“New f-Block and Mixed d,f-Block Molecular Nanomagnets”

“New f -Block and Mixed d,f -BlockMolecular Nanomagnets”

A DISSERTATION SUBMITTED TO THE UNIVERSITY OF MANCHESTER

FOR THE DEGREE OF

Doctor of PhilosophyIN THE FACULTY OF ENGINEERING AND PHYSICAL SCIENCES

ByEufemio Moreno Pineda

School of Chemistry

2014

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Contents

Abstract 13

Declaration 15

Copyright 17

Acknowledgements 19

1 Introduction 231.1 Rationale for submitting by alternative format . . . . . . . . . . . . . 231.2 Organisation of the thesis . . . . . . . . . . . . . . . . . . . . . . . . 231.3 Contributing Authors . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2 Molecular Magnetism and Molecular Nanomagnets 272.1 Magnetism: Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2 Molecular Nanomagnets . . . . . . . . . . . . . . . . . . . . . . . . 282.3 Molecular Magnetism: Origin . . . . . . . . . . . . . . . . . . . . . 302.4 Molecular Magnetism: Spin clusters . . . . . . . . . . . . . . . . . . 312.5 Molecular Magnetism: 4f -based MNMs . . . . . . . . . . . . . . . . 33

2.5.1 4f -based Systems . . . . . . . . . . . . . . . . . . . . . . . . 362.6 Lanthanide Cages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.6.1 Toroidal moment in {Dy3} . . . . . . . . . . . . . . . . . . . 372.6.2 [Dy5O(OiPr)13] and [Dy4K2O(O2

tBu)12] . . . . . . . . . . . 382.6.3 3d/4f Complexes . . . . . . . . . . . . . . . . . . . . . . . . 39

3 Magnetocaloric Effect 453.1 First steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2 Adiabatic Demagnetisation . . . . . . . . . . . . . . . . . . . . . . . 453.3 MCE: Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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3.4 Enhancing MCE using MNMs . . . . . . . . . . . . . . . . . . . . . 473.4.1 Ligand Effects and Solvothermal Synthesis . . . . . . . . . . 483.4.2 Ferromagnetic Interactions . . . . . . . . . . . . . . . . . . . 49

3.5 Recent Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4 MNMs as Coolers 534.1 Magnetism of Molecular Coolers . . . . . . . . . . . . . . . . . . . . 53

4.1.1 Molecular amino−phosphonate cobalt−lanthanide clusters . . 534.1.2 Wells−Dawson Cages as Molecular Refrigerants . . . . . . . 534.1.3 Iron Lanthanide Phosphonate Clusters: {Fe6Ln6P6} Wells-Dawson-

like Structures with D3d Symmetry . . . . . . . . . . . . . . 53

5 Single Molecule Magnets 935.1 SMMs: Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 935.2 4f-SMMs: Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 935.3 3d/4f-SMMs: Interactions . . . . . . . . . . . . . . . . . . . . . . . 95

6 4f and 3d/4f SMMs 996.1 4f-4f and 3d-4f interactions . . . . . . . . . . . . . . . . . . . . . . . 99

6.1.1 Direct measurement of DyIII· · ·DyIII interactions in a single-molecule magnet . . . . . . . . . . . . . . . . . . . . . . . . 99

6.1.2 Systematic study of a family of butterfly-like {M2Ln2} molec-ular magnets . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7 Quantum Computing 1597.1 Beginnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1597.2 Qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1607.3 Requirements for Qubits . . . . . . . . . . . . . . . . . . . . . . . . 1607.4 MNMs in QC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

8 QC using MNMs 1658.1 QC using AF-Wheels . . . . . . . . . . . . . . . . . . . . . . . . . . 165

8.1.1 A supramolecular assembly for implementation of the√

SWAPgate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

9 Conclusions 1899.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

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9.1.1 Molecular Coolers . . . . . . . . . . . . . . . . . . . . . . . 1899.1.2 Single Molecule Magnets . . . . . . . . . . . . . . . . . . . 1909.1.3 Quantum Computing . . . . . . . . . . . . . . . . . . . . . . 190

Appendices 191

A Magnetism 193A.1 Atoms in a Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . 193A.2 Magnetisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196A.3 Magnetic Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . 197A.4 Exchange coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . 198A.5 Alternating Current Magnetic Susceptibility . . . . . . . . . . . . . . 199

B EPR Spectroscopy 203B.1 EPR Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203B.2 Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204B.3 Zero Field Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 204B.4 Spin Effective formalism . . . . . . . . . . . . . . . . . . . . . . . . 205B.5 Exchange interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 205

C Quantum Gates 207C.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207C.2 Two Qubit Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207C.3 Three Qubit Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

D Contribution to other Projects 211D.1 Contribution to other Projects . . . . . . . . . . . . . . . . . . . . . . 211

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List of Figures

2.1 (a) p-nitrophenyl nitronyl nitroxide radical; (b) diazaadamantane dini-troxide radical; (c) benzo-fused dithiazolyl radical. . . . . . . . . . . 28

2.2 Left to right 0→3D compounds: a)[Fe14(bta)6O6(OMe)18Cl6], wherebta is benzotriazolate; b) [CsLn(Ph2acac)4]n chain; c) [Mn(N3)2(pyz)]layer, where pyz is pyrazine; and d) [Sm(HCOO)3]n network. Colourcode: M, blue; O, red; N, light blue; Ln, purple; W, grey; Mn, palepink; C, light grey; no H atoms are shown for clarity. . . . . . . . . . 29

2.3 (a) Crystal structure of [Mn12O12(OAc)16(H2O)4] viewed down thetetragonal C4v (z), where light blue spheres represent MnIII and darkblue spheres represent MnIV; (b) Representation of relative orienta-tions of MnIII (S = 2) and MnIV (S = 3

2 ) spins in the ground state.Colour code: O, red; C, grey. Hydrogens omitted for clarity . . . . . . 30

2.4 Strutures of: (a) [Fe4(µ-OMe)6(dpm)3]; (b) [Mn6(hfac)12(NITPh)6];(c) [NHn

2Pr2][Cr7M(µ-F)8(O2CtBu)16]; (d) [Fe8(µ3-O)2(OH)12(tacn)6]+4.Colour code: O, red; C, grey; F, light yellow; Cr, green; Fe, dark or-ange; Mn, blue; N, light blue. Hydrogens omitted for clarity. . . . . . 32

2.5 (a) Structure of [LnPc2]– (Ln = TbIII, DyIII, HoIII, ErIII, TmIII andYbIII); (b) View along the tetragonal axis of the molecular structure ofthe complex. Colour code: C, grey; Ln, purple, N, blue. Hydrogensomitted for clarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.6 (a) Molecular structure of [Dy3(µ3-OH)2L3Cl(H2O)5]Cl3 triangle (Hy-drogen atoms, the chloride counter ion and solvent molecules omittedfor clarity); (b) Scheme of the spin structure of the {Dy3} complexand of the local easy axes orientation in respect of the laboratory XYZ

reference frame. Colour code: C, grey; O, red; Ln, purple, N, blue.Hydrogens omitted for clarity. . . . . . . . . . . . . . . . . . . . . . 38

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2.7 (a) Crystal structure of: [Dy5O(OiPr)13] and (b) [Dy4K2O(O2tBu)12].

Colour code: C, grey; O, red; Ln, purple; K, dark grey. Hydrogensomitted for clarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.8 Structures of CuGd molecules: (a) [CuSALtn)2Gd(H2O)(NO3)]; (b)[Dy(hfac)3CuSatnOH]2; (c) [CuHAPen)2Gd(H2O)3](ClO4)3. Colourcode: C, grey; Gd, purple, N, blue; Cu, aqua; F, yellow; O, red. Hy-drogens omitted for clarity. . . . . . . . . . . . . . . . . . . . . . . . 40

3.1 Schematic showing two basic processes of the MCE when a magneticfield is applied or removed in a magnetic system: (a) the isothermalprocess leading to an entropy change, and (b) the adiabatic process,which yields a variation in temperature; (c) Molar magnetisation ofsuper-paramagnet with spin S, as a function of temperature and mag-netic field. Isothermal process A→B renders higher−∆Sm, whilst adi-abatic process A→C yields ∆Tad, leading to decrease of the temperature. 47

3.2 3d/4f metal complexes with high magnetic entropy change (−∆Sm): (a){Gd42Co10}[28] (−∆Sm = 41.3 J kg-1 K-1); (b) {Mn4Gd6}[29] (−∆Sm =33.7 J kg-1 K-1); (c) {Gd36Ni12}[30] (−∆Sm = 36.3 J kg-1 K-1); Colourcode: Gd, purple; M (transition metal), blue; N, cyan; P, green; O, red;C grey. Hydrogens omitted for clarity. . . . . . . . . . . . . . . . . . 49

5.1 Structures of mononuclear lanthanide SMMs: (a) Na[Dy(DOTA)(H2O)];(b) [Dy(paaH∗)2(NO3)2]; (c) [DyCp∗COT]. Colour code: Dy, purple;blue; N, cyan; O, red; C grey, Na, blue. Hydrogens omitted for clarity. 94

5.2 (a) Radical-bridge dysprosium dimer SMM [[(Me3Si)2N]2Dy(THF)2(µ-η 2:η 2-N2)]−; (b) Magnetisation (M) vs. field (H) from 11 to 15 K forDy-radical bridge compound. Colour code: Dy, purple; blue; N, cyan;O, red; C grey, Si, pink. Hydrogens omitted for clarity. . . . . . . . . 94

5.3 Structures of 3d/4f cages: (a) [(µ 3-C9H3O6){LCuDy(NO3)2}3]; (b)[Co2Dy2(L)4(NO3)2(THF)2]; (c) [Cr2Dy2(OMe)2(mdea)2(acac)4(NO3)2];(d) [Cr4Dy4(µ3-OH)4(µ-N3)4(mdea)4(piv)4]. Colour code: Dy, pur-ple; blue; N, cyan; O, red; C grey, Co, light purple; Cu, blue. Hydro-gens omitted for clarity. . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.1 Structure of Molecular qubits candidates: (a) {Cu3W18}17; (b) {Tb2}18;(c) {CuTb}19; (d) {GdW5}20. Colour code: Ln, purple; Cu, blue; N,cyan; O, red; C grey; Sb, pink. Hydrogens omitted for clarity. . . . . . 162

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7.2 Crystal structures of antiferromagnetic wheels: (a) {[NH2nPr2][Cr7Ni(µ-

F)8(O2CtBu)15]}2(Cu(NO3)2)[24] known as green wheel and (b) {[Cr7Ni(µ-F)3(O2CtBu)15(Etglu)(L)]}[26], also known as purple wheel. Colourcode: Cr, purple and green; Cu, blue; N, cyan; O, red; C grey; Ni,grey-blue. Hydrogens omitted for clarity. . . . . . . . . . . . . . . . 163

A.1 (a) Saturation of the magnetisation for S = 12 , 3

2 , 52 and 7

2 for a g = 2.0;(b) Zeeman splitting for S = 5

2 under application of a magnetic field. . 196A.2 (a) Behaviour of S = 5

2 state. The degeneracy is partially removedbefore the application of the applied magnetic field. . . . . . . . . . . 197

A.3 (a) χMT vs. T graphs for ferromagnetic, antiferromagnetic and non-interacting (paramagnetic) coupled spins; (b) Ground and excited staterepresentation for two s = 1

2 spins with ferromagnetic and antiferro-magnetic interactions using a −2J formalism. . . . . . . . . . . . . . 198

A.4 Representation of the potential energy vs. the magnetisation directionfor a single molecule with an S = 10 spin ground state ion, {Mn12},split by axial zero field splitting. . . . . . . . . . . . . . . . . . . . . 199

A.5 (a) Frequency dependence of the real and imaginary component of themagnetic susceptibility. χT and χS are the isothermal and adiabaticsusceptibility respectively; (b) Argand plot (or Cole-Cole) χ ′′ vs. χ ′ ata given temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

B.1 (a) Zeeman splitting of S = 12 separated by gµBH; (b) Zeeman splitting

for S = 12 interacting with I = 1

2 . . . . . . . . . . . . . . . . . . . . . . 203B.2 (a) Zeeman splitting for an S = 1, with a zero-field splitting D > 0 and

(b) D > 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204B.3 EPR simulation and Zeeman diagram along the z-axis for two coupled

S = 1 in axial crystal field and an isotropic exchange interaction: (a) J

= +1 cm-1 and D = 0; (b) J = −1 cm-1 and D = 0; (c) ) J = +1 cm-1 andD = +1 cm-1; (d) J = −1 cm-1. . . . . . . . . . . . . . . . . . . . . . 206

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To the memory of Anselma Catillo, Francisco Saavedra, Juan Bautista Moreno and Tilsa Newell, whom touched my life and I will always remember.

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Abstract

"New f-Block and Mixed d,f-Block Molecular Nanomagnets" is a thesis submitted toThe University of Manchester for the degree of Doctor of Philosophy in the Faculty ofEngineering and Physical Sciences.

Molecular Nanomagnets have been proposed as plausible candidates in a varietyof futuristic applications. Thorough understanding of the magnetic properties of thesesystems is therefore necessary to develop devices that include such units.

The aim of this thesis is to synthesise and structurally and magnetically characterisea range of systems that could be used as elementary units in three proposed applicationssuch as: data storage devices, magnetic refrigerants and qubits for quantum computing.

A series of mixed 3d/4f metal complexes were synthesised through solvothermalreactions and characterised by X-ray single crystal diffraction and SQUID magnetom-etry. Through indirect methods it was possible to obtain high magnetic entropy changefor some systems. It was also possible to obtain some insight into the magnetic inter-actions within the systems through modelling the magnetic data.

The role of the 4f-4f and 3d-4f interactions in two sets of molecules is also de-scribed. The first study is in an asymmetric dysprosium dimer, where through a rangeof experimental techniques and advanced theoretical methods, such ab-initio calcula-tions we are able to explain the role of the intramolecular interactions and their effecton the SMM properties of this system. Similarly, insight into the role of the 3d-4finteractions is achieved through the observation of the magnetic behaviour of a familyof 27 tetranuclear systems, though SQUID data and ab-initio calculations.

Finally, Chemical functionalization of a well-proposed qubits, namely {Cr7Ni}and subsequent reaction with a redox active metal ion, CoII/III, two {Cr7Ni} systemsare linked. The magnitude of the exchange interaction between the {Cr7Ni}-CoII-{Cr7Ni} was determined through Electron Paramagnetic Resonance. Furthermore,by chemical oxidation/reduction of the cobalt between paramagnetic and diamagneticstates, i.e. CoII and CoIII respectively, we demonstrate that the interaction can beswitched ON/OFF. This characteristic makes of these systems candidates to functionas a√

SWAP gate.

Eufemio Moreno PinedaOctober 2014

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Declaration

No portion of the work referred to in this dissertation hasbeen submitted in support of an application for another de-gree or qualification of this or any other university or otherinstitute of learning.

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Copyright

i. The author of this thesis (including any appendices and/or schedules to this the-sis) owns certain copyright or related rights in it (the “Copyright”) and s/he hasgiven The University of Manchester certain rights to use such Copyright, includ-ing for administrative purposes.

ii. Copies of this thesis, either in full or in extracts and whether in hard or electroniccopy, may be made only in accordance with the Copyright, Designs and PatentsAct 1988 (as amended) and regulations issued under it or, where appropriate,in accordance with licensing agreements which the University has from time totime. This page must form part of any such copies made.

iii. The ownership of certain Copyright, patents, designs, trade marks and other in-tellectual property (the “Intellectual Property”) and any reproductions of copy-right works in the thesis, for example graphs and tables (“Reproductions”), whichmay be described in this thesis, may not be owned by the author and may beowned by third parties. Such Intellectual Property and Reproductions cannotand must not be made available for use without the prior written permission ofthe owner(s) of the relevant Intellectual Property and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication andcommercialisation of this thesis, the Copyright and any Intellectual Propertyand/or Reproductions described in it may take place is available in the Univer-sity IP Policy (see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any relevant Thesis restriction declarations deposited in the Uni-versity Library, The University’s policy on presentation of Theses and The Uni-versity Library’s regulations (see http://www.manchester.ac.uk/library/aboutus/regulations).

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Acknowledgements

First of all I would like to thank Almighty God, because without Him nothing wouldbe possible.

This research project would not have been possible without the support of manypeople. I would like to thank my supervisors Professors Eric J. L. McInnes and RichardE. P. Winpenny for their advice, guidance and support, whom were abundantly helpfuland offered invaluable assistance during my studies.

My deepest gratitude to Dr. Floriana Tuna for supervising and teaching me aboutSQUID and EPR measurements, for having always time to answer my many questionsand most importantly for being my friend and give me many advice during the MScand PhD studies.

I’d like to thank Prof David Collison for helpful discussion, ideas and guidance.Thanks to Dr. Grigore A. Timco for all his invaluable time explaining everything

about the synthesis of wheels.To Dr. Robin Pritchard, Dr. Chris Muryn, Dr. Iñigo Victorica-Irezabal and Dr.

George Whitehead for their time explaining and teaching me X-ray data collection andsolution.

Thanks to Dr. Antonio Fernandez Mato for teaching me organic synthesis andbeing patient with my many questions.

To Professor Jürgen Schnack for his help modelling the magnetic data for some ofthe huge cages herein described.

To Professor Joris van Slageren for his kind attention while I was in Stuttgart per-forming HF-EPR and MCD measurements. Similarly thanks to all the members ofhis group, especially Andreas Döring, Raphael Marx, Yvonne Rechkemmer and PetrNeugebauer for their help and kind attention.

Thanks to James for his help when I was stuck using LateX and solving issuesusing different programs.

To everybody in the magnets group Asad, Karzan, Joseph, Sam, Rob, Maria,James, Nick, Simon, Morten, Yan-Zhen Zheng, Antonio and Jesus for their supportand friendship all this time.

Thanks to all my brothers in Manchester, Asad, Khalid, Karzan, Antonio, Jesus,Mohammed, Jaffar, Hamzan, Joe and Bekir.

I thank the SENACYT-IFARHU scholarship program of the Government of Panamafor their financial support during my studies. The author would also like to conveythanks to the Faculty for laboratory facilities such as elemental microanalysis, X-ray

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facilities, mass spectrometry, etc.Finally and most importantly, the author wishes to express his love and gratitude to

his beloved family for their understanding and endless love through the duration of hisstudies. I would like to thank my wife, Concepcion Molina and all my family mem-bers, especially my mother, Maribel de Moreno and father, Eufemio Moreno Fuentes;my sisters, Maria del Carmen, Maria Elena y Gloria Elena and grandfather, AlejandroPineda, uncles, aunts and all members of all my family for supporting and encouragingme to pursue this degree. To my wife’s family, especially Mrs. Sofia and Mr. Molinafor their support and love.

Eufemio Moreno Pineda

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...when he imagined his education was completed, it had in fact not commenced; andthat, although he had been at the public school and a university, he in fact knew

nothing. To be conscious that you are ignorant is a great step to knowledge.

Benjamin Disraeli, Sybil or The Two Nations

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Chapter 1

Introduction

1.1 Rationale for submitting by alternative formatWell-defined publications of closely related work are suitable for the alternative formatthesis. The high impact nature of the results obtained for the author of this thesishas resulted in the publication in peer-reviewed journals. Slow publication of resultsobtained would significantly diminish the impact of the work, in a fast growing areasuch as molecular magnetism. Moreover, well-timed publication is critical in sciencefor several reasons. Firstly, the work is highly collaborative, with collaboration withtheorists and physicists, therefore getting the research into the public domain is highlyimportant. Secondly, the research is equipment demanding and access to expensiveand sought after national facilities (such as Diamond Light Source, Harwell Campus,Oxfordshire, UK and Advanced Light Source, Berkeley, California, USA) is dependenton quality research invariably demonstrated by publications in high impact journals. Ithas therefore been necessary and preferable to publish during the course of the author’sPhD studies. The published papers cover all aspects of the work undertaken and so aredeemed suitable for submission as part of this thesis. As the thesis author’s workis exemplified by publications and manuscripts and publications presented here, thealternative format is deemed appropriate.

