Lanthanoid pyridyl-β-diketonate 'triangles'. New examples of single molecule toroics

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Trans., 2020, DOI: 10.1039/D0DT02855J.

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DOI: 10.1039/D0DT02855J

ARTICLE

Lanthanoid pyridyl-β-diketonate ‘triangles’. New examples of

single molecule toroics

Chiara Caporale,^aAlexandre N. Sobolev,^bWasinee Phonsri,^cKeith S. Murray,^cAbinash Swain,^d

Received 00th January 20xx,

Accepted 00th January 20xx

Gopalan Rajaraman,^dMark I. Ogden, ^aMassimiliano Massi ^aand Rebecca O. Fuller ^a,e

*

DOI: 10.1039/x0xx00000x

Trinuclear lanthanide clusters have been synthesised and investigated as toroidal spin systems. A pyridyl functionalised -

diketonate, 1,3-bis(pyridin-2-yl)propane-1,3-dione(o-dppdH) has been used to synthesise a family of clusters of the form

[Dy₃(OH)₂(o-dppd)₃Cl₂(H₂O)₄]Cl₂7H₂O (1), [Tb₃(o-dppd)₃(μ₃-OH)₂(CH₃CH₂OH)₃Cl₃][Tb₃(o-dppd)₃(μ₃-OH)₂(H₂O)(CH₃CH₂OH)₂

Cl₃]Cl₂H₂O (2), [Ho₃(OH)₂(o-dppd)₃Cl(H₂O)₅]Cl₃3H₂O (3) and [Er₃(OH)₂(o-dppd)₃Cl₂(H₂O)₃(CH₃OH)]Cl₂3H₂OCH₃OH (4).

Despite the previous occurrence of this structural motif in the literature, these systems have not been widely investigated

in terms of torodic behaviour. Magnetic studies were used to further characterise the complexes. DC susceptiblity studies

support weak antiferromanetic exchange in the complexes. Slow magnetic relaxation behaviour is observed in the dynamic

AC magnetic studies for complex 1. Theoretical studies predict that complex 1 and 3 have a non-magnetic ground state

based on a toroidal arrangement of spins. Changes to the coordination environment in 2 do not support a toroic spin state.

The prolate nature of Er^IIIcentres in complex 4 and large transverse anisotropy do not support the toroidal arrangement of

lanthanoid spins in the complex.

Functionalisation of the diketonate scaffold or the addition of co-

ligands can be used to alter the coordination environment. ^{11, 13}

Introduction

Developing a synthetic methodology to obtain specific lanthanoid

The wealth of functionalities available for the -diketonate family

provides good opportunity to develop structural-magnetic

clusters for applications such as single molecule magnets (SMMs)^{1, 2}

a

4

and luminescence^3,

is a

major current area of interest.⁵

property relationships in a family of structures. This statement may

at first seem counter intuitive, as the development of lanthanoid

SMMs is centred on using the ligand field symmetry to enhance the

inherent anisotropy of the Ln^IIIions with large magnetic moments.^1,

^{14 15}The best examples of Ln-SMMs involve only a single lanthanoid

Understanding how the structure and coordination environment

impacts on the measured properties is key for the advancement of

these molecules into future applications. -diketones are a versatile

and highly functionalisable ligand class which have been shown to

7

support polynuclear lanthanoid cluster formation.^6,

Such

17

ion (e.g. mononuclear complexes).^16,Polynuclear Ln complexes

complexes are normally comprised of a hydroxo-bridged polynuclear

usually only display very weak SMM behaviour due to a lack of

lanthanoid cluster core encapsulated by -diketonate ligands.

19

interaction through -bridging between ions.^18,

The lack of

9

Examples of mononuclear,^8,dinuclear,¹⁰trinuclear¹¹and larger

exchange and the poor anisotropy does not lead to a stabilisation of

a bistable ground state at notable temperatures (with the exception

of Dy). However, polynuclear clusters comprised of an appropriate

geometry can result in an ideal environment for alternative spin

arrangements.²⁰

clusters¹²supported by -diketonate ligands are known.

Coordination with these molecules generally occurs through the

bidentate backbone of the -diketonate ligand together with

additional co-ligands contained within the coordination sphere.

^a.School of Molecular and Life Sciences, Curtin University, Bentley WA 6102,

Australia.

Triangular spin arrangements are well known avenues for producing

interesting properties.²¹Oxo-bridged transition metal complexes

have long been known to exhibit spin frustration.^{22, 23}More recently,

triangular Dy₃cluster complexes have been shown to display a

toroidal spin arrangement in these single molecule toroics (SMTs).²⁴

Depending on the type of SMTs, these systems may have a

nonmagnetic ground state which exists based on a toroidal

arrangement of spins.²⁰This non-magnetic state does not interact

with the applied magnetic field and is observed as a tail in the field

dependent magnetisation measurements. These materials have

unique spin transport properties based on their strongly anisotropic

^b.School of Molecular Sciences and CMCA, M310, The University of Western

Australia, Crawley WA 6009, Australia.

^c.School of Chemistry, Monash University, Clayton VIC 3800, Australia

^d.Department of Chemistry, Indian Institute of Technology BombayPowai, Mumbai,

Maharashtra, 400076, India

^e.School of Natural Sciences-Chemistry, University of Tasmania, Hobart TAS 7001,

Australia. E-mail: rebecca.fuller@utas.edu.au

Electronic Supplementary Information (ESI) available: Reaction scheme and

characterisation for o-dppdH (¹H NMR; ¹³C NMR, IR); Structural representations

including packing arrangements and complexes 1-4; Selected interatomic distances

and angles; Polyhedra view complexes 2-4; magnetic measurements complexes 2-

4; Poly_aniso calculated susceptibility; Dynamic calculations for complex 1 and 4;

Magnetic exchange in complexes 2-4; Tabulated energies and ground-state g

tensors. See DOI: 10.1039/x0xx00000x

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nature, resulting in their suitability for a number of potential

applications including quantum computers and spintronic devices. ^25,

²⁶In addition to Dy based SMTs, non-triangular analogues for other

lanthanoids have also been recently reported, Ln = Tb, Ho, Er.^{27, 28}

for the production of these systems. Collection of the product was

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achieved after a series of washing steps^Du^Os^Ii^:n¹g^0.1a⁰c³e⁹t^/o^Dn⁰i^Dtr^Til⁰e²⁸a⁵n⁵d^J

pyridine to remove unreacted o-dppdH and lanthanoid salt from the

target compound. The target clusters were then collected as a

powder and crystals suitable for X-ray diffraction were grown using

slow evaporation or diffusion techniques. If required, the bulk

sample was recrystallised for magnetic measurements as well as

analysis.

Trigonal Dy₃complexes provided the first examples of SMTs.²⁹In

these complexes the ring-like arrangement of spins is strongly

anisotropic and aligns with the plane of the array. However, as the

SMT field has matured, a wealth of structures has been developed.^27,

30, 31

New examples with a range of structural motifs have been

Crystallography

reported, including square,³²wheel,³³cubane³⁴and 3d-linked pair

of Dy₃heptanuclear clusters.³¹In this work we have focused on

developing complexes with a similar structural motif to the trigonal

complexes. ^{11, 24}

Figure 2 shows the structure of the complex cation of [Dy₃(OH)₂(o-

dppd)₃Cl₂(H₂O)₄]Cl₂7H₂O (1). The compound crystallises in the

ퟏ

triclinic space group P . Each of the -diketonate ligands binds to

two of the Dy^IIIcentres. One of the oxygens from the -diketone

binds exclusively to one Dy^IIIatom. The other oxygen is shared (₂-O)

between the two centres (Dy-O-Dy angles in the 97.96-98.37° range).

