Observation of Slow Relaxation and Single-Molecule Toroidal Behavior in a Family of Butterfly-Shaped Ln4Complexes

DOI: 10.1002/chem.201603640

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Single-Molecule Magnets

Observation of Slow Relaxation and Single-Molecule Toroidal

Behavior in a Family of Butterfly-Shaped Ln₄Complexes

Sourav Biswas,^[a]Sourav Das,^[b]Tulika Gupta,^[c]Saurabh Kumar Singh,^[d]Michael Pissas,^[e]

Gopalan Rajaraman,*^[c]and Vadapalli Chandrasekhar*^{[a, f]}

Abstract: A family of five isostructural butterfly complexes

with a tetranuclear [Ln₄] core of the general formula

[Ln₄(LH)₂(m₂-h¹h¹Piv)(h²-Piv)(m₃-OH)₂]·xH₂O·yMeOH·zCHCl₃(1:

Ln=Dy^III, x=2, y=2, z=0; 2: Ln=Tb^III, x=0, y=0, z=6; 3:

Ln=Er^III, x=2, y=2, z=0; 4: Ln=Ho^III, x=2, y=2, z=0; 5:

Ln=Yb^III, x=2, y=2, z=0; LH₄=6-{[bis(2-hydroxyethyl)ami-

no]methyl}-N’-(2-hydroxy-3-methoxybenzylidene)picolinohy-

drazide; PivH=pivalic acid) was isolated and characterized

both structurally and magnetically. Complexes 1–5 were

probed by direct and alternating current (dc and ac) mag-

netic susceptibility measurements and, except for 1, they

did not display single-molecule magnetism (SMM) behavior.

The ac magnetic susceptibility measurements show frequen-

cy-dependent out-of-phase signals with one relaxation pro-

cess for complex 1 and the estimated effective energy barri-

er for the relaxation process was found to be 49 K. We have

carried out extensive ab initio (CASSCF+RASSI-SO+SINGLE_

ANISO+POLY_ANISO) calculations on all the five complexes

to gain deeper insights into the nature of magnetic anisotro-

py and the presence and absence of slow relaxation in these

complexes. Our calculations yield three different exchange

coupling for these Ln₄complexes and all the extracted J

values are found to be weakly ferro/antiferromagentic in

nature (J₁= +2.35, J₂=ꢀ0.58, and J₃=ꢀ0.29 cm^ꢀ1for 1;

J₁= +0.45, J₂=ꢀ0.68, and J₃=ꢀ0.29 cm^ꢀ1for 2; J₁= +0.03,

J₂=ꢀ0.98, and J₃=ꢀ0.19 cm^ꢀ1for 3; J₁= +4.15, J₂=ꢀ0.23,

and J₃=ꢀ0.54 cm^ꢀ1for 4 and J₁= +0.15, J₂=ꢀ0.28, and

J₃=ꢀ1.18 cm^ꢀ1for 5). Our calculations reveal the presence

of very large mixed toroidal moment in complex 1 and this

is essentially due to the specific exchange topology present

in this cluster. Our calculations also suggest presence of

single-molecule toroics (SMTs) in complex 2. For complexes

3–5 on the other hand, the transverse anisotropy was com-

puted to be large, leading to the absence of slow relaxation

of magnetization. As the magnetic field produced by SMTs

decays faster than the normal spin moments, the concept of

SMTs can be exploited to build qubits in which less interfer-

ence and dense packing are possible. Our systematic study

on these series of Ln₄complexes suggest how the ligand

design can help to bring forth such SMT characteristics in

lanthanide complexes.

single-chain magnets,^[3]and single-ion magnets.^[3b,4]Although

initially polynuclear complexes containing 3d^[5]metal ions were

being investigated for SMM behavior, very soon 3d/4f hetero-

metallic complexes^[6]and subsequently homometallic 4f^[7,9]

complexes have been found suitable for SMM applications. In

particular, complexes containing Dy^III, Tb^III, and Ho^IIIhave been

Introduction

Research on lanthanide-ion-based molecular magnetic materi-

als is a fast developing area.^[1]Since the seminal discovery

of

single-molecule

magnet

(SMM)

behavior

in

Mn₁₂O₁₂(OAc)₁₆(H₂O)₄]·2HOAc^.4H₂O^[2]this field has expanded to

[a] S. Biswas, Prof. V. Chandrasekhar

Department of Chemistry, Indian Institute of Technology Kanpur

Kanpur 208016 (India)

[e] Dr. M. Pissas

Institute of Advanced Materials, Physicochemical Processes

Nanotechnology and Microsystems

E-mail: vc@iitk.ac.in

NCSR Demokritos, 15310 Ag. Paraskevi, Attiki, (Greece)

[b] Dr. S. Das

[f] Prof. V. Chandrasekhar

Department Of Chemistry

Institute of Infrastructure Technology Research and Management

Near Khokhara Circle, Maninagar East, Ahmedabad 380026 (India)

National Institute of Science Education and Research

Institute of Physics Campus, Sachivalaya Marg, PO: Sainik School

Bhubaneswar 751 005, Orissa (India)

[c] T. Gupta, Dr. G. Rajaraman

Supporting information for this article can be found under htt p ://

dx.doi.org/10.1002/chem.201603640. It contains the molecular structures of

2–5 (Figures S1–S4), list of bond length and bond angles (Tables S1–S4), lit-

erature reported butterfly shaped complexes, CASSCF+RASSI-SO+SINGLE_

ANISO computed energies, SINGLE_ANISO computed crystal field parame-

ters of 1–5 (Tables S5–14), angle between main anisotropy axes (Table S15)

of 1, temperature dependence of the a) in-phase and b) out-of-phase ac

susceptibility plot of 1 (Figure S6).

Department of Chemistry, Indian Institute of Technology Bombay

Powai, Mumbai 400076 (India)

E-mail: rajaraman@chem.iitb.ac.in

[d] Dr. S. K. Singh

Department of Molecular Theory and Spectroscopy

Max-Planck Institute for Chemical Energy Conversion

Stiftstr 34-36, 45470 Mꢀlheim an der Ruhr (Germany)

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investigated extensively, since these ions possess a relatively

high ground state spin along with significant unquenched or-

bital angular momentum. These two parameters are important

in generating energy barriers for the reversal of magnetization.

Among the homometallic lanthanide ion complexes, the tetra-

nuclear family offers considerable structural diversity and

varied structural topologies such as linear,^[8]distorted cubane,^[9]

square-grid,^[10]tetrahedron,^[11]trigonal pyramid,^[12]zig-zag,^[13]

butterfly^[14a–l]rhombus,^[15]and irregular (Y-shaped,^[16]ladder

type,^[17]sea-saw^[18]) are known. This family also contains some

like 4f orbitals of Ln^IIIions, significant progress in the post Har-

tree–Fock multiconfigurational ab initio methodology has

been achieved towards resolving these issues. The CASSCF+

RASSI-SO+SINGLE_ANISO^[25]approach has been employed to

depict the magnetic properties of individual metal ions. This

can be followed by the estimation of anisotropic interaction

between the Ln^IIIsites within the Lines model as implemented

in the POLY_ANISO code.^[26]

Our laboratory has been investigating the tetranuclear lan-

thanide ion complex family.^[7g,9,27]Thus, we have reported

cubane-shaped [Ln₄(L)₄(m₂-h¹h¹Piv)₄] (LH₂=2-{[6-(hydroxyme-

thyl)pyridin-2-yl]methyleneamino}phenol)^[9]and rhombus-

shaped complexes, [Ln₄(LH)₂(m₂-O)₂(H₂O)₈]^[27a](LH₃=(6-hydroxy-

methyl)-N’-[(8-hydroxyquinolin-2-yl)methylene]picolinohydra-

zide). Interestingly the Dy^IIIanalogue of both of these families

shows two relaxation pathways in their ac susceptibility stud-

ies. Recently we were also able to prepare [Ln₄(L)₄(m₄-OH)(m₃-

examples

such

as

[Dy₄K₂O(OtBu)₁₂]^[12]and

[Dy₄(m₃-

OH)₂(bmh)₂(msh)₄Cl₂]^[14g](bmh=1,2-bis(2-hydroxy-3-methoxy-

benzylidene) hydrazone; msh=methoxysalicy-laldehyde hydra-

zone) which showed very high energy barriers for magnetiza-

tion reversal. Recently, a review summarizing the SMM behav-

ior of tetranuclear Dy^IIIfamily has appeared.^[1d]

In addition to SMM behavior, in recent years, the importance

of single-molecule toroics (SMTs)^[15]is becoming important. The

electromagnetic response of a toroidal arrangement of mag-

netic moments in complexes has several potential applica-

tions.^[16]Toroidal moments^[17]in SMTs are expected to arise

from wheel-shaped vortex arrangements of local magnetic mo-

ments and are essentially governed by magnetic exchange in-

teraction between the metal centers. Besides, the toroidal

magnetic states are promising for building quantum comput-

ing and information storage as they are insensitive to homoge-

neous magnetic fields.^[16–18]This renders a more protective en-

vironment (with respect to the application of magnetic field)

to the two components of the toroidal magnetic state and the

respective circular arrangement of magnetic moments in re-

verse directions^[17b](in comparison with spin-projected eigen-

states of true spin S=1/2).^[18]Moreover, since the magnetic

field produced by a net toroidal moment decays much faster

than the field of a normal magnetic dipole, qubits designed^[18a]

on the basis of toroidal moments will be much less interfering

and, therefore, could be packed much more densely than spin

OH)₂(NO₃)₄]^[7g]

(LH=2-methoxy-6-(pyridin-2-ylhydrazonome-

thyl)phenol) with a see-saw topology and [Ln₄(LH)₂(LH₂)₂(m₂-

h¹h¹Piv)₂(h¹-Piv)₄] (LH₃=N’-(2-hydroxy-3-methoxybenzylidene)-

6-(hydroxymethyl)picolinohydrazide}),^[27b]which contains two

dimeric subunits.

Motivated by these results, we designed a new flexible com-

partmental aroyl hydrazone ligand, 6-{[bis(2-hydroxyethyl)ami-

no]methyl}-N’-(2-hydroxy-3-methoxybenzylidene)picolinohydra-

zide (LH₄), which upon reaction with Ln(NO₃)₃·5H₂O (Ln=Dy,

Tb, Er, Ho and Yb) afforded butterfly-shaped homometallic

tetranuclear

complexes

[Ln₄(LH)₂(m₂-h¹h¹Piv)(h²-Piv)(m₃-

OH)₂]·xH₂O·yMeOH·zCHCl₃(1: Ln=Dy^III, x=2, y=2, z=0; 2:

Ln=Tb^III, x=0, y=0, z=6; 3: Ln=Er^III, x=2, y=2, z=0; 4:

Ln=Ho^III, x=2, y=2, z=0; 5: Ln=Yb^III, x=2, y=2, z=0)

(Scheme 1). The synthesis, structure and magnetism of 1–5 are

described herein, along with detailed theoretical studies on

these complexes.

qubits.^[18a]Also, the toroidal magnetic moment interacts with Result and Discussion

a dc current passing through the molecule^[19]or a time-varying

Synthetic aspects

electric field^[20]by means of magneto-electric coupling^[21]and

this allows the moment to be controlled and manipulated

purely by electrical means, a property much sought after in

molecular devices.^[18a]Despite these features, the number of

molecules exhibiting toroidal moments are relatively small, as

concrete efforts to control the direction of the anisotropic axes

is needed to achieve toroidal moments at the ground state.