1.2 Organisation of the thesisChapter Two is a general introduction to molecular nanomagnets (MNMs), with partic-ular emphasis on 3d, 4f and 3d/4f mixed metal MNMs. Chapter Three sets out a briefintroduction to the origin and theory of the magnetocaloric effect (MCE) and the ap-plication of MNMs in this expanding field. In Chapter Four three papers are described,where the goal is the synthesis, structural and magnetic characterisation of four fami-lies of cages, i.e. {Co4Ln10P8}, {Co6Ln4P6}, {Ni6Ln6P6} and {Fe6Ln6P6}. In thesepapers, we have investigated the MCE and the magnetic interactions of some of thecages. Chapter Five gives a brief introduction to single molecule magnets (SMMs),and the 4f/4f and 3d/4f interactions. In Chapter Six two manuscripts are explained,

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1.3. CONTRIBUTING AUTHORS

where the main goal is to explain and understand the role of the intramolecular mag-netic interactions in the performance of SMMs. The 4f-4f interaction study has beenundertaken using an asymmetric {Dy2} molecule. We have also investigated the roleof 3d-4f interactions in the SMM behaviour of an isostructural butterfly-like familyof tetramers. In Chapter Seven a concise explanation of quantum computing and theincreasingly growing interest of MNMs as qubits is explained. A manuscript describ-ing the synthesis and magnetic and spectroscopic characterisation of a possible quan-tum√

SWAP gate using the archetypal molecular nanomagnets {Cr7Ni} is describedin Chapter Eight. Chapter Nine contains some conclusions of the work undertaken.Chapter Ten contains the appendices, where a brief description of magnetochemistryand EPR are addressed. In the appendices papers which the author of the thesis hascontributed through crystallography, SQUID and EPR measurements, and the process-ing and simulation of the data obtained are included.

1.3 Contributing AuthorsChapter 4, Paper 1, "Molecular Amino-phosphonate Cobalt-lanthanide Clusters" isan original research communication written by Professors Richard E. P. Winpennyand Eric J. L. McInnes and the author of the thesis. The work covers a new familyof 3d/4f phosphonate cages. The author of the thesis with the helpful guidance ofDr. Andrew C. Regan conducted the synthesis of the organic ligand. The author ofthe thesis performed structural characterisation, X-ray crystallography, data collection,refinement and the generation of the crystallographic information files (.cifs), with thehelp and advice of Dr. Robin G. Pritchard and Professor Yan-Zhen Zheng. Dr. FlorianaTuna and the author of the thesis performed SQUID measurements and processing ofthe data.

Paper 2 in Chapter 4, "Wells-Dawson Cages as Molecular Refrigerants" is an orig-inal research full paper written by Professors Richard E. P. Winpenny and Eric J. L.McInnes and the author of the thesis, with helpful comments from Professor Yan-ZhenZheng. The work establishes a family of 3d/4f cages {Ni6Ln6P6}, where enhancementof the magnetic entropy was achieved through modification of the R group of the phos-phonates. The author of the thesis performed synthesis and X-ray crystallography. Theauthor of the thesis and Dr. Floriana Tuna jointly performed SQUID measurements andprocessing of the data.

Paper 3 in Chapter 4, "Iron Lanthanide Phosphonate Clusters: {Fe6Ln6P6} Wells-Dawson-like Structures with D3d" is an original research full paper written by the au-thor and his supervisors, Professors Richard E. P. Winpenny and Eric J. L. McInnes.The work establishes a family of 3d/4f cages {Fe6Gd6P6}, where despite having themaximum multiplicity of spin for the 3d metal ion, i.e. Fe(III) 6S5/2 and Gd(III) 8S7/2,strong antiferromagnetic interactions between the 3d-3d pair diminishes the ∆Sm. Theauthor of the thesis performed the synthesis. Dr. Simon J. Teat at Berkeley synchrotronfacility and the author of the thesis jointly collected crystallographic data. The authorof the thesis performed the refinement of the crystallographic data and .cif generation.

24 PhD. Eufemio Moreno Pineda 2014


The author of the thesis and Dr. Floriana Tuna jointly performed SQUID measure-ments and processing of the data. Professor Jürgen Schnack modelled the magneticdata for the cages.

Paper 1 in Chapter 6, "Direct measurement of DyIII · · ·DyIII interactions in a single-molecule magnet" is a full paper written by the author of the thesis, Nicholas F. Chilton,Professors Richard E. P. Winpenny and Eric J. L. McInnes with input from all co-authors. This piece of research explains the effect of the 4f-4f interaction in an asym-metric lanthanide dimer. The author of the thesis performed the synthesis, single crys-tal X-ray data collection and processing and SQUID measurements and processing ofthe data. Low frequency, i.e. S-, X-, K- and Q-band Electron Paramagnetic Resonancedata were undertaken by the author of the thesis and Daniel O. Sells. Petr Neuge-bauer, Shang-Da Jiang and Raphael Marx performed high frequency-high field EPRmeasurements in Stuttgart in Professor Joris van Slageren’s group. Raphael Marx andMaría Dörfel collected far infrared data also in Professor Joris van Slageren’s group.Ab-initio calculations and modelling of magnetic data was performed by Nicholas F.Chilton. The model to describe the EPR spectra of {Dy2} molecule was achievedthrough joint efforts of Professor Eric J. L. McInnes, Professor Richard E. P. Win-penny, Professor David Collison and Nicholas F. Chilton. The author of the thesis andNicholas F. Chilton performed EPR simulations with guidance from Professors DavidCollison, Eric J. L. McInnes and Richard E. P. Winpenny.

Paper 2 in Chapter 6, "Systematic study of a family of butterfly-like {M2Ln2} molec-ular magnets (M = MgII, MnIII, CoII, NiII and CuII; Ln = YIII,GdIII, TbIII, DyIII, HoIII

and ErIII)" is an research full paper written by the author of the thesis and Profes-sors Richard E. P. Winpenny and Eric J. L. McInnes. In this work a description ofthe 3d/4f interactions in a tetranuclear family of cages was obtained through DC andAC magnetic data and ab-initio calculations. The author of the thesis performed thesynthesis, single crystal X-ray data collection and processed the data. Dr. FlorianaTuna and the author of the thesis jointly performed SQUID measurements. Processingand modelling of magnetic data was performed by the author of the thesis. Ab-initiocalculations was performed by Nicholas F. Chilton.

Paper 1 in Chapter 8, "Switching Interactions in Two Spin Qubits Gates" is an orig-inal current research manuscript written by the author of the thesis, Professors RichardE. P. Winpenny and Eric J. L. McInnes. Two molecular systems are described and pro-posed as feasible qubits for a

√SWAP quantum gate. Dr. Antonio Fernandez and the

author of the thesis carried out the synthetic part of this work with the helpful adviceof Dr. Grigore A. Timco and Dr. Floriana Tuna. Dr. Iñigo J. Vitorica-Yrezabal and theauthor of the thesis carried out crystallographic data collection and processing of thedata. James Walsh and the author of the thesis collected the EPR data. Electrochemicalcharacterisation was carried out for the author of the thesis. Oxidation and reduction ofthe compound and the EPR data collection was obtained jointly between Dr. AntonioFernandez, James Walsh and the author of the thesis. The thesis’ author and ProfessorEric J. L. McInnes carried out simulation of the EPR data. Theoretical calculations forthe√

SWAP gate proposal were conducted by Professors Stefano Carretta and PaoloSantini.

PhD. Eufemio Moreno Pineda 2014 25



Chapter 2

Molecular Magnetism and MolecularNanomagnets

2.1 Magnetism: OriginThe phenomenon of magnetism has been known for millennia. The first account ofa material showing magnetic behaviour dates back to around 900 B.C. in the ancientGreek city of Magnesia in Asia Minor. The ancient Greeks were impressed with theproperties of lodestone (Fe2O3), material supposedly used to pull nails out of theirsandals; whilst the Chinese used the magnetic properties of lodestone to develop thecompass, used for navigation, despite not completely understanding the physical forcesdriving the behaviour of this material.

At that time many interpretations were given to this interesting phenomenon; how-ever, it was not untill the nineteenth and twentieth centuries when full account of thenature of this intriguing phenomenon was achieved. The relationship between electric-ity and magnetism commenced in 1819 with Hans Christian Oersted who first observedthe influence of electric currents in compass needles. This was further investigated byother researchers leading to the unification of Magnetism and Electricity in the so-called Maxwell’s equations in the 1860s. Since then magnetic materials have becomeindispensable in modern applications and devices. Common devices such as: medicalinstruments, magnetic separators, loudspeakers, microphones, switches, sensors, datastorage devices, motors, and generators are some examples of devices exploiting mag-netic materials. These materials are based on inorganic transition or lanthanide metaloxides.

A new era for magnetic materials arose at the end of the twentieth century withthe discovery that molecular organic materials can show magnetic ordering belowa critical temperature (Tc) also known as the Curie temperature. The first organic-based magnet comprised p-nitrophenyl nitronyl nitroxide radical (Figure 2.1a), ab-breviated p-NPNN, showing ferromagnetic ordering and spontaneous magnetisationbelow Tc = 0.65 K[1]. This behaviour was observed in just one (β ) of the four phases(αβγδ ). Studies performed on this system revealed that the magnetisation in this

27

2.2. MOLECULAR NANOMAGNETS

organic molecule was due to long range ordering of the magnetic moments in thesolid state (3D). Unfortunately, despite showing ferromagnetic ordering, nitroxide rad-icals show magnetic ordering at very low temperature, with the highest temperatureTc = 1.48 K observed in the compound diazaadamantane dinitroxide radical[2] (Figure2.1b). The reason behind such low Tc lies in the fact that its magnitude depends onthe strength of the interactions, therefore stronger interactions were needed in orderto overcome the low temperature regime observed in nitroxide radical organic materi-als. The quest for new organic materials showing stronger interactions consecutivelyled to a benzo-fused dithiazolyl radical (Figure 2.1c), with Tc = 35 K[3]. Moreover,application of hydrostatic pressure of 16 kbar leads to transition temperatures of 65K[3]. Nonetheless, despite this astonishing behaviour in organic molecules, quite lowtemperatures were yet needed to observe the ordered phases.

NSS

N

F

FF

F

CN

NN

H

HH

H

NO O

H3C CH3H3C CH3

OO

N

N

CH3

CH3

CH3H3C

O

O

(a) (b) (c)

Figure 2.1: (a) p-nitrophenyl nitronyl nitroxide radical; (b) diazaadamantane dinitroxide radi-cal; (c) benzo-fused dithiazolyl radical.

Despite showing ferromagnetic ordering, it was obvious that in order to achievethe room temperature magnetic ordering regime in molecular based systems, metalions with d and/or f electrons had to be introduced. This rationale soon led to abreakthrough discovery in molecule-based materials. In the 1990’s it was first discov-ered that slow relaxation of the magnetisation could also be observed at pure molec-ular level with no necessity of long range ordering. This astonishing behaviour wasfirst observed in the complex [Mn12O12(OAc)16(H2O)4][4,5] comprising eight Mn(III)and four Mn(IV) sandwiched between sixteen acetate organic ligands and four wa-ter molecules that magnetically isolate the [Mn12O12(OAc)16(H2O)4] complex fromneighbouring molecules thus minimizing intermolecular interactions.

2.2 Molecular NanomagnetsParamagnetic metal co-ordination complexes are molecular materials with at leastone paramagnetic metal ion connected to ligands. Depending on their structural di-mensionality, they can be classified in four different types: zero-dimensional (0-D)molecules[9], infinite 1-D chains[10], 2-D layers[11] and 3-D networks[12] (Figure 2.2).


2.2. MOLECULAR NANOMAGNETS

Figure 2.2: Left to right 0→3D compounds: a)[Fe14(bta)6O6(OMe)18Cl6], where bta is ben-zotriazolate; b) [CsLn(Ph2acac)4]n chain; c) [Mn(N3)2(pyz)] layer, where pyz is pyrazine; andd) [Sm(HCOO)3]n network. Colour code: M, blue; O, red; N, light blue; Ln, purple; W, grey;Mn, pale pink; C, light grey; no H atoms are shown for clarity.

MNMs are 0-D systems that exhibit super-paramagnet-like properties[13]; com-monly possessing high spin ground states. A difference between MNMs compared toconventional magnetic materials is that these systems are much smaller than metalnanoparticles and they can be easily organized into single crystals allowing accu-rate measurements[14]. Furthermore, they can be investigated in solution allowing themagnetic study of single entities without spurious effects arising from intermolecularinteractions[15].

MNMs have been extensively studied due to their interesting magnetic propertiesobserved when subjected to an external magnetic field and/or low temperatures[5].They also provide an enormous number of architectures obtained from combinationof different metal ions and organic ligands[16]. The wide variety of organic ligandsalong with the different metal ions and oxidation states have led to different struc-tural motifs with diverse physical properties such as: spin crossover compounds[17],molecules with toroidal moment[18], SMMs[19], etc. These materials have been exten-sively proposed in a wide range of applications, ranging from contrast agents in mag-netic resonance imaging[20], spintronics[21], high density memory in storage devicesusing single-molecule magnets (SMMs)[6], low temperature refrigerants[8] to qubitsfor logical gates in quantum computing (QC)[7,22]. Furthermore, these systems are amilestone for physicists and chemists for the understanding of physical phenomena


2.3. MOLECULAR MAGNETISM: ORIGIN

occurring at the pure molecular level[23].

2.3 Molecular Magnetism: OriginMagnetochemistry has been known for decades[24,25]; it is a part of chemistry wherephysical techniques are used to characterise paramagnetic species.

The field came about with the discovery molecular systems can retain magnetisa-tion at the pure molecular level at zero applied magnetic field[15]. The first observationof this, common in alloys and metal oxide magnets, was first observed in a manganesecomplex, [Mn12O12(OAc)16(H2O)4]·4H2O·2AcOH[4,5] in the 1990’s (Figure 2.3), set-ting a new scenario for organometallic complexes.

Figure 2.3: (a) Crystal structure of [Mn12O12(OAc)16(H2O)4] viewed down the tetragonal C4v(z), where light blue spheres represent MnIII and dark blue spheres represent MnIV; (b) Repre-sentation of relative orientations of MnIII (S = 2) and MnIV (S = 3

2 ) spins in the ground state.Colour code: O, red; C, grey. Hydrogens omitted for clarity .

The manganese cage, from here after {Mn12}, can be described as an internal tetra-hedron of MnIV and an external octagon of MnIII, with overall S4 symmetry bridgedby µ3 oxide ions and by carboxylate bridges from acetate anions.

The first account of a {Mn12} complex dates back to 1921 when Weinland andFischer proposed the synthesis of such a molecule[26], nonetheless due to the limita-tion of characterisation techniques at the time, no crystal structure was obtained. Inthe 1990’s the growing interest towards the understanding of biological systems com-prising paramagnetic sites, drew the attention of researchers towards the synthesis ofinorganic complexes that could mimic the interactions observed in their complex bio-logical analogues[27]. The quest to understand the Photosystem II led Christou’s groupto the synthesis of [Mn12O12(OAc)16(H2O)4][28]. The former complex fascinatingly


2.4. MOLECULAR MAGNETISM: SPIN CLUSTERS

has a metallic core analogue reported in the 1980’s with just standard variable tem-perature magnetic susceptibility measurements and no further characterisation. Laterit was observed that both {Mn12} clusters exhibit a spin-ground state S = 10[4,5,29,30],being astonishingly anisotropic systems. The anisotropic character led to an inusualobservation in paramagnetic molecules, the observation of hysteresis loops[5]. Thishighly anisotropic character imposed a barrier to the reorientation of the magnetisationbelow certain temperatures leading to the spin reversal of the magnetisation.

The spin ground state of {Mn12} can be explained by the MnIV ions preferringto align in a ferromagnetic fashion. Each MnIV has a magnetic spin (S) equal to 2,whereas each MnIII has a magnetic spin (S) equal to 3

2 . In the complex, each of thefour MnIII spins is aligned in opposite spin direction to the MnIV ions, resulting in atotal spin-ground state of S = 10 (Figure 2.3)[4,5,29,39].

A technique of paramount importance for the characterisation of {Mn12} is Elec-tron Paramagnetic Resonance (EPR)[28,31]. Through EPR it was found that {Mn12}has a large zero-field splitting (ZFS) of D = −0.5 cm–1 in its ground state. This re-moves the 2S + 1 degeneracy, even when the spins are not in an applied magneticfield. In the case of {Mn12} the lowest lying populated levels are ms = ±10 andms = ±9, at only ∼ 10 cm–1. The origin of the large zero-field splitting is associ-ated with Jahn-Teller distortion that affects the MnIII ions (d4) and the near co-parallelalignment of the eight Jahn-Teller axes. The large and negative ZFS leads to a largemagnetic anisotropy, reflected in {Mn12} as a blocking of the reversal of the magneti-sation; where the anisotropy represents how easy a net molecular spin polarizes in thepresence of a magnetic field. This means that if a molecule with high anisotropy issubjected to an applied magnetic field, which is then removed, in the absence of thefield the spin of the molecule remains oriented along the easy axis for a long periodof time below a certain temperature, making {Mn12} a good prospect for data storagedevice and a plausible building block for quantum computers[7].

In the light of studies made on {Mn12}, it can be concluded that big spin clus-ters are promising for SMMs. It is also known that high nuclearity spin-clusters canstabilise high-spin ground states. A disadvantage of this kind of SMMs is that theirapplication for data storage is only available under the temperature regime where thespins block their magnetisation; nevertheless clearly the {Mn12} molecule opened upa new field and many new possible applications for molecular magnets. In the quest ofsuch magnetic behaviour in molecule-based systems other magnetic behaviours havebeen observed. For example multinuclear clusters, homo- and mixed-metal, withoutSMMs characteristics have been proposed as magnetic cooling devices and quantumbits, among other applications (see Chapter 3, 5 and 7).

2.4 Molecular Magnetism: Spin clustersThe chemical stability to variation of carboxylate groups in the archetypal {Mn12} ledto the synthesis of numerous analogues of {Mn12}, most of them exhibiting blocking


2.4. MOLECULAR MAGNETISM: SPIN CLUSTERS

of the spin reversal of the magnetisation[32,33]. Similarly, other variations in the syn-thetic procedure led to various other manganese-based complexes. Basically, the maininterest in manganese-based MNMs was due to two main reasons: i) manganese ionscan possess a relatively high spin ground state (S); ii) due to Jahn-Teller distortions,manganese(III) usually possesses a high Zero Field Splitting (D), where frequentlythese two features jointly impart SMM properties to its compounds.

Besides the great deal of research towards manganese complexes[32,33], many otherimportant non-manganese-based MNMs have been obtained. For example, cages withinteresting magnetic properties such as: [Fe8(µ3-O)2(OH)12(tacn)6]Br8(H2O)9 (tacn= 1,4,7-triazayclononane)[34], [Fe4(µ-OMe)6(dpm)3] (dpm = dipivaloylmethane)[35],[Mn6(hfac)12(NITPh)6] (hfac = hexafluoroacetylacetonate; NITPh = imidazolyl-1-oxyl3-oxide radical)[36] and [NHn

2Pr2][Cr7M(µ-F)8(O2CtBu)16][37], have been thoroughlycharacterised (Figure 2.4).

Figure 2.4: Strutures of: (a) [Fe4(µ-OMe)6(dpm)3]; (b) [Mn6(hfac)12(NITPh)6]; (c)[NHn

2Pr2][Cr7M(µ-F)8(O2CtBu)16]; (d) [Fe8(µ3-O)2(OH)12(tacn)6]+4. Colour code: O, red;C, grey; F, light yellow; Cr, green; Fe, dark orange; Mn, blue; N, light blue. Hydrogens omit-ted for clarity.

A particularly appealing family of molecules is the antiferromagnetic rings, withmolecular formula [NHn

2Pr2][Cr7M(µ-F)8(O2CtBu)16][36] where the divalent metal,


2.5. MOLECULAR MAGNETISM: 4F-BASED MNMS

can be changed at will, i.e. M = MnII, FeII, CoII, NiII, CdII and ZnII (Figure 2.4c).This family of clusters stems from an octametallic CrIII parent [Cr8(µ-F)8(O2CtBu)16],firstly described in 1984, where it was the subject of catalytic studies[38]. Investiga-tion of the magnetic properties of [Cr8(µ-F)8(O2CtBu)16] resulted in antiferromag-netic coupling between neighbouring CrIII centres (S = 3

2 ), resulting in an S = 0 groundstate[39]. A rich family of molecules developed around this, containing homo- andhetero-metallic wheels and chains[40,41]. They are characterized by having a cyclicmotif and by containing CrIII ions which are bridged by fluorides and carboxylates.Their formation is controlled by the use of templating molecules, typically an ammo-nium cation.

The choice of heterometal ion in the {Cr7M} wheel can be used to tune the mag-netic and electronic properties of the wheel, whilst retaining isostructural geome-try. The carboxylate functionality provides delocalised π-electrons and hence a path-way for magnetic superexchange around the circle of metal ions. Particularly the[NHn

2Pr2][Cr7Ni(µ-F)8(O2CtBu)16] or {Cr7Ni} analogue gained a great deal of interestdue to its magnetic properties and chemical robustness. {Cr7Ni} is synthesised in highyield where the octahedral CrIII, being a relatively chemically inert ion, makes the ringextremely stable once formed. There is a great deal of scope for functionalisation, byvarying R of the templating amine or by changing the carboxylates for ones conveyingother functional groups[43]. For example, functionalisation of ammonium cations ledto inorganic rotaxanes[44], whilst introduction of carboxylates with functional groupslead to linked wheels[45].