The second of the dysprosium centres is also bound to a nitrogen

from the pyridyl group, so that each ligand is bound through 

²(N,O);²(O,O’) to the lanthanoid centres with the other pyridyl

nitrogen atom left unbound. The lanthanoid centres and ligand

bridging oxygen atoms form an essentially planar 6 membered ring

(deviation 0.06 Å). The metal array approximates an equilateral

triangle, with deviation from the ideal Ln-Ln-Ln angle of less than

0.24°. The three eight-coordinate Dy^IIIcentres are bridged by two

central ₃-OH oxygens which lie above and below the metal plane by

1.211 and 1.175 Å, respectively. Two of the Dy^IIIcations are

coordinated to chloride anions. The final positions in the Dy^III

coordination sphere contain H₂O molecules. One of the unbound

pyridyl rings is distorted over two positions with occupancies set to

0.6667 and 0.3333. As a result, the neighbouring H₂O contained in

the lattice is disordered. Selected bond lengths for all the complexes

are given in Table 1 with additional data contained in the ESI (Table

S1 and S2).

Pyridyl functionalised -diketonates have shown potential as

supporting ligands for SMTs. The pyridin-4-yl analogue has been

used in the synthesis of a cubane-shaped Dy₄complex.²⁷A Ho^III

complex with the bis(pyridin-2-yl) -diketonate has been shown to

consist of a coordination environment similar to o-vanillin Dy^III

triangles which exhibited a toroidal spin arrangement.^{11, 24}Despite

the similarity of the core and bridging atoms, the magnetic behaviour

exhibited by the holmium complex was distinctly different to the

dysprosium system. It was postulated to be likely due to the result of

the difference in the magnetic anisotropy of the holmium and

dysprosium centres. In this vein we have synthesised a family of

triangular molecules based on Dy^III, Tb^III, Ho^IIIand Er^IIIwith the

deprotonated 1,3-bis(pyridin-2-yl)propane-1,3-dione (Figure 1)

ligand (o-dppdH). This family of lanthanide complexes has been used

to investigate the role of the lanthanoid centre in the spin structure

of the metal core. In this work we aim to further elucidate the impact

of the lanthanoid anisotropy on the ligand field and magnetic

exchange by undertaking a detailed experimental and theoretical

investigation on these systems.

Using continuous SHAPE measurements, the 8-coordinate

environment approximates a triangular dodecahedron (TDD8) with

D2d symmetry and based on the shape distortion parameter given in

Table 1 for all studied complexes, this is valid for all Ln metal

centres.³⁶The polyhedral representations are given in Figure S3 (ESI)

Figure 1: Structure of the o-dppdH ligand, 1,3-bis(pyridin-2-yl)propane-1,3-dione.

Results and discussion

Synthesis and characterisation of complexes

A series of trinuclear lanthanoid clusters with the formula [Ln₃(₃-

OH)₂(o-dppd)₃Cl_xL_y]^4-xwhere Ln= Dy^III, Tb^III, Ho^IIIor Er^III; x+y=6; L =

H₂O or CH₃CH₂OH or CH₃OH have been prepared. o-dppdH was

synthesised via a Claisen condensation of ethyl-2-picolinate and 2-

35

acetylpyridine using a literature procedure (Scheme S1).^11,The

ligand (2 eq.) was treated with a lanthanoid salt of the form

LnCl₃.6H₂O (where Ln= Dy^III, Tb^III, Ho^IIIand Er^III) in the presence of

triethylamine. Although a stoichiometry of 1:1 appears to be more

appropriate for the production of a trigonal system, the 2:1 ratio and

complexation proceeding at elevated temperatures was necessary

Figure 2: Molecular structure of complex 1. Dy…Dy distances are 3.54-3.55 Å. Thermal

ellipsoids are set to 30 % probability. For clarity, hydrogen atoms and lattice solvent are

omitted.

2 | J. Name., 2012, 00, 1-3

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DOI: 10.1039/D0DT02855J

Table 1: Selected interatomic distances and SHAPE parameter for [Dy₃(OH)₂(o-dppd)₃Cl₂(H₂O)₄]Cl₂7H₂O 1, {[Tb₃(o-dppd)₃(OH)₂(CH₃CH₂OH)₃Cl₃] [Tb₃(o-dppd)₃(μ₃-

OH)₂(H₂O)(CH₃CH₂OH)₂Cl₃]Cl₂H₂O} 2, [Ho₃(OH)₂(o-dppd)₃Cl(H₂O)₅]Cl₃3H₂O 3 and [Er₃(OH)₂(o-dppd)₃Cl₂(H₂O)₃(CH₃OH)]Cl₂3H₂OCH₃OH 4.

1

2

3

4

Dy1

Dy2

Dy3

-

Tb1

Tb2

Tb3

Ho1

Ho2

Ho3

Er1

Er2

Er3

-

distances (Å)

Ln-Cl

Ln-O123 (₃-O)

Ln-O321 (₃-O)

Ln-N

2.644(2) 2.543(6)

2.672(1) 2.672(1) 2.712(1)

2.390(3) 2.392(3) 2.376(3)

2.386(3) 2.397(3) 2.377(3)

2.530(4) 2.522(4) 2.520(3)

2.645(4)

2.383(8) 2.363(8)

2.356(8) 2.354(7)

2.51(1)

1.213

-

2.577(4) 2.642(1)

2.394(5) 2.382(6) 2.359(4)

2.356(5) 2.350(4) 2.374(6)

2.498(7) 2.486(7) 2.486(7)

2.36(1)

2.38(1)

2.511(9)

2.353(3) 2.339(3) 2.357(3)

2.371(3) 2.373(3) 2.331(3)

2.494(4) 2.498(3) 2.498(3)

2.50(1)

0.811

Distortion

SHAPE (D_2d)*

1.230

0.854

1.033

1.307

1.296

1.571

0.985

0.814

1.217

0.901

*D_2dsymmetry for triangular dodecahedral polyhedral

for complexes 2-4. The closer the SHAPE index is to zero the less

distortion from the ideal environment. The geometry of the Dy^III

centres in 1 appears to approximate a triangular dodecahedron

(TDD8) with D_2dsymmetry (Figure 3). The metal bond distances and

angles for 1 are similar to those in the Dy^IIIo-vanillin complexes which

have the form [Dy₃(₃-OH)₂L₃Cl₂(H₂O)₄] where L = 2-hydroxy-3-

methoxybenzaldehyde.²⁹Continuous shape measurements

performed on the Dy^IIIo-vanillin systems found the geometry of the

complexes also approximates a triangular dodecahedron (TDD8)

with D_2dsymmetry. In complex 1, the lattice contains large voids

which are occupied by non coordinated Cl ions and H₂O. The solvent

system used to isolate the complex is also shown to impact on the

solvent contained within the voids of complex 2 and 4.