Another aspect that remains intriguing among lanthanide

complexes is that the underlying complexity of the ligand field

environment around Ln^IIIions complicates a precise estimation

of the anisotropic axes of these complexes. Though various ex-

perimental tools, that is, inelastic neutron scattering,^[22]multi-

frequency high-field EPR,^[23]field- and orientation-dependent

magnetic susceptibility, have been utilized to probe the mag-

netic anisotropy,^[24]precise estimation of the directions of local

anisotropy axes remains, nevertheless, challenging. This can be

remedied by fragment quantum chemistry calculations, ac-

counting for spin-orbit coupling in a non-perturbative manner.

Despite difficulties in analyzing the single-ion nature of core-

Multidentate ligands containing various functional groups (car-

boxylate, hydroxyl, oxime, methoxy, ethoxy and amine) have

been employed to construct polynuclear lanthanide complex-

es.^[7g,9,14,27]Among these, multidentate, flexible aroylhydrazone-

based Schiff base ligands appear to be very promising. First,

these ligands can display keto–enol tautomerism, in which

both the isomeric forms of the ligand are anticipated to exhibit

different binding modes to the metal centers depending upon

the conditions. Second, CꢀC bond rotation (conformational

isomers)^[7a,27b,28]in these ligands opens up an additional source

of coordination flexibility. Utilizing these characteristics in N’-

(2-hydroxy-3-methoxybenzylidene)-6-(hydroxymethyl)picolino-

hydrazide (LH₃), we have previously assembled Ln₄and Ln₆

complexes (Scheme 2).

In order to introduce further versatility in the above ligand

system, we have prepared 6-{[bis(2-hydroxyethyl)amino]meth-

yl}-N’-(2-hydroxy-3-methoxybenzylidene)picolinohydrazide

(LH₄), which is similar to LH₃except that the pendent ꢀCH₂OH

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in the latter is replaced by the ꢀ[CH₂N(CH₂CH₂OH)₂] motif. The

choice of pendent was dictated by the knowledge that while

the ꢀCH₂CH₂OH arm acts as a chelating ligand (along with the

nitrogen), in its deprotonated form it acts as a bridging ligand.

LH₄was synthesized by following a five-step synthetic protocol

(Scheme 3). LH₄contains eight potential coordinating sites

with two unsymmetrical pockets: one of these is tetradentate

and consists of a methoxy, a hydroxy, an imine nitrogen and

an enolized hydrazone oxygen atom, while the other is penta-

dentate and possesses a diethanol amine, a pyridine nitrogen,

and a common enolizable oxygen atom (Figure 1). The reac-

tion of LH₄with the Ln(NO₃)₃·5H₂O and pivalic acid in the pres-

Figure 1. a) The two coordinating pockets of [LH]^3ꢀin its enolized form.

b) Coordination mode of the ligand [LH]^3ꢀ

.

Scheme 1. Synthesis of tetrametallic Ln₄complexes 1–5.

Scheme 2. a) A Ln₄complex containing both keto and enol forms of the ligand.^[27b]b) A Ln₆complex containing only the enol form of the ligand.^[7a]

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Scheme 3. Synthesis of the ligand LH₄.

ence of triethylamine as a base (1:2:2:5) afforded butterfly-

shaped homometallic tetranuclear complexes, [Ln₄(LH)₂(m₂-

h¹h¹Piv)(h²-Piv)(m₃-OH)₂]·xH₂O·yMeOH·zCHCl₃(1: Ln=Dy^III, x=2,

y=2, z=0; 2: Ln=Tb^III, x=0, y=0, z=6; 3: Ln=Er^III, x=2, y=

2, z=0; 4: Ln=Ho^III, x=2, y=2, z=0; 5: Ln=Yb^III, x=2, y=2,

z=0) (Scheme 1).

two Dy^IIIions simultaneously in its two multidentate flexible

pockets [pentadentate (OONNO) and tridentate (ONO)] (Fig-

ure 1a). Both the metal centers within the pockets of [LH]^3ꢀ

are effectively linked by the enolized hydrazone oxygen. Each

X-ray crystal structures of 1–5

Single-crystal X-ray diffraction studies reveal that compounds

1, 3, 4 and 5 crystallize in the monoclinic system in space

group P2₁/n with Z=2. Compound 2 crystallizes in the space

group P2₁/c. Although the asymmetric units of 1–5 contain

half of the total molecule, their structural motifs are not identi-

cal: 1 possess a [Dy₂(LH)(m₂-h¹h¹Piv)(h²-Piv)(OH)] motif (Fig-

ure 2a), while 2–5 possess [Ln₂(LH)(h²-Piv)(h¹-Piv)(m₂-OH)]

motifs. All the compounds are neutral and possess the same

structural topology with a butterfly-shaped tetrametallic core.

In view of their similarity, compound 1 has been chosen as

a representative example to describe the structural features of

this family of complexes. Selected bond parameters of 1 are

given in Table 1. The molecular structures and selected bond

parameters of 2–5 are given in the Supporting Information

(Figure S1–S4 and Tables S1–S4). A perspective view of the mo-

lecular structure of 1 is portrayed in Figure 2b.

The homometallic tetranuclear complex [Ln₄(LH)₂(m₂-

h¹h¹Piv)₂(h²-Piv)₂(m₃-OH)₂] is formed by the cumulative coordi-

nation action of two triply deprotonated ligands, [LH]^3ꢀalong

with four pivalate ligands. Although the ligand LH₄contains

nine potential coordinating sites, only seven of these are in-

volved in assembling the tetranuclear complex. The other two,

namely, the OMe group and the hydrazine nitrogen (near the

carbonyl carbon) do not participate in binding. Within complex

1, it has been found that each ligand can accommodate the

Figure 2. a) Asymmetric unit of 1. b) Molecular structure of 1 (selected hy-

drogen atoms and the solvent molecules have been omitted for clarity).

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can be expanded to two edge-sharing triangular units (Dy1-

Dy2-Dy1* and Dy1-Dy1*-Dy2*). One face of each triangular

unit is capped by a m₃-OH ligand.

Table 1. Selected bond lengths [ꢁ] and bond angle [8] parameters of 1.

Bond lengths

around Dy1

Bond lengths

around Dy 2

Bond angles

around Dy

Overall, 1 contains two structurally distinct eight-coordinat-

ed Dy^IIIions with distorted triangular dodecahedron geome-

tries; one of them possesses a 7O, 1N coordination environ-

ment (Figure 4a), while the other has a 6O, 2N coordination

environment (Figure 4b). Among the three Dy-m₃-OH bonds

two are significantly shorter (2.338, 2.351 ꢁ) than the other

(2.458 ꢁ). Among the other DyꢀO distances, those involving

DyꢀO_phen(2.216 ꢁ) are the shortest. The average Dy···Dy dis-

tance is 4.274 ꢁ (shortest distance being 3.678 ꢁ, largest dis-

tance, 6.606 ꢁ).

Dy1ꢀO7

2.259(2) Dy2ꢀO5

2.216(2) Dy1-O10-Dy2*

2.272(2) Dy1-O7-Dy2

2.305(3) Dy1-O9-Dy1^[a]

113.68(10)

108.57(10)

108.35(10)

110.26(10)

99.61(9)

Dy1ꢀO4

Dy1ꢀO9

2.314(2) Dy2ꢀO7

2.340(3) Dy2ꢀO3

Dy1ꢀO10 2.348(2) Dy2ꢀO10* 2.358(2) Dy1-O9-Dy2^[a]

Dy1ꢀO9^[a]2.353(2) Dy2ꢀO1

2.432(3) Dy1^[a]-O9-Dy2^[a]

2.462(2)

2.518(3)

2.521(3)

Dy1ꢀO8

Dy1ꢀN1

Dy1ꢀN3

2.409(3) Dy2ꢀO9*

2.520(3) Dy2ꢀN4

2.641(3) Dy2ꢀO2

[a] Atoms are generated by the symmetry operation *: 0.5ꢀx, 0.5+y,

0.5ꢀz.

pentadentate pocket of two [LH]^3ꢀcontains two ethanolamine

arms. One of these is neutral and functions as a chelating

ligand, while the other is de-protonated and acts as a bridging

ligand (m-O) between two metal centers connecting the two

Dy₂sub-units. In addition to the binding provided by the

ligand [LH]^3ꢀ, the tetranuclear ensemble is further strength-

ened by two m₃-OH ligands and four pivalate ions; two of

these are chelating (h²) while the other two are bridging (m₂-

h¹:h¹). Thus, overall, each [LH]^3ꢀadopts a m₃-h¹:h²:h¹:h²:h¹:h¹co-

ordination mode (Figure 1b) and, along with four pivalate and

two m₃-OH groups, enables the construction of the butterfly-

shaped tetranuclear core, [Dy₄(m₂-O)₄(m₂-OH)₂]⁶⁺(Figure 3). This

core contains four coplanar Dy^IIIcenters, Dy1 and Dy1* repre-

sent the central region, while Dy2 and Dy2* represent the

wing-tips.

Figure 4. a) Distorted triangular dodecahedral geometry containing 6O, 2N.

b) Distorted triangular dodecahedral geometry containing 7O, 1N.

The butterfly-shaped core topology observed in the present

instance has been seen earlier, but the preparation of such

complexes has involved different ligand systems (Supporting

Information). A comparison of the structural and magnetic

properties of the butterfly-shaped tetranuclear lanthanide

complexes is listed in Table 2.

Further analysis of the core of the complex 1 reveals some

interesting structural features. The central core [Dy₄(m₃-OH)₂]¹⁰⁺

Magnetic studies

The direct-current (dc) magnetic susceptibility measurements

of complexes 1–5 were performed in the 2–300 K temperature

range and under an applied magnetic field of 0.1 or 1 T (Fig-

ures 5 and 6). The room-temperature c_MT values (56.51, 46.44,

44.45, 55.52 and 9.52 cm³Kmol^ꢀ1, for 1–5, respectively) are

close to the calculated values of 56.68, 47.25, 45.90, 56.25 and

10.29 cm³Kmol^ꢀ1for the ground state of the four magnetically

non-interacting Dy^IIIions (4f⁹, J=15/2, S=5/2, L=5, g=4/3;

⁶H_15/2), Tb^IIIions (4f⁸, J=6, S=3, L=3, g=3/2; ⁷F₆), Er^IIIions

4

(4f¹¹, J=15/2, S=3/2, L=6, g=6/5; I_15/2), Ho^IIIions (4f¹⁰, J=8,

5

S=2, L=6, g=5/4; I₈) and Yb^IIIions (4f¹³, J=7/2, S=1/2, L=3,

2

g=8/7; F_7/2). In complex 1, upon cooling, the c_MT product

steadily increases up to 40 K to reach

a

value of

60.04 cm³Kmol^ꢀ1and this is followed by a gradual decrease to

reach a value of 21.31 cm³Kmol^ꢀ1at 2 K (in presence of 1 T ap-

plied magnetic field). The gradual increase of c_MT up to 40 K is

a clear signature of the presence of weak ferromagnetic inter-

actions in the system (Figure 5a). The decrease in c_MT upon

further cooling can be attributed to the combined effects from

Figure 3. Butterfly-shaped core containing two triangular units and two

defect-cubane units.