There is antiferromagnetic coupling between adjacent CrIII centres, JCr-Cr ≈ +6cm-1 and JCr-Ni ≈ +0.6 cm-1 (in a +2J Hamiltonian, where JCr-Cr and JCr-Ni are theexchange interactions between Cr· · ·Cr and Cr· · ·Ni centres respectively), resulting ina non-zero net spin ground state determined through magnetic measurements[42]. Theexchange interaction between the CrIII, d3, s = 3

2 and the NiII, d8, s = 1 leads to anet S = 1

2 for the whole ring in the ground state[42]. At low temperature this doublydegenerate ground state is well separated from the S = 3

2 first excited state[46]. Appli-cation of a field induces Zeeman splitting of the ms = ±1

2 states leading to a pseudotwo-level system. It has been proposed that these levels could represent the states ofa quantum binary digit (qubit) within a future quantum information processing (QIP)system, its decoherence time along with the chemical stability toward functionalisationmake them ideal candidates. Winpenny’s group have demonstrated that with chemi-cal functionalisation of these units, entanglement between qubits can be attained[46,47];moreover it has also been possible to introduce functional groups for its depositiononto gold surfaces[48].

2.5 Molecular Magnetism: 4f -based MNMsA drawback observed in 3d-based SMMs is that in order to observe the blocking ofthe magnetisation, a cooperative behaviour between the metal ions and the single sitemagnetic anisotropy has to be additive, i.e. the ZFS of each metal ion must be as



collinear as possible otherwise they tend to cancel[15].A new alternative was presented in 2003 with the discovery of SMM behaviour in

single ion lanthanide systems[49]. Intensive investigation of their magnetic propertiesarose from the discovery that monometallic complexes of 4f-ions can also show slowrelaxation of magnetisation, without requiring cooperative anisotropic behaviour[50].The single ion anisotropic character observed in lanthanides is a result of the strongspin orbit interaction and crystal field observed in such systems[49,51].

The electronic configuration of rare-earth elements is [Xe]4fn5d16s2 where the dif-ference between the fourteen elements depends upon the electrons filling the 4f or-bitals. Due to the internal characteristics of 4f electrons, i.e. effective shielding by6s and 5d electrons, these are not strongly influenced by the environment involved instrong bonding and/or redox processes[52], yielding an extremely stable +3 oxidationstate with just a few of them showing well developed alternative oxidation states, e.g.divalent Eu(II), Sm(II) and Yb(II) and tetravalent Ce(IV), when 4f 0, 4f 7 and 4f 14 areattained. To a first approximation lanthanides in molecular materials behave as freeions and conversely to its 3d counterparts the spin-orbit coupling in rare earths is muchstronger. The electronic configuration of free lanthanide ions are characterised by theRussell-Saunders scheme as 2S+1LJ, with S and L the spin and orbital quantum numberand J varying from |L − S| ≤ J ≤ L + S. The result of the strong spin-orbit couplinggiven by Hund’s rules is the large separation between the ground state J multiplet andthe first excited states. When the single ion is in the presence of a ligand field envi-ronment the 2S+1LJ degenerate magnetic ground state splits into 2J + 1 components,with wavefunctions of linear combinations of |J,mJ〉 and mJ varying from −J to +J(see Scheme 2.1)[53].

4f n-1 5d1

4f n

2S+1L

2S+1LJ

Electronic configuration Interelectronic

repulsion(Spectroscopic terms) Spin-orbit

coupling(Spectroscopic levels)

Crystal Field(Stark Levels)

2·104 cm-1

104 cm-1

102 cm-1

Scheme 2.1: Schematic energy diagram showing the relative magnitude of the interelectronicrepulsion, the spin-orbit coupling, and ligand-field effects.



In contrast to 3d-based MNMs, where the spin orbit coupling is often quenchedrendering the determination of the magnetic properties of such systems to the spinonly value, the determination of magnetic properties of 4f-based systems is far fromtrivial. An example is given to clarify this point: the inter-electronic repulsion in aDy(III) ion splits the electronic configuration in spectroscopic terms. According toHund’s rules the state with the highest multiplicity (2S+1) lies lowest in energy.

Then the degeneracy of each term is lifted by the spin-orbit coupling i.e. 6H, 6F,etc., states split into 6H15/2, 6H13/2, 6F11/2, 6F9/2 etc. For a 4fn configuration where n <7 the value taken by the ground state is the lowest possible J, i.e. |L − S|, converselywhere n >7 the ground state is the lowest possible value of J, i.e. |L + S|. The spinorbit coupling in Dy(III) (4f9) would lead to a ground state 6H15/2, where S = 5

2 ; L =5 and J = 15

2 . The crystal field lifts the degeneracy of the state obtained from the firstperturbation i.e. the spin-orbit coupling, splitting the states involved. For Dy(III) thecrystal field breaks the degeneracy of the 16-fold degenerate ground state 6H15/2 intomJ =±15

2 ,±132 ,±11

2 ,±92 ,±7

2 ,±52 ,±3

2 and±12 (+mJ, mJ − 1, mJ − 2, . . .−mJ), being

the projections of the total angular momentum quantum number. At low temperaturessolely the ground state is considered due to the separation of this and the first excitedstate. This interaction of the spin orbit-coupled J state and the crystal field generatesthe anisotropic character imposing an energy barrier to the reorientation for the Dy(III)case and for lanthanide based systems (Scheme 2.2)[54].

Electronrepulsion

Crystalfield

Spin-orbit coupling

6F

6F15/2

6H

6F7/2

6H5/2

6F11/2

6H13/2

6H15/2

6H9/26H7/2

6F11/26F9/2

0

5

10

Ene

rgy

(cm

-1 x

103 )

±13/2

±15/2

±9/2

±5/2

±7/2 ±11/2

±3/2 ±1/2

mJ

Scheme 2.2: Low energy electronic structure of the Dy(III) ion with sequential perturbations ofelectron-electron repulsions, spin-orbit coupling, and the crystal field. The crystal field splittingis constructed from a model for the complex, Dy[(Me3Si)2N]3. Energy is measured relative tothe ground crystal field (mJ) state. Further complications due to mixing between states havebeen neglected in favour of clarity.



2.5.1 4f -based SystemsWhile in 3d-based molecular nanomagnets the anisotropic character is a cooperativebehaviour between the easy axis magnetic anisotropy (D) and the total spin-groundstate (S) yielding an energy barrier to the reversal of the magnetisation, the SMMbehaviour observed in single-ion lanthanide containing systems is given by the ligandfield (LF) in which the lanthanide resides[51]. In 2003 Ishikawa et al. reported for thefirst time the observation of single molecule magnet behaviour in complexes with asingle metal ion entity comprising Tb(III) or Dy(III)[49]. The molecule comprised alanthanide sandwiched between two phthalocyanines, giving a series of double-deckercomplexes of formula [LnIIIPc2]·TBA+ (being Pc = phthalocyanine dianion; TBA+ =N(C4H9)+). Four N donors atoms of the phthalocyaninate ligand bind the central metal,which are staggered above and below (Figure 2.5).

Figure 2.5: (a) Structure of [LnPc2]– (Ln = TbIII, DyIII, HoIII, ErIII, TmIII and YbIII); (b) Viewalong the tetragonal axis of the molecular structure of the complex. Colour code: C, grey; Ln,purple, N, blue. Hydrogens omitted for clarity.

The energy barrier for the terbium analogue turns out be one of the highest yetobserved[49,55-57]. Alternating-current (AC) magnetic susceptibility measurements per-formed on the pure system showed a frequency dependence of the magnetic behaviour,characteristic of SMMs. A frequency dependence out-of-phase susceptibility (χ ′′) wasobserved for the Tb(III) analogue without applied dc field (Hdc) at about 40 K (1 kHz),whilst a more diminished behaviour was obtained for the Dy(III) complex. To ensurethat the magnetic behaviour observed was intrinsic to the molecular species, AC mea-surements were carried out on magnetically diluted systems revealing χ ′′ and in-phasesusceptibility (χ ′) curves shifted toward higher temperatures[49]. This shifting clearlydemonstrates that the SMM behaviour is intrinsic to the molecule and that shifting to-wards higher temperatures is due to the removal of intermolecular interactions[49]. De-termination of the low-lying electronic structure through magnetic susceptibility and1H-NMR for the [TbIIIPc2]·TBA+ complex reveals a highly axial ground state with mJ


2.6. LANTHANIDE CAGES

= ±6, the maximum possible for Tb, whereas for [DyIIIPc2]·TBA+ the mJ = ±132 , the

second largest in the mJ = ±152 ground state manifold. For [TbIIIPc2]·TBA+, Tb(III)

with a 7F6 ground term, these studies revealed a large separation between the groundstate (mJ =±6) and the first excited state (mJ =±5) of 576 cm-1; whereas a smaller sep-aration was obtained for [DyIIIPc2]·TBA+, indicating that a large separation betweenthe ground and excited state is a key requirement for a high Ueff. Small separationpromotes relaxation pathways for the relaxation of the magnetisation through ∆mJ =±1 steps for thermal process.

2.6 Lanthanide CagesAstonishing behaviour has been observed in several polymetallic dysprosium contain-ing systems, such as spin chirality observed in a [Dy3(µ3-OH)2L3Cl(H2O)5]Cl3

[18]

(where L = ortho-vanillin) molecule, and high Ueff observed in [Dy5O(OiPr)13][55] and[Dy4K2O(O2

tBu)12][56] systems, whilst introduction of radical bridging ligands has ledto the observation of magnetic hysteresis at 14 K[52,58,59], the highest yet observed. Themagnetic behaviour of three of these compounds is briefly described below.

2.6.1 Toroidal moment in {Dy3}The crystal structure of {Dy3} consists of a triangle of dysprosium centres capped bytwo µ 3-hydroxo centres (Figure 2.6). The deprotonated o-vanillins bridge two Dy(III)metals and cap them with three O donors, with Cl or H2O groups also connecting toeach Dy(III), giving a coordination number of eight. The overall point symmetry ofthe molecules is close to C3h.

The static magnetic behaviour of {Dy3} shows a room temperature χ MT valueclose to the expected for three non-interacting Dy(III) ions whilst the low tempera-ture value goes practically to zero[18,60]. The magnetisation versus field, MB(H), con-firms the presence of a diamagnetic ground state. MB(H) starts slowly increasing withhigher magnetic field confirming antiferromagnetic interactions operating within thecluster[18,60]. Above H = 0.95 T the MB(H) increases up to 15.3 µ B in good agreementfor three non interacting Dy(III). Similar results were obtained through micro-SQUIDtechnique[18,60].

The intriguing non-magnetic ground state behaviour observed for these moleculesresults from the canting of the magnetic anisotropy axis of the Dy(III) ions, lying inthe plane at an angle of 120◦ from one another (See Figure 2.6b), leading to a vortexspin-chiral ground state[18,60]. The dynamic behaviour likewise shows an interestingprofile demonstrating that despite having a diamagnetic ground state {Dy3} behaves asan SMM. The dynamic behaviour of this intriguing molecule was investigated throughAC-SQUID measurements. Frequency dependent behaviour was observed below 20K, where substantial energy barriers of 36 K (in zero-applied field) and 120 K (3 kG)correspond to the reorientation of spins pointing in opposite directions in the plane.



Figure 2.6: (a) Molecular structure of [Dy3(µ3-OH)2L3Cl(H2O)5]Cl3 triangle (Hydrogenatoms, the chloride counter ion and solvent molecules omitted for clarity); (b) Scheme of thespin structure of the {Dy3} complex and of the local easy axes orientation in respect of thelaboratory XYZ reference frame. Colour code: C, grey; O, red; Ln, purple, N, blue. Hydrogensomitted for clarity.

These compounds led to the long-held idea that information can be maintained in anon-magnetic ground state.

2.6.2 [Dy5O(OiPr)13] and [Dy4K2O(O2tBu)12]

An interesting behaviour was also observed in two related alkoxide Dy(III) cages. Thefirst one, [Dy5O(OiPr)13][55,56] has a square-based pyramid of Dy(III) bridged by iso-propoxide groups and a µ5−oxide in the centre of the pyramid, whilst the secondcage is a [Dy4K2O(O2

tBu)12][56] oxo-centred octahedron with a cis arrangement ofpotassium ions (Figure 2.7). A strong frequency dependent behaviour features for bothcomplexes, giving energy barriers of Ueff = 528 and 692 cm-1 for {Dy5} and {Dy4K2}respectively [56].

Surprisingly, the high-energy barriers observed in these systems can be further im-proved by magnetic dilution into their diamagnetic analogues, i.e. {Y5} and {Y4K2}[56].Magnetic dilution of {Dy5} into {Y5} and {Dy4K2} into {Y4K2} shows an insignif-icant role is played by intermolecular interactions between {Dy5} and neighbouringparamagnetic molecules. Astonishingly, dilution of 5 % of Dy(III) into the synthe-sis of {Y5} and {Y4K2} showed an improved Ueff for both systems, leading to 804and 842 cm-1 respectively[56]. The cause of such improvement has been attributedto transverse magnetic fields from intramolecular neighbours, which induces quantumtunnelling (QT)[56,61].

The occurrence of the QT has been related to the crystal field environment aroundthe lanthanide ion. For pure axial systems, (i.e. pure ±mJ), the QT is forbidden,



Figure 2.7: (a) Crystal structure of: [Dy5O(OiPr)13] and (b) [Dy4K2O(O2tBu)12]. Colour code:

C, grey; O, red; Ln, purple; K, dark grey. Hydrogens omitted for clarity.

leading to the desired SMM performance. Nevertheless, although QT is forbidden inpurely axial Kramers ions, it has been frequently seen that neighbouring paramagneticions can induce QT due to the transverse magnetic fields. QT can be prevented in AC-susceptibility experiments by the application of a magnetic field changing the relativeenergies of previously resonant states by the Zeeman effect, i.e. the relaxation of themagnetisation of an SMM from one magnetic (+Si or −Si) state to that of opposite spin(−Si or +Si) can be faster than predicted from the barrier height because of tunnellingthrough the energy barrier[62].

2.6.3 3d/4f ComplexesThe studies of the magnetic influence of a 3d metal on the magnetic behaviour of a4f ion at molecular level were conducted by Gatteschi and colleagues in the 1980’s,on Gd(III) and Cu(II) pairs[63-65] (See figure 2.8). The magnetic interaction was sur-prisingly ferromagnetic, contrary to the antiferromagnetic behaviour expected from theoverlap of at least one electron with the semi-occupied orbital of Cu(II) as observed forCu(II) and Mn(II) ions[66]. Many other Cu-Ln mixed-metal systems have since beeninvestigated, showing ferromagnetic interactions for most of them[67-69]. At first mostof the effort was dedicated to transition metal systems and the isotropic lanthanide,Gd(III) 8S7/2.

The reason behind the burgeoning interest of researchers in such materials lies inthree principal aspects: i) 3d metal ions can propagate strong exchange interactions[70]

(often rather weak in lanthanides due to the inner nature of 4f orbitals); ii) 3d-4f areprompted to exhibit ferromagnetic interactions, which can lead to high spin groundstate (important for SMMs[15] and magnetocaloric[8,71,72] application; and iii) the strongspin orbit coupling intrinsic to lanthanide systems can give improved SMM character-istics (when Ln = Tb(III), Dy(III), Ho(III) and Er(III)), while when Gd(III) is the ion



h]

Figure 2.8: Structures of CuGd molecules: (a) [CuSALtn)2Gd(H2O)(NO3)]; (b)[Dy(hfac)3CuSatnOH]2; (c) [CuHAPen)2Gd(H2O)3](ClO4)3. Colour code: C, grey; Gd, pur-ple, N, blue; Cu, aqua; F, yellow; O, red. Hydrogens omitted for clarity.

then higher magnetic entropy[8,70,72] can be achieved (see Chapter 3).

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Chapter 3

Magnetocaloric Effect

3.1 First stepsIn 1881 the German physicist, Emil Gabriel Warburg, described for the first timethe so-called magnetocaloric effect (MCE). In his work entitled, "Magnetische Unter-suchungen", Warburg described the behaviour of iron, which releases and/or absorbsthermal energy under the application/and removal of an applied magnetic field [1]. Thisclearly implies that under adiabatic conditions the application and removal of the mag-netic field can cause heating or cooling of the magnetic materials[1-5]. However, itwas not until the late 1900’s when further investigations into this effect and magneticcooling applications were made.

Langevin in 1905 conducted the first demonstration of the effect, when he firstdetermined the reversible temperature change in the magnetisation of a paramagneticmaterial[6]. Later, independently Debye and Giauque explained the effect and proposedthe use of the reversible field change to achieve temperatures lower than liquid heliumusing adiabatic demagnetisation[7,8]. This revolutionary idea latter resulted in Giauqueand MacDougall obtaining the Nobel Prize in physics in 1949 for their studies of matterat temperatures close to absolute zero. On the basis of this effect it was proposedto create magnetic refrigerators where instead of gas, working body in conventionalcooling systems, the working body would be replaced by magnetic materials. Thescientific community was immediately engaged with such proposals due to its energy-saving and cheaper-cost potential, efficiency and reliability. Moreover, cryocoolerscould potentially be used in ultra low temperature applications, where the expensive3He is currently used and becoming scarce, such as: ultra-low radiation detectors forouter space research and SQUID magnetometers among others[9-12].

3.2 Adiabatic DemagnetisationIn 1933, Giauque and MacDougall conducted the first experiments on the adiabaticdemagnetisation[13]. In their first experiment Giauque and MacDougall used a para-magnetic lanthanide salt, gadolinium sulphate Gd2(SO4)2·8H2O to reach the minimal

45

3.3. MCE: ORIGIN

temperature of 0.25 K from the initial temperature of 1.5 K after the application andadiabatic removal of a magnetic field of 8 kG[13] therein demonstrating the feasibil-ity of this process to achieve sub-Kelvin temperatures. The temperature below 1 Kin these experiments was determined indirectly through magnetic susceptibility mea-surements and the Curie law extrapolation[5,13] . These experiments set up a new erafor magnetocooling applications, leading to a great number of researchers investigatingdifferent materials such as garnets, oxides, superparamagnetic materials and ultimatelymolecular nanomagnets[5].

3.3 MCE: OriginThe basic understanding of the magnetocaloric effect lies in the thermodynamic rela-tionships that relate the magnetic entropy change (∆Sm), the magnetisation of a system(M

β) and the temperature (T). The origin of the MCE is the interaction between the

magnetic sublattice to the applied magnetic field (H), which changes the magneticcontribution to the entropy of the solid[2,3].

The magnitude of the entropy (ST) of a ferromagnet occurs due to a distribution ofthe total entropy associated to the contribution of the lattice (Slat), electronic (Sel) andmagnetic (Sm) (eq. 3.1).

ST(T,H)= Slat(T,H)

+Sel(T,H)+Sm(T,H)

(3.1)

Application of a magnetic field to a system composed of spins will align its mag-netic moments, lowering the magnetic entropy, formerly disordered due to thermalagitation. If a spin system undergoes a similar situation under adiabatic conditions(adiabatic application of magnetic field), then due to the lack of heat exchange, thedecrease in magnetic entropy (Sm), will cause an increase of the other entropies associ-ated to the systems, i.e. Slat , Sel. To preserve the total entropy of the system (ST ), dueto the absence of contact with the surroundings, the system therefore should increaseits lattice entropy (Slat), which implies the system should heat up (see Figure 3.1a).

Similar behaviour is observed if the opposite is the case i.e. adiabatic removal ofthe applied magnetic field (See Figure 3.1b and c). When the applied magnetic field isswitched on isothermally, the temperature of the system (T) remains constant and thetotal entropy decreases due to the decrease of the magnetic entropy Sm (eq 3.2).

∆Sm = S(T0,H0)−S(T0,H1) (3.2)

Under adiabatic removal of the magnetic field, the magnetic entropy increases, butdue to the lack of heat exchange with the surroundings, the increase of the magneticentropy (Sm) causes the entropy of the lattice to decrease (Slat), resulting in a change inthe temperature of the material. This is known as adiabatic temperature change (∆Tad).