Figure 3: Polyhedral view of the eight coordinate geometry of

Dy1 in complex the two 3-O(H) are positioned above the LnIII

centre (O321 and O123). This depiction from CrystalMaker®

v9.1.3 supports a TDD-8 coordination environment around the

lanthanoid centre. Purple= DyIII, red=O, green=Cl and blue=N

atom.

A

similar metal array is seen in the {[Tb₃(o-dppd)₃(μ₃-

Cl ][Tb (o-dppd) (μ OH) (H O) Cl ]Cl 

OH)

₂(CH₃CH₂OH)₃(CH₃CH₂OH)₂

3

2

3

2

H₂O} (2), [Ho₃(OH)₂(o-dppd)₃Cl(H₂O)₅]Cl₃3H₂O (3) and [Er₃(OH)₂(o-

dppd)₃Cl₂(H₂O)₃(CH₃OH)]Cl₂3H₂OCH₃OH (4) complexes (ESI Figure

S2). The three lanthanoid centres are in an equilateral arrangement

with similar coordination to the -diketonate ligand and central

hydroxide groups as discussed for 1. Selected bond lengths are given

in Table 1 and in the ESI (Table S1 and S2) Depending on the

lanthanoid atom, the coordination sphere contains between one and

three Cl anions with the other positions consisting of solvent

molecules, dependent on the recrystallisation method (H₂O, CH₃OH,

CH₃CH₂OH). Using continuous SHAPE measurements, the 8-

coordinate environment approximates a triangular dodecahedron

(TDD8) with D_2dsymmetry, the polyhedral representations are

contained in Figure S3 (ESI). The structure of the holmium analogue

(3) is distorted in a similar manner to 1, namely one of the unbound

pyridyl rings occurs in two positions (occupancy 0.5) with

neighbouring lattice solvent also being disordered.

are found to link together through the chloride counter ions and the

pyridyl ring with either a coordinated water and/or hydroxide ligands

(Figure 4). The hydrogen bond is indirect as it does not occur solely

between donor atoms coordinated to the Dy^IIIcentres. Rather, it

involves both donor and lattice solvent/counter ions. However, since

it is the triangular arrangement of the spins and the associated

Using CrystalExplorer 3.1³⁷the packing arrangement of molecules is

found to be influenced by - interactions as well as coordinated Cl

anions hydrogen bonding to the pyridyl rings on the adjacent

molecule and lattice solvent (ESI Figure S1a). The metal arrays are

arranged in parallel planes (Figure 4). Intermolecular  stacking

interactions between the delocalised diketonate and pyridyl ring or

between two adjacent pyridyl rings, with a maximum centroid to

centroid distance of 3.9 Å noted in 1 (ESI Figure S1b). The molecules

Figure 4: CrystalExplorer 3.1 is used to depict the hydrogen bonding

network in 1. Purple=Dy^III, red=O, green=Cl, light blue=N, grey=C and

white=H.

anisotropy which impact on the stabilisation of a non-magnetic

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toroidal spin states, the extended network will not significantly affect g[J(J+1)]^0.5values of 10.65 (Dy³⁺), 9.72(Tb³⁺), 10.61 (Ho³⁺) and 9.58

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3+

the occurrence of a toroidal state.²⁴

(Er ) _Bper Ln centre. As the temperature is decreased from room

temperature to about 100 K we see a slight decrease occurs in _MT

that is likely the result of the depopulation of the excited Ln^IIIStark

DOI: 10.1039/D0DT02855J

Both lattice and coordinated solvents were impacted by conditions

used for crystallisation. When comparing complex 3, to

the previously reported analogue¹¹an additional water and one less

chloride were refined as co-ligands with further water contained in

the lattice. In complex 2 the co-ligands are disordered, whereby one

of the coordinated H₂O molecules is replaced by a CH₃CH₂OH

molecule. To ensure that the variations between reaction batches

only represented the slight changes mentioned, two structural

analyses for crystals from the erbium system were fully refined.

[Er₃(OH)₂(o-dppd)₃Cl₂(H₂O)₃(CH₃OH)]Cl₂5H₂O (4a) highlights the

variable solvation for different crystallisations. Full details of this

complex can be found in the ESI (Table S1) Metal analysis was used

to confirm lanthanide content. These results were consistent with

the proposed formulations as well as values inferred from the room

temperature susceptibility.

The extended structures for complexes 2-4 are dependent on -

interactions and coordinated Cl anions linked to neighbouring pyridyl

rings in the way depicted for complex 1 in Figure S1. The coordination

environments in the lanthanoid triangles is different for Tb^IIIbut Ho^III

and Er^IIIare similar to that in Dy^III. The linking of the metal arrays for

both 3 and 4 is also similar to that seen for complex 1. In 3, the Ho^III

metal array of neighbouring molecules are connected through a

hydrogen bonding network involving the lattice Cl anions being

linked from a pyridyl ring of one molecule to coordinated H₂O and

₃-O of another. In an analogous manner, the complex 4 metal arrays

are linked through two slightly different lattice Cl anion

environments. The first is identical to that observed in 1 and 3. The

second involves a pyridyl ring and coordinated CH₃CH₂OH from one

Figure 5:Temperature dependent _MT products in a DC field of 1 T for the series of

[Ln₃(₃-OH)₂(o-dppd)₃Cl_xL_y]^4-xcomplexes, where Ln = Dy (1) blue; Tb (2) pink; Ho (3) red

and Er (4) green.

levels. At lower temperatures, a more rapid decrease is observed,

which is likely a result of the thermal depopulation of the low-lying

Zeeman levels possibly combined with weak antiferromagnetic

coupling between the centres.

Magnetisation (M) isotherms (2-20 K) for each of the complexes were

determined in DC fields of 0 to 5 T. The results for 1 are shown in

Figure 6 with similar results being observed for 2-4 (ESI Figure S6). In

molecule being linked through the lattice Cl anions to a coordinated each of the complexes, the measurements made at 2 K do not reach

a saturation value at 5 T (i.e. M has a value of 15.60, 13.64, 14.56 and

13.94 N for 1-4, respectively). Similarly, a saturation in the

H₂O and central ₃-O of the neighbouring molecule. A different

arrangement is seen for the Tb^IIImetal arrays (2). Neighbouring

molecules are still linked through lattice Cl anions. However, in this

case the coordinated CH₃CH₂OH (or H₂O) groups are also linked with

the neighbouring molecule pyridyl, with the central ₃-O playing no

role. In the absence of coordinated CH₃CH₂OH, water in the lattice is

also involved. Figure S4 in the ESI contains representations for each

of the complexes. The alternative environments are not expected to

alter any exchange interaction between the centres as it is the

triangular arrangement of the spins and the associated anisotropy

which governs these processes.

magnetisation is not seen in

5 T fields at 3 K. The non-

superimposability of the curves when plotted as M vs H/T supports

the occurrence of low-lying levels that are energetically close to the

ground state supporting the role of zero field splitting or Zeeman

depopulation effects, arising from magnetic anisotropy. Despite the

coordination environment being reminiscent of reported systems

with a toroidal ground states, the shape of the M vs H plots at low

fields does not have the S-shape that is often, but not always,

associated with toroidal systems.^15,18,20-22However since these

toroidal arrangements are influenced by molecular symmetry and

the moment in addition to interaction one cannot rule out the

possibility that there is a small energy gap between the nonmagnetic

ground state and the first excited state which precludes the S-shape

being observed.³⁴At present ab initio calculations based on CASSCF

method are best suited to identify such behaviour while

experimental evidence would require methods such as micro-Squid

magnetisation/hysteresis plots³¹and NMR to unambiguously detect

and describe such states.