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Table 2. Structural and magnetic features of tetranuclear lanthanide assemblies having butterfly-shaped core topology.

Compound

Dy₃ꢀ(m₃-OH)

Coordination numbers

(local geometries around Ln^IIIcenters)

Magnetic

properties

Ref.

distances [ꢁ]

[Dy₄(m₃-OH)₂-(hmmpH)₂(hmmp)₂(Cl)]

hmmpH₂=C₁₀H₁₃NO₃

2.344, 2.347, and 2.381

2.333, 2.405 and 2.408

2.337, 2.367 and 2.402

2.373, 2.334 and 2.447

2.359, 2.354 and 2.411

2.362, 2.302, and 2.447

2.342, 2.340 and 2.378

eight coordinate

(distorted square-antiprism)

SMM

U_eff=7 K

t₀=3.8ꢂ10^ꢀ5s

SMM

U_eff=80 K

t₀=5.75ꢂ10^ꢀ6s

SMM

U_eff=6.25 K

t₀=3.75ꢂ10^ꢀ5

SMM

U_eff=6.2

t₀=2.4ꢂ10^ꢀ5

[14a]

[Dy₄(m₃-OH)₂(m-OH)₂(2,2-bpt)₄(NO₃)₄(EtOH)₂]

2,2-bptH=C₁₂H₉N₅

eight coordinate

(distorted square-antiprism)

[14b]

[14c]

[14d]

[14e]

[14f]

[14g]

[Dy₄(m₃-OH)₂(o-van)₄(O₂CC(CH₃)₃)₄(NO₃)₂]

o-van=C₈H₈O₃

eight coordinate

(distorted square antiprismatic geometry)

[Dy₄(m₃-OH)₂(mdeaH)₂(piv)₈]

mdeaH₂=C₅H₁₃NO₂

eight coordinate

(between dodecahedral and bicapped

trigonal-prismatic; distorted dodecahedral)

eight coordinate

(distorted square antiprismatic and

distorted bicaped trigonal prismatic)

seven and eight coordinate

[Dy₄(m₃-OH)₂(ampdH₄)₂(piv)₁₀]

ampdH₄=C₆H₁₅NO₂

SMM

U

_eff=5.4 K

t₀=1.1ꢂ10^ꢀ5

s

[Dy₄(m₃-OH)₂(bmh)₂(msh)₄Cl₂]

bmh=C₁₆H₁₆N₂O₄

msh=C₈H₁₀N₂O₂

[Dy₄(m₃-OH)₂L₂(acac)₆]

H₂L=C₂₀H₂₂N₂O₂

U_eff=9.7 K; 170 K

t₀=3.2ꢂ10^ꢀ5s;

4 X10^ꢀ7s

eight coordinate

(distorted square-antiprism)

U_eff=22 K

t₀=3.66ꢂ10^ꢀ6s

acac=C₅H₈O₂

[Dy₄(m₃-OH)₂(php)₂(OAc)₆(H₂O)₂]

H₂php=C₁₉H₁₅N₇O₂

[Dy₄(LH)₂(m₃-OH)₂(h²-piv)₂(m₂- h¹:h¹Piv)₂]

LH₄=C₁₉H₂₄N₄O₅

2.343, 2.320 and 2.469

2.338, 2.351 and 2.458

eight and ten coordinate

slow relaxation

of magnetization

U_eff=49.03 K

t₀₌5.78ꢂ10^ꢀ8

[14h]

eight coordinate

(distorted triangular dodecahedral)

this work

thermal depopulation of excited state ꢁm_jStark levels of Dy^III

ions and intra/intermolecular exchange interactions between

the Dy^IIIions.^[14c,37m]Contrary to this observed variation, in com-

plex 2 (Figure 5c) the c_MT product gradually decreases up to

almost saturation for magnetic fields larger than 2 T (Figures 5

and 6). Notably, the field dependence of magnetization up to

6 K (some cases 8 K) does not get saturated even at 7 T. This is

necessarily due to inherent large magneto-anisotropy of the

Ln^IIIions along with weak intramolecular interactions inducing

accessibility of low-lying excited states even at 2 K. In 1–5, the

field dependence of magnetization reaches a maximum value

of about 21.5, 17.7, 17.8, 20.8, and 7.6 Nm_B, respectively, which

are approximately half of the expected values for four weakly

coupled lanthanide ions, and can be attributed to the crystal-

field effects leading to significant magnetic anisotropy.

45 K and then drops rapidly to reach

a

value of

18.31 cm³Kmol^ꢀ1at 2 K (at 0.1 T). For complex 3 (Figure 5e)

also the c_MT product gradually decreases up to 50 K and then

drops rapidly to reach a value of 16.94 cm³Kmol^ꢀ1at 2 K (at

1 T). In complex 5, (Figure 6c) the c_MT product decreases rapid-

ly starting from the room temperature to reach a value of

5.12 cm³Kmol^ꢀ1at 2 K (at 1 T). This behavior in complexes 2,

3, and 5 can be ascribed to the progressive depopulation of

excited state ꢁm_jstark levels of Tb^III, Er^III, and Yb^IIIions, respec-

tively, arising from the ⁷F₆, ⁴I_15/2, ²F_7/2ground terms, respectively,

by the existent antiferromagnetic interactions between the lan-

thanide ions. For complex 4, (Figure 6a) the c_MT product re-

mains almost constant till 20 K and then finally drops off

abruptly to reach values of 20.03 cm³Kmol^ꢀ1(at 1 T). This is

mainly due to the depopulation of the crystal field ꢁm_jstates

and also possible weak intermolecular interactions between

the Ho^IIIions, which could be responsible for the sharp de-

creases in c_MT at low temperatures. Comparative analysis on all

the complexes suggests that, for complex 5, c_MT starts to de-

cline at a higher temperature and this is essentially due to the

Dynamics of magnetization in 1 and 2

In order to probe the dynamics of magnetization, alternating-

current (ac) magnetic susceptibility measurements were carried

out on complex 1 at 0 and 0.15 T dc field in the temperature

range of 2–20 K. At both 0 and 0.15 T magnetic fields, complex

1 displays variable-frequency temperature dependence of the

in-phase (c’) and out-of-phase (c’’) susceptibility signals with

maxima at 10 and 7.5 K, respectively, at the highest employed

frequency of 4111 Hz. Clear, temperature-dependent maxima in

the c’ and c’’ signals were observed at and below 10 K. This

clearly affirms the presence of SMM behavior. The ac measure-

ments in the presence of static dc field were undertaken in

order to suppress the QTM efficiently. Observation of single-

peak relaxation behavior is notable as generally Ln^IIIcomplexes

show multiple relaxation phenomena owing to substantial

quantum tunneling of magnetization (QTM) at zero field and

the presence of crystallographically independent lanthanide

2

larger splitting of F_7/2ground multiplet and preponderant de-

population of the excited state ꢁm_jstark levels.

Isothermal magnetization measurements were performed on

the polycrystalline samples of 1–5. The field dependence of

the magnetization for 1–5 at 2, 4, and 6 K (sometimes 8 K)

shows a relatively rapid increase in the magnetization to reach

&

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Figure 6. Temperature-dependent c_MT plot for complexes a) 4 and c) 5;

blue-filled circles represent experimental data and green-filled squares corre-

spond to ab initio simulations using three different exchange interactions

and constant intermolecular interaction (zJ) of ꢀ0.025 cm^ꢀ1. Field depend-

ence of molar magnetization plot for complexes b) 4 and d) 5; filled trian-

gles imply experimental data and solid lines correlate to ab initio simulations

using three different exchange interactions and constant intermolecular in-

teraction (zJ) of ꢀ0.025 cm^ꢀ1. It is worth noting that all the J values provided

in the graphs correspond to J^exchcontribution of the total magnetic interac-

tion. [Note: In complex 5, the ab initio simulated data could not produce

a nice fit with respect to the experimental data.]

Figure 5. Temperature-dependent c_MT plot for complexes a) 1, c) 2, and e) 3;

blue-filled circles represent experimental data and green-filled squares corre-

spond to ab initio simulations using three different exchange interactions

and constant intermolecular interaction (zJ) of ꢀ0.025 cm^ꢀ1. Field depend-

ence of molar magnetization plots for complexes b) 1, d) 2, and f) 3; filled

triangles imply experimental data and solid lines correlate to ab initio simu-

lations using three different exchange interactions and constant intermolec-

ular interaction (zJ) of ꢀ0.025 cm^ꢀ1. It is worth noting that all the J values

provided in the graphs correspond to J^exchcontribution of the total magnetic

interaction.

susceptibility shows a more pronounced frequency depend-

ence (below 20 K; 2–20 K range), but in this case also

a maxima could not be detected accurately (except that at low

temperatures that is, ca. 5 K a clear maxima was observed).

Upon cooling, c’’ shows a maximum and starts to reduce in

the 4–8 K range. The characteristic frequency (maximum of c’’

vs. u plot) at about 5 K for 1 progressively decreases with an

increasing dc magnetic field (Figure 7 f). This is suggestive of

an operative thermal relaxation mechanism.^[29]Hence, analysis

of the relaxation dynamics clearly reveals that, despite the in-

herent fast QTM of lanthanide complexes, the thermally assist-

ed Orbach process seems to be the prevalent relaxation pro-

cess at low temperature in complex 1. We have also undertak-

en ac measurements on complex 2 at 0 and 0.15 T dc field in

the temperature range of 2–20 K. In the variable-frequency

temperature-dependence plots, no temperature-dependent c’

signal was detected in 0 and 0.15 T of magnetic field (Figure S6

in the Supporting Information). However, a very weak tempera-

ture-dependent c’’ signal was observed in the 0 and 0.15 T

magnetic fields. In contrast, in the absence of frequency de-

pendent c’/c’’ signal both at 0 and 0.15 T field suggests the ab-

sence of SMM behavior of complex 2 (Figure S6 in the Sup-

porting Information). Moreover, the divergence of c’’ peaks at

low temperatures (<4 K) in 2 indicates the presence of a fast

relaxation process within the ground doublet precluding SMM

characteristics in 2.

sites. The maximum peaks corresponding to c’’/c’ (0/0.15 T) do

not go to zero below the maxima at low temperature, suggest-

ing the existence of fast QTM, transverse anisotropy, and hy-

perfine and dipolar interactions. Detailed analysis of the c’’/c’

versus T plots indicates that for c’ dependence of temperature,

relaxation becomes temperature-independent at higher tem-

perature (quantum regime), while the thermally activated re-

laxation process prevails at lower temperature. On the other

hand, for c’’ dependence of temperature is dictated by thermal

processes throughout the temperature-variation regime. In

temperature-dependent relaxation plots, below the maximum

peak, a drop of c’’/c’ is detected with a slight increase of ac re-

sponse for few frequencies. This increase is attributed to super-

paramagnetism in conjunction with paramagnetism and preva-

lent QTM, transverse anisotropy, and hyperfine and dipolar in-

teractions. Besides, alternating-current (ac) magnetic suscepti-

bility measurements were carried out on complex 1 at 0.15 T

dc field in the frequency range of 0–4000 Hz. Though variable-

temperature frequency dependence behavior of in-phase com-

ponent of ac susceptibility was visible (below 20 K), no clear

signature of maxima could be detected. The out-of-phase ac

The frequency dependence of c’’ has been fitted to a gener-

alized Debye model to extract the relaxation time t. The fitting

of t to the Arrhenius law leads to the deduction of an effective

Chem. Eur. J. 2016, 22, 1 – 20

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ꢀ1

t_QTMrepresents the relaxation frequency of the quantum tun-

neling relaxation process. The fit of the data leads to an effec-

tive energy barrier for magnetization reorientation U_eff=

49.03 K (34.08 cm^ꢀ1) with t₀=5.78ꢂ10^ꢀ8s and t_QTM=4.13ꢂ

10^ꢀ4s for complex 1 (Orbach+QTM). Moreover, fitting of the

high-temperature relaxation times to the Arrhenius law (linear

Orbach process) results in U_eff=40.92 K (28.44 cm^ꢀ1) with t₀=

1.5ꢂ10^ꢀ7s. This again reiterates the prevalence of Orbach

mechanism in regulating the relaxation even in the low-tem-

perature region.