The mathematical relationship between the magnetic field H, the magnetisation ofa material and the temperature and the magnetocaloric effect-related values, ∆Tad(T,∆H) and ∆Sm(T, ∆H) is specified by the Maxwell relations:


3.4. ENHANCING MCE USING MNMS

Sm = ln (2S+1)

TfTi

Hi

Hf

Si

Sf

ΔSm

A B

C0

Disorder

Disorder

Order

Order

S2 S1

T2T1

Isothermal process ΔS ≠ 0 (S2 > S1)

Adiabatic process ΔT ≠ 0 (T2 > T1)

H = 0

H ≠ 0 H = 0

H ≠ 0(c)(a)

(b)

max

Figure 3.1: Schematic showing two basic processes of the MCE when a magnetic field is ap-plied or removed in a magnetic system: (a) the isothermal process leading to an entropy change,and (b) the adiabatic process, which yields a variation in temperature; (c) Molar magnetisationof super-paramagnet with spin S, as a function of temperature and magnetic field. Isothermalprocess A→B renders higher −∆Sm, whilst adiabatic process A→C yields ∆Tad, leading todecrease of the temperature.

(∂S(T,H)

∂H

)=

(∂M(T,H)

∂T

)H

(3.3)

Which for an isothermal and isobaric process led to:

∆Sm(T,∆H) =∫ H2

H1

(∂M∂T

)H

dH (3.4)

Equation (3.4) indicates that the magnetic entropy change is proportional to boththe derivative of magnetisation with respect to temperature at constant field and to thefield variation.

3.4 Enhancing MCE using MNMsThe enhancement of the MCE was observed in nanosize particles and crystalline su-perparamagnetic materials. Studies performed on monodisperse and non-interactingmagnetic cages diluted in a nonmagnetic matrix performed by McMichael[14,15] andShull[16,17] showed a significant enhancement of the magnetic entropy change whencompared with conventional materials.

In this respect MNMs have been envisioned as working materials to reach sub-Kelvin temperatures, due to being magnetically isolated and their big spin groundstate, which can in principle offer better properties than those found in superparam-agnetic materials[18]. Intensive research of the application of MNMs, the MCE and theadiabatic demagnetisation processes have led to the proposal of key requirements forthe synthesis of plausible candidates for such applications[3].



In order to obtain a significant change in the magnetic entropy and therefore a sig-nificant change in temperature, the system must contain a large magnetic moment[3].This is due to the fact that the magnetic entropy, which is related to the temperaturechange, has a direct relationship between the magnetic degrees of freedom of a systembetween T = 0 and T = ∞. Therefore a high ground state would render a big magneticentropy change ( ∆Sm) and temperature change ( ∆Tad). Additionally, low-lying ex-cited states and weak ferromagnetic interactions are also desirable because they willcontribute to the magnetic entropy through Sm = nRln(2S+1) where n is the number ofparamagnetic entities in the system.

Several alternatives have been proposed to achieve these requirements. In the fol-lowing sections these requirements will be briefly described.

3.4.1 Ligand Effects and Solvothermal SynthesisThe existence of large spin ground state and low-lying excited states is important fora significant MCE as previously described. One chemical strategy to achieve this re-quirement is to bring many paramagnetic metals together in a single entity through theuse of multidentate ligands.

Several authors have described many polydentate ligands, as key features towardsobtaining polymetallic cages[19-22]. For example, one important ligand family used insynthetic routes to obtain complexes has been organophosphates or phosphonates[20].This family of ligands offers a wide variety of coordination modes (Scheme 3.1); more-over, further modulation of structure can be achieved with modification of the alkyl oraryl R group bound to the phosphorus atom.

P

R

O OO

M

MM

M

MM

M MM

P

R

O OO

M

MM

M

MM M

P

R

O OO

M

M

M

MM M

P

R

O OO

M M

MM

MM

P

R

O OO

MM

MM M

P

R

O OO

MM

MM

9.333 7.322 6.222

4.2115.2215.222

Scheme 3.1: Coordination availability of phosphonate ligands (Harris notation).

Unfortunately, phosphonates tend to form polymeric materials that are often highlyinsoluble, limiting the synthesis of single molecular systems. This issue has beenaddressed by the introduction of co-ligands and/or the introduction of bulky R groupsthat prevent polymerisation.

Secondly, reactions under extreme synthetic conditions, such as solvothermal syn-thesis, have proved efficient to achieve bigger cages[23]. The solubility of ligands,metal sources and co-ligands, and the temperature and pressure limit can be enhanced



through the use of non-conventional techniques. In solvothermal synthesis the reac-tion is carried out using heat in a sealed vessel, where the temperature achieved canexceed 250◦ C and high pressures using conventional organic solvents. Moreover, in-soluble starting materials and more polar solvents can be employed because the hightemperatures and pressures improve their miscibility at these extreme temperatures andthe enhanced diffusion of the molecules involved in the reaction favours polymetallicmolecules formation[23].

3.4.2 Ferromagnetic InteractionsThe introduction of small ferromagnetic interactions is desired for good MCE prospect[2,24]. Ferromagnetic interactions introduce a fast response of the spins to the appliedmagnetic field. This response in turns manifest itself as a quick magnetisation of thecompound at lower fields, which is an important requirement for efficient and low-costmagnetic cooling devices.

3d/4f mixed metal systems have gained remarkable attention due to their tendencyto promote ferromagnetic interactions[25,27] (Chapter 2 Section 2.7). Many polymetal-lic 3d/4f cages have been obtained showing remarkable magnetic entropy change,showing the feasibility of such approaches.

Another important requirement for an efficient adiabatic demagnetisation processis a negligible anisotropy of the molecule. In order to achieve the maximum entropychange after the adiabatic removal of the applied magnetic field, the system must beable to achieve its maximum state of entropy (randomness), which is diminished ifanisotropy is present in the system. The effect of the anisotropy is to align the magneticvectors in certain directions of the magnetic field; therefore good MNMs must containisotropic 3d or 4f metal ions. For lanthanide based MNMs a good choice is Gd(III)8S7/2, due to its high spin ground state and its negligible anisotropy. Figure 3.2 containssome examples of high nuclearity 3d/Gd cages[28-30].

Figure 3.2: 3d/4f metal complexes with high magnetic entropy change (−∆Sm): (a){Gd42Co10}[28] (−∆Sm = 41.3 J kg-1 K-1); (b) {Mn4Gd6}[29] (−∆Sm = 33.7 J kg-1 K-1); (c){Gd36Ni12}[30] (−∆Sm = 36.3 J kg-1 K-1); Colour code: Gd, purple; M (transition metal), blue;N, cyan; P, green; O, red; C grey. Hydrogens omitted for clarity.


3.5. RECENT TRENDS

3.5 Recent TrendsWhile synthetically the previously mentioned approaches offer a wide variety of 0-Dcages, from the physical point of view and the desired properties for magnetic coolants,other approaches have been employed. Recently a widely used approach is related tomaximising the effect of the molecular weight. Due to the mass dependence of themagnetic entropy, 1D to 3D systems with high numbers of unpaired electrons andlow molecular mass have been studied, leading to remarkably high magnetic entropychanges. For example, magnetic entropy changes of 56 J kg-1 K-1, 47.7 J kg-1 K-1 and66.4 J kg-1 K-1 have been observed in [Gd(CO2H)3]n

[31], [Gd(OAc)3(H2O)0.5]n[32] and

[Gd(OH)CO3]n[33] respectively for a field change (∆H = 0 − 7 T).

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[5] A. M. Tichin and Y. I. Spichkin, The Magnetocaloric Effect and its Applications,Institute of Physics Publishing, Bristol and Philadelphia, 2003.

[6] P. Langevin, Ann. Chem. Phys., 1905, 4, 70.

[7] P. Debye, Ann. Physik, 1926, 81, 1154.

[8] W. F. Giauque, J. Am. Chem. Soc., 1927, 49, 1864.

[9] T. Feder, Phys. Today, 2009, 62, 21.

[10] J. A. Barclay and W. A. Steyert, Cryogenics, 1982, 22, 73.

[11] B. Daudin, A. A. Lacaze and B. Salce, Cryogenics, 1982, 22, 439.

[12] B. Daudin, R. Lagnier and B. Salce, J. Magn. Magn. Mater., 1982, 27, 315.

[13] W. F. Giauque and D. P. MacDougall, Phys. Rev., 1933, 43, 768.

[14] R. D. McMichael, J. J. Ritter and R. D. Shull, J. Appl. Phys., 1993, 73, 6946.

[15] R. D. Shull, R. D. McMichael and J. J. Ritter, Nanostructured Mater., 1993, 2,205.

[16] R. D. Shull, AIP Conf. Proc., 1993, 273, 628.

[17] R. D. Shull, IEEE Trans. Magn., 1993, 29, 2614.


3.5. RECENT TRENDS

[18] F. Torres, J. M. Hernandez, X. Bohigas and J. Tejada, Appl. Phys. Lett., 2000,77, 3248.

[19] S. Accorsi, A. Barra, A. Caneschi, G. Chastanet, A. Cornia, A. C. Fabretti, D.Gatteschi, C. Mortalo, E. Olivieri, F. Parenti, P. Rosa, R. Sessoli, L. Sorace, W.Wernsdorfer, and L. Zobbi, J. Am. Chem. Soc., 2006, 126, 4742.

[20] T. C. Stamatatos, C. G. Efthymiou, C. C. Stoumpos and S. P. Perlepes, Eur. J.Inorg. Chem., 2009, 23, 3361.

[21] M. Manoli, R. D. L. Johnstone, S. Parsons, M. Murrie, M. Affronte, M. Evange-listi, and E. K. Brechin, Angew. Chem. Int. Ed., 2007, 46, 4456.

[22] S. Khanra, M. Helliwell, F. Tuna, E. J. L. McInnes and R. E. P. Winpenny, DaltonTrans., 2009, 31, 6166.

[23] R. H. Laye and E. J. L. McInnes, Eur. J. Inorg. Chem., 2004, 14, 2811.

[24] D. Gatteschi, R. Sessoli and J. Villain, Molecular nanomagnets, Oxford Univer-sity Press, Oxford, 2006.


[26] C. Bencini, C. Benelli, A. Caneschi, A. Dei and D. Gatteschi, Inorg. Chem.,1986, 25, 572.


[28] J.-B. Peng, Q.-C. Zhang, X.-J. Kong, Y.-Z. Zheng, Y.-P. Ren, L.-S. Long, R.-B.Huang, L.-S. Zheng, Z. Zheng, J. Am. Chem. Soc., 2012, 134, 3314.

[29] Y.-Z. Zheng, E. Moreno-Pineda, M. Helliwell, R. E. P. Winpenny, Chem. Eur.J., 2012, 18, 4161.

[30] J.-B. Peng, Q.-C. Zhang, X.-J. Kong, Y.-P. Ren, L.-S. Long, R.-B. Huang, L.-S.Zheng, Z. Zheng, Angew. Chem., Int. Ed., 2011, 50, 10649.

[31] G. Lorusso, J. W. Sharples, E. Palacios, O. Roubeau, E. K. Brechin, R. Ses-soli, A. Rossin, F. Tuna, E. J. L. McInnes, D. Collison and M. Evangelisti, Adv.Mater., 2013, 25, 4653

[32] F.-S. Guo, J.-D. Leng, J.-L. Liu, Z.-S. Meng and M.-L. Tong, Inorg. Chem.,2012, 51, 405.

[33] Y.-C. Chen, L. Qin, Z.-S. Meng, D.-F. Yang, C. W. Z. Fu, Y.-Z. Zheng, J.-L. Liu,R. Tarasenko, M. Orendác, J. Prokleška, V. Sechovskc and M.-L. Tong, J. Mater.Chem. A, 2014, 2, 9851.


3.5. RECENT TRENDS


Chapter 4

MNMs as Coolers

4.1 Magnetism of Molecular CoolersThe aim of this chapter is to explore new MNMs and their magnetic properties. Insuch a quest we have explored four families of polymetallic cages where the phospho-nates ligands have played a key role in the synthetic strategy. In order to try to obtainferromagnetic interactions we have employed a 3d/4f mixed metal system approach.Through solvothermal synthesis we show that high nuclearity cages can be obtained,an important feature to maximise magnetic entropy change. All molecules were struc-turally characterised through single crystal X-ray diffraction and the magnetic char-acterisation was achieved through SQUID measurements. We developed models todescribe the magnetic properties for some cages in order get insight into the role of theexchange interaction and its effect on the entropy change.

4.1.1 Molecular amino−phosphonate cobalt−lanthanide clustersChem. Commun. 2013, 49, 3522−3524.

4.1.2 Wells−Dawson Cages as Molecular RefrigerantsInorg. Chem. 2013, 52, 13702−13707.

4.1.3 Iron Lanthanide Phosphonate Clusters: {Fe6Ln6P6} Wells-Dawson-like Structures with D3d Symmetry

Inorg. Chem. 2013, 53, 3032−3038.

53

4.1. MAGNETISM OF MOLECULAR COOLERS


3522 Chem. Commun., 2013, 49, 3522--3524 This journal is c The Royal Society of Chemistry 2013

Cite this: Chem. Commun.,2013,49, 3522

Molecular amino-phosphonate cobalt–lanthanideclusters†

Eufemio Moreno Pineda, Floriana Tuna, Robin G. Pritchard, Andrew C. Regan,Richard E. P. Winpenny* and Eric J. L. McInnes*

The use of 1-amino-1-cyclohexyl phosphonic acid, a functionalised

phosphonate, leads to the synthesis of two new structural types

for 3d–4f phosphonate cages with unusual structural cores and

which show high magnetocaloric effects.

Phosphonates of general formula RPO32� are now well estab-

lished as binding groups for molecular d-block transition metalclusters through use of large R groups or co-ligands that inhibitformation of polymeric materials.1 Such compounds are beingintensively studied for their magnetic properties. However, withsome exceptions,2 the range of R groups used has tended to belimited to aliphatic or aromatic organic groups. Here we report theuse of phosphonates where R contains an additional bindinggroup, and the synthesis of two families of 3d–4f molecular clustersusing an amino-functionalised phosphonate, which exploits thedifferences in donor atom preferences of the 3d and 4f ions. Thereis very little literature on phosphonate-bound molecular 3d–4fclusters,3 although recent results have shown that 3d–4f clustersin general can display impressive magnetocaloric effects.3,4 Thereare a few examples of the use of imine- and amino-phosphonates in3d and metalloid clusters2a,b and coordination polymers,2c,d and a3d–4f 2D materials using R = CH2N(CH2CO2)2.2e,f 1-Amino-1-cyclo-hexylphosphonic acid, (1-NH2-1-C6H10)PO3H2, was prepared bya modification of a literature method5 (Scheme 1; see ESI† forsynthetic details).

Reaction of (1-NH2-1-C6H10)PO3H2 with [Co2(m-OH2)(O2CtBu)4-(HO2CtBu)4]6 and [Ln2(O2CtBu)6(HO2CtBu)6],7 (Ln = Gd or Dy)with Et3N as base, in MeCN at 150 1C under solvothermalconditions, followed by slow cooling to room temperature givespink crystals of [Co4Ln10(O2CtBu)12(O3PC6H10NH2)8(PO4)2(O2CMe)2-(O3PC6H10NH3)2] (Ln = Gd, 1; Dy, 2) in 10% yield (Fig. 1).

Equivalent reactions with other LnIII ions failed to give crystal-line products. Compounds 1 and 2 both crystallise in the triclinicspace group P%1 and have the same molecular structures (Fig. 1).‡The {Dy10P12} core of 2 can be described as based on two centered12-vertex polyhedra sharing a face (Fig. 2). The two atoms at thecentre of each polyhedron (P11 and P12) are from m6-bridgingphosphates (a 6.222 binding mode in Harris notation),8 with thecentres in the shared face being P5, P6, Dy5 and Dy6. The 12-vertexpolyhedra are distorted, but can be derived from an icosahedron,with the distortion increasing dramatically towards the sharedface, i.e. in an icosahedron there should be triangular faces, not adiamond face as in P5-Dy5-P6-Dy6. One icosahedron consists ofDy1 to Dy6 and P1 to P6; if P5 and P6 moved towards the centre ofthe polyhedron (Fig. 2a) the distortion would be much less,however as these sites are shared between the icosahedra thenthis might be the reason for the distortion. We have previouslynoted the tendency of phosphorus centres to act as additional

Scheme 1 Synthesis of 1-amino-1-cyclohexylphosphonic acid.

Fig. 1 Crystal structure of the {Co4Dy10P12} cluster. Scheme: Dy, purple; Co, blue;P, green; O, orange; C, grey; N, cyan; (H omitted for clarity).

School of Chemistry and Photon Science Institute, The University of Manchester,

Oxford Road, Manchester, M13 9PL, UK. E-mail: [email protected];

Fax: +44 (0)161-275-4606

† Electronic supplementary information (ESI) available: Synthetic method,crystallographic details, crystallographic figures, magnetic information. Experi-mental details, magnetism and Diamond figures. CCDC 922115 (2), 922116 (1),922117 (3). For ESI and crystallographic data in CIF or other electronic format seeDOI: 10.1039/c3cc40907d

Received 2nd February 2013,Accepted 8th March 2013

DOI: 10.1039/c3cc40907d

www.rsc.org/chemcomm

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vertices of larger polyhedra in phosphonate clusters, including{M9P3} icosahedra (M = FeIII, VIII).9 The {Ln10P12} core structures of1 and 2 are then an extension of this. Bi-icosahedral structures areknown, including an {Au13Ag12} cluster reported by Teo, whichfeatures a single shared vertex.10

The four CoII ions cap the {Ln10P12} core, sitting above triangularfaces P2-P4-Dy4, P1-P3-Dy3, P8-P10-Dy9 and P7-P9-Dy7 in 2. This isa direct consequence of the second functional group in theaminophosphonates. Eight of the aminophosphonates (P1–4 andP7–10) each bind three DyIII ions, with each O-arm binding a singleDy, with the amino-group binding to a cobalt (giving a 4.2111coordination mode; Fig. 2b).8 Hence, each Co is N,O-chelated bytwo aminophosphonates, with a final coordination site being takenby a carboxylate giving a distorted cis-N2O3 geometry at Co. All Dyions are exclusively O-bound, with either capped octahedral ordodecahedral geometry. Hence, the preferential binding of theamino-phosphonate O- and N-donors for LnIII and CoII, respec-tively, forces the Co centres to the periphery of the molecule. Theremaining two aminophosphonates (P5, 6), which form part of theshared face of the {Ln10P12} core, only bind to three Dy centres(3.1111 mode; Fig. 2b), with the amino group uncoordinated.

Neither the acetates nor the phosphates in the structure of 1 and 2were present in the reaction starting materials; hence presumablythey result from hydrolysis of acetonitrile and phosphonate under thesolvothermal reaction conditions. We attempted to improve the yieldsof 1 and 2 by introducing Na3PO4 as a phosphate source. However,under otherwise identical reaction conditions, we instead obtained[Na2Co6Ln4(m3-OH)2(O2CtBu)12(O3PC6H10NH2)6(MeCN)2] (Fig. 3; Ln =Gd, 3; Dy, 5) in low yields. The syntheses can be modified to giveimproved yields of 15–20%. This reaction also works for Ln = Tb (4).Curiously, these products do not contain phosphate, but do incorpo-rate Na ions and a much less regular structure results.

Compounds 3–5 crystallize in the space group P21/n.‡ Theseinversion-symmetric {Ln4Co6P6Na2} clusters contain proportio-nately much more cobalt than 1–2, and with three differentgeometric environments (tetrahedral, distorted 5-coordinate,and octahedral). Three different amino-phosphonate bindingmodes are found. There is also a higher proportion of carboxylatein the products.

Two CoII ions (Co2 and symmetry equivalent, s.e.) with octa-hedral {O5N} geometry sit at the centre of the cluster, bridged bytwo m3-hydroxides which further bridge to a LnIII ion (Gd1 and s.e.).Three amino-phosphonates bridge this butterfly-like core, oneither side, to a further two cobalts, a lanthanide and a sodiumion. Co2 is N,O-chelated by one amino-phosphonate (P2), as above.Co1 and s.e. have a distorted {N2O3} coordination sphere, com-prising one N,O-chelating amino-phosphonate (P1) and oneN-bound (P3). The remaining cobalt sites (Co3 and s.e.) havetetrahedral {O4} geometry from two phosphonates and twocarboxylates. The amino-phosphonates adopt three differentbinding modes (Fig. 3b): that containing P1 is 5.2221 bound(Gd2Co2Na; including an N,O-chelated Co1); that containing P2is 4.2111 bound (Gd2Co2; N,O-chelating Co2); that containing P3 is5.2211 bound (Gd2Co3). In each case the amino group is terminallybound to Co. As in 1 and 2, all the Ln ions are exclusively O-bound.