Magnetic Properties

Polycrystalline samples of 1-4 were used for the collection of

magnetic susceptibility data. DC measurements (2-300 K) in fields of

1 T (Figure 5) and 0.1 T (ESI Figure S5) gave similar results. The room

temperature _MT values for complexes 1-4 are 40.6, 33.4, 39.6 and

34.0 cm³mol^-1K, respectively. The value obtained for 3 is consistent

with the previous literature reports for a structural analogue (39.7

cm³mol^-1K).¹¹At 300 K the _effper Ln^IIIin complex 1-4 are 10.40,

9.43, 10.27 and 9.53 _B. These are consistent with the calculated

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Figure 7: The temperature dependent (2-10 K) out of phase susceptibility, χ_M”, for

complex 1 in 0 T DC field.

Limitations of the MOLCAS packaged means calculations on the full

complex 1 are not possible. Instead calculations were undertaken in

two stages. Firstly, calculations are performed on each Dy centre by

substitution of the other two Dy^IIIions by diamagnetic Lu^IIIions.

Secondly, the single-ion anisotropy of all three Dy^IIIare combined

together to understand the relaxation of the states. All calculations

were performed using the X-ray crystal structure data as input.

Figure 6: Magnetisation isotherms (2-20 K) in applied fields 0 to 5 T for complex 1.

Variable temperature (2-10 K) AC dynamic measurements were also

undertaken for each of the complexes both with and without an

applied bias DC field for a range of frequencies between 20 and 1488

Hz. The bias field applied in experiments was optimised for each

sample by measuring changes _M” in a static DC field under an

applied oscillating field (1488 Hz and 498 Hz) at 3 K. The out of phase

component, _M” for the [Dy₃(OH)₂(o-dppd)₃Cl₂(H₂O)₄] complex is

shown in Figure 7 in zero applied DC field. The Dy^IIIKramer’s ion

complex 1 is found to have an out of phase signal below 8 K which

varies with frequency. However, no maxima are observed in _M”

plots, even in an applied field (ESI Figure S7). Nevertheless, the

signals are consistent with slow magnetic relaxation occurring for a

multicentred Dy^IIIcomplex with insufficient anisotropy. The results

for complexes 2-4 are given in the ESI (Figure S7). The DC fields

applied in complexes 2-4 were used in an attempt to obtain efficient

quantum tunnelling and, hopefully, observe frequency dependence

of _M”. However, a weak signal to noise (both with and without an

applied DC field) was seen in the _M” vs. temperature or vs.

frequency plots for complexes 2-4 (ESI Figure S7), a result similar to

cases involving Ln₆toroics.³⁸The _M” vs. frequency log-plots for 2- 4

showed that the weak, noisy data varied little upon applying the DC

field (Figure S8) with no clear evidence for frequency dependent

maxima. In the case of 1, there is a hint of a maximum at ~1000 Hz,

between 2-3 K, but a Debye analysis to estimate a U_effvalue was not

feasible.

The local g tensors for the low-lying Ising doublets in 2 and 3 and the

Kramers doublets (KDs) for 1 and 4 are given in Tables S5-S9 in the

ESI. The local g tensor for complexes 1-3 is Ising in nature with

diminishing contribution towards the transverse anisotropy, as the

combination of six O, one N and one Cl (for one centre seven O and

one N) providing axial approach of ligand field around the oblate Ln^III

ions in the eight coordinated square antiprism environment,

whereas for the prolate Er ion, the g tensor is not axial in nature and

they have significant transverse anisotropy.

Since the lanthanide centres are not completely symmetric to one

another, the theoretical analysis confirms that, for the above ligand

field environment when the oblate ion like Dy^IIIis approached by two

different ligand from two different directions (keeping the other six

coordination sites same), the Cl reduces the axiality compare to the

O coordination. This is due to the increase in bond length for the

former (around 2.54 Å) compared to 2.32 Å to the latter, which in

response decreases the interaction of ligand with the metal centre.

For the complexes 1-4 the arrangement of each ground state

anisotropy has been plotted (Figure 8) for all the Ln^IIIcentres. In

complex 1 the arrangement is in a circular pattern suggesting

toroidal behaviour for the complex and the same is seen also in

complex 3. Interestingly in 2, two of the Tb^IIIcentres have the ground

state anisotropy aligned along the triangular plan similar to 1 and 3,

however the g_zzaxis of the Tb3 centre is perpendicular to the

triangular plane, destroying the possible toroidal moments in this

complex. This arises from the significant change in the coordination

environment of Tb1 centre where in one water molecule is found

coordinated trans to Cl position compared to ethanol coordination

which is found in the other Tb2 and Tb3 centres. Hence the

arrangement of anisotropic axis around the Tb1 centre is more or less

Theoretical analysis

In the absence of the S-shape in the low temperature magnetisation

isotherms, theoretical studies were undertaken to predict whether

these systems have a toroidal spin arrangement. For a triangular Ln^III

complex to display

a toroidal spin arrangement, a planar

arrangement of local anisotropy axes and the polynuclear Ln^III

complex requires cyclic symmetry.³⁹

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similar to that of complex 1 (Dy1 in Dy₃complex), whereas the In complex 4, the ligand field is completely reversed to what is

View Article Online

DOI: 10.1039/D0DT02855J

anisotropic axis for the Tb2 and Tb3 centres are parallel to each needed for the prolate ions. It is expected for complex 4 that slow

other. For the prolate Er^IIIion, the ligand fields present are not relaxation will not be observed. Indeed this was confirmed from the

suitable as they offer strong axial ligand and weaker equatorial experiments, where

a

large Quantum tunnelling of the

ligation and this leads to significant transverse anisotropy at the magnetisation was found for all the three Er^IIIcentres. For 1 there are

ground state and hence no toroidal behaviour can be expected

(Figure 8). Large transverse anisotropy arises due to significant

mixing of the m_Jstates as shown in Figure S11 in ESI. The higher

LoProp charge is present at the bridging O of the diketo group and

less for the ₃-O and the terminal water O for all the complexes

making the anisotropy axis lying in the direction of the bridging keto

oxo group for the oblate ion complex 1-3 whereas for the prolate Er

for complex 4, the anisotropy axis moves away from above the diketo

oxo group as shown in Figure 8.