Ab initio calculations

To gain insights into the nature of the local anisotropy of the

Ln^IIIcenters and to understand their electronic structural prop-

erties, ab initio calculations were performed on all five com-

plexes. For each complex, we have undertaken two sets of cal-

culations: primarily, using the SINGLE_ANISO program, we

have calculated the single-ion magnetic anisotropy of the indi-

vidual Ln^IIIions; later, the POLY_ANISO program was employed

to extract the exchange-coupled energy levels and the ex-

change parameters.

Single-ion analysis on complexes 1–5

Complex 1: The energy data for eight Kramers doublets (KDs)

6

of the ground H_15/2multiplet for the four Dy^IIIions and g ten-

sors of ground state in compound 1 are shown in the Support-

ing Information, with the excited states lying at 3000 cm^ꢀ1. In

1, the ground state KD shows an almost axial type anisotropy

for all the four metal sites (see Table S5 in the Supporting In-

formation); that is, g_z(Figure 8, yellow dashed lines for orienta-

tion of main anisotropy axis for ground KDs in all the four Dy^III

sites) is close to that expected for a pure m_j= ꢁ15/2 state. It is

worthwhile mentioning that all the computed g tensors corre-

Figure 7. Temperature dependence of the a) in-phase and b) out-of-phase ac

susceptibility at 0 T dc applied magnetic field for complex 1. Temperature

dependence of the c) in-phase and d) out-of-phase ac susceptibility at 0.15 T

dc applied magnetic field for complex 1. Frequency dependence of the

e) in-phase and f) out-of-phase ac susceptibility at 0.15 T dc applied magnet-

ic field for complex 1 [Note: all the real/imaginary component of magnetic

susceptibilities (c’/c’’) have unit of cm³mol^ꢀ1]. g) Arrhenius plots for the re-

laxation times (t) extracted from the c’’ versus frequency data in zero Oe dc

fields for compound 1. The solid blue line corresponds to the best fits to

QTM plus Orbach (black void circles). The solid red line represents linear fit-

ting of the high-temperature data which consequently signifies Orbach re-

laxation process.

˜

spond to an effective spin s=1/2 of the KDs. Besides, in all the

Dy sites, the angle between g_zdirections of ground and first

excited KD lies in the range of about 30–508. This invoked re-

laxation to be operative by means of first excited KDs in all

four metal centers. Based on single-ion analysis, the calculation

energy barrier (U_calcd) for magnetization reorientation turns out

to be 146 and 118 cm^ꢀ1for two types of non-equivalent Dy^III

centers (Dy1, Dy3 and Dy2, Dy4, respectively). Crystal field

analysis shows predominant non-axial terms and axial contri-

butions reiterating considerable competitiveness between

them (see Table S6 in the Supporting Information). This corre-

sponds to the significant ground KD QTM and affirms the SMM

characteristic only in the presence of an applied dc magnetic

field in 1.

energy barrier for magnetization reorientation (U_eff). The linear

dependence of ln(t) at high temperatures suggests a predomi-

nant Orbach relaxation mechanism. The data deviate from line-

arity in the low-temperature region due to operative QTM and

confirms consideration of other spin-lattice relaxation mecha-

nism processes. These relaxation times can be fitted with the

Equation (1),^[26]and accounts for relaxation through quantum

tunneling and Orbach thermal processes.

Comparatively larger values of g_zand negligible magnitude

of transverse anisotropy clearly reveals axial nature of the

ground KD of each KD involved in exchange interaction. This

axial nature essentially ensures interaction between the neigh-

boring Dy^IIIions to be of Ising type.

t^ꢀ1¼ t_QTMþ t₀^ꢀ1expðꢀU_eff=k_BTÞ

ꢀ1

ð1Þ

Complex 2: The energy data for the thirteen energy levels of

7

This resulted in larger U_effvalues and smaller flipping rates

the ground F₆multiplet for the four Tb^IIIions and g tensors of

as compared to the simple Arrhenius law. In Equation (1),

ground state in compound 2 are shown in the Supporting In-

&

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Figure 9. a) Crystal structure of complex 2 showing main anisotropy axis

(yellow dashed lines) on four Tb^IIIions and local magnetization (light green

arrows) in the ground state. The diagram also illustrates exchange pathways

employed for our calculations. b) Low-lying exchange spectrum in complex

2. Every exchange state (represented by thick blue lines) has been arranged

based on the corresponding magnetic moment. The curved green arrows

signify tunneling transition (D_tun;tunnel splitting or tunnel gaps) within each

doublet.

Figure 8. a) Crystal structure of complex 1 showing main anisotropy axis

(yellow dashed lines) on four Dy^IIIions and local magnetization (purple

arrows) in the ground state. The diagram also illustrates exchange pathways

employed for our calculations. b) Low-lying exchange spectrum and the po-

sition of the magnetization blocking barrier (red dotted line) in complex 1.

Every exchange state (represented by thick blue lines) has been arranged

based on the corresponding magnetic moment. The curved green arrows

signify tunneling transition (D_tun;tunnel splitting or tunnel gaps) within each

doublet, orange bent arrows indicate spin-phonon transitions (numbers are

averaged transition moments in m_Bconnecting the corresponding states). It

is worth noting that the spin-phonon transition among the lowest energy

states are not mentioned as they lie in the range of about 10^ꢀ1to 10^ꢀ4m_B.

field analysis shows the competitive nature of significant axial

and non-axial terms (see Table S8). This corroborates the earlier

observed large tunnel splitting and is responsible for the lack

of SMM characteristics in complex 2.

Complex 3: The energy data for eight KDs of the ground

⁴I_15/2multiplet for the four Er^IIIions and g tensors of ground

state in compound 3 are shown in the Supporting Information

(see Table S9), with the excited states lying at 6600 cm^ꢀ1. In 3,

the ground state KD possesses significant transverse anisotro-

py for all four metal sites promoting QTM probability within

the ground KD (g_z=16, g_x=0.3, g_y=0.7; see Figure 10: yellow

dashed lines represent orientation of main anisotropy axis for

ground KD in all the four Er^IIIsites). Besides, in all the Er sites,

the angle between g_zdirections of ground and first excited KD

lies in the range of about 65–1328. This invoked relaxation to

be operative through the first excited KD in all the four metal

centers. Based on single-ion analysis, substantial QTM relaxa-

tion pathway completely removes the possession of SMM char-

acteristics in complex 3. Based on crystal field analysis, non-

axial contributions prevail (see Table S10) and this precludes

SMM behavior in complex 3.

formation (see Table S7), with the excited states lying at

2200 cm^ꢀ1. In 2, the ground as well as excited state pseudo-

doublets show an Ising type anisotropy (due to completely

zero g_xycontribution in non-Kramers ions in accordance with

Griffith Theorem) for all four metal sites, that is, g_z(Figure 9,

yellow dashed lines for orientation of main anisotropy axis for

ground pseudo-doublet in all the four Tb^IIIsites) is close to

that expected for a pure m_j= ꢁ6 state. Based on single-ion

analysis, significant D_tunwas computed within the ground

pseudo-doublets as 5 and 1 cm^ꢀ1for two types of non-equiva-

lent Tb^IIIcenters (Tb1,Tb3 and Tb2,Tb4, respectively) . This is

evidence for substantial ground multiplet crystal field pertur-

bation and precludes any SMM behaviour in complex 2. Crystal

Complex 4: The energy spectrum for seventeen energy

5

levels of the ground I₈multiplet for the four Ho^IIIions and g

tensors of ground state in compound 4 are shown in the Sup-

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Figure 10. a) Crystal structure of complex 3 showing main anisotropy axis

(yellow dashed lines) on four Er^IIIions and local magnetization (purple

arrows) in the ground state. The diagram also illustrates exchange pathways

employed for our calculations. b) Low-lying exchange spectrum in complex

3. Every exchange state (represented by thick blue lines) has been arranged

based on the corresponding magnetic moment. The curved green arrows

signify tunneling transition (D_tun;tunnel splitting or tunnel gaps) within each

doublet.

Figure 11. a) Crystal structure of complex 4 showing main anisotropy axis

(yellow dashed lines) on four Ho^IIIions and local magnetization (purple

arrows) in the ground state. The diagram also illustrates exchange pathways

employed for our calculations. b) Low-lying exchange spectrum in complex

4. Every exchange state (represented by thick blue lines) has been arranged

based on the corresponding magnetic moment. The curved green arrows

signify tunneling transition (D_tun;tunnel splitting or tunnel gaps) within each

doublet.

porting Information (see Table S11), with the excited states

lying at 5200 cm^ꢀ1. In 4, the ground as well as excited state

pseudo-doublets show an pure Ising type anisotropy for all

four metal sites; that is, g_z(see Figure 11: yellow dashed lines

represent orientation of main anisotropy axis for ground

pseudo-doublet in all the four Ho^IIIsites) is close to that ex-

pected for a pure m_j= ꢁ8 state. Based on single-ion analysis,

significant D_tunwas computed within the ground pseudo-dou-

blets as 1.1 and 0.7 cm^ꢀ1for two types of non-equivalent Ho^III

centers (Ho1,Ho3 and Ho2,Ho4) respectively. This precludes

any SMM behaviour in complex 4. Crystal field analysis (see

Table S12) shows preponderant non-axial terms and leads to

the absence of SMM behaviour in complex 4.

relaxation within ground state itself, deterring attainment of

any energy barrier for magnetization reversal. Based on single-

ion analysis, substantial QTM relaxation pathway completely

removes the possession of SMM characteristics in complex 5.

Crystal field analysis (see Table S14) shows significantly larger

non-axial terms and leads to the absence of SMM behavior in

complex 5.