The magnetic behaviour of 1 to 5 was studied on polycrystallinesamples using a SQUID magnetometer (Fig. 4 and Fig. S3–S5, ESI†).The room temperature values of wT (w = molar magnetic suscepti-bility) for 1 is 91 emu K mol�1, decreasing slowly with decreasingtemperature down to about 10 K, before decreasing more rapidly. Forthe dysprosium analogue 2, wT is 154 emu K mol�1 and decreasesmore steadily with decreasing temperature. This more rapid decreasereflects the nature of the orbitally degenerate DyIII ions in 2 cf.the spin-only GdIII ions of 1. Compounds 3, 4 and 5 have room

Fig. 2 (a) 12-Vertex polyhedral sharing a face {Dy10P12} core; (b) phosphonatecoordination modes in {Co4Dy10P10} (colours as Fig. 1).

Fig. 3 (a) Crystal structure of {Co6Gd4P6} cluster (pivalate groups were omitted forsimplicity); (b) phosphonate coordination modes in {Co6Gd4P6} (colour as Fig. 1).

Fig. 4 Magnetization as a function of applied field at 2 K for 1–5.

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3524 Chem. Commun., 2013, 49, 3522--3524 This journal is c The Royal Society of Chemistry 2013

temperature wT values of 52, 65 and 81 emu K mol�1, respectivelywhich are close to the values calculated for non-interacting ions52 emu mol�1 K (for six CoII, g = 2.70,3f,11 S = 3/2 and four GdIII, g =2.00, S = 7/2), 68 emu mol�1 K (for six CoII, g = 2.70, S = 3/2 and fourTbIII, gJ = 3/2, J = 6) and 77 emu mol�1 K (for six CoII, g = 2.70, S = 3/2and four DyIII, gJ = 4/3, J = 15/2). For all three complexes there is aminimum in wT at a few K; this may be a signature of weak intra-molecular magnetic interactions. Given the typically weak nature ofinteractions between phosphonate-bridged metal ions, and alsothat it is observed in all three compounds, this may be due to thecentral {Co2O2} unit. The molar magnetisations (M) as a functionapplied magnetic field (H) of 1–5 at 2 K rise to values of 64, 58, 41,32 and 35 Nb, respectively, at 7 T without achieving saturation(Fig. 4). We have not attempted any quantitative analysis given thecomplexity of both the molecular structures and the orbitallydegenerate nature of most of the metal ions.

Given the recent interest in 3d–4f clusters as potentialmagnetic refrigerants, particularly those with the isotropic andhigh spin GdIII ion, we have investigated the magnetocaloricproperties of the Gd-containing compounds 1 and 3. The magneticentropy changes of 1 and 3 for changing applied field werecalculated indirectly from the magnetization behaviour as a func-tion of applied field and temperatures (Fig. 4, Fig. S4 and S5, ESI†)using the standard relationship DS ¼

R½@MðT ;MÞ=@T �HdH.

This gives magnetic entropy changes for 1 and 3 of 32.6 and19.7 J kg�1 K�1 for DH = 0–7 T at 2 K.

The magnetic entropy value observed for 1 is among the highestobserved to date for a 3d–4f mixed metal clusters,3,4 surpassed onlyby {Co10Gd42} 41.3 J kg�1 K�1, {Ni10Gd42} 38.2 J kg�1 K�1,{Ni12Gd36} 36.3 J kg�1 K�1, {Mo4Gd12} 35.3 J kg�1 K�1 and{Mn4Gd6P6} 33.7 J kg�1 K�1. 1 has the second highest magneticentropy change for 3d–4f phosphonate compounds, justexceeded by {Mn4Gd6P6}. Gd-cage complexes with higherentropy values have been reported.12

In conclusion, functionalization of phosphonate ligands is avery promising route to 3d–4f clusters, with the potential to exploitthe differing coordination preferences of d-block and f-block ions.

This work was supported by the EPSRC (UK), the University ofManchester and the Panamanian government agency SENACYT-IFARHU. REPW thanks the Royal Society for a Wolfson Merit Award.

Notes and references‡ Crystal data for 1 [C124H214Co4Gd10N10O66P12�3(C2H3N)]: Mr =5226.25, triclinic, space group P%1, T = 100.15 K, a = 18.2190(2), b =22.4563(3), c = 27.5752(4) Å, a = 70.1022(12), b = 84.5267(11),g = 79.3776(12)1, V = 10420.1(2) Å3, Z = 2, r = 1.666 g cm�3, total data84 001, independent reflections 42 000 (Rint = 0.083), m = 3.61 mm�1,1975 parameters, R1 = 0.095 for I Z 2s(I) and wR2 = 0.218. Crystal datafor 2 [C124H228Co4Dy10N10O66P12�C4N2H6]: Mr = 5229.68, triclinic, spacegroup P%1, T = 100.15 K, a = 17.0917(3), b = 20.9589(3), c = 30.4298(4) Å,a = 108.0775(13), b = 101.8103(13), g = 92.1947(12)1, V = 10082.3(3) Å3,Z = 2, r = 1.725 g cm�3, total data 79 235, independent reflections 40 171(Rint = 0.062), m = 4.14 mm�1, 1877 parameters, R1 = 0.087 for I Z 2s(I) andwR2 = 0.194. Crystal data for 3 [C100H186Co6Gd4N8Na2O44P6�2(C2H3N)]:Mr = 3501.06, triclinic, space group P21/n, T = 100.15 K, a = 15.8683(5),b = 27.0973(8), c = 19.4683(6) Å, b = 112.274(3)1, V = 7746.5(4) Å3, Z = 2,r = 1.501 g cm�3, total data 42 633, independent reflections 15 760(Rint = 0.060), m = 2.45 mm�1, 771 parameters, R1 = 0.055 for I Z 2s(I) andwR2 = 0.139. Crystal data for 4 (unit cell) [C100H186Co6Tb4N8Na2O44P6]:monoclinic, space group P21/n, T = 100.15 K, a = 15.8615(4),

b = 27.2388(6), c = 19.440(5) Å, b = 111.837(3)1, V = 7797.9(3) Å3. Crystaldata for 5 (unit cell) [C100H186Co6Dy4N8Na2O44P6]: monoclinic, spacegroup P21/n, T = 100.15 K, a = 15.810(3), b = 27.065(6), c = 19.386(4) Å,b = 111.888(5), V = 7697.12 Å3.

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Supporting Information

Molecular Amino-Phosphonate Cobalt-Lanthanide Clusters

Eufemio Moreno Pineda, Floriana Tuna, Robin Pritchard, Andrew Regan, Richard E. P. Winpenny* and Eric J. L. McInnes* School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK. Fax: 44 -161-275-4606; E-mail: [email protected] Experimental Details Synthesis of starting materials

Unless stated otherwise, all reagents and solvents were purchased from Aldrich Chemicals and used without further purification. [Co2(µ-OH2)(O2CtBu)4(HO2CtBu)4]6 6 was prepared according to established methods. [Ln2(O2CtBu)6(HO2CtBu)6]7 (Ln = Gd, 7; Tb, 8, Dy, 9) were synthesized by refluxing Ln2O3 (3.62 g, 10 mmol) and excess pivalic acid (30 g, 300 mmol) at 160 ºC for 5 hrs to form a clear solution. Followed by cooling the solution to room temperature and white precipitate came out. 50 ml toluene was added to dissolve the access pivalic acid and filtered in vacuum and 50 ml n-hexane were used to wash the product (yield ca. 13 g, 87 %). Synthesis of (1-amino-1-cyclohexyl)phosphonic acid5

Diethyl 1-aminocyclohexylphosphonate: a solution of cyclohexanone (9.1

mL, 0.088 mol), diethyl phosphite (11.2 mL, 0.087 mol) and 52 mL of NH3/EtOH (2M, 0.1 mol) was heated in an ampule to 100 ºC for 7 hours. Excess NH3 and EtOH were removed under reduced pressure. The resultant oil was a mixture of diethyl 1-aminocyclohexylphosphonate and diethyl phosphite. The oily product (22 g) was dissolved in acetone (38 mL) and a solution of oxalic acid (5.4 g, 60 mmol) in acetone (13.7 mL) was added. The mixture was refrigerated overnight and the precipitated product was separated by filtration and washed with cold acetone (3 x 25 mL). The dry product was treated with a saturated solution of NaHCO3 and extracted with DCM until the extracted DCM became colourless. The solution was concentrated under reduced pressure to afford pure diethyl 1-aminocyclohexylphosphonate (13.13 g, 84 %).

1-aminocyclohexylphosphonate acid: diethyl 1-aminocyclohexylphosphonate (3 g, 13 mmol) and HCl 6M (45 mL) were heated in an ampule for 3 hours at 120 ºC. then the solution was evaporated until the odour of HCl

Electronic Supplementary Material (ESI) for Chemical CommunicationsThis journal is © The Royal Society of Chemistry 2013



disappeared. The product was then dissolved in H2O and precipitated with MeCN to give 1-aminocyclohexylphosphonic acid (2.0 g, 88 %). The product contains one molecule of water of crystallization. Elemental analysis, calcd (%) for C6H14NPO3 � H2O: C36.55, H 8.18, N 7.10, P 15.71; Found: C 36.53, H 7.92, N 7.05, P 15.57. Synthesis of compound 1 to 2

1 was obtained by mixing 6 (0.036 g, 0.04 mmol), 7 (0.165 g, 0.1 mmol), Et3N (0.1 ml, 1 mmol) and H2O3PC6H10NH2 (0.036 g, 0.2 mmol) in MeCN (8 ml) were stirred at room temperature for a few minutes. The resulting slurry was transferred into a 10 mL Teflon-lined autoclave, which was heated at 150 oC for 12 hrs. and then cooled to room temperature at a rate of 0.05 oC min-1. Pink block-shape crystals were collected (yield 10 mg, 10 %, based on 7). EA for Co4Gd10P12N10O66C124H236, found (calc); C 28.96 (29.18), H 4.67 (4.66), Co 4.34 (4.62), Gd 29.65 (30.81), N 2.65 (2.74) and P 7.21 (7.28). 2 was obtained by mixing 6 (0.036 g, 0.04 mmol), 9 (0.165 g, 0.1 mmol), Et3N (0.1 ml, 1 mmol) and H2O3PC6H10NH2 (0.036 g, 0.2 mmol) in MeCN (8 ml) were stirred at room temperature for a few minutes. The resulting slurry was transferred into a 10 mL Teflon-lined autoclave, which was heated at 150 oC for 12 hrs. and then cooled to room temperature at a rate of 0.05 oC min-1. Pink block-shape crystals were collected (yield 10 mg, 10 %, based on 9). EA for Co4Dy10P12N10O66C124H236, found (calc); C 28.47 (28.89), H 4.53 (H 4.61), Co 4.48 (4.57), Dy 31.23 (31.52), N 2.65 (2.72) and P 7.18 (7.21). Synthesis of compound 3 to 5

3 to 5 were synthesized from similar reaction, replacing the lanthanide source. 6 (0.095 g, 0.1 mmol), 7, 8 or 9 (0.075 mmol), Et3N (0.1 ml, 0.7 mmol), Na3PO3 (0.05g, 0.3 mmol) and H2O3PC6H10NH2 (0.018 g, 0.1 mmol) in MeCN (8 ml) were stirred at room temperature for a few minutes. The resulting slurry was transferred into a 10 mL Teflon-lined autoclave, which was heated at 150 oC for 12 hrs. and then cooled to room temperature at a rate of 0.05 oC min-1. Block-shape purple crystals were collected. EA for 3 (yield 20 mg, 18.50 % based on 7) Co6Gd4Na2O46N6P6C96H186, found (calc for 3 with loss of 2 MeCN and gain of 2 H2O); C 32.52 (34.16), H 5.12 (5.55), Co 10.44 (10.48), Gd 17.90 (18.64), P 5.63 (5.51), N 3.12 (2.49) and Na 1.37 (1.36). EA for 4 (yield 18 mg, 16.6 % based on 8) Co6Tb4Na2O46N6P6C96H186, found (calc for 4 with loss of 2 MeCN and gain of 2 H2O); C 32.72 (34.09), H 5.35 (5.54), Co 10.85 (10.46), Tb 18.31 (18.79), P 5.21 (5.49), N 3.20 (2.5) and Na 1.23 (1.35). EA for 5 (yield 16 mg, 14.6% based on 9) Co6Dy4Na2O44N8P6C100H188, found (calc); C 35.23 (34.89), H 5.28 (5.50), Co 10.98 (10.27), Dy 18.46 (18.88), P 5.71 (5.39), N 2.98 (3.25) and Na 1.41 (1.33). Crystallography

The data of 1 to 5 were collected on a Bruker SMART CCD diffractometer with MoKα radiation (λ = 0.71073 Å). The data of 5 were collected on a oxford SMART CCD diffractometer with MoKα radiation (λ = 0.71073 Å). The structures were solved by direct methods and refined on F2 using SHELXTL. CCDC 922115-922117 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/conts/retrieving.html (or from the




Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB21EZ, UK; fax: (+44)1223-336-033; or [email protected]).

Crystal data for 1 [C124H214Co4Gd10N10O66P12·3(C2H3N)]: Mr = 5226.25, triclinic, space group P-1, T = 100.15 K, a = 18.2190 (2), b = 22.4563 (3), c = 27.5752 (4) Å, α = 70.1022 (12), β = 84.55267 (11), γ = 79.3776 (12)º, V = 10420.1 (2) Å3, Z = 2, ρ = 1.666 g cm-3, total data 84001, independent reflections 42000 (Rint = 0.083), µ = 3.61 mm-1, 1975 parameters, R1 = 0.095 for I ≥ 2σ(I) and wR2 = 0.218. CCDC 922116

Crystal data for 2 [C124H228Co4Dy10N10O66P12·C4N2H6]: Mr = 5229.68, triclinic, space group P-1, T = 100.15 K, a = 17.0917 (3), b = 20.9589 (3), c = 30.4298 (4) Å, α = 108.0775 (13), β = 101.8103 (13), γ = 92.1947 (12)º, V = 10082.3 (3) Å3, Z = 2, ρ = 1.725 g cm-3, total data 79235, independent reflections 40171 (Rint = 0.062), µ = 4.14 mm-1, 1877 parameters, R1 = 0.087 for I ≥ 2σ(I) and wR2 = 0.194. CCDC 922115

Crystal data for 3 [C100H186Co6Gd4N8Na2O44P6·2(C2H3N)]: Mr = 3501.06, triclinic, space group P21/n, T = 100.15 K, a = 15.8683 (5), b = 27.0973 (8), c = 19.4683 (6) Å, β = 112.274 (13)º, V = 7746.5 (4) Å3, Z = 2, ρ = 1.501 g cm-3, total data 42633, independent reflections 15760 (Rint = 0.060), µ = 2.45 mm-1, 771 parameters, R1 = 0.055 for I ≥ 2σ(I) and wR2 = 0.139. CCDC 922117

Crystal data for 4 (unite cell) [Co6Tb4P6N9O43C100H188]: monoclinic, space group P21/n, T = 100.15 K, a = 15.8615(4), b = 27.2388(6), c = 19.440(5) Å, γ = 111.837(3)º, V = 7797.9(3) Å3.

Crystal data for 5 (unite cell) [Co6Dy4P6N10O44C104H192]: monoclinic, space

group P21/n, T = 100.15 K, a = 15.810(3), b = 27.065(6), c = 19.386(4) Å, β = 111.888(5), V = 7697.12 Å3.

Figure S1. Polyhedral representation of Co4Dy10P12. Scheme: Dy, purple; Co, blue; P, green; O, orange; C, grey; N, cyan.




Figure S2. a) Full structure and polyhedral representation of Co6Gd4P6 cluster; b) Polyhedral representation of Co6Gd4P6. Scheme: Gd, purple; Co, blue; P, green; O, orange; C, grey; N, cyan; (H omitted for clarity).




Magnetic measurements

The magnetic properties of polycrystalline samples of 1-5 were performed with a Quantum Design MPMS-XL7 SQUID. The samples were ground, placed in a gel capsule and fixed with a small amount of eicosanoid acid to avoid movement during the measurement. The data were corrected for diamagnetism from the gel capsule, diamagnetic contribution from the eicosanoid acid and diamagnetic contribution calculated from Pascal constants.

Figure S3. a) Molar magnetic susceptibility (χT) vs. T plot for 1-5 under 1 kG DC field.




Figure S4. a) M/Nµβ magnetization of 1 at different temperatures; b) Magnetic Entropy change of 1.




Figure S5. a) M/Nµβ magnetization of 3 at different temperatures; b) Magnetic Entropy change of 3.




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Wells−Dawson Cages as Molecular RefrigerantsEufemio Moreno Pineda, Floriana Tuna, Yan-Zhen Zheng,† Richard E. P. Winpenny,*and Eric J. L. McInnes*

School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.

*S Supporting Information

ABSTRACT: Five clusters with the general formula [Ni6Gd6(μ3-OH)2(μ2-OA-c)2(O3PR)6(O2C

tBu)16], where R = methyl (1), phenyl (2), n-hexyl (3), benzyl (4), n-octyl(5), have been prepared. All of the clusters have a {Ni6Gd6P6} core that can be related to theWells−Dawson ion. We have also prepared analogues where the gadolinium is replaced withdiamagnetic yttrium: [Ni6Y6(μ3-OH)2(μ2-OAc)2(O3PR)6(O2C

tBu)16] (R = methyl (6), n-hexyl (7), benzyl (8), n-octyl (9)), allowing the magnetic exchange within the {Ni3} units to beanalyzed by modeling as the sum of two noninteracting isosceles triangles. The variation in themagnetic entropy changes for magnetization (−ΔSM) among compounds 1−5 could beattributed not only to the molecular weight of the compounds but also to intramolecularmagnetic interactions.

■ INTRODUCTION

Paramagnetic cage complexes, sometimes called molecularnanomagnets (MNMs), have been extensively studied due totheir interesting physics and the possibility of exploiting theirmagnetic behavior in technological applications.1 The mostexplored family of MNMs are the single-molecule magnets(SMMs), where the molecules show slow relaxation ofmagnetization. Other applications that have been proposedfor MNMs include quantum information processing, spin-tronics, and magnetic refrigerants. Magnetic refrigerants arebased on the magnetocaloric effect (MCE), where an adiabaticdemagnetization process leads to cooling. MNMs can be usedto achieve very low (sub-Kelvin) temperatures.2 Goodcandidate molecules have negligible magnetic anisotropy buta high-spin ground state or at least a highly degenerate set oflow-lying states that can saturate in applied field. Ferromagneticinteractions between the metal centers can be favorable, sincethis gives rise to faster magnetization in low applied fields. Thefrequent observation of ferromagnetic interactions in 3d−4fmixed-metal cages has led to recent studies of such compoundsfor this application, often involving the isotropic GdIII ion (S =7/2) to obtain high magnetic entropy changes (−ΔSM) on(de)magnetization.3

We, and others, have recently reported the use ofphosphonates (R-PO3

2−) to make 3d−4f cage complexes.4

The tendency of metal phosphonates to form insolublepolymeric materials can be controlled by the addition ofcoligands or by the use of bulky R groups. Our first study withnickel lanthanides produced a {Ni6Ln6P6} rugby-ball-shapedmolecule4c that showed weak ferromagnetic coupling within the{Ni3} moiety with consequent high MCE. One importantcharacteristic of molecules for MCE is the molecular weight,because ultimate exploitation depends on the mass (or density)

of the material. Herein we report systematic variations of the{Ni6Ln6P6} cage by changing the phosphonate. We find thatthe metal core is robust and insensitive to modification of the Rgroup, but there are subtle changes in the MCE parametersbeyond those predicted simply from mass changes. Diamag-netic lanthanide analogues are prepared to quantify changes inthe magnetic interactions within the cages across the series.

■ EXPERIMENTAL SECTIONMaterials and Physical Measurements. All reagents and

solvents were purchased from Aldrich Chemicals and used withoutfurther purification. [Ni2(μ2-OH2)(O2C

tBu)4(HO2CtBu)4] and

[Ln2(O2CtBu)6(HO2C

tBu)6] (Ln = Gd, Y) were prepared by reportedmethods.5,6 Analytical data and yields are given in Table 1.