The computed energy spectra for the low-lying Ising doublets for 2

and 3 or the KDs for complexes 1 and 4 are given in Tables S3 and S4

of ESI. From the Tables, one can clearly see that the Dy3 centre

possessing two aqua ligands coordinated (and no –Cl) is found to

have the largest ground-state excited state gap of 159 cm^-1

compared to other to Dy centres (82 cm^-1and 50 cm^-1respectively

Figure 9: Arrangement of anisotropic axis for the ground state KDs and Ising

doublets for complex 1-4. Violet= Dy, green = Ho, Yellow= Tb, Pink= Er, Red=

O, Grey= C, Blue= N, Green= Cl, H are omitted for clarity.

no clear maximum seen in the out of phase susceptibility plots,

making it not possible to derive any relaxation time for

magnetisation or magnetic blocking barrier. At the individual Dy^III

centre, the ground state is not completely pure m_j=±15/2 in nature

with significant mixing from the excited m_jlevels causing fast QTM

between the degenerate ground state KDs. Moving from ground to

first excited state the angle between the anisotropy axes for both

states did not coincide with each other with very large angle of

Figure 8: Dynamics for magnetic blocking relaxation through ab initio

computation for Dy1. The thick blue line represents the Kramers

deviation causing the Raman and Orbach process between ground to

first excited levels. The relaxation diagram for the individual

lanthanide ions for Kramers ion are given in Figure 9 and ESI Figure

S10 - S11.

doublets as a function of computed magnetic moment. The green

dotted arrows show the possible pathway through Orbach/Raman

relaxation, the dotted red lines and blue represent the presence of

QTM/TA-QTM between the connecting pairs. The numbers provided at

each arrow are the mean absolute value for the corresponding matrix

element of transition magnetic moment. The numbers at the KDs

represents the contribution of different states for the corresponding

wave functions.

Toroidal Behaviour and Exchange Coupling:

for Dy1 and Dy2). Moving to complexes 2 and 3, for the Ising

doublets, the tunnel splitting for complexes 2 and 3 occurs and is

found to be in the range of 0.0005 to 0.1 cm^-1for the former and in

the range of 2 to 3 cm^-1for the later which is in agreement with the

previously reported molecule.¹¹Due to the non-Kramers nature and

high tunnel splitting it is very much expected that these molecules

lack SMM behaviour and hence no significant peak for the out of

phase susceptibility has been observed from the AC magnetic

dynamics measurement.

The inputs from the SINGLE_ANISO calculations have been used in

the POLY_ANISO module to compute the exchange interactions

between the Ln-Ln centre for all the four complexes and the energy

levels for the exchange coupled state have been obtained. For

calculating the exchange interaction, the Lines model has been taken

into account with the Hamiltonian represented in the equations 1-3

(see below in Experimental). Since all the lanthanide centres are in

distinctive ligand environments i.e. they have different terminal

coordination, the exchange interactions between the Ln-Ln centres

are expected to differ. We have considered three different exchange

parameters for the three Ln centres represented in the Figure 10

6 | J. Name., 2012, 00, 1-3

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ground state anisotropy which is responsible for the predicted

View Article Online

toroidal moment. For these two complexes,^Dt^Oh^Ie^{: 1}t⁰o^.1r⁰o³id⁹a^/Dl ⁰p^Dro^Tp⁰e²⁸rt⁵i⁵e^Js

have been exploited using POLY_ANISO module^{42, 43}to obtain the

toroidal states at the different energy levels. For this the magnetic

interaction has been simulated by considering the magnetic dipole-

dipole interaction and the exchange interaction explicitly within

Lines model approximation. The Hamiltonian used for the approach

is provided in the Experimental section, equations 1-3.

It has been observed that the flipping of spins occurs moving from

the ground to first excited state causing switching to the reversal

arrangement. The ground state vectors in 1 are found to be in almost

perfect triangular arrangement where the angle of deviation of the

g_zvector from the Dy₃plane for complex 1 is 2.8°, 3.0 ° and 5.7° for

Dy1, Dy2 and Dy3 respectively. Similarly for complex 3 these values

are 3.9°, 1.5° and 1.9° for Ho1, Ho2 and Ho3 centres. The lack of

toroidal behaviour for complexes 2 and 4 arises from the deviation

of the g_zvector from the respective lanthanide Ln3 plane being too

high. These values are 3.5° ,19.7° and 35.4° for complex 2, whereas

Figure 10: Mode of exchange between the Dy-Dy

ions in complex 1.

below (see also ESI Figure S12). For complexes 2-4 all the three

exchange interactions are found to be antiferromagnetic in nature as

obtained by fitting both the experimental susceptibility and

magnetisation data. For complex

1

there are two weak for complex 4, no in plane vectors are found. The g_zis out of plane

with respect to the Er₃triangle.^{27, 30}The energy profile diagram is

ferromagnetic and one weak antiferromagnetic exchange

interactions. A closer look at the structure reveals that there are

some differences in the geometrical parameters apart from the

variation in the terminal ligand. Particularly one of ₃-OH, has

significant asymmetry in Dy1-O(H)-Dy angles with one angle being

slightly larger than the other two (98.05 vs. 97.15 and 96.45°). This

large angle which corresponds to the J1 interaction is between two

given in Figure 11.

Dy centres possessing terminal –Cl ions. As shown earlier by us in

41

magneto-structural correlations for several Dy2 dimers,^40,

the

angle here is at the border line where even a marginal change

(approximately one degree) could switch the nature of exchange

from weakly ferro to antiferromagnetic. These values are reflected in

the bond angle analysis of the other three complexes as well. The

corresponding Ln-O-Ln for the complex 2 are found to be 96.86,

96.95 and 96.42˚, for complex 3 it was 97.78, 97.13 and 97.60˚, and

for complex 4, 96.49, 96.43 and 97.06˚. In all of these cases the

magnetic interactions are found to be antiferromagnetic in nature.

Moreover the smaller bond angles in complex 4 favours a greater

antiferromagnetic contribution compared to the other complexes.

The experimental and POLY_ANISO calculated temperature

dependent _MT for complexes 1-4 are contained in the ESI in Figure

S9.

Table 2 The exchange interactions between the Ln-Ln for complexes

1-4; in cm^-1.

J³

J¹

J²

J³

J¹

J²

J³

J¹

J²

dipo

tot

exch

dipo

-0.65

-0.16

-0.25

-1.95

-0.05

-0.18

-0.23

-1.80

-0.05

-0.18

-0.23

-1.80

-0.25

-0.04

-0.10

-0.45

-0.15

-0.06

-0.10

-0.40

-0.15

-0.06

-0.10

-0.40

-0.12

-0.15

-1.50

0.20

1

2

3

4

-0.12

-0.13

-1.40

-0.12

-0,13

-1.40

Figure 11: Low-lying exchange spectrum for complexes 1 (upper) and 3

(lower). The exchange coupled states (KDs) are placed on the diagram

according to their magnetic moments (bold blue and green lines).

From the SINGLE_ANISO calculations at the individual Ln centres it

was found that in 1 and 3 there is a circular arrangement of the

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The ground toroidal state shows an energy difference of

̴

View Article Online

DOI: 10.1039/D0DT02855J

the first excited state where the flipping of one spin occurs (non-

toroidal state). For complex 2 the anisotropy axes for the ground

Ising doublet are similar to that of toroidal arrangement, (the angle

has been reported above). However slight deviation of the gz axis

from the triangle plane and weaker coupling leads to smaller

toroidal-non-toroidal state gap and hence a smaller barrier ( ̴

0.5 cm^-

¹) compared to complex 1. In contrast, the axis for the complex 3

shows unusual behaviour due to the significant change in the

terminal coordination for Tb-1 centre which we have already

discussed above, causing two of the ground state axes to be parallel

to each other. Moving to complex 4, as a result of the prolate nature All NMR spectra were calibrated to residual solvent signals. Infrared

of the Er^IIIion very large transverse anisotropy in the ground state

was observed, and thus it is expected that there should not be any

toroidal properties. This is confirmed from the theoretical studies.

spectra were recorded using an attenuated total reflectance Perkin

Elmer Spectrum 100 FT-IR with a diamond stage. IR spectra were

recorded from 4000–650 cm^-1. Characterisation data (¹H NMR; ¹³C

NMR, IR) for the ligand are contained as figures within the ESI (pp 1-

2). The intensity of the band is reported as strong (s), medium (m),

or weak (w), with broad (br) bands also specified. Melting points

were determined using a BI Barnsted Electrotermal 9100 apparatus.