Exchange interaction and SMT behavior analysis on com-

plexes 1–5

Complex 5: The energy spectrum for eight KDs of the

Due to the Ising nature of the Dy^IIIsites, we have simulated

the magnetic interactions between Dy^IIIions by incorporating

contributions from magnetic dipole–dipole and exchange in-

teractions within an Ising exchange Hamiltonian. We have

computed the exchange interaction between the Dy^IIIions

within the Lines^[38]model, with an effective Heisenberg Hamil-

tonian [Eq. (2)],^[17b,c](in which J_i¼ J_i^dipolarþ J_i^exch; that is, J_iis the

total magnetic interaction in combination of calculated J_i^dipolar

and fitted J_i^exchparameters; this summation depicts the interac-

tion between all the neighboring Dy^IIIcenters) corresponding

to local S=5/2 spins on Dy^IIIcenters in the absence of spin-

2

ground F_7/2multiplet for the four Yb^IIIions and g tensors of

ground state in compound 5 are shown in the Supporting In-

formation (see Table S13), with the excited states lying at

10000 cm^ꢀ1. In 5, the ground state KD transverse component

prevails with g_x=5.23, g_y=3.34, g_z=0.92 for all the metal cen-

ters. This clearly corresponds to the stabilization of m_j= ꢁ1/2

state and occurrence of pronounced QTM relaxation pathway

(Figure 12a yellow dashed lines for orientation of main aniso-

tropy axis for ground KD in all the four Yb^IIIsites). This solely

blocks the magnetization within ground state KD and forces

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X

3

~

~ ~ ~

_i¼1J_lS_izS_iþ1z

ð3Þ

H_ex¼ ꢀ

Concepts based on the Lines model and Equation (3) has led

to the deduction of Equation (4) in which f corresponds to

i,j+1

angle between the anisotropy axes on the centers i and i+1.

~

ð4Þ

As f_i,j+1ꢃ2p/3, J_i=ꢀ12.5 J_i. For our calculations, we will

J_i¼ 25 cos ꢀ_i;jþ1J_i

[30]

~

assume J_i=J (J_i=J). Now, based on this approximation, we

~

can state that J₁, J₂, and J₃will be antiferromagnetic, ferro-

magnetic, and ferromagnetic, respectively, for ferromagnetic,

antiferromagnetic, and antiferromagnetic J₁, J₂, and J₃, respec-

tively This results in ferromagnetic alignment of the pseudo-

spins (as represented by local magnetization vector in Fig-

ure 8a purple arrows) along the anisotropy axis (as represent-

ed by yellow dashed line in Figure 8a). This leads to tangential

orientation of local magnetization vectors along the four Dy^III

centers. Lines model calculations leads to the formation of ex-

change spectrum of lowest exchange levels. The resultant

Ising doublets are represented by one single direction of mag-

netization Z and this varies in accordance with the doublets as

well as zero transversal magnetization (g_x=g_y=0). Our data

clearly reveals comparatively stronger dipolar Dy^III–Dy^IIIcou-

pling (Table 3) than the corresponding exchange contribution

and this is in line with the expected behavior for Dy^III–Dy^IIIcou-

pling. Non-compensation of the spins owing to the non-paral-

lel axes leads to a non-zero magnetic ground state (g_z=32.42,

g_z=g_z=ca. 10^ꢀ8; highly anisotropic ground exchange doublet)

with the next-higher exchange doublet state lying at 4.86 cm^ꢀ1

Figure 12. a) Crystal structure of complex 5 showing main anisotropy axis

(yellow dashed lines) on four Yb^IIIions and local magnetization (light green

arrows) in the ground state. The diagram also illustrates exchange pathways

employed for our calculations. b) Low-lying exchange spectrum in complex

5. Every exchange state (represented by thick blue lines) has been arranged

based on the corresponding magnetic moment. The curved green arrows

signify tunneling transition (D_tun;tunnel splitting or tunnel gaps) within each

doublet.

above the ground state possessing g_zof 39.61. This results in

large ground state magnetic moment as m_z=¹= g_zm_B

=

27

orbit coupling which has been diagonalized based on the KDs

procured from fragment ab initio calculations.

2

16.21 m_B, that is, almost twice the moment of an individual Dy^III

center. It is notable that, along with ground state, all the ex-

X

3

^

ð2Þ

H_ex¼ ꢀ

_i¼1J_iꢂ S_iꢂ S_iþ1

Table 3. Parameters of the magnetic interaction between the Tb^III, Er^III,

Ho^IIIand Yb^IIIions in complexes 1–5.

The fitting was performed with three different exchange in-

teractions J₁–J₃, while the intermolecular interaction (zJ) was

kept constant for all complexes. It is worth noting that in the

POLY_ANISO code, the dipolar contribution is treated explicitly,

while the exchange part has been estimated from fit to the

magnetic data. Magnetic coupling between Ln ions incorpo-

rate contributions from magnetic dipole–dipole and exchange

interactions. This approach proves to be appropriate in this

regard due to the resemblance of the KDs to jM_J= ꢁ15/2i

state. We also calculated the exchange spectrum (Figure 8b) of

complex 1 using the POLY_ANISO program. Nice agreement

between the simulated and experimental magnetic data (c_MT

(T) and M (H)) was (Figure 5a,b) observed with the parameters

J₁= +2.35 cm^ꢀ1, J₂=ꢀ0.58 cm^ꢀ1, and J₃=ꢀ0.29 cm^ꢀ1at an in-

J₁

J₂

J₃

complex 1

J_i^dipolar

3.10

+2.35

+5.45

ꢀ1.30

ꢀ0.58

ꢀ1.88

ꢀ1.30

ꢀ0.29

ꢀ1.59

J_i^exch

J_i

complex 2

J_i^dipolar

+1.00

+0.45

+1.45

ꢀ0.40

ꢀ0.68

ꢀ1.08

ꢀ0.50

ꢀ0.29

ꢀ0.79

J_i^exch

J_i

complex 3

J_i^dipolar

+0.60

+0.03

+0.63

ꢀ0.50

ꢀ0.98

ꢀ1.48

ꢀ0.70

ꢀ0.19

ꢀ0.89

J_i^exch

J_i

complex 4

J_i^dipolar

ꢀ1.10

+4.15

+3.05

ꢀ0.90

ꢀ0.23

ꢀ1.13

ꢀ1.10

ꢀ0.54

ꢀ1.64

termolecular interaction (zJ)=ꢀ0.025 cm^ꢀ1

.

J_i^exch

Considering the small value of exchange, it is expected to

J_i

~

be of Ising type [Eq. (3)], in which S_izrepresents projection of

complex 5

J_i^dipolar

J_i^exch

J_i

+0.70

+0.15

+0.85

ꢀ0.40

ꢀ0.28

ꢀ0.68

ꢀ0.60

ꢀ1.18

ꢀ1.78

the pseudo-spin on the anisotropy axis of i^thcenter and also

depicts two states with reverse maximal magnetization on this

center.

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magnetization vector in Figure 9a purple arrows) along the

anisotropy axis (as represented by yellow dashed line in Fig-

ure 9a) in 2. This leads to tangential orientation of local mag-

netization vectors along the four Tb^IIIcenters forming a paralle-

logram along the Tb₄plane. Our data clearly reveals compara-

tively stronger dipolar Tb^III–Tb^IIIcoupling (see Table 3) than the

corresponding exchange contribution. Non-compensation of

the spins owing to the non-parallel axes leads to a non-zero

magnetic ground state (g_z=30.10, g_x=g_y=ca. 10^ꢀ8) with the

next- higher exchange doublet state lying at 7.29 cm^ꢀ1above

the ground state possessing g_zof 0.34. This results in large

Table 4. Energies [cm^ꢀ1], corresponding tunnel splitting (D_tun) and g_z

values of the low-lying exchange doublet state in complex 1:

Energy

D_tun

g_z

Energy

D_tun

g_z

0

4.86

9.70

28.96

32.44

35.93

118.97

10^ꢀ8

10^ꢀ10

10^ꢀ8

10^ꢀ10

10^ꢀ8

32.42

39.61

39.59

71.90

0.05

39.26

0.02

118.97

121.03

123.83

125.87

147.12

10^ꢀ8

10^ꢀ5

34.05

31.47

31.48

50.79

60.74

14.76

14.78

34.09

ground state magnetic moment as m_z=¹= g_z=15.05 m_B; that is,

2

almost twice the moment of an individual Tb^IIIcenter. It is no-

table that excited exchange doublets higher than the ground

state are associated with zero magnetic moment while few of

the excited exchange doublets contain large magnetic

moment (Table 5). From Figure 9a, it is evident that the mag-

change excited doublets are associated with substantial mag-

netic moment (Table 4). Such a low-energy gap between the

ground and excited states (4.86 cm^ꢀ1) in conjunction with

large magnetic moment of first excited exchange doublet (g_z=

39.61) is probably the reason behind the absence of a promi-

nent S-shape in the low-field M(H) curve (Figure 5b). Due to

the magnetic exchange, the local magnetization vector and

main anisotropy axis are found to be collinear, leading to

a non-compensated ground state magnetic moment. Hence,

the combination of ferromagnetic orientation of the pseudo-

spins on Dy sites and the significant magnetic moment of Dy

sites in the ground exchange doublet leads to the presence of

a toroidal magnetic moment in complex 1 and categorizes it

under a mixed moment single-molecule toroic (SMT).

Table 5. Energies [cm^ꢀ1], corresponding tunnel splitting (D_tun) and g_z

values of the low-lying exchange doublet state in complexes 2–5.

Energy

D_tun

g_z

Energy

D_tun

g_z

complex 2

0

7.29

7.97

0.05

0.002

0.08

30.10

0.34

0.06

8.34

14.42

14.56

0.10

0.006

0.10

0.06

26.50

23.92

complex 3

0

0.48

0.64

0.001

0.004

0.003

20.67

18.97

16.47

2.04

2.24

2.63

0.001

0.0002

21.46

22.78

45.85

The pure Ising nature of the pseudo-doublets for all the four

Tb^IIIand Ho^IIIsites in complexes 2 and 4, respectively, ensures

the interaction between the neighboring Tb^IIIand Ho^IIIions to

be of Ising type. However, substantial transverse components

in all the eight/four KDs for all the four Er^IIIand Yb^IIIsites in

complex 3 and 5, respectively, prevents the interaction be-

tween the neighboring Er^IIIand Yb^IIIions to be of pure Ising

type. In all four complexes, we have simulated the magnetic

interactions by incorporating contributions from magnetic

dipole–dipole and exchange interactions within an Ising ex-

change Hamiltonian using the POLY_ANISO program. A nice

agreement between the simulated and experimental magnetic

data (c_MT(T) and M(H)) was observed (see Figure 5c,d,e,f and

Figure 6a,b,c,d for complexes 2, 3, 4 and 5 respectively) with

the parameters J₁= +0.45 cm^ꢀ1, J₂=ꢀ0.68 cm^ꢀ1and J₃=

ꢀ0.29 cm^ꢀ1at intermolecular interaction (zJ)=ꢀ0.025 cm^ꢀ1in

complex 2, J₁= +0.03 cm^ꢀ1, J₂=ꢀ0.98 cm^ꢀ1and J₃=

ꢀ0.19 cm^ꢀ1at intermolecular interaction (zJ)=ꢀ0.025 cm^ꢀ1in

complex 3, J₁= +4.15 cm^ꢀ1, J₂=ꢀ0.23 cm^ꢀ1and J₃=

ꢀ0.54 cm^ꢀ1at intermolecular interaction (zJ)=ꢀ0.025 cm^ꢀ1for

complex 4 and J₁= +0.15 cm^ꢀ1, J₂=ꢀ0.28 cm^ꢀ1and J₃=

ꢀ1.18 cm^ꢀ1at intermolecular interaction (zJ)=ꢀ0.025 cm^ꢀ1in

complex 5 (Table 3). Now, based on this approximation, we can

complex 4

0

2.70

2.74

complex 5

0

0.002

0.003

16.12

11.11

11.09

5.42

28.05

30.99

0.002

0.001

0.002

73.43

0.13

37.80

0.02

0. 02

0.06

7.59

3.65

6.81

0.40

0.43

0.47

0.03

0.04

5.31

6.68

5.47

0.22

0.32

netic moments of the four Tb ions are projected onto the Tb₄

plane with a toroidal arrangement. Such a low-energy gap be-

tween the ground and excited states (7.29 cm^ꢀ1) in conjunc-

tion with a weakly magnetic (g_z=0.34) first excited state ex-

plains the absence of prominent S shape in low-field experi-

mental M(H) curve (Figure 5d). Due to the magnetic exchange,

local magnetization vector and main anisotropy axis are found

to be collinear leading to non-compensated ground state mag-

netic moment. Hence, combination of ferromagnetic orienta-

tion of the pseudo-spins on Tb sites and significant magnetic

moment of Tb sites in ground exchange doublet leads to the

presence of toroidal magnetic moment in complex 2 and cate-

gorizes it under a mixed-moment single-molecule toroic (SMT).