Synthesis. Cages 1−9 were synthesized under similar conditions.[Ni2(μ2-OH2)(O2C

tBu)4(HO2CtBu)4] (0.1 g, 0.1 mmol),

[Gd2(O2CtBu)6(HO2C

tBu)6] (0.075 mmol), RPO3H2 (R = methyl,phenyl, n-hexyl, benzyl, n-octyl) (0.1 mmol), and triethylamine (Et3N)(0.1 mL, 1 mmol) in acetonitrile (MeCN) (8 mL) were stirred atroom temperature for 5 min. The resulting slurry was transferred intoa 10 mL Teflon-lined autoclave, which was heated to 150 °C for 12 hand then cooled to room temperature at a rate of 0.05 °C min−1.Yellow X-ray-quality crystals were obtained for methyl (1), phenyl (2),n-hexyl (3), benzyl (4), and n-octyl (5) phosphonic acids directly fromthe autoclave. Similar conditions of reactions but replacing the[Gd2(O2C

tBu)6(HO2CtBu)6] source with [Y2(O2C

tBu)6(HO2CtBu)6]

yielded analogous clusters for methyl (6), n-hexyl (7), benzyl (8) andn-octyl (9) phosphonic acid. Attempts to synthesize the Y analogue ofcomplex 2 {Ni6Gd6P6} (R = phenyl) were unsuccessful.

Crystallography. Single-crystal X-ray diffraction measurements for1−4 were carried out on a Bruker SMART CCD diffractometer withMo Kα radiation (λ = 0.71073 Å) at 100 K. The data collection of 5−7

Received: September 10, 2013Published: November 12, 2013

Article

pubs.acs.org/IC

© 2013 American Chemical Society 13702 dx.doi.org/10.1021/ic402296t | Inorg. Chem. 2013, 52, 13702−13707



Table 1. Elemental Analysis and Yield (%) for Compounds 1−9

elemental analysis: found (calcd)

compd formula yielda C H N Ni Ln P

1 [Ni6Gd6(μ3-OH)2(OAc)2(O3PMe)6(O2CtBu)16] 35 30.12 (29.76) 4.60 (4.77) 0 (0) 9.54 (9.69) 26.06 (25.98) 5.18 (5.12)

2 [Ni6Gd6(μ3-OH)2(OAc)2(O3PPh)6(O2CtBu)16]·

2MeCN20 36.04 (36.45) 4.82 (4.69) 0.87 (0.68) 8.34 (8.62) 23.29 (23.1) 4.69 (4.55)

3 [Ni6Gd6(μ3-OH)2(OAc)2(O3PHex)6(O2C

tBu)16]·2MeCN46 35.76 (36.02) 5.86 (5.80) 0.74 (0.68) 8.69 (8.52) 23.11 (22.82) 4.75 (4.50)

4 [Ni6Gd6(μ3-OH)2(OAc)2(O3PCH2Ph)6(O2C

tBu)16]·2MeCN

77b 37.90 (37.85) 4.88 (4.93) 1.25 (1.32) 8.21 (8.28) 22.14 (22.19) 4.46 (4.37)

5 [Ni6Gd6(μ3-OH)2(OAc)2(O3POct)6(O2C

tBu)16]·2MeCN53 38.17 (37.96) 5.89 (6.14) 0.56 (0.65) 7.98 (8.18) 21.83 (21.92) 4.37 (4.32)

6 [Ni6Y6(μ3-OH)2(OAc)2(O3PMe)6(O2CtBu)16]·

2MeCN28 34.00 (34.17) 5.49 (5.43) 0.81 (0.85) 10.51 (10.66) 15.98 (16.14) 5.39 (5.62)

7 [Ni6Y6(μ3-OH)2(OAc)2(O3PHex)6(O2CtBu)16]·

2MeCN49 39.60 (39.99) 6.52 (6.44) 0.73 (0.75) 9.25 (9.45) 13.78 (14.32) 4.99 (4.98)

8 [Ni6Y6(μ3-OH)2(OAc)2(O3PCH2Ph)6(O2C

tBu)16]·4MeCN

70b 41.63 (41.89) 5.51 (5.46) 1.33 (1.46) 9.12 (9.16) 13.79 (13.88) 4.81 (4.84)

9 [Ni6Y6(μ3-OH)2(OAc)2(O3POct)6(O2CtBu)16]·

2MeCN54 42.20 (41.97) 6.52 (6.78) 0.63 (0.72) 9.15 (9.04) 13.83 (13.70) 4.93 (4.77)

aCalculated on the basis of the lanthanide pivalate starting material. bCalculated on the basis of the lanthanide phosphonate starting material.

Table 2. Crystallographic Information for Clusters 1−9

1 2 3 4 5

chem formula C90H170Gd6Ni6P6O56·2CH3CN

C120H182Gd6Ni6P6O56·2CH3CN

C120H230Gd6Ni6P6O56 C126H184Gd6Ni6P6O56 ·4CH3CN

C132H256Gd6Ni6P6O56·4CH3CN

fw 3711.94 4084.33 4050.61 4252.62 4383.13cryst syst triclinic monoclinic triclinic monoclinic triclinicspace group P1 P21/n P1 P21/n P1a/Å 15.4495(5) 18.3716(8) 16.5791(4) 18.8556(14) 16.4562(4)b/Å 16.0319(5) 20.4859(8) 20.5132(4) 16.0904(12) 17.6336(4)c/Å 16.3513(6) 21.8809(9) 25.5694(5) 28.384(2) 18.5683(4)α/deg 104.512(3) 90.00 84.2046(17) 90.00 79.888(2)β/deg 101.152(3) 94.926(4) 89.3037(18) 94.9300(10) 70.274(2)γ/deg 100.934(3) 90.00 89.3726(18) 90.00 68.785(2)V/Å3 3723.9(2) 8204.6(6) 8650.4(3) 8579.68 4719.5(2)Z 1 2 2 2 1ρcalcd/g cm−3 1.655 1.653 1.555 1.646 1.542T/K 104(2) 100.15 100.15 100.00 100.15μ(Mo Kα)/mm−1

3.511 3.195 3.029 3.060 2.783

R1(I > 2σ(I))a 0.0509 0.0916 0.0841 0.0464 0.0574wR2a 0.1028 0.1854 0.1822 0.1121 0.1298

6 7 8 9

chem formula C94H176N2Ni6O56P6Y6·2CH3CN C120H228Ni6O56P6Y6 C134H208N4Ni6O56P6Y6·4CH3CN C132H248Ni6O56P6Y6

fw 3301.90 3640.57 3842.48 3806.86cryst syst triclinic triclinic monoclinic triclinicspace group P1 P1 P21/n P1a/Å 15.5870(7) 16.6447(4) 18.8806(9) 16.2833(9)b/Å 16.0533(7) 20.5345(4) 16.0529(7) 17.5109(15)c/Å 16.3662(7) 25.1562(6) 28.2345(13) 18.3682(9)α/deg 104.895(4) 84.0060(18) 90.00 81.023(6)β/deg 101.521(4) 88.9737(18) 94.8310(10) 70.241(5)γ/deg 100.704(4) 89.5098(16) 90.00 69.087(7)V/Å3 3754.4(3) 8549.6(3) 8527.1(7) 4600.6(6)Z 1 2 2 1ρcalcd/g cm−3 1.460 1.414 1.497 1.374T/K 128.35(10) 128.40(10) 100(2) 150.03(18)μ(Mo Kα)/mm−1 3.162 2.784 2.797 2.590R1(I > 2σ(I))a 0.0733 0.0678 0.0576 0.0931wR2a 0.1511 0.1708 0.1435 0.2279

aR1 = ||Fo| − |Fc||/|Fo|; wR2 = [w(|Fo| − |Fc|)2/w|Fo|

2]1/2.

Inorganic Chemistry Article

dx.doi.org/10.1021/ic402296t | Inorg. Chem. 2013, 52, 13702−1370713703



was carried out on Agilent SUPERNOVA diffractometer with Mo Kαradiation (λ = 0.71073 Å) at 150 K. Data reduction and unit cellrefinement were performed with Crysallis software. The structureswere solved by direct methods using SHELXS-97 and were refined byfull-matrix least-squares methods using Olex2.7 Crystal data andrefinement parameters are given in Table 2. Selected bond lengths andangles are given in the Supporting Information. CCDC depositionnumbers: 958734−958740, 805050, and 805052.Magnetic Measurements. The magnetic properties of poly-

crystalline samples of 1−9 were measured with a Quantum DesignMPMS-XL7 SQUID magnetometer. The samples were ground, placedin a gel capsule, and fixed with a small amount of eicosane to avoidmovement during the measurement. The data were corrected for thediamagnetism from the gel capsule and the eicosane with thediamagnetic contribution from the complexes calculated from Pascalconstants.

■ RESULTS AND DISCUSSION

Synthetic Description. Solvothermal synthesis has provedto be effective in producing high-nuclearity polymetallic cages,8

and we have previously reported 3d−4f phosphonate cagessynthesized through this technique.4 Here we found optimalconditions for synthesis of the {Ni6Ln6P6} cages to be 150 °Cin MeCN, giving yields obtained between 20 and 60%.Structure. The compounds crystallize in two different space

groups, P1 (1, 3, 5−7, and 9) and P21/n (2, 4, and 8); however,

there is little difference between the molecular structures andthe description below serves for all molecules. In each case thecage lies on an inversion center. The cage can be described as arugby ball (Figure 1 and Figure S1 (Supporting Information)).The two ends of the rugby ball are capped by a {Ni3(μ3-OH)}triangle, in which the μ3-OH group is displaced ca. 0.47(2)−0.49(2) Å out of the {Ni3} plane (see Table S1 (SupportingInformation)). There are two chemically distinct Ni···Ni edges(Figure S7 (Supporting Information)). To describe the bindingmodes of the polynucleating ligands, we use Harris notation,14

X.Y1Y2Y3, where X is the overall number of metals bound by thewhole ligand, and each value of Y refers to the number of metalatoms attached to the different donor atoms (Figure S2(Supporting Information)). The Ni1···Ni2 and Ni2···Ni3 edgesare each bridged by a 2.11 pivalate (exo to the cage) and onearm of a 5.222 phosphonate (P1 or P3), also bridging to threeLn ions. The Ni1···Ni3 edge is bridged by a 2.20 acetate (exo tothe cage) and a 5.221 phosphonate (P2). Hence, the {Ni3}triangles approximate very closely isosceles triangles with ashort Ni1···Ni3 edge (Figure S7 (Supporting Information)).Note that although acetate was not added to the reaction,hydrolysis of MeCN under solvothermal conditions is known9

and in situ formation of carboxylates in solvothermal cagesynthesis is well established.4g,10 Deliberate addition of acetatedoes not improve the yield of crystalline material, and we have

Figure 1. (a) Crystal structure and (b) {Ni6Ln6P6} core of 1-9. Scheme: Gd/Y, purple; Ni, blue; P, green; O, orange; C, gray; H omitted for clarity.(c) Polyhedral view of {Ni6Ln6P6} core and comparison with the {M18} Wells-Dawson core.





also been unable to include other bridging ligands in thestructure. The bridging between the Ni and Ln ions iscompleted by three pivalates using either the 2.11 or the 2.21coordination modes.The alternating arrangement of the Ln and P atoms forms a

{Ln3P3} six-membered ring, which connects to its centrosym-metric-related counterpart through six 2.11 pivalates. The Gd···Gd separations within the {Gd3P3} six-membered rings in 1−5fall into the range 6.05−6.57 Å, whereas those between the{Gd3P3} rings are shorter, in the range 3.9−4.9 Å. In theyttrium cages 6−9 the analogous Y···Y ranges are 5.9−6.50 and3.138−4.60 Å, respectively. If the P atoms are treated as part ofthe core of these cages, the resulting {Ni6Ln6P6} units resemblethe Wells−Dawson polyoxometalate (Figure 1c right). Thiscomplements the paramagnetic “Keggin” ions that have beenreported.13

Magnetism. The magnetic behavior of 1−9 has beenstudied on polycrystalline samples (Figure 2 and Figure S3(Supporting Information)). At room temperature 1−5 all haveχMT values (where χM is the molar magnetic susceptibility)close to the sum of the calculated value (54.1 emu K mol−1) forsix S = 1, g = 2.2 and six S = 7/2, g = 2.00 centers. Upon cooling,χMT changes little down to about 50 K, before increasing slowlyto a maximum at around 15 K. Magnetization (M) versusapplied field (H) measurements at low temperature all saturateat around 55 μB (Figure 2b and Figures S3 and S5 (SupportingInformation)), consistent with the maximum possible value forfull alignment of spins.Compounds 6−9 were studied in order to understand the

magnetic interactions in and between the {Ni3} moieties. Thebehaviors of the four compounds are very similar (Figure 3 andFigure S4 (Supporting Information)). At room temperature theχMT value is slightly above that calculated for six S = 1 centers

with g = 2.2 (7.26 cm3 K mol−1), with observed values of 7.8,8.2, 7.9, and 7.9 cm3 K mol−1 for 6−9, respectively. In each casethe χMT value increases smoothly to a maximum at near 10 K,before falling at lower temperatures. Low-temperature M vs Hstudies show a steady increase up to 7 T, tending towardsaturation at slightly above 12 μB (Figure 3 and Figures S4 andS5 (Supporting Information)).The behavior of 6, 7 and 9 was modeled using PHI

software11 with Hamiltonian (1), fitting χMT vs T and M vs Hsimultaneously. Data and fits for 8 were reported previously.4c

Hamiltonian (1) assumes an isosceles triangle (see above)with the first term being the isotropic exchange interactionbetween Ni(1)···Ni(2) and Ni(2)···Ni(3) and the second termthat between Ni(1)···Ni(3), the chemically unique edge (Figure3, inset). The third and fourth terms are the axial zero fieldsplitting (ZFS) and Zeeman terms, respectively, of each Nicenter. No meaningful simultaneous fits to χMT vs T and M vsH could be obtained without inclusion of the ZFS terms or withan equilateral model. For simplicity the ZFSs are taken ascollinear and identical for all three Ni ions. Best statistical fits(Figure 3) to the experimental data were found using theparameters in Table 3.The two {Ni3} triangles are treated as noninteracting, i.e. the

results of Hamiltonian (1) are simply multiplied by a factor of2. In each case we find two ferromagnetic and one

Figure 2. Magnetic studies of 1: (a) χMT vs T measured in a 1 kG applied magnetic field and (b) M vs H at the temperatures indicated.

Figure 3.Magnetic measurements on compound 6: (left) χMT vs T measured in a 1 kG field; (right)M vs H at the temperatures indicated. Red linesare the best simultaneous fits to Hamiltonian (1).

∑

∑

= − + − + + μ

=

=

H J S S S S J S S D S g

H S

2 ( ) 2 ( )i

iz B

ii

1 1 2 2 3 2 1 31

32

1

3

(1)





antiferromagnetic interaction within the {Ni3} triangles. Theunique interaction (J2) is presumably for the significantlyshorter Ni(1)···Ni(3) edge ,which has a correspondingly muchsmaller Ni(1)−O−Ni(3) angle of ca. 104−105°: cf. the 118−121° angles found for the other two edges (Table 4).

The magnitudes of D obtained for 6−9 seem at firstsurprisingly large for {NiO6} coordination environments(Table 3). However, these environments are far from

homoleptic, and the ligand fields at Ni are likely to be stronglyaxial, dominated by the short Ni···μ3-OH interactions of1.960(6)−2.009(7) Å, with the remaining O donors fromphosphonate and carboxylate in the range 1.975(8)−2.229(3)Å (see Figure S7 and Table S1 (Supporting Information)).Even small deviations from regular octahedral environmentscan give rise to significant ZFS values for NiII.12

In order to understand the interaction between Ni···Gd andGd···Gd within the clusters, the magnetization curve for sixnoninteracting GdIII ions was calculated using the Brillouinfunction and added to the experimental data for the {Ni6Y6P6}cages. These curves were then compared with the experimentaldata for the analogous {Ni6Gd6P6} compounds (Figure 4). Forcages 3−5 the curves agree well; hence, the Ni···Gd interactionsmust be negligible. However, the magnetization curve of 1 isslightly higher than that calculated from 6 plus six GdIII. Thissuggests that weak ferromagnetic Ni···Gd interactions areoperating in 1 but not in 3−5.The rapid magnetization observed for the {Ni6Gd6P6} cages,

due to the ferromagnetic coupling, with achievement of fullspin alignment, led us to study the magnetic entropy changesfor these processes (Table 3 and Figure S6 (SupportingInformation)). The maximum magnetic entropy change valueper mass was achieved for the methylphosphonate derivative 1,with a value of 32 J kg−1 K−1: this is entirely predictable, as 1has the lowest molecular weight. However, this does not appearto be the only factor, as the increase is greater than predictedpurely on the grounds of mass change.Comparing the molar magnetic entropy change for each case,

we can clearly see that the molar magnetic entropy is higher for1 (116.1 J mol−1 K−1), followed by 5 (115.4 J mol−1 K−1), 3(114.2 J mol−1 K−1), 2 (111.7 J mol−1 K−1), and 4 (105.5 Jmol−1 K−1) (Table 3). On examination of the magneticbehavior of these compounds it is clear that the two MePO3

2−

cages differ from the other cages. In the {Ni6Y6P6} cages, the

Table 3. Magnetic Data for 1−9

R group in RPO32−

Me Ph hexyl CH2Ph octyl

Gd complex 1 2 3 4 5Y complex 6 7 8 9J1/cm

−1 (for Y complex) 2.4 4.8 2.83 4.5J2/cm

−1 (for Y complex) −1.0 −3.5 −1.18 −2.7D/cm−1 (for Y complex) 6.2 4.3 5.7 5.8g (for Y complex) 2.28 2.32 2.28 2.27−Δ∑μ/J kg

−1 K−1 (for Gdcomplex)a

32 27.9 28.2 26.5 26.6

−Δ∑μ/J mol−1 K−1 (for Gd

complex)a116.1 111.7 114.2 105.5 115.4

aCalculated for a ΔH = 0−7 T, at 3 K.

Table 4. Ni(i)···OH···Ni(j) Angles (deg) (See Figure 3 Inset)in the {Ni3} Moiety

α β γ

methyl 104.4(2) 119.2(2) 119.5(2)benzyl 104.2(1) 120.4(2) 118.7(2)hexyla 103.50(4) 119.3(4) 119.93(4)octyl 104.2(3) 120.8(3) 118.0(3)

aAverage distance of the two molecules in the asymmetric unit cell.

Figure 4. Comparison between experimental 2 K magnetization data for {Ni6Gd6P6} (red curves) and those for the analogous {Ni6Y6P6} cage plusthe Brillouin function for six GdIII ions (black curves): (a) cages 1 and 6; (b) cages 3 and 7; (c) cages 4 and 8; (c) cages 5 and 9.





Ni···Ni exchanges are found to be smaller in 6 in comparisonwith 7−9, while in the {Ni6Gd6P6} cages there is evidence forferromagnetic interactions in 1 and not in 3−5 (see Figure 4).A weak ferromagnetic interaction between Ni and Gd couldexplain the increase in magnetic entropy found in 1 being largerthan would be predicted purely on molecular weightconsiderations. Ferromagnetic interactions are ideal for MCE,as these interactions allow saturation of the magnetization atlower magnetic fields; however, in order to allow fasterdemagnetization of the molecule after the removal of theapplied field, weak ferromagnetic interactions are preferable.The variations observed are very small, and there is a danger

of making too much of a very subtle change: i.e., even if there isa Ni···Gd ferromagnetic exchange, it is barely observable. Itdoes seem that MePO3

2− is subtly different from the otherphosphonates, and perhaps this is due to the electron-releasingnature of the methyl group leading to greater electron densityon the phosphonate and hence stronger superexchange.

■ CONCLUSIONSA family of 3d−4f cages has been synthesized that resemble theWells−Dawson ion. The structure seems insensitive to thephosphonate used. The magnetic entropy change of the clusterwas improved through the reduction of the molecular massusing methylphosphonate; however, the increase seems slightlygreater than would be expected if it were entirely due to masschange. Analysis of magnetization data suggests a weakferromagnetic interaction between Gd and Ni, which couldaccount for this difference.The structural chemistry of phosphonate cages is intriguing.

The coordinative flexibility of phosphonates allows the metalsites to adopt multiple different structures, and it is possiblethat the use of solvathermal methods favors a high-symmetrycore in the structures. By regarding the P center as a “metal”center, we can describe this compound as akin to the Wells−Dawson ion. The question of whether there is a more generalcorrelation between phosphonate cages and polyoxometalatesis worth exploring. For example, while phosphonates support a{Ni12} cage containing a truncated tetrahedron similar to theKeggin ion,13b in that structure the P centers are not regardedas part of the polyhedron. Comparing the structures of thesetwo extensive families of polymetallic cages might beinstructive.

■ ASSOCIATED CONTENT*S Supporting InformationFigures and CIF files giving crystallographic data, additionalviews of the crystal structures, a schematic of the bondingmodes adopted by the ligands in the structure, and themagnetic measurements on all compounds. This material isavailable free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authors*E-mail for R.E.P.W.: [email protected].*E-mail for E.J.L.M.: [email protected] Address†Center for Applied Chemical Research, Frontier Institute ofScience and Technology, Xi’an Jiaotong University, Xi’an710054, People’s Republic of China.NotesThe authors declare no competing financial interest.