Elemental analyses were carried out on bulk samples using a Thermo

Finning EA 1112 Series Flash. Inductively coupled plasma atomic

emission spectroscopy (Murdoch-Marine and Freshwater Research

Laboratory) was used to evaluate the lanthanoid content of the

complexes. The metal analysis for the lanthanoid gave results

consistent with the proposed formulations after extensive drying.

Conclusions

Triangular arrangements of lanthanoid spins have been shown to

exhibit a nonmagnetic ground state based on a vortex arrangement

of spins. We have synthesised a family of trinuclear lanthanide

complexes using pyridyl functionalised -diketonate to investigate

this phenomenon. The metal array has the general form [Ln₃(₃-

OH)₂(o-dppd)₃Cl_xL_y] where Ln= Dy^III, Tb^III, Ho^IIIor Er^III. We have

undertaken magnetic studies and theoretical calculations on the

complexes. Despite the inability to observe an S-shape at low

temperatures and fields in the magnetisation isotherms, theoretical

studies have predicted that complexes 1 and 3 support a toroidal spin

arrangement. 1 is found to have a large ground state with Ising

anisotropy, and the spins are arranged toroidally. Complex 3 is also

predicted to show toroidal behaviour which is slightly inferior to 1.

For 2, a large ground state anisotropy is present, but due to

significant change in the coordination environment, it does not

possess any toroidal behaviour. The inability to observe a flattening

in the magnetic isotherms for these complexes is likely due to the

nonmagnetic ground state which is not energetically well separated

from the first excited state. Unsurprisingly, the prolate nature of Er

in 4 and the large transverse anisotropy does not support a toroidal

arrangement.

Crystallographic data for the structure were collected at 100(2) K on

an Oxford Diffraction Gemini diffractometer with Mo Kα or Cu Kα

radiation. Following absorption corrections and solution by direct

methods, the structures were refined against F²with full-matrix

least-squares using the program SHELXL-2014.⁴⁴All hydrogen atoms

were added at calculated positions and refined by use of riding

models with isotropic displacement parameters based on those of

the parent atoms. Anisotropic displacement parameters were

employed throughout for the non-hydrogen atoms. Structure

refinement data are reported in the SI.

1,3-bis(pyridin-2-yl)propane-1,3-dione (o-dppdH):

2-Acetylpyridine (5.60 mL, 0.050 mol) was dissolved in anhydrous

THF (200 mL) and NaH (60% dispersion in paraffin oil, 2.40 g, 0.060

mol) was carefully added. Ethyl-2-picolinate (6.80 mL, 0.050 mol) was

added dropwise and the mixture was vigorously stirred at 60 °C for

12 hours. More portions of THF were added as the mixture thickened

(30 mL x 2). The solvent was removed under reduced pressure and

the red/orange solid was acidified in a 1:5 v/v glacial acetic

acid:water solvent mixture. The solid was filtered out and washed

with multiple portion of 1:5 v/v glacial acetic acid:water solvent

mixture. The solid was then recrystallised from methanol. The target

product was collected as an off-white powder. Yield: 6.16 g (54.5%).

MP: 102 – 103 °C. IR ( / cm^-1): 3053 w (C-H asym stretch), 2922 w (C-

H sym stretch), 1603 s (C=O stretch), 1317 m (C-N stretch). ¹H NMR

( / ppm, DMSO-d₆): 8.77 (d, 2H, J = 4.3 Hz), 8.20 – 7.94 (m, 6H), 7.64

– 7.62 (m, 2H). ¹³C NMR ( / ppm, DMSO-d₆): 196.6, 183.5, 151.9,

151.5, 149.7, 149.1, 137.7, 127.9, 127.2, 121.9, 121.5, 93.7, 48.1.

The Dy-Dy distance in 1 is similar (3.537 Å to 3.553 Å) to the

previously reported Dy₃toroidal molecule by Powell and co-

workers²⁴(3.514 to 3.540 Å) and is shorter than another Dy₃toroidal

(Dy-Dy distance is 3.73 Å) reported by Murray et al.³⁹The angle

between the ground state g_zzaxis for 1 is found to be 6.13°, 10.6° and

2.7° for Dy1, Dy2 and Dy3 respectively and this is also similar to

Powell’s Dy3 system (4.1° , 8.8° and 2.4°) and is significantly smaller

than Dy₃toroidal system report by Murray et al. (~12°). Due to the

striking similarity of 1 to earlier Dy₃system by Powell, we expect that

their toroidal moments are comparable and is expected to be better

than the Dy₃system reported by Murray et al.

The present work confirms that a combination of both theoretical

and experimental studies is essential in the determination of a

toroidal state in triangular (and other) lanthanoid STMs.

8 | J. Name., 2012, 00, 1-3

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Anal. Calcd for o-dppdH C₁₃H₁₀N₂O₂: C 69.02, H 4.46, N 12.38%.

[Er₃(OH)₂(o-dppd)₃Cl₂(H₂O)₃(CH₃OH)]Cl₂3H₂OCH₃OH_View(4_A)_r:_ticleY_Oi_ne_ll_ind_e:

DOI: 10.1039/D0DT02855J

0.155 g (12.3%). Crystals suitable for X-ray analysis were obtained by

Found: C 69.23. H 4.31, N 12.53%.

slow evaporation of a methanol solution of the cluster over a week.

MP: 322 °C (dec). IR ( / cm^-1): 3355 w (OH stretch), 3005 w (C-H

asym stretch), 2923 w (C-H sym stretch), 1526 s (C-O stretch), 1312

General synthesis for the lanthanide trinuclear clusters

m

(C-N

stretch).

Anal.

Calcd

for

o-dppdH (0.317 g, 0.0014 mol) was dissolved in dry methanol (40 mL)

[Er₃(OH)₂(C₁₃H₉N₂O₂)₃Cl₂(H₂O)₃(CH₃OH)]

and triethylamine (0.2 mL) was added dropwise to deprotonate the

Cl₂(H₂O)(C₅H₅N)₂(CH₃CH₂OH)₃=C₅₆H₇₃Er₃N₈O₁₈Cl₄: C 37.40; H 4.26; N

6.65 %. Found: 37.49; H 4.30; N 6.86 %; % Er calculated 28.0 % found

27.4 %. _eff=9.53 B.M. per Er³⁺.