The three exchange interactions in complex 3, 4, and 5

result in ferromagnetic alignment of the pseudospins (Figures

10a, 11a and 12a for 3, 4, and 5, respectively, as indicated by

purple and light green arrows respectively; see, also Table 3)

along the anisotropy axis (as represented by yellow dashed

line in Figures 10a, 11a and 12a for 3, 4, and 5, respectively).

~

state that.J₁, J₂, J₃will be antiferromagnetic, ferromagnetic,

and ferromagnetic, respectively, for ferromagnetic, antiferro-

magnetic, and antiferromagnetic J₁, J₂, and J₃, respectively, in

all four complexes (2–5).

The three different exchange interactions result in ferromag-

netic alignment of the pseudospins (as represented by local

&

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Despite this ferromagnetic orientation, the corresponding

magnetic moments do not form a wheel-shaped topology,

which is a signature for toroidal behavior. Instead they lie in

very random fashion and preclude possession of any toroidal

magnetic moment in the complexes 3–5.

ation processes, which are known to play a proactive role in

the relaxation of magnetization.^[37h,j,39]

To gain further insights into the relaxation pathways opera-

tive in complex 2 we need to analyze the exchange spectrum

(Figure 9b). The tunnel splitting within the ground state itself

is very large (10^ꢀ2cm^ꢀ1) (Figure 9b, green curved arrows). This

promotes QTM/TA-QTM efficiently and precludes any SMM be-

havior. Hence, though complex 1 shows both SMM and SMT

behavior, complex 2 only shows SMT characteristics (the lack of

SMM behavior is due to large tunneling transition within the

ground exchange doublet).

Non-compensation of the spins owing to the non-coparallel

axes leads to a non-zero magnetic ground state g_z=30.10, g_x=

g_y=ca. 10^ꢀ7in 3, g_z=16.12, g_x=g_y=ca. 10^ꢀ8in 4 and g_z=7.59,

g_x=g_y=ca. 10^ꢀ8in 5 (see Table 5). In all the three complexes,

the next-higher exchange doublet state lies at 0.48, 2.70, and

0.22 cm^ꢀ1with respect to the ground state possessing g_zof

18.97, 11.11, and 3.65 for 3, 4, and 5, respectively. This results

In a similar manner, with an aim to analyze relaxation path-

ways operative in complexes 3, 4, 5 we need to analyze the ex-

change spectrum (see Figure 10b, Figure 11b and Figure 12b).

The tunnel splitting within the ground state itself is very large:

10^ꢀ3, 10^ꢀ3, 10^ꢀ2cm^ꢀ1for complexes 3, 4, and 5, respectively

(Figures 10b, 11b, and 12b green curved arrows for 3, 4, and

5, respectively). This promotes QTM/TA-QTM efficiently and

precludes any SMM behavior. Hence, complex 3, 4, and 5 lack

both SMM and SMT characteristics.

in a large ground state magnetic moment of m_z=¹= g_z=10.34_,

2

8.06, and 3.79 m_Bfor 3, 4, and 5, respectively (see Table 5). In all

the three complexes, the magnetic moment for the exchange

coupled system is almost equal to the magnetic moment of an

individual Er^III, Ho^III, and Yb^IIIcenter.

Analyzing the mechanism of magnetization relaxation in

complexes 1–5

To gain further insights into the relaxation pathways operative

in complex 1, we need to analyze the exchange spectrum (Fig-

ure 8b). The tunnel splitting of the ground state is very small

till the sixteenth exchange doublet (<10^ꢀ5cm^ꢀ1) (Figure 8b,

green curved arrows). This suppresses the ground state QTM

completely and TA-QTM within the higher excited energy

levels up to sixteenth exchange doublet and promotes relaxa-

tion through higher levels. The seventeenth and eighteenth

exchange doublet possess D_tunof about 10^ꢀ5cm^ꢀ1and this un-

folds a channel for tunneling relaxation of magnetization

through these states. Towards estimating the energy barrier,

we need to consider spin–phonon mechanisms (Orbach,

Raman) through the excited states. This relies on the largest

transition magnetic moments corresponding to the connecting

exchange states (orange bent arrows in Figure 8b). Though

significant matrix elements corresponding to a spin–phonon

transition have been detected between the ꢁ14 and ꢁ15

states (0.76 m_B), due to concomitant negligible tunnel splitting,

relaxation through this pathway can be discarded. On this

note, the relaxation path through ꢀ17, ꢀ18, +18, and +17

should be efficient, as tunnel splitting between these states is

intrinsically large; that is, at the cut-off range of 10^ꢀ5cm^ꢀ1. In

addition, a large magnetic moment matrix element between

the ꢀ17, +18 and ꢀ18, +17 states (1.27 m_B) separated by

0.005 cm^ꢀ1essentially induces the relaxation by this pathway.

Moreover, spin-phonon transition from the ground state ꢀ1 to

ꢀ18 and ꢀ1 to +18 is associated with magnetic moment

matrix element of about 10^ꢀ2and 10^ꢀ1m_B, respectively. This re-

laxation mechanism outlines the computed energy barrier for

magnetization reorientation approximately as about 147 cm^ꢀ1

in complex 1. The intra-square exchange coupling within the

four Dy^IIIcenters has been well represented by the exchange

energy^[29c]spectrum in Figure 13. The U_calcdvalue estimated is

larger than that obtained from the experiments (U_eff) and the

discrepancy could be attributed to various factors, such as in-

termolecular interactions and non-Orbach multi-phonon relax-

Comparative studies on complexes 1–5

The pre-requisite for SMT behavior is strong uniaxial anisotropy

in a low-symmetry ligand field environment.^[15a]Additionally,

large intramolecular dipolar coupling induced by the local

magnetic moments on the interacting magnetic centers con-

tributes to the observation of SMT characteristics.^[15a]As per

these two criteria, Dy^IIIhas the largest anisotropy due to an in-

trinsically large angular momentum and spin-orbit coupling.

Among the complexes studied, 1 possesses the strongest intra-

molecular dipolar coupling (J₁= +3.10 cm^ꢀ1, J₂=ꢀ1.30 cm^ꢀ1,

J₃=ꢀ1.30 cm^ꢀ1; see Table 3). These factors cumulatively are re-

sponsible for the observation of toroidal moment in the

ground state in 1. On the other hand, in the rest of the four

complexes, intramolecular J_dipolaris weaker than in 1 lying in

the range of about ꢀ1 to +1 cm^ꢀ1. Despite possessing second

strongest dipolar exchange (after Dy), complex 4 lacks SMT

characteristic. However, with relatively weaker dipolar coupling

(J₁= +1.00 cm^ꢀ1, J₂=ꢀ0.40 cm^ꢀ1, J₃=ꢀ0.50 cm^ꢀ1; see Table 3),

complex 2 is predicted to exhibit mixed moment SMT behav-

ior. This is due to incumbent vortex-type wheel-shaped ar-

rangement between the local magnetic moments on the four

interacting Tb^IIIsites in 2. On the other hand, local magnetic

moments on the four interacting Ho^IIIcenters are oriented in

a random fashion and prevent SMT behavior in 4 and this may

be attributed to the decrease in the oblate nature as we move

from Dy^IIIto Ho^IIIions.^[1c]This consequentially leads to a reduc-

tion in the overall negative charged axial crystal field around

Ho, deterring perfect perpendicular orientation of g_zwith re-

spect to the oblate electron density. Except complex 1, none

of other complexes exhibit SMM behavior. This is also associat-

ed with the presence of strong exchange interactions in com-

plex 1 which suppress the QTM to promote relaxation via

higher energy levels. Absence of SMM behavior in complex 4,

despite the presence of strong exchange, is due to very weak

Chem. Eur. J. 2016, 22, 1 – 20

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Figure 13. Computed exchange energy spectrum for complex 1 where energies are expressed in cm^ꢀ1. The orange lines for each degenerate energy level cor-

respond to the number of degenerate states associated to that level. The tetranuclear core Dy₄structural motifs have been used to represent the local mag-

netic moments of the Ising quantum states. The eigenstates are correlated to each other by flips of magnetic moments (blue arrows) on the four individual

Dy^IIImagnetic centers. The pink numbers indicate number of the exchange doublet. For each exchange doublet two time reversed components possessing +

and ꢀ opposite magnetization exist and are shown in the above picture.

exchange promoted among these ions, leading to prominent

QTM effects at the ground state.

intrinsic metal centers, lack SMT behavior. This can be attribut-

ed to the inability of accurate communication between the

magnetic moments of the neighboring magnetic sites to

induce SMT characteristic. In addition, absence of SMM in 3, 4,

and 5 is suggestive of prevalent single-ion behavior over ex-

change interaction. Strong exchange interaction is expected to

quench the QTM probability to promote relaxation via higher

excited states.

Conclusions

In summary, we have synthesized a series of homometallic tet-

ranuclear complexes by employing a new aroylhydrazone

based Schiff base ligand. These complexes possess a butterfly-

shaped structural topology. Ab initio calculations were carried

out on these isostructural Ln^III(Ln=Dy^III, Tb^III, Er^III, Ho^III, and

4

Yb^III) complexes with an aim to understand the anisotropy ori-

entation, exchange coupled spectra, and toroidal magnetic

moments. Complex 1 shows both SMM and SMT (mixed

moment) behavior with a calculated barrier of 119 cm^ꢀ1. Com-

plex 2 shows SMT behavior, but SMM characteristics could not

be detected. Our comparative analysis reveals that complexes

3, 4 and 5, with total magnetic moments equal to that of their

Experimental Section

Solvents and other general reagents used in this work were puri-

fied according to standard procedures.^[31]Pyridine-2,6-dicarboxylic

acid, sodium borohydride, Dy(NO₃)₃·5H₂O, Tb(NO₃)₃·5H₂O,

Ho(NO₃)₃·5H₂O, Er(NO₃)₃·5H₂O and Yb(NO₃)₃·5H₂O were obtained

from Sigma Aldrich Chemical Co. and were used as received. o-Va-

nillin, hydrazine hydrate (80%), PBr₃, pivalic acid, diethanolamine

&

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14

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and sodium sulphate (anhydrous) were obtained from S.D. Fine

Chemicals, Mumbai (India). Methyl-6-(hydroxymethyl) picolinate^[27a]

and methyl 6-(bromomethyl)picolinate, were prepared according

to literature procedures.^[27a]

have been generated using Diamond 3.1e software.^[32f]The crystal

data and the cell parameters for compounds 1–3 are summarized

in Table 6. CCDC 1490848 (1), 1490849 (2), 1490850 (3), 1490851

(4), and 1490852 (5) contain the supplementary crystallographic

data for this paper. These data can be obtained free of charge

from The Cambridge Crystallographic Data Centre.