■ REFERENCES(1) (a) Kahn, O. Molecular Magnetism; VCH: New York, 1993.(b) Gatteschi, D.; Sessoli, R.; Villain, J. Molecular Nanomagnets;Oxford University Press: Oxford, U.K., 2006.(2) (a) Sessoli, R. Angew. Chem., Int. Ed. 2012, 51, 43. (b) Evangelisti,M.; Brechin, E. K. Dalton Trans. 2010, 39, 4672. (c) Evangelisti, M.;Candini, A.; Ghirri, A.; Affronte, M.; Brechin, E. K.; McInnes, E. J. L.Appl. Phys. Lett. 2005, 87, 072504. (d) Sharples, J. W.; Collison, D.Polyhedron 2013, 54, 91.(3) (a) Karotsis, G.; Evangelisti, M.; Dalgarno, S. J.; Brechin, E. K.Angew. Chem. int. Ed. 2009, 48, 9928. (b) Langley, S. K.; Chilton, N.F.; Moubaraki, B.; Hooper, T. N.; Brechin, E. K.; Evangelisti, M.;Murray, K. S. Chem. Sci. 2011, 50, 6606. (c) Hooper, T. N.; Schnack,J.; Piligkos, S.; Evangelisti, M.; Brechin, E. K. Angew. Chem., Int. Ed.2012, 51, 4633. (d) Zheng, Y.; Zhang, Q.-C.; Long, L.-S.; Huang, R.-B.; Muller, A.; Schnack, J.; Zheng, L.-S.; Zheng, Z. Chem. Commun.2013, 49, 36.(4) (a) Baskar, V.; Gopal, K.; Helliwell, M.; Tuna, F.; Wernsdorfer,W.; Winpenny, R. E. P. Dalton Trans. 2010, 39, 4747. (b) Wang, M.;Yuan, D.-Q.; Ma, C.-B.; Yuan, M.-J.; Hu, M.-Q.; Li, N.; Chen, H.;Chen, C.-N.; Liua, Q.-T. Dalton Trans. 2010, 39, 7276. (c) Zheng, Y.-Z.; Evangelisti, M.; Winpenny, R. E. P. Angew. Chem., Int. Ed. 2011, 50,3692. (d) Zheng, Y.-Z.; Evangelisti, M.; Winpenny, R. E. P. Chem. Sci.2011, 2, 99. (e) Zheng, Y.-Z.; Pineda, E. M.; Helliwell, M.; Evangelisti,M.; Winpenny, R. E. P. Chem. Eur. J. 2012, 18, 4161. (f) Zheng, Y.-Z.;Evangelisti, M.; Tuna, F.; Winpenny, R. E. P. J. Am. Chem, Soc. 2012,134, 1057. (g) Pineda, E. M.; Tuna, F.; Zheng, Y.-Z.; Pritchard, R. G.;Regan, A. C.; Winpenny, R. E. P.; McInnes, E. J. L. Chem. Commun.2013, 49, 3522.(5) (a) Chaboussant, G.; Basler, R.; Gudel, H.-U.; Ochsenbein, S. T.;Parkin, A.; Parsons, S.; Rajaraman, G.; Sieber, A.; Smith, A. A.; Timco,G. A.; Winpenny, R. E. P. Dalton Trans. 2004, 2758. (b) Aromi, G.;Batsanov, A. S.; Christian, P.; Helliwell, M.; Parkin, A.; Parsons, S.;Smith, A. A.; Timco, G. A.; Winpenny, R. E. P. Chem. Eur. J. 2003, 9,5142.(6) (a) Fomina, I. G.; Kiskin, M. A.; Martynov, A. G.; Aleksandrov,G. G.; Dobrokhotova, Z. V.; Gorbunova, Y. G.; Shvedenkov, Y. G.;Tsivadze, A. Y.; Novotortsev, V. M.; Eremenko, I. L. Zh. Neorg. Khim.2004, 49, 1463. (b) Zoan, T. A.; Kuzmina, N. P.; Frolovskaya, S. N.;Rykov, A. N.; Mitrofanova, N. D.; Troyanov, S. I.; Pisarevsky, A. P.;Martynenko, L. I.; Korenev, Y. M. J. Alloys Compd. 1995, 225, 396.(7) Dolomanov, O. V.; Bourthis, L. J.; Gildea, R. L.; Howard, J. A. K.;Puschmann, H. J. Appl. Crystallogr. 2009, 42, 339.(8) Laye, R. H.; McInnes, E. J. L. Eur. J. Inorg. Chem. 2004, 14, 2811.(9) Belsky, A. J.; Brill, T. B. J. Phys. Chem. A 1999, 103, 3006.(10) Shaw, R.; Tidmarsh, I. S.; Laye, R. H.; Breeze, B.; Helliwell, M.;Brechin, E. K.; Heath, S. L.; Murrie, M.; Ochsenbein, S.; Gudel, H. U.;McInnes, E. J. L. Chem. Commun. 2004, 1418.(11) Chilton, N. F.; Anderson, R. P.; Turner, L. D.; Soncini, A.;Murray, K. S. J. Comput. Chem. 2013, 34, 1164.(12) (a) Packov, A.; Miklovic, J.; Titis, J.; Koman, M.; Boca, R. Inorg.Chem. Commun. 2013, 32, 9. (b) Charron, G.; Bellot, F.; Cisnetti, F.;Pelosi, G.; Rebilly, J.-N.; Riviere, E.; Barra, A.-L.; Mallah, T.; Policar, C.Chem. Eur. J. 2007, 13, 2774. (c) Boca, R. Coord. Chem. Rev. 2004,248, 757.(13) (a) [Fe13O4F24(OMe)12]

5− reported in: Bino, A.; Ardon, M.;Lee, D.; Spingler, B.; Lippard, S. J. J. Am. Chem. Soc. 2002, 124, 4578.(b) [Ni12(OH)4(O3PPh)4(O2C

tBu)12L6], where L is a disorderedmixture of solvents. See: Breeze, B. A.; Shanmugam, M.; Tuna, F.;Winpenny, R. E. P. Chem. Commun. 2007, 5185.(14) Coxall, R. A.; Harris, S. G.; Henderson, D. K.; Parsons, S.;Tasker, P. A.; Winpenny, R. E. P. Dalton Trans. 2000, 2349.






Wells-Dawson Cages as Molecular Refrigerants

Eufemio Moreno Pineda, Floriana Tuna, Yan-Zhen Zheng,a Richard E. P. Winpenny* and Eric J. L. McInnes*

School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road,

Manchester M13 9PL, UK.

a. Current address: Center for Applied Chemical Research, Frontier Institute of Science and

Technology, Xi'an Jiaotong University, Xi'an 710054, China.

Figure S1. Crystal structures of 1 – 5: a) 1; b) metal core (top view); c) 2; d) 3; e) 4 and f) 5. Scheme: Gd, purple; Ni, blue; P, green; O, red; C, grey; (H omitted for clarity).

5.221 5.222 2.11 2.21 2.20

Figure S2. Coordination mode of phosphonates and acetates in compounds 1 – 5 described using the Harris notation.

a)

d)

b) c)

f )e)



Figure S3. Susceptibility and magnetisation plots for Ni6Gd6P6: a) 2; b) 3; c) 4 and d) 5.

Figure S4. Susceptibility (top) and magnetisation (bottom) for Ni6Y6P6: a) 7; b) 8 and d) 9.



Figure S5. Magnetisation at 2 K from 0 - 7 T for complexes: a) 1 - 5; b) 6 - 9.

Figure S6. Magnetic entropy change calculated from isothermal magnetisations for a) 1; b) 2; c) 3; d) 4 and e) 5 for a ∆H = 0 - 7 T.



Table S1. Selected angles and bond distances of 1 - 9.

a. Average distance of the two molecules in the asymmetric unit cell.

Figure S7. {Ni3} moiety for Ni6Ln6P6 clusters. Ni, blue; P, green; O, red; C, grey; (H and some C omitted for clarity).

Ni1 Ni3

Ni2

O1

O3

O2O6

O4

O8

O7

OH

O10

O11

O9

O13 O12

O15

O14

1 2 3a 4 5 6 7

a 8 9

Ni3 (plane)-OH /Å 0.490(2) 0.474(2) 0.484(3) 0.478(1) 0.483(2) 0.476(1) 0.470(2) 0.472(1) 0.483(2)

Ni(1)…Ni(2) /Å 3.418(1) 3.460(2) 3.443(2) 3.427(2) 3.398(2) 3.418(2) 3.431(1) 3.424(9) 3.404(3)

Ni(2)…Ni(3) /Å 3.430(2) 3.433(2) 3.445(2) 3.425(2) 3.459(1) 3.429(2) 3.413(1) 3.419(9) 3.440(2)

Ni(1)…Ni(3) /Å 3.138(1) 3.168(2) 3.166(2) 3.138(2) 3.158(1) 3.156(2) 3.152(1) 3.141(8) 3.161(2)

Ni(1)…OH…Ni(2) /° 119.3(2) 119.9(4) 119.3(4) 118.8(2) 120.7(2) 119.2(2) 119.82(2) 118.7(2) 118.0(3)

Ni(2)…OH…Ni(3) /° 119.2(2) 118.9(4) 119.93(4) 120.2(2) 118.0(2) 119.2(2) 119.94(2) 120.4(2) 120.8(3)

Ni(3)…OH…Ni(1) /° 103.6(2) 104.7(4) 103.50(4) 103.9(2) 104.0(2) 104.4(2) 104.62(2) 104.2(1) 104.2(3)



Iron Lanthanide Phosphonate Clusters: {Fe6Ln6P6} WellsDawson-like Structures with D3d SymmetryEufemio Moreno Pineda,† Floriana Tuna,† Yan-Zhen Zheng,†,⊥ Simon J. Teat,‡

Richard E. P. Winpenny,*,† Jurgen Schnack,§ and Eric J. L. McInnes*,†

†School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.‡Advanced Light Source, Lawrence Berkeley Laboratory, 1 Cyclotron Road, MS2-400, Berkeley, California 94720, United States§Faculty of Physics, University of Bielefeld, Universitatsstr. 25, D-33615 Bielefeld, Germany


ABSTRACT: Reaction of [Fe3(μ3-O)(O2CtBu)6(HO2C

tBu)3](O2CtBu) and

[Ln2(O2CtBu)6(HO2C

tBu)6] (Ln = lanthanide) with three different phosphonic acids producea family of highly symmetrical {Fe6Ln6P6} clusters with general formula [Fe6Ln6(μ3-O)2(CO3)(O3PR)6(O2C

tBu)18], where R = methyl 1, phenyl 2, or n-hexyl 3. All the clusterspresent an analogous metal frame to the previously reported {Ni6Ln6P6} both being related tothe well-known Wells−Dawson ion from polyoxometallate chemistry. These highlysymmetrical clusters have, or approximate very closely to, D3d point symmetry. Both FeIII

and GdIII ions are magnetically isotropic and could thus exhibit promising magnetocaloricproperties; hence we investigated the {Fe6Gd6P6} compounds accordingly. Modeling themagnetic data of [Fe6Gd6(μ3-O)2(CO3)(O3PPh)6(O2C

tBu)18] by the finite-temperatureLanczos method gave a strong antiferromagnetic Fe···Fe interaction (JFe−Fe = −30 cm−1)and very weak Gd···Gd and Gd···Fe exchange interactions (|J| < 0.1 cm−1). The strongantiferromagnetic Fe···Fe interaction could account for the relatively smaller −ΔSm valueobserved, compared against the {Ni6Gd6P6} analogues.

■ INTRODUCTION

The magnetic properties of molecular transition-metal cageshave received a great deal of attention since it wasdemonstrated that some examples display memory effects, theso-called single molecule magnets.1 This Study has led toresearch in related areas such as molecular spintronics,quantum information processing, and magnetocalorics.1,2 We,and others, have been exploring the synthetic chemistry of 3d−4f cages to probe the effect of combining the very differentmagnetic properties of 3d and 4f ions in one molecule.3,4 Wehave found that phosphonates, although usually requiringcoligands to prevent formation of insoluble polymers, areparticularly good ligands for binding such materials because theRPO3

2− can bridge many metal ions, compared to carboxylatesfor example, with a favorable ligand set for the oxophiliclanthanides.5,6 Moreover, their solubility and bulk can bereadily tuned via choice of R, and it is also possible to introducefurther functional groups.6

We recently reported a family of {Ni6Gd6P6} cages of generalformula [NiII6Gd

III6(μ3−OH)2(O3PR)6(O2C

tBu)16(HO2Ac)2].7

These molecules are both structurally and magneticallyintriguing. Structurally, the molecules are layered, and if thephosphorus atoms are considered as part of the core then the3:6:6:3 (Ni3:Gd3P3:Gd3P3:Ni3) structure strongly resemblesthat of the classic Wells−Dawson8 [X2M18O62]

n− ion (X = e.g.P, Si), which may suggest wider correlation betweenphosphonate cages and polyoxometallate chemistry. Magneti-

cally, the {Ni6Gd6P6} cages display rather large magnetocaloriceffects (MCEs). The MCEs can be exploited in adiabaticdemagnetisation experiments, and certain molecular cages haveproved good candidates for very low-temperature refrigeration,9

even at the molecular level,10 due a highly degenerate set oflow-lying spin states that can saturate in applied field, resultingin large magnetic entropy changes on application of an externalmagnetic field. In the case of {Ni6Gd6P6} the large MCE effectsare due to a combination of the high spin multiplicity (NiII, S =1; GdIII, S = 7/2) and the presence of ferromagnetic internalcoupling within the cage, meaning that relatively large magneticentropy changes can be achieved with small applied fieldchanges.We have examined whether this Wells−Dawson-like family

could be extended to other 3d metal systems. In this Work wereport the successful replacement of the divalent NiII ions in{Ni6Gd6P6} for the isotropic trivalent FeIII. This was toinvestigate (i) whether trivalent 3d ions could be incorporatedinto the same structure and, if so, how the differing chargebalance would be accommodated and (ii) the effect on themagnetic, including magnetocaloric, behavior of replacing theanisotropic NiII, S = 1 spins with relatively isotropic and higherspin FeIII, S = 5/2 spins. We further report substitution of theGdIII ion with other 4f ions.

Received: November 13, 2013Published: March 6, 2014

Article

pubs.acs.org/IC

© 2014 American Chemical Society 3032 dx.doi.org/10.1021/ic402839q | Inorg. Chem. 2014, 53, 3032−3038



■ EXPERIMENTAL SECTIONStarting Materials. [FeIII3(μ3-O)(O2C

tBu)6(HO2CtBu)3]-

(O2CtBu)11 and [LnIII2(O2C

tBu)6(HO2CtBu)6]

12 (Ln = Gd, Tb, Dy,or Ho) were prepared by reported methods. All other startingmaterials and solvents were of reagent grade and used as purchased.Synthetic Method. [FeIII3(μ3-O)(O2C

tBu)6(HO2CtBu)3]-

(O2CtBu) (0.1 g, 0.075 mmol), [GdIII2(O2C

tBu)6(HO2CtBu)6] (0.1

g, 0.1 mmol), RPO3H2 (R = methyl, phenyl, or n-hexyl) (0.1 mmol),and triethylamine (0.1 mL, 1 mmol) in acetonitrile (8 mL) werestirred at room temperature for 5 min. The resulting slurry wastransferred into a 10 mL Teflon-lined autoclave, which was heated at150 °C for 12 h under solvothermal conditions13 and then cooled toroom temperature at a rate of 0.05 °C min−1. Reddish-brown crystals( o f X - r a y d iff r a c t i o n qu a l i t y ) o f [ F e I I I

6Gd I I I6 (μ 3 -

O)2(O2CtBu)18(O3PR)6(CO3)], with R = Me (1), Ph (2), and n-

hexyl (3) were obtained directly from the autoclave in 40−50% yield.Similar reactions with [LnIII2(O2C

tBu)6(HO2CtBu)6], where Ln = Tb,

D y , H o , g a v e a n a l o g o u s [ F e I I I6 L n I I I

6 ( μ 3 -O)2(O2C

tBu)18(O3PR)6(CO3)] clusters (R = Me [Ln = Dy (4), Ho(5)] and Ph [Ln = Tb (6)]), in similar yields. (Elemental analyses andyields are in Supporting Information, Table S1; IR data are inSupporting Information, Figure S1.)X-ray Data Collection and Structure Solution. Data for 1 were

collected on a Bruker APEX II diffractometer (synchrotron, λ =0.77490) at the Advanced Light Source, Berkeley Lab, U.S.A. Datareduction was performed with Bruker SAINT software. Single-crystalX-ray diffraction measurements for 2 and 6 were carried out on aBruker SMART CCD diffractometer with Mo Kα radiation (λ =0.71073 Å) at 100 K. Data for 3 were collected on a RigakuSaturn724+ diffractometer (synchrotron, λ = 0.68890 Å) at beamlineI19 at Diamond Light Source, U.K. Data reduction and unit cellrefinement for 2, 3, and 6 were performed with Crysallis software. Thestructures were solved by direct methods using SHELXS-9714a andwere refined by full-matrix least-squares methods using Olex2.14b In allcases the crystals were mounted on a tip using crystallographic oil andplaced in a cryststream. Data were collected using ϕ and ω scanschosen to give a complete asymmetric unit. All non-hydrogen atomswere refined anisotropically. Hydrogen atoms were calculatedgeometrically and were riding on their respective atoms.Some degree of disorder was found in all clusters. For compounds 2

and 6 the carbon atoms of the tBu groups of the pivalate ligands arefound to be disordered over two sites. The tBu groups were modeledsplitting their occupancy into parts. Bond and angle (DANG) andthermal (ISOR) restraints were also used to model these atoms. Some

disorder was found on the oxygen atoms of the pivalates, which werealso modeled splitting them into parts.

Reduction of the data of compound 1 yielded the nonstandardspace group P21/n. Transformation of the unit cell from P21/n to the

standard space group P21/c was performed with the matrix

⎛⎝⎜

⎞⎠⎟

1 0 00 1 01 0 1

using XPREP for posterior solution. Compound 1 was highlydisordered, and some gadolinium and oxygen atoms were alsomodeled splitting their occupancy into parts. ISOR and DANGrestraints were used to model some thermal ellipsoids. In this clusterwe were not able to completely solve the carbonate group within the{Fe6Gd6P6} cage, probably due to the high level of disorder observed.Because of the hexyl chain on the R group in compound 3 moredisorder was observed. tBu and hexyl groups were restrained using(DANG), (ISOR), and (SADI) commands. The hexyl groups werealso modeled using these commands. Several attempts to collect andsolve diffraction data for clusters 4 and 5 were performed (seeSupporting Information); however, due to the poor quality of the datawe were not able to obtain the crystal structures. The unit cells ofthese compounds were obtained (see Supporting Information), havingsimilar parameters to 1 confirming, along with the elemental analyses,that these are isostructural. Full crystallographic details can be found inCIF format: see the Cambridge Crystallographic Data Centre database(971523−971526) for 1−3 and 6. Crystal data and refinementparameters are given in Table 1.

Magnetic Measurements. The magnetic properties of poly-crystalline samples of 1−6 were measured with a Quantum DesignMPMS-XL7 SQUID magnetometer. The samples were ground, placedin a gel capsule, and fixed with a small amount of eicosane to avoidmovement during the measurement. The data were corrected for thediamagnetism from the gel capsule and the eicosane, with thediamagnetic contribution from the complexes calculated from Pascalconstants.