.

diketone. LnCl₃6H₂O (0.0007 mol) was added to the reaction mixture

and heated at the reflux temperature for 48 hours. The solvent was

evaporated under reduced pressure and the solid was dissolved in 40

mL of acetonitrile (to remove excess of ligand) and centrifuge for 5

minutes at 7500 rpm. The insoluble solid was retained and dissolved

in 40 mL of pyridine, before being centrifuged again (unreacted

lanthanoid salt precipitates out). The solution was collected and

evaporated under reduced pressure and the solid was washed

multiple times with diethyl ether (20 mL x 3). The target complex

used for characterisation and magnetic measurements was either

Crystallography

Experimental data for the structures were measured at 100(2) K on

an Oxford Diffraction Gemini diffractometer or an Oxford Diffraction

Xcalibur X-Ray diffractometers. In complexes 1, 3, 4 and 4a the lattice

Cl are disordered between several positions. During the refinement,

their populations were forced to maintain a balance between the

collected directly as a crystalline powder or recrystallised from positively and negatively charged components of the complexes. The

data were corrected for Lorentz and polarization effects and

absorption. The structures were solved by direct methods and

refined against F²with full-matrix least-squares using the programs

suit SHELX.⁴⁵Anisotropic displacement parameters were employed

for the non-hydrogen atoms. All hydrogen atoms were added at

calculated positions and refined by use of a riding model with

isotropic displacement parameters based on those of the parent

atom. Crystallographic data for the structures reported in this paper

have been deposited at the Cambridge Crystallographic Data Centre.

Copies of the data with CCDC numbers 2022326-2022330 can be

obtained free of charge via https://www.ccdc.cam.ac.uk/structures/,

or from the Cambridge Crystallographic Data Centre, 12 Union Road,

Cambridge CB2 1EZ, U.KCB21EZ, UK (fax +441223336033; email

deposit@ccdc.cam.ac.uk).

methanol, ethanol or ethanol:hexanes mixture. With the exception

of 2, complexes have the general form [Ln₃(μ₃-OH)₂(o-dppd)₃Cl_xL_6-x-y

L’_y]Cl_4-x, where: L and L’ = H₂O or CH₃CH₂OH or CH₃OH. Metal analysis

for the lanthanides gave results consistent with the proposed

formulations. Elemental analysis was performed on bulk crystalline

material.

[Dy₃(OH)₂(o-dppd)₃Cl₂(H₂O)₄]Cl₂7H₂O (1): Yield: 0.210 g (19.7 %).

Crystals suitable for X-ray analysis were obtained by slow

evaporation of a methanol solution of the cluster over a week. MP:

323 °C (dec). IR ( / cm^-1): 3195 w (OH stretch), 3005 w (C-H asym

stretch), 2923 w (C-H sym stretch), 1521 s (C-O stretch), 1310 m (C-N

stretch). Anal. Calcd for [Dy₃(OH)₂(C₁₃H₉N₂O₂)₃Cl₂(H₂O)₄]

(CH₃CH₂OH)₅=C₄₉H₆₇N₆O₁₇Cl₂Dy₃: C 37.47; H 4.30; N 5.35 %. Found: C

37.56; H 4.66; N 5.83 %. % Dy calculated 31.04 % found 31.9 %.

(1): C₃₉H₅₁Cl₄Dy₃N₆O₁₉, M = 1537.16, colourless needle, 0.192 × 0.048



_eff=10.40 B.M. per Dy³⁺.

3

1

× 0.028 mm , triclinic, space group P (No. 2), a = 10.1440(3), b =

17.5135(4), c = 17.9653(4) Å, α = 62.865(2), β = 73.868(2), γ =

78.120(2)°, V = 2716.81(13) Å³, Z = 2, D_c= 1.879 g cm^-3, μ = 4.353 mm^-

¹. F₀₀₀= 1490, MoKα radiation, λ = 0.71073 Å, 2θ_max= 64.5°, 58606

reflections collected, 17881 unique (R_int= 0.0847). Final GooF =

1.002, R1 = 0.0613, wR2 = 0.1201, R indices based on 10524

{[Tb (o-dppd) (μ -OH)

Cl ][Tb (o-dppd) (μ -

₂(CH₃CH₂OH)₃

3

OH) (H O)

Cl ]Cl H O} (2): Yield: 0.177 g (15.0 %).

(CH₃CH₂OH)₂

2

3

Crystals suitable for X-ray analysis were obtained by slow diffusion of

hexane in an ethanol solution of the cluster over a week. MP: 318 °C

(dec). IR ( / cm^-1): 3183 w (OH stretch), 3005 w (C-H asym stretch),

2923 w (C-H sym stretch), 1520 s (C-O stretch), 1306 m (C-N stretch). reflections with I > 2σ(I) (refinement on F²), |Δρ|_max= 2.5(2) e Å^-3, 745

Anal. Calcd for [Tb (C₁₃H₉N₂O₂) (OH) (H O)

_2.5Cl₃]

_0.5(CH₃CH₂OH)

parameters, 133 restraints. CCDC-2022326

3

2

(CH₃CH₂OH)C₅H₅N= C₅₁H₅₆N₇O₁₂Cl₃Tb₃: C 39.72, H 3.66 N 6.35%.

Found: C 39.41, H 3.67, N 6.35%. % Tb calculated 28.3 % found 28.7

%. _eff=9.43 B.M. per Tb³⁺.

(2): C₈₈H₉₂Cl₈N₁₂O₂₃Tb₆, M = 2922.85, pale yellow blade, 0.291 ×

3

ퟏ

0.119 × 0.030 mm , triclinic, space group P (No. 2), a = 13.3953(3),

b = 14.2766(3), c = 14.9895(4) Å, α = 92.506(2), β = 97.712(2), γ =

95.225(2)°, V = 2824.30(12) Å³, Z = 1, D_c= 1.718 g cm^-3, μ = 3.961 mm^-

¹. F₀₀₀= 1414, MoKα radiation, λ = 0.71073 Å, 2θ_max= 64.7°, 61139

reflections collected, 18702 unique (R_int= 0.0516). Final GooF =

1.001, R1 = 0.0458, wR2 = 0.0987, R indices based on 13555

reflections with I > 2σ(I) (refinement on F²), |Δρ|_max= 0.25(2) e Å^-3,

648 parameters, 10 restraints. CCDC-2022327

[Ho₃(OH)₂(o-dppd)₃Cl(H₂O)₅]Cl₃3H₂O (3): Yield: 0.181 g (16.8 %).

Crystals suitable for X-ray analysis were obtained by slow

evaporation of a methanol solution of the cluster over a week. MP:

314 °C (dec). IR ( / cm^-1): 3375 w (OH stretch), 3053 w (C-H asym

stretch), 2922 w (C-H sym stretch), 1521 s (C-O stretch), 1310 m (C-N

stretch).

Anal.

Calcd

for

[Ho₃(OH)₂(C₁₃H₉N₂O₂)₃Cl(H₂O)₅]

Cl₂(CH₃CH₂OH)₂(H₂O) = C₄₃H₅₃N₆O₁₆Ho₃Cl₃: C 34.17; H 3.53; N 5.56 %.

Found: C 34.45; H 3.79; N 5.91 %. % Ho calculated 32.7 % found 32.9 (3): C₃₉H₄₅Cl₄Ho₃N₆O₁₆, M = 1490.40, colourless block, 0.161 × 0.126

%. _eff=10.27 B.M. per Ho³⁺.