Instrumentation: Melting points were measured using a JSGW

melting point apparatus and are uncorrected. IR spectra were re-

corded as KBr pellets on a Bruker Vector 22 FT IR spectrophotome-

ter operating at 400–4000 cm^ꢀ1. Elemental analyses of the com-

pounds were obtained from Thermoquest CE instruments CHNS-O,

Magnetic measurements: Magnetic data were measured using

a Quantum Design MPMS-XL SQUID magnetometer. All samples

were 3 mm diameter pellets molded from ground crystalline sam-

ples. Magnetic susceptibility measurements were carried out in the

2–300 K temperature range in a 0.1 or 1 T applied magnetic field,

and diamagnetic corrections were considered by Pascal’s con-

stants. Isothermal magnetization measurements were undertaken

up to 7 T at 2, 4, 6 and in somecases 8 K. The ac susceptibility

measurements under different applied static fields were performed

using an oscillating ac field of 3.5 Oe and ac frequencies ranging

from 10 to 10000 Hz.

Computational details: The magnetic properties of all the Ln^III

sites in complexes 1–5 were studied by fragment ab initio calcula-

tions. In order to have good illustration of the 3d or 4f ligand field

states within a fragment we needed to consider the impact of

neighboring metal centers. Owing to the concomitant limitations

of MOLCAS (8.0 version)^[25a–e]of computing magnetic properties of

single paramagnetic metal ion at a time, we undertook calculations

on individual metal fragments. In all the complexes, four types of

calculations were carried out. For each fragmented calculation, one

Ln^IIIion of interest was kept intact, while the other three atoms

were replaced by the diamagnetic Y^IIIion. All the calculations were

carried out on X-ray crystal structures using the basis sets^[33]shown

in Table 7, embedded in MOLCAS suite:

1

EA/110 model. H NMR spectra were recorded in CDCl₃and CD₃OD

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).

X-ray crystallography: The crystal data for the compounds have

been collected on a Bruker SMART CCD diffractometer (MoKa radi-

ation, l=0.71073 ꢁ). The program SMART^[32a]was used for collect-

ing frames of data, indexing reflections, and determining lattice pa-

rameters, SAINT^[32a]for integration of the intensity of reflections

and scaling, SADABS^[32b]for absorption correction, and

SHELXTL^[32c,d]for space group and structure determination and

least-squares refinements on F². All the structures were solved by

direct methods using the program SHELXS-97^[32e]and refined by

full-matrix least-squares methods against F²with SHELXL-97.^[32e]Hy-

drogen atoms were fixed at calculated positions and their positions

were refined by a riding model. All the non-hydrogen atoms were

refined with anisotropic displacement parameters. All the struc-

tures encounter thermal disorder for few atoms, especially in the

tertiary butyl groups of the main residues. Hence we had to

employ some restrains/constrains for the refinement stability. In

complex 2, the carbon atom of the ꢀOMe and interstitial CHCl₃

were showing large thermal displacements. Hence, electron densi-

ties of corresponding atoms were partitioned into two positions

and refined with suitable constraints. The crystallographic figures

In each fragment calculation, multi-configurational approach rela-

tivistic effects were treated in two steps based on a Douglas–Kroll

Hamiltonian. For the generation of basis sets, scalar terms were in-

Table 6. Crystal data and structure refinement parameters of 1–5.

1

2

3

4

5

formula

C₆₀H₉₂Dy₄N₈O₂₄

1959.42

monoclinic

P2₁/n

12.661(6)

16.590 (7)

16.934(7)

94.421(1)

3546.5(3)

2

C₆₄H₈₆Cl₁₈N₈O₂₀Tb₄

2561.23

monoclinic

P2₁/c

11.484(3)

20.047(5)

20.750(5)

103.869 (3)

4638(2)

C₆₀H₉₂Er₄N₈O₂₄

1978.46

monoclinic

P2₁/n

12.634(3)

16.602(4)

16.906(4)

94.630(4)

3534.5(15)

2

C₆₀H₉₂Ho₄N₈O₂₄

1969.14

monoclinic

P2₁/n

12.642(5)

16.632(5)

16.943(5)

94.424(5)

3552(2)

2

C₆₀H₉₀N₈O₂₄Yb₄

1999.56

monoclinic

P2₁/n

12.635(5

16.646(5)

16.848(5)

94.612(5)

3532(2)

2

M_w[g^ꢀ1

crystal system

space group

a [ꢁ]

]

b [ꢁ]

c [ꢁ]

b [8]

V [ꢁ^ꢀ3

]

Z

2

1_calcd[gcm^ꢀ3

]

1.835

4.246

1928.0

1.834

3.596

2504.0

1.859

4.781

1944.0

1.841

4.487

1936.0

1.880

5.327

1956.0

m [mm^ꢀ1

F(000)

]

crystal size [mm³]

q range [8]

0.0046ꢂ0.0031ꢂ0.0025 0.059ꢂ0.052ꢂ0.037

0.0082ꢂ0.0056ꢂ0.0049 0.0096ꢂ0.0091ꢂ0.0065 0.059ꢂ0.052ꢂ0.037

4.08 to 25.03

ꢀ15ꢄhꢄ15

ꢀ19ꢄkꢄ19

ꢀ20ꢄlꢄ20

19795

4.09 to 25.03

ꢀ13ꢄhꢄ13

ꢀ18ꢄkꢄ23

ꢀ24ꢄlꢄ24

28257

4.09 to 25.03

ꢀ15ꢄhꢄ14

ꢀ19ꢄkꢄ19

ꢀ17ꢄlꢄ20

22329

4.08 to 25.03

ꢀ10ꢄhꢄ15

ꢀ19ꢄkꢄ19

ꢀ20ꢄlꢄ20

23853

4.10 to 25.03

ꢀ14ꢄhꢄ15

ꢀ19ꢄkꢄ9

ꢀ20ꢄlꢄ18

17858

limiting indices

reflns collected

independent reflns

completeness to q [%]

data/restraints/parameters

goodness-of-fit on F²

final R indices

6227 [R(int)=0.0357]

99.5

6227/4/458

1.027

R₁=0.0252

wR₂=0.0483

R₁=0.0370

wR₂=0.0510

8121 [R(int)=0.0682] 6205 [R(int)=0.0477]

6236 [R(int)=0.0281]

99.5

6236/2/440

1.079

R₁=0.0187

wR₂=0.0448

R₁=0.0205

wR₂=0.0455

6171 [R(int)=0.0386]

99.2

6171/1/377

1.077

R₁=0.0347

wR₂=0.0822

R₁=0.0441

wR₂=0.0964

99.2

99.5

8121/9/474

1.044

6205/4/439

1.019

R₁=0.0540

wR₂=0.1410

R₁=0.0676

wR₂=0.1520

R₁=0.0258

wR₂=0.0530

R₁=0.0359

wR₂=0.0561

[I>2q(I)]

R indices (all data)

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constant stirring, triethylamine (3.62 mL, 27.3 mmol) was added

added dropwise and the reaction mixture was allowed to stir for

20 min at room temperature. Then, methyl 6-(bromomethyl)picoli-

nate (2.1 g, 9.1 mmol) in THF was added dropwise over a period of

15 min. The reaction mixture was stirred for 24 h at room tempera-

ture. The white turbid solution was filtered and evaporated in

vacuo to get a light yellow oily residue, which was dissolved in di-

chloromethane (30 mL) and washed with water (30 mL) and brine

(20 mL). The aqueous layer was extracted twice with dichlorome-

thane (2ꢂ30 mL) and the combined organic layer was dried

(Na₂SO₄) and filtered, and the solvent was removed in vacuo af-

Table 7.

Elements

Basis set

Elements

Basis set

Dy

Tb

Er

Ho

Yb

ANO-RCC..8s7p5d3f2g1h.

Y

ANO-RCC..6s5p3d.

ANO-RCC..3s2p1d.

ANO-RCC..3s2p.

ANO-RCC..2s.

N

O

C

H

cluded that were used to determine spin-free wave functions and

energies through the use of complete active space self-consistent

field (CASSCF)^[34]methods. Spin-orbit coupling was taken into ac-

count by using RASSI-SO,^[35]which uses CASSCF wave functions as

the basis sets and multi-configurational wave functions as input

states. The resulting wave functions and the energies of the molec-

ular multiplets were used for the evaluation of the magnetic prop-

erties, and g tensors of the lowest multiplets of the isolated frag-

ments were calculated using a specially designed routine SINGLE_

ANISO.^[25f]The basis of this approach is essentially ab initio calcula-

tion of all orbital moment and magnetic moment matrix elements

on the relevant spin-orbit multiplets acquired from CASSCF/RASSI-

SO calculations. These matrix elements were subsequently utilized

in SINGLE_ANISO routine to compute:

1

fording a light yellow oily product. Yield: 1.95 g, 83.51%; H NMR

(500 MHz, CDCl₃): d=2.84 (t, 4H; NCH₂), 3.57 (t, 4H; CH₂O), 3.94 (s,

3H; OMe), 3.97 (s, 2H; NCH₂), 5.28 (s, 1H; OH), 7.43 (d, 1H; Py-H),

7.79 (t, 1H; Py-H), 8.01 ppm (d, 1H; Py-H); elemental analysis calcd

for C₁₂H₁₈N₂O₄(254.28): C 56.68, H 7.13, N 11.02; found: C 56.62, H

7.01, N 11.15.

Methyl 6-{[bis(2-hydroxyethyl)amino]methyl}picolinohydrazide:

A solution of methyl 6-[{bis(2-hydroxyethyl)amino}methyl]picoli-

nate (1.8 g, 7.08 mmol) in ethanol (15 mL) was added dropwise to

a stirred solution of hydrazine hydrate (0.425 g, 8.5 mmol) at room

temperature and the resulting solution was heated to reflux for

5 h. After allowing the reaction mixture to come to room tempera-

ture, ethanol was removed off in vacuo to produce a light yellow

solid residue, which was recrystallized from MeOH/CHCl₃(1:1) to

get the final product as a light yellow solid. Yield: 1.6 g, 88.92%;

1) experimentally measured magnetic proprties (temperature-de-

pendent Van Vleck susceptibility tensor, field-dependent magneti-

zation for different temperatures and temperature-dependent

magnetization at various frequencies)

1

m.p. 978C; H NMR (500 MHz, CD₃OD): d=2.72 (t, 4H; NCH₂), 3.62

(t, 4H; CH₂O), 3.90 (s, 2H; NCH₂), 7.64 (d, 2H; Py-H), 7.89 ppm (t,

1H; Py-H); elemental analysis calcd for C₁₁H₁₈N₄O₃(254.13)_:C 51.96,

H 7.13, N 22.03; found: C 52.02, H 7.50, N 22.11.

2) parameters of magnetic spin Hamiltonians for different spin-

orbit multiplets, spin states represented by the corresponding

pseudospin (g tensors).