■ RESULTS AND DISCUSSION

Synthetic Description. The {Ni6Gd6P6} family of clusterswas prepared by reaction of a nickel carboxylate dimer,[NiII2(μ2−OH2)(O2C

tBu)4(HO2CtBu)4], with the gadolinium

carboxylate dimer [GdIII2(O2CtBu)6(HO2C

tBu)6] and phos-phonic acid with base in MeCN under solvothermalconditions.7 To prepare analogous structures with trivalent d-block ions we replaced the nickel starting material with themost straightforward FeIII carboxylatesthe oxo-centered

Table 1. Crystallographic Information for Clusters 1−3 and 6

1 2 3 6

chem formula Fe6Gd6P6O60C96H180 Fe6Gd6P6O59C127H192 Fe6Gd6P6O59C127H240 Fe6Tb6P6O59C127H192

fw 3758.81 4127.21 4175.60 4137.23cryst system monoclinic trigonal trigonal trigonalspace group P21/c R3 c R3c R3ca/Å 15.590(3) 16.8883(3) 34.2470(4) 16.8951(2)b/Å 15.565(3) 16.8883(3) 34.2470(4) 16.8951(2)c/Å 31.774(6) 103.9530(2) 103.4064(12) 103.8149(15)α/deg 90 90 90 90β/deg 109.13(3) 90 90 90γ/deg 90 120 120 120V/Å3 7285(3) 25676.6(11) 104667(3) 25663.2(7)Z 2 6 24 6ρ calcd/g cm−3 1.714 1.601 1.590 1.606T/K 173.0 100.0 100.0 100.0μ (Mo Kα)/mm−1 3.414 2.914 2.643 3.070R1 (I > 2σ)(I)a 0.0935 0.0717 0.0994 0.0950wR2

a 0.2733 0.1433 0.2940 0.1972aR1 = ||Fo| − |Fc||/|Fo|, wR2 = [w(|Fo| − |Fc|)

2/w|Fo|2]1/2


dx.doi.org/10.1021/ic402839q | Inorg. Chem. 2014, 53, 3032−30383033



triangles. Analogous solvothermal reactions with [FeIII3(μ3-O)(O2C

tBu)6(HO2CtBu)3](O2C

tBu) successfully gave the{Fe6Gd6P6} clusters 1−3 in good yield (40−50%) in crystallineform directly on slowly cooling. Single-crystal X-ray diffractionidentified the products as [FeIII6Gd

III6(μ3-O)2(CO3)-

(O2CtBu)18(O3PR)6]; these structures are much more sym-

metrical than their {Ni6Gd6P6} analogous (see Figure 1), andthe key differences in the structures are detailed below.Attempts to extend the syntheses to other lanthanide ions (4−6) were only partially successful in terms of getting cleancrystalline products; the reason for this is not clear.Crystallography. Compounds 1−6 have very similar

structures, and here we describe the structure of 2 in detailas representative (Figure 1 and Supporting Information, FigureS2). Compound 2 crystallizes in the R3 c space group, and themolecule has crystallographic D3d symmetry with only one Fe,one Gd, and one P in the asymmetric unit. (Compound 3 alsocrystallizes in the R3c space group, while 1 crystallizes in P21/c:although the latter then strictly has only C2h point symmetrythe structure is very close to D3d). The cluster core thenconsists of 6 FeIII and 6 GdIII ions, bound by 6 phosphonates,18 pivalates, and 2 oxides. The structure is layered, with two{Fe3} triangles capping two central Gd layers, overall giving arugby ball-like shape (Figure 1). The {Fe3} and {Gd3} planesare separated by 3.677(3) Å, while the {Gd3}···{Gd3}interplane distance is 2.20(2) Å. The six Gd ions canalternatively be described as forming a ring in a chairconformation, with Gd···Gd edges of 3.931(2) Å. The twoequilateral {Fe3(μ3-O)} triangles are oxo-centered with the μ3-O2− in the {Fe3} plane. The {Fe3} triangles sit eclipsed over theadjacent {Gd3} triangle (Figure 2 and Supporting Information,Figure S3) with nearest Fe···Gd distances of 3.677(3) Å. EachFe···Fe edge (3.315(4) Å) is bridged by one pivalate (which

adopts a 2.11 coordination mode in Harris notation)15 and bytwo arms of a phosphonate. The phosphonates adopt a 5.222coordination mode, further binding to two GdIII ions in theadjacent {Gd3} layer and one in the other {Gd3} layer. The Gdand Fe ions are further bridged by 2.11 pivalates, as are the two{Gd3} layers. Finally, a carbonate ion is found in the middle ofthe cage, disordered over two sites, binding to all the Gd ions(6.222 binding mode). This must arise from atmospheric CO2fixation; there is ample precedent for this in lanthanideclusters.16

The {Gd3} and {P3} triangles in each half of the molecule arestaggered with an interplane distance of just 1.485(1) Å. Hence,the alternating arrangement of Gd and P atoms can be definedas a puckered {Gd3P3} ring. Treating the P atoms as part of thecore in this way then gives a layered 3:6:6:3 {Fe6Ln6P6}structure which, as we noted for the {Ni6Ln6P6} family, stronglyresembles the Wells−Dawson polyoxometallate (Figure 1b).The additional 6+ charge on the {M6Ln6P6} core of

{Fe6Ln6P6} cf. {Ni6Ln6P6} requires changes in the ligand setto retain charge balance (Figure 2): (i) The {Fe3} triangles in{Fe6Ln6P6} incorporate μ3-oxide rather than μ3-hydroxide as inthe equivalent {Ni3} triangles, presumably carrying throughfrom the {Fe3O} starting material. As a consequence, the{Fe3O} fragments are planar, while in {Ni3(OH)} thehydroxide is displaced ca. 0.5 Å from the {Ni3} plane towardthe center of the cage (Figure 2a). (ii) In the {Ni3} triangles of{Ni6Ln6P6} two edges have conventional 1,3-carboxylatebridges (2.11 binding mode in Harris notation), but the thirdedge has instead a 1,1-bridging carboxylic acid (i.e., via a singleO atom; 2.20 binding) (Figure 2c). This makes the {Ni3}triangle isosceles, with the unique edge ca. 0.3 Å shorter thanthe other two (Ni···Ni distances ca. 3.15 and 3.45 Å). In{Fe6Ln6P6} all the carboxylates are 1,3-bridges, and the {Fe3}

Figure 1. Crystal structure of the {Fe6Gd6P6} cage 2 viewed (a) (left) perpendicular to the C3 axis and (right) down the C3 axis. (b) Polyhedralrepresentation of (left to right) {Fe6Gd6P6} core, Wells−Dawson polyoxometallate, and {Ni6Gd6P6} core. Colors: Gd, purple; Fe, blue; Ni, cyan; P,green; O, red; C, gray; H omitted for clarity.





triangle is equilateral. (iii) The Ln sites in the {Ni6Ln6P6} cagesare seven-coordinate, with a capped octahedral geometry, whilein the {Fe6Ln6P6} the Ln sites are eight-coordinate with adodecahedral coordination geometry.These changes to the ligand set are accompanied by less

variation in the phosphonate binding modes in {Fe6Ln6P6}. In{Ni6Ln6P6} two binding modes are observed: each half of themolecule has two 5.222 phosphonates (as in {Fe6Ln6P6}) whilethe third (on the unique Ni···Ni edge) is only 5.221 bound. In{Fe6Ln6P6} all the phosphonates are equivalent and 5.222

bound (Supporting Information, Figure S3). This affects theLn···Ln distances; for example, in the {Fe6Gd6P6} complex 2these are 3.931(2) Å, each pair being bridged by one 1,1 arm ofa phosphonate (i.e., single-atom bridging) and one 1,3-bridgingphosphonate (Supporting Information, Figure S3). In the{Ni6Gd6P6} complex with the same phosphonate (R = Ph)there are two Gd···Gd edges of 3.889(1) Å and four that aremuch longer (5.035(1) and 5.018(1) Å) corresponding to two1,3-bridging phosphonates. Finally, the nearest neighbor Fe···Ln distances are slightly longer than Ni···Ln, for example,3.677(3) Å in 2 and 3.360(2) to 3.509(2) Å in the equivalent{Ni6Gd6P6} molecule.The net result of these changes is that {Fe6Ln6P6} is a much

more regular and higher-symmetry system compared to{Ni6Ln6P6}. Schematically, {Fe6Ln6P6} is an equilateral trigonalantiprism (D3d; crystallographically imposed for 2 and 3) while{Ni6Ln6P6} is an isosceles trigonal antiprism (C2h, with the 2-fold axis corresponding to one of the perpendicular C2′ axes ofthe D3d structure; crystallographically there is only inversionsymmetry). This has direct consequences for the magneticinteractions in the molecules.

Magnetic Description. Magnetic susceptibility studies on1−6 were performed on polycrystalline samples in thetemperature range of 1.8−300 K under an applied direct-current (dc) magnetic field (H) of 1000 Oe. Magnetisation as afunction of applied field was investigated in the field and in thetemperature ranges of 0−7 T and 2−10 K, respectively (Figure3 and Supporting Information, Figure S4).For 1−3, room-temperature χMT values (where χM is the

molar magnetic susceptibility) of 52.4, 51.1, and 52.3 emu Kmol−1, respectively, were observed. These values are substan-tially lower than those calculated for the sum of six independentFeIII (S = 5/2) and six GdIII (S = 7/2) centers (73.5 emu Kmol−1, assuming g = 2.0 for both ions), but they are onlyslightly higher than expected for six GdIII ions (47.25 emu Kmol−1). On cooling, the χMT products decrease relatively slowlyuntil ca. 20 K, below which they decrease more rapidly,reaching 37.2, 27.8, and 36.5 emu K mol−1 for 1−3,respectively, at 2 K. The molar magnetization (M) as afunction of applied field at base temperature (2 K) rises slightlymore slowly than the calculated Brillouin function for sixnoninteracting GdIII (Figure 3), and the saturation values (atμ0H > ca. 4 T) are only slightly higher than they are for six GdIII

ions (42 μB), being 44.9, 43.4, and 44.9 μB for 1−3,respectively.

Figure 2. Comparison of {Fe6Gd6P6} and {Ni6Gd6P6}. (a) {Fe3(μ3-O)} (left) and {Ni3(μ3-O)} (right) fragments; (b) {Fe6Gd6P6} vieweddown the C3 axis (left) and equivalent {Ni6Gd6P6} (right); (c){Fe3Gd3P3} (left) and {Ni3Gd3P3} (right) fragments (the Ni1···Ni3edge is unique with a 1,1-bridging carboxylic acid). Colors: Gd, purple;Fe, blue; Ni, cyan; P, green; O, red; C, gray; H omitted for clarity.

Figure 3. (left) Molar magnetic susceptibility (χMT) vs T plot for 1−6 under 1 kG dc field. (right) Molar magnetization (M) as a function of appliedmagnetic field (H) at 2 K for 1−6.





Hence, the χMT(T) and M(H) behaviors are dominated bythe six GdIII ions. This implies that the magnetic moments dueto the six FeIII ions are largely canceled out by comparativelystrong antiferromagnetic interactions. If we assume that each{Fe3} triangle is strongly coupled with an S = 1/2 ground state,the saturation magnetization at 2 K corresponds to the sum ofsix S = 7/2 and two S = 1/2 centers, which is 44 μB (for g =2.0), close to the experimental values.As a representative example, the magnetic behavior of 2 was

modeled with an isotropic Heisenberg Hamiltonian:

∑ μ = − · +<

H J S S g BS2i j

ij i J B z(1)

Here si denotes the individual spin operators at site i (7/2 or

5/2) and Sz denotes the z component of the total spin operator.Because the dimension of the Hilbert space is a staggering 12230 590 464, an exact matrix diagonalization is impossible, butobservables can be approximated using the finite-temperatureLanczos method (FTLM).17 We considered three possibledistinct exchange interactions: J1 within the {Fe3} triangles, J2between nearest Gd ions within the buckled {Gd6} ring, and J3between each Fe ion and the closest Gd ion on the {Gd6} ring(Figure 4 and Supporting Information, Figure S5). An isotropicg = 2.00 was used. The poor radial extent of the Gd 4f functionsmeans that |J2| and |J3| are likely to be very small; hence, J1 is thedominant interaction. If we assume J3 = 0, to make thecalculations relatively simple, then good simultaneous agree-ment with the experimental χMT(T) andM(H) data is obtainedwith antiferromagnetic exchange interactions of J1 = −30 cm−1

and J2 = −0.04 cm−1 (Figure 4). If we instead assume J2 = 0,then we get a poorer approximation both in χMT(T) and M(H)(Supporting Information, Figure S5). We then investigatedparameters sets allowing both J2 and J3 to be nonzero, with J2varied in a narrow range of about −0.04 cm−1 (SupportingInformation, Figure S5). To summarize, good results could beobtained with nonzero |J3| < 0.1 cm−1, in accord with earlierfindings in 3d−4f cages3d and with slightly better agreement forferromagnetic coupling, with a slight decrease in the magnitudeof J2. A larger antiferromagnetic J3 coupling can be excludedbecause then the magnetization rises too slowly with appliedfield. A similar reason precludes smaller Fe···Fe (J1) couplingsbecause then the magnetization would rise to much largervalues.The very weak J1 and J2 interactions involving Gd ions is

expected. The Fe···Fe exchange is typical of that in the classicbasic metal carboxylate triangles [Fe3(μ3-O)(O2CR)6L3]

+;18

this is at first surprising because the exchange interactionmediated by phosphonates is generally much weaker than thatby carboxylates. However, the triangular fragments in 1−3 canbe written as [Fe3(μ3-O)(O2C

tBu)3(O2P(O)R)3(O2CtBu)3]

where the first three carboxylates are 1,3-bridging within thetriangle, while the second set of carboxylates are the “terminal”ligands; that is, they do not bridge within the triangle. Hence,with respect to [Fe3(μ3-O)(O2CR)6L3]

+, we have simplyreplaced three 1,3-bridging carboxylates for 1,3-bridgingphosphonates. Presumably the exchange interaction is carriedpredominantly by the oxide and remaining 1,3-bridgingcarboxylates.To assess the magnetocaloric behavior of 1−3, the magnetic

entropy changes were determined indirectly from the magnet-ization as a function of applied field and temperature data usingthe Maxwell relationship −ΔSm = ∫ [∂M(T,M)/∂T]H dH(Supporting Information, Figure S4). We obtain maximummagnetic entropy changes for ΔH = 0−7 T at 3 K of −ΔSm =25.4, 22.0, and 22.9 J kg−1 K−1 for 1−3, respectively. The largervalue for 1 is simply because of its lower molecular weight(phosphonate substituent R = Me vs Ph, hexyl): in molar unitswe have 95.1, 90.8, and 95.6 J mol−1 K−1, respectively.It is instructive to compare these results to those for

{Ni6Gd6P6} under the same experimental conditions: these arein the range of 105−116 J mol−1 K−1, depending on R. Hence,we have much larger magnetic entropy changes for {Ni6Gd6P6}cf. {Fe6Gd6P6} despite the lower spin and greater magneticanisotropy of NiII cf. FeIII. Moreover, for the former we areaccessing much more of theoretically possible magnetic entropygiven by the total multiplicity of the spin system, Sm = Πi ln(2Si+ 1) R (where R is the gas constant). For {Fe6Gd6P6} with six S= 5/2 and six S = 7/2 centers, this gives Sm = 193 J mol−1 K−1.Hence, under our experimental magnetization conditions weare only accessing ca. 50% of the available magnetic entropy.For {Ni6Gd6P6} with six S = 1 and six S = 7/2 centers, this givesSm = 159 J mol−1 K−1. Hence, for these compounds we areaccessing ca. 70% of the available magnetic entropy.This can be explained by the strength of the exchange

interaction within the 3d metal {M3} triangles. For {Fe6Gd6P6}we have JFe−Fe = −30 cm−1 (see above). For an isolatedequilateral {Fe3} triangle this would give a doubly degeneratetotal spin S = 1/2 ground state, with the lowest excited states (S= 3/2) at 90 cm−1. At low temperature only the S = 1/2 statesare accessible, even at high field. Magnetic data for {Ni6Gd6P6}could only be modeled with two unique JNi−Ni exchange values,consistent with the isosceles {Ni3} symmetry: two interactions

Figure 4. The (left) χMT(T) and (right) M(H,T) fittings for compound 2. (inset) Schematic sketch of the magnetic core 1−3; dashed lines indicateexchange interactions. The J3 coupling (not shown) acts between nearest Fe and Gd ions.





of +2 to +5 cm−1 (depending on R), and one interaction of −1to −4 cm−1 (depending on R). For an isolated {Ni3} trianglethis would give the entire 27-fold energy spectrum within 30−60 cm−1 (depending on R). There are two important points: (i)the couplings are much weaker for Ni, and (ii) there areferromagnetic interactions for Ni. These result in a muchgreater proportion of the magnetic spectrum (and hence theproportion of the possible magnetic entropy) being accessibleat low temperature and low field, combined with the ability tofully saturate the magnetization (M = 55 μB at 7 T and 2 K for{Ni6Gd6P6}, consistent with the full alignment of spins). Thesetwo factors enhance the magnetocaloric response for{Ni6Gd6P6} cf. {Fe6Gd6P6}, far outweighing the effect of thelower spin of NiII. These factors also override the significantzero-field splittings of NiII, which are in the range of 4−6 cm−1,from magnetic studies of {Ni6Y6P6}. The FeIII ions in{Fe6Gd6P6} could be treated as isotropic.Comparing the molar magnetic entropy for compounds 1−3,

it is clear than the value obtained for 2 is lower than that for 1and 3. This has also been observed in {Ni6Gd6P6} where themagnetic entropy of the phenyl phosphonate cluster wasslightly lower than that of the alky-phosphonate analogues.Comparing the magnetic data for 1−3 we can see that χMT(T)and M(H) are lower for 2 than they are for 1 and 3, suggestingslightly stronger antiferromagnetic interactions within thecluster.The χMT values at room temperature for 4−6 were: for 4,

101.4 emu K mol−1 (calcd. 111.25 emu K mol−1 for six FeIII, g =2.00, S = 5/2 and six DyIII, gJ = 4/3, J = 15/2); for 5, 99.4 emuK mol−1 (calcd. 110.6 emu K mol−1 for six FeIII, g = 2.00, S = 5/2 and six HoIII, gJ = 5/4, J = 8); and for 6, 80.7 emu K mol−1

(calcd. 97.1 emu K mol−1 for six FeIII, g = 2.00, S = 5/2 and sixTbIII, gJ = 3/2, J = 6). All these experimental room-temperaturevalues are lower than the sum of the constituent ions, againlikely due to the magnitude of the antiferromagnetic exchangeinteraction within the {Fe3O} moieties. In magnetizationexperiments M(H) for 4−6 at 2 K reaches values of 34.2,33.3, and 31.2 μB, respectively, at 7 T. None of the clustersshowed any out-of-phase response in alternating-currentsusceptibility measurements down to 2 K.

■ CONCLUSIONSSubstitution of the nickel dimer starting material for an ironsource allowed us to synthesize a family of {Fe6Ln6P6} cageswith a metal core analogous to the {Ni6Ln6P6} and the well-known Wells−Dawson polyoxometallates. These clusters aremore symmetrical than the nickel counterparts, possessing D3dpoint symmetry. Structurally three differences distinguish the{Fe6Ln6P6} from the {Ni6Ln6P6} clusters: the presence of 18carboxylates, 2 oxides, and 1 carbonate charge balancing thecage. Simultaneous fitting of the magnetic data χMT(T) andM(H) showed strong antiferromagnetic interactions betweenthe Fe···Fe pairs (JFe···Fe = −30 cm−1), which are responsible forthe lower observed MCE response than in {Ni6Gd6P6} despiteintroducing a more isotropic ion with higher spin multiplicity(FeIII, S = 5/2, 6S5/2). The model assumes an equilateral {Fe3}triangle, consistent with the crystallography, which would be ahighly frustrated system with a doubly degenerate pair of S = 1/2 states at lowest energy;19 Type 1 frustration by theclassification we have recently introduced.20 In general {Fe3}triangles show distortions at low temperature,18 losing thedegeneracy. The results we report here do not suggest any suchdistortion; however, we have not yet been able to make the

Wells−Dawson structure for {Fe6Y6P6}, which would allow usto investigate the frustration more carefully, for example byelectron paramagnetic resonance spectroscopy.

■ ASSOCIATED CONTENT*S Supporting InformationThis includes cif files, further synthetic details, structuraldrawings, further modeling of magnetic data, and magneticplots. This material is available free of charge via the Internet athttp://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: [email protected] (E.J.L.M.).*E-mail: [email protected] (R.E.P.W.).Present Address⊥Center for Applied Chemical Research, Frontier Institute ofScience and Technology, Xi’an Jiaotong University, Xi’an710054, China.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSE.M.P. thanks the Panamanian agency SENACYT-IFARHU.J.S. thanks the Deutsche Forschungsgemeinschaft (SCHN/615-15) for continuous support. Supercomputing time at the LRZGarching (Germany) is gratefully acknowledged. R.E.P.W.thanks the Royal Society for a Wolfson Merit Award. We alsothank Dr. David Allan and his team for help in use of X-ray atthe synchrotron at Diamond Light Source, and we thank DLSfor beam-time. The ALS is supported by the Director, Office ofScience, Office of Basic Energy Sciences, of the U.S.Department of Energy under Contract No. DE-AC02-05CH11231.

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(c) Zheng, Y.-Z.; Evangelisti, M.; Winpenny, R. E. P. Chem. Sci. 2011,2, 99. (d) Zheng, Y.