Complex 1−3

Ab Initio-Fitted (in cm⁻¹

)

DFT-Computed (cm⁻¹

)

complex

J_ex

J_dip

J_tot

J

1

2

3

−0.60

+0.45

−

+0.15

+0.13

−

−0.45

+0.58

−

−0.55

+0.60

+0.10

Figure 11. DFT computed spin density plot for complex 3, the Gd^IIIanalogue of complex 1 obtained from broken symmetry calculations; α and β

densities are represented by red and violet lobes, respectively.

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bridged by μ-oxo bridges.³⁰The nature of magnetic

interactionis is strongly dependent on the Gd−O−Gd bond

angles. A change of angle, even by 1°, can lead to a change in

the nature of the coupling between the lanthanide ions. For

complexes 2 and 3, one of these angles between Tb−O−Tb

and Gd−O−Gd are ∼114°, and for Dy−O−Dy it is 115°.

These angles lie in the borderline area and may be responsible

for the switch in the nature of exchange.

SINGLE_ANISO computed crystal ﬁeld parameters 1

and 2, DFT computed spin density on Ln center using

Broken symmetry approach for complexes 1−3 (PDF)

Accession Codes

CCDC 2026242, 2026261, 2026262, and 2058082 contain the

supplementary crystallographic data for this paper. These data

can be obtained free of charge via www.ccdc.cam.ac.uk/

data_request/cif, or by emailing data_request@ccdc.cam.ac.

uk, or by contacting The Cambridge Crystallographic Data

Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44

1223 336033.

CONCLUSION

■

In summary, we have utilized a multidentate aroylhydrazone-

based Schiﬀ base ligand, 6-((bis(2-hydroxyethyl)amino)-N′-

(2-hydroxybenzylidene)picolinohydrazide (LH₄) to assemble

homometallic dinuclear lanthanide(III) complexes containing

nonequivalent lanthanide metal centers [Ln₂(LH₂)(LH)-

(CH₃OH)(N₃)]·xMeOH·yH₂O [1, Ln = Dy^III, x = 0, y = 2;

2, Ln = Tb^III, x = 1, y = 1]. The nonequivalence of the

lanthanide ions in these complexes arises from the variation of

one terminal ligand. Thus, while one of the lanthanides has

methanol as the ligand, the other has an azide. In all cases, the

lanthanide ions are nine-coordinate in a spherical capped

square antiprism geometry (as determined by SHAPE

analysis). Detailed magnetic studies revealed that 1 is a zero-

ﬁeld SMM with an eﬀective energy barrier (U_eff) 59(3) K of

magnetization reversal and a relaxation time of τ₀= 10(4) ×

10⁻⁶s, while 2 shows a ﬁeld-induced SMM behavior.

Combined ab initio and DFT calculations were performed to

understand the observed magnetism. This reveals, that apart

from the Kramers vs non-Kramers nature of the lanthanide ion,

the individual variations in the coordination geometry around

the lanthanide ions seem to play a subtle and important role in

dictating the overall magnetic behavior. The change in the

behavior of the nature of exchange has also been addressed in

relation to the Ln−O−Ln bond angle which agrees with the

earlier reported examples. The same magnetic structural

correlation of the nature of exchange with metal oxo metal

bond angle also holds true for the nine-coordinated

asymmetric dinuclear lanthanide systems.

AUTHOR INFORMATION

Corresponding Authors

■

Vadapalli Chandrasekhar − Department of Chemistry, Indian

Institute of Technology−Kanpur, Kanpur 208016, India;