6-{[Bis(2-hydroxyethyl)amino]methyl}-N’-(2-hydroxy-3-methoxy-

benzylidene)picolinohydrazide (LH₄): To a stirred solution of

For the estimation of magnetic properties, all spin-orbit multiplets

of crystal field on the Ln^IIIcenters were considered. This feature

was imperative for precise quantitative depiction of the impact of

strong magnetic anisotropy and applied magnetic field.

methyl

6-{[bis(2-hydroxyethyl)amino]methyl}picolinohydrazide

(1.5 g, 5.9 mmol) in methanol (40 mL), o-vanilin (0.898 g, 5.9 mmol)

in methanol (20 mL) was added dropwise at room temperature,

and the resulting solution was heated to reflux for 5 h. After allow-

ing the reaction mixture to come to room temperature, the yellow

solution was concentrated in vacuo and kept in a refrigerator over-

night. An off-white precipitate was filtered, washed with cold

methanol (30 mL) and diethyl ether (20 mL) before being dried to

get the title product. Yield: 1.63 g, 71.11%; m.p. 1048C; ¹H NMR

(500 MHz, CDCl₃): d=2.86 (t, 4H; NCH₂), 3.71 (t, 4H; CH₂O), 3.92 (s,

3H; OMe), 4.00 (s, 2H; NCH₂), 6.83 (t, 1H; Ar-H), 6.92 (d, 1H; Ar-H),

7.16 (d, 1H; Ar-H), 7.25 (d, 1H; Py-H), 7.61 (t, 1H; Py-H), 8.04 (d,

2H; Py-H), 8.39 (s, 1H; imine-H), 11.32 (br, 1H; NH), 11.78 ppm (s,

1H; OH); FT-IR (KBr): n˜ =3438 (OꢀH), 3231 (NꢀH); 1682 (C=O), 1607

(C=N_imine), 1594 cm^ꢀ1(C=N_py); ESI-MS: m/z: [M+H]⁺: 389.17; ele-

mental analysis calcd for C₁₉H₂₄N₄O₅(388.42): C 58.75, H 6.23, N

14.42; found: C 58.96, H 6.03, N 14.97.

Upon describing the individual metal ion properties, we attempted

to elucidate the exchange coupling between the Ln^IIIcenters

within the Lines model as implemented in the POLY_ANISO^[26]rou-

tine and validated earlier.^{[14c,15,18a,34,36,37]}This uses a single-parame-

ter exchange Hamiltonian to explain the isotropic interaction be-

tween spin terms in absence of spin-orbit coupling. Spin-orbit mul-

tiplets on monometallic fragments were generated usually in terms

of Heisenberg Hamiltonian. Diagonalization of this matrix led to

the evaluation of anisotropic interaction between the respective

metal centers. It is notable that the Lines model^[38,15–17]employs

only single parameter for the effective isotropic interaction in

order to simulate the anisotropic interaction between metal pair

fragments. This allowed the use of specific different exchange pa-

rameters corresponding to the accurate description of respective

spin terms of the metal fragments. The Lines model considers

three cases : 1) two strong anisotropic centers (Ising exchange),

2) two isotropic (spin-only) magnetic sites (Heisenberg exchange/

Ising exchange), and 3) one isotropic and one strong anisotropic

center (Ising+Heisenberg). In the POLY_ANISO code, we used the

Ising exchange Hamiltonian (as equation mentioned in main

manuscript) in which the Lines model precisely incorporates aniso-

tropic dipolar and exchange interactions.

General synthetic procedure for the preparation of the com-

plexes 1–5: All the metal complexes (1–5) were synthesized ac-

cording to the following procedure. To a stirred solution of LH₄

(0.046 g, 0.12 mmol) in methanol (20 mL), Ln(NO₃)₃·5H₂O

(0.24 mmol) was added affording a yellow solution, which was

stirred for a further period of 10 min. After that, triethylamine

(0.09 mL, 0.6 mmol) was added dropwise to the mixture at room

temperature and the reaction mixture was continued to stir for

a further period of 15 min. At this stage pivalic acid (0.025 g,

0.24 mmol) was added dropwise and the stirring was continued for

12 h to get a yellow precipitate. This was filtered, washed with di-

ethyl ether (2ꢂ20 mL), dried, re-dissolved in (1:1) v/v mixture of

methanol and chloroform and kept for crystallization. Within

a week, yellow block-shaped crystals, suitable for X-ray crystallogra-

Synthesis

Methyl 6-{[bis(2-hydroxyethyl)amino]methyl}picolinate: To a solu-

tion of diethanolamine (0.956 g, 9.1 mmol) in THF (40 mL), under

&

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Full Paper

phy study, were obtained by slow evaporation the solvents. The

details of each reaction and characterization data for these com-

plexes (1–5) are given below.

Acknowledgements

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

India, for financial support, including support for a single-crys-

tal CCD X-ray diffractometer facility at IIT-Kanpur. V.C. is grate-

ful to the DST for a J. C. Bose Fellowship. S.B. thanks the Coun-

cil of Scientific and Industrial Research, India, for Senior Re-

search Fellowship. G.R. acknowledges IITB for the High Per-

formance Computing Facility.

[Dy₄(LH)₂(m₂-h¹h¹Piv)₂(h²-Piv)₂(m₃-OH)₂]·2H₂O·2MeOH (1): Quanti-

ties: LH₄(0.046 g, 0.12 mmol), Dy(NO₃)₃·5H₂O (0.107 g, 0.24 mmol),

Et₃N (0.09 mL, 0.6 mmol), PivH (0.025 g, 0.24 mmol). Yield: 0.069 g,

59.48% (based on the ligand); m.p. >2508C (decomp); IR (KBr):

n˜ =3645 (w), 3532 (b), 3051 (b), 2957 (s), 2908 (b), 2863 (w), 1610

(s), 1557 (s), 1480 (s), 1446 (s), 1423 (s), 1375 (s), 1360 (s), 1349 (s),

1237 (s), 1213 (s), 1181 (w), 1167 (w), 1132 (w), 1081 (s), 1034 (w),

1017 (w), 974 (w), 951 (s), 908 (w), 892 (s), 862 (w), 850 (s), 791 (s),

760 (w), 732 (w), 691 (w), 598 (w), 569 (w), 537 (w), 487 cm^ꢀ1(w);

elemental analysis calcd for C₆₀H₉₂Dy₄N₈O₂₄(1959.42): C 36.78, H

4.73, N 5.72; found: C 36.97, H 4.51, N 5.13.

Keywords: cluster compounds

properties · Schiff base · single-molecule magnets

· lanthanides · magnetic

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[Er₄(LH)₂(m₂-h¹h¹Piv)₂(h²-Piv)₂(m₃-OH)₂]·2H₂O·2MeOH (3): Quanti-

ties: LH₄(0.046 g, 0.12 mmol), Er(NO₃)₃·5H₂O (0.106 g, 0.24 mmol),

Et₃N (0.09 mL, 0.6 mmol), PivH (0.025 g, 0.24 mmol); Yield: 0.065 g,

54.16% (based on ligand); m.p. >2508C (decomp); IR (KBr): n˜ =

3645 (w), 3531 (b), 3039 (b), 2957 (s), 2897 (b), 2861 (w), 1604 (s),

1557 (s), 1481 (s), 1444(s), 1415 (s), 1379 (s), 1361 (s), 1346 (s), 1237

(s), 1201 (s), 1173 (w), 1156 (w), 1122 (w), 1073 (s), 1034 (w), 1012

(w), 978 (w), 946 (s), 902(w), 887 (s), 869 (w), 841 (s), 799 (s), 763

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N 5.66; found: C 36.75, H 4.33, N 5.79.

[HO₄(LH)₂(m₂-h¹h¹PIV)₂(h²-PIV)₂(m₃-OH)₂]·2H₂O·2MeOH (4): Quanti-

ties: LH₄(0.046 g, 0.12 mmol), Ho(NO₃)₃·5H₂O (0.105 g, 0.24 mmol),

Et₃N (0.09 mL, 0.6 mmol), PivH (0.025 g, 0.24 mmol); Yield: 0.071 g,

61.2% (based on ligand); m.p. >2508C (decomp); IR (KBr): n˜ =

3639 (w), 3537 (b), 3033 (b), 2955 (s), 2891 (b), 2859 (w), 1602 (s),

1559 (s), 1473 (s), 1447(s), 1410 (s), 1373 (s), 1364 (s), 1343 (s), 1232

(s), 1205 (s), 1177 (w), 1153 (w), 1121 (w), 1068 (s), 1031 (w), 1014

(w), 973 (w), 947 (s), 908(w), 889 (s), 863 (w), 847 (s), 799 (s), 765

(w), 731 (w), 683 (w), 591 (w), 558 (w), 526(w), 472 cm^ꢀ1(w); ele-

mental analysis calcd for C₆₀H₉₂Ho₄N₈O₂₄(1969.14): C 36.60, H 4.71,

N 5.69; found: C 36.94, H 4.79, N 6.01.

[Yb₄(LH)₂(m₂-h¹h¹Piv)₂(h²-Piv)₂(m₃-OH)₂]·2H₂O·2MeOH (5): Quanti-

ties: LH₄(0.046 g, 0.12 mmol), Yb(NO₃)₃·5H₂O (0.105 g, 0.24 mmol),

Et₃N (0.09 mL, 0.6 mmol), PivH (0.025 g, 0.24 mmol); Yield: 0.063 g,

53.38% (based on ligand); m.p. >2508C (decomp); IR (KBr): n˜ =

3634 (w), 3531 (b), 3037 (b), 2956 (s), 2892 (b), 2853 (w), 1599 (s),

1558 (s), 1471 (s), 1443(s), 1407 (s), 1374 (s), 1368 (s), 1341(s), 1237

(s), 1201 (s), 1173 (w), 1157 (w), 1119 (w), 1061 (s), 1026 (w), 1012

(w), 977 (w), 942 (s), 903(w), 882 (s), 867 (w), 841 (s), 798 (s), 763

(w), 725 (w), 681 (w), 594 (w), 553 (w), 521(w), 468 cm^ꢀ1(w); ele-

mental analysis calcd for C₆₀H₉₀N₈O₂₄Yb₄(1999.56): C 36.04, H 4.54,

N 5.60; found: C 36.34, H 4.12, N 5.89.

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Received: July 31, 2016

Published online on && &&, 0000

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Full Paper

FULL PAPER

Magnetic butterflies: A series of five

isostructural tetranuclear complexes

with molecular formula [Ln₄(LH)₂(m₂-

h¹h¹Piv)(h²-Piv)(m₃-OH)₂] have been as-

sembled by employing an aroyl hydra-

zine-based Schiff base ligand in con-

junction with pivalic acid. Detailed mag-

netochemical analysis including ab initio

calculation reveals the presence of

single-molecule magnet behavior of the

Dy derivative coupled with very large

mixed toroidal moment, while other

compounds display none.

&

Single-Molecule Magnets

S. Biswas, S. Das, T. Gupta, S. K. Singh,

M. Pissas, G. Rajaraman,*

V. Chandrasekhar*

&& – &&

Observation of Slow Relaxation and

Single-Molecule Toroidal Behavior in

a Family of Butterfly-Shaped Ln₄

Complexes

&

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www.chemeurj.org

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Article Doi

Observation of Slow Relaxation and Single-Molecule Toroidal Behavior in a Family of Butterfly-Shaped Ln4Complexes

DOI: 10.1002/chem.201603640

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Article abstract of DOI:10.1002/chem.201603640

Full text of DOI:10.1002/chem.201603640

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