3

ퟏ

× 0.093 mm , triclinic, space group P (No. 2), a = 10.1060(6), b =

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8s7p5d3f2g1h.] basis set for Ln^IIIatoms, the [ANO-RCC...3s2p.] basis

DOI: 10.1039/D0DT02855J

set for C atoms, the [ANO-RCC...2s.] basis set for H atoms, the [ANO-

17.3501(9), c = 18.1704(11) Å, α = 110.050(5), β = 105.850(5), γ =

101.302(4)°, V = 2727.2(3) Å³, Z = 2, D_c= 1.815 g cm^-3, μ = 10.157 mm^-

¹. F₀₀₀= 1436, CuKα radiation, λ = 1.54178 Å, 2θ_max= 134.8°, 25032

reflections collected, 9622 unique (R_int= 0.0769). Final GooF = 1.001,

R1 = 0.0819, wR2 = 0.1944, R indices based on 5808 reflections with

I > 2σ(I) (refinement on F²), |Δρ|_max= 1.4(2) e Å^-3, 748 parameters,

177 restraints. CCDC-2022328

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RCC...3s2p1d.] basis set for N and O the [ANO-RCC...4s3p1d.] basis

set for the Lu atom, [ANO-RCC...5s4p2d1f.] atoms. The Guessorb step

involves for selecting the suitable active space, followed by the spin

averaged CASSCF calculations. The active space taken for the Dy, Tb

, Ho and Er are (9,7), (8,7), (10,7) and (11,7) respectively, indicating

distribution of corresponding number of electrons in the seven 4f

(4): C₄₁H₄₉Cl₄Er₃N₆O₁₆, M = 1525.44, pale brown needle, 0.272 ×

3

ퟏ

0.140 × 0.056 mm , triclinic, space group P (No. 2), a = 10.0875(3), orbitals. For the configuration Interaction procedure 21 sextet roots

has taken for Dy^III, for the Tb^IIIion seven septet, one hundred and

forty quintet excited states and one hundred and ninety-five triplet

excited states for the Ho^IIIion two hundred and ten triplet excited

states and one hundred and ninety-five singlet excited states, for the

Er^IIIion thirty five quartet and one hundred twelve doublet excited

states has been included. After computing all the excited state, all

the low excited states (<50000 cm^-1) has been mixed through RASSI-

SO module.⁴⁸Finally the SINGLE_ANISO module helps in calculating

the anisotropy factor of the low lying state as well as the nature of

magnetic behaviour at individual Ln centre.

b = 17.5576(4), c = 18.0809(4) Å, α = 110.687(2), β = 105.565(2), γ =

100.854(2)°, V = 2739.91(13) Å³, Z = 2, D_c= 1.849 g cm^-3, μ = 4.814

mm^-1. F₀₀₀= 1474, MoKα radiation, λ = 0.71073 Å, 2θ_max= 64.8°,

56013 reflections collected, 18104 unique (R_int= 0.0284). Final GooF

= 1.002, R1 = 0.0390, wR2 = 0.1024, R indices based on 15201

reflections with I > 2σ(I) (refinement on F²), |Δρ|_max= 4.3(2) e Å^-3, 656

parameters, 40 restraints. CCDC-2022329

(4a): C₃₉H₄₇Cl₄Er₃N₆O₁₇, M = 1515.40, pale brown needle, 0.167 ×

0.111 × 0.082 mm³, triclinic, space group P-1 (No. 2), a = 10.1697(2),

b = 17.4740(3), c = 17.7993(3) Å, α = 62.933(2), β = 74.798(2), γ =

79.589(2)°, V = 2711.1(1) Å³, Z = 2, D_c= 1.856 g cm^-3, μ = 4.866 mm^-

¹. F₀₀₀= 1462, MoKα radiation, λ = 0.71073 Å, T = 100(2) K, 2θ_max

65.7°, 61314 reflections collected, 18503 unique (R_int= 0.0531).

=

The above results gives the inputs for performing the POLY_ANISO

module for the entire molecule to derive the exchange and dipolar

interaction between the Ln-Ln centres. The Hamiltonian for

calculating the exchange values has been given below.^{51, 52}

Final GooF = 1.003, R1 = 0.0521, wR2 = 0.1165, R indices based on

12677 reflections with I > 2σ(I) (refinement on F²), |Δρ|_max= 2.2(2) e

Å^-3, 634 parameters, 18 restraints. Lp and absorption corrections

applied. CCDC-2022330

∑

퐻_푒푥= ― 퐽_푖푆_푖푆_{푖 + 1}

(1)

푖

Magnetism

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

this describes the interaction between all the neighbouring metal

centres.

Magnetic susceptibility measurements were performed using a

Quantum Design MPMS-XL

7

SQUID magnetometer. DC

measurements were carried out at temperatures between 1.8 and

300 K in fields ranging from 0–5 T. AC susceptibility measurements

were carried out in an oscillating ac field of 3.5 Oe and frequencies

ranging from 0.1 to 1500 Hz. Measurements were made on

polycrystalline samples contained in Vaseline to prevent torqueing

effects.

퐷푦^푖― 퐷푦^{푖 + 1}

푑푖푝

퐷푦^푖― 퐷푦^{푖 + 1}

)푠_퐷푦푠_퐷푦

_{푖 + 1}(2)

푖

푒푥푐ℎ

퐻 = ―( ― 퐽

+ 퐽

휇_퐵²

퐷푦^푖― 퐷푦^{푖 + 1}

푑푖푝

퐽

=

푔²_퐷푦

(3)

푖 + 1

푅³_퐷푦

푖

― 퐷푦

Computational Details

Conflicts of interest

There are no conflicts to declare

Theoretical investigation were performed using ab initio calculations

based on the coordinates from the X-ray crystal structures with the

MOLCAS 8.0 package.⁴⁶The calculations involve the stepwise

Acknowledgements

procedure of guessing the active orbitals followed by CASSCF and

48

RASSI calculations.^47,

Doughlass Kroll Hamiltonian has been

ROF thanks the ARC for a Discovery Early Career research Award

(DE180100112). The authors acknowledge the CMCA Research

Facility at UWA. KSM thanks the ARC for a Discovery grant. GR would

like to than SERB and DST for funding (CRG/2018/000430;

included to take account of the relativistic effect which is more

pronounced for the heavier lanthanide elements.⁴⁹CASSCF

calculations helps in achieving the spin free eigenstate.

SINGLE_ANISO module is used to calculate the magnetic properties

at individual lanthanide centre.⁵⁰Using the inputs obtained from the

SINGLE_ANISO module POLY_ANISO calculations has been done to

plot the toroidal states as well the exchange interaction between the

Ln-Ln centre. For the Ln ions TZVP level of basis set has been taken

from the ANO…RCC library where as for the coordinated O and Cl TZV

level of basis set has been used. For the remaining atoms DZV level

basis has been used. We have employed the [ANO-RCC...

DST/SJF/CSA-03/2018-10;

SB/SJF/2019-20/12).

Dr

Thomas

Rodemann of the UTas Central Science Laboratory is thanked for

elemental analysis.

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DOI: 10.1039/D0DT02855J

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Lanthanoid pyridyl-β-diketonate 'triangles'. New examples of single molecule toroics

DOI: 10.1039/d0dt02855j

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