Tata Institute of Fundamental Research, Gopanpally,

Hyderabad 500107, India; orcid.org/0000-0003-1968-

2980; Email: vc@iitk.ac.in, vc@tifrh.res.in

Fabrice Pointillart − Université de Rennes, CNRS, ISCR

(Institut des Sciences Chimiques de Rennes)-UMR 6226, F-

35000 Rennes, France; orcid.org/0000-0001-7601-1927;

Email: fabrice.pointillart@univ-rennes1.fr

Gopalan Rajaraman − Department of Chemistry, Indian

Institute of Technology−Bombay, Powai 400076, Mumbai;

orcid.org/0000-0001-6133-3026; Email: rajaraman@

chem.iitb.ac.in

Authors

Pawan Kumar − Department of Chemistry, Indian Institute of

Technology−Kanpur, Kanpur 208016, India

Sourav Biswas − Department of Geo-Chemistry, Keshav Deva

Malaviya Institute of Petroleum Exploration, Dehradun

248915, India

Abinash Swain − Department of Chemistry, Indian Institute of

Technology−Bombay, Powai 400076, Mumbai

Joydev Acharya − Department of Chemistry, Indian Institute

of Technology−Kanpur, Kanpur 208016, India;

orcid.org/0000-0002-9480-4725

Vierandra Kumar − Department of Chemistry, Indian

Institute of Technology−Kanpur, Kanpur 208016, India

Pankaj Kalita − Tata Institute of Fundamental Research,

Gopanpally, Hyderabad 500107, India; orcid.org/0000-

0002-1240-5633

ASSOCIATED CONTENT

* Supporting Information

■

sı

The Supporting Information is available free of charge at

https://pubs.acs.org/doi/10.1021/acs.inorgchem.1c00249.

Crystal data information for 3, simulated single-crystal

data and experimental XRD pattern for 1−2, ESI-MS

spectrum of complex 2 and 3, molecular structure and

bond length and bond angle of 2 and 3, continuous

shape measure calculations, supramolecular interactions.

Field dependence of molar magnetization plot at 2 K

and ﬁeld dependence of molar magnetization plot in

complexes and in-phase component of the ac magnetic

susceptibility data for 1, normalized Cole−Cole plot at

several temperatures between 2 K and 15 K for 1 under

0 and 800 Oe, ac magnetic susceptibility data and

normalized Cole−Cole plot at several temperatures

between 2 K and 15 K for 1_5%,in-phase and out-of-phase

components of the ac magnetic susceptibility for 2 at 2 K

in an applied DC magnetic ﬁeld from 0 to 3000 Oe, in-

phase (χ_M′ ) and out-of-phase (χ′_M′) components of the ac

magnetic susceptibility data for 2 in 2800 Oe applied

magnetic ﬁeld, CASSCF + RASSI-SO+SINGLE_ANI-

SO computed energies of the eight low-lying KDs and

Jessica Flores Gonzalez − Université de Rennes, CNRS, ISCR

(Institut des Sciences Chimiques de Rennes)-UMR 6226, F-

35000 Rennes, France

Olivier Cador − Université de Rennes, CNRS, ISCR (Institut

des Sciences Chimiques de Rennes)-UMR 6226, F-35000

Rennes, France; orcid.org/0000-0003-2064-6223

Complete contact information is available at:

https://pubs.acs.org/10.1021/acs.inorgchem.1c00249

Notes

The authors declare no competing ﬁnancial interest.

ACKNOWLEDGMENTS

■

We thank the Department of Science and Technology (DST),

India; the CNRS, Université de Rennes 1, the European

Commission through the ERC-CoG 725184 MULTI-

PROSMM (Project No. 725184) for ﬁnancial support, and

also support for the Single Crystal CCD X-ray Diﬀractometer

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dysprosium(iii) metallocenium single-molecule magnets. Chem. Sci.

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facility at IIT-Kanpur. V.C. is grateful to the DST for a J. C.

Bose fellowship. P.K. and A.S. thank the University Grants

Commission (UGC), India for Senior Research Fellowships.

G.R. acknowledges DST/SERB for funding (Nos. CRG/2018/

000430, DST/SJF/CSA-03/2018-10, SB/SJF/2019-20/12).

We sincerely thank Mr. Prakash Nayak, NISER, Bhubanswar,

Odisha, India, for the PXRD measurements.

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Azide-Coordination in Homometallic Dinuclear Lanthanide(III) Complexes Containing Nonequivalent Lanthanide Metal Ions: Zero-Field SMM Behavior in the Dysprosium Analogue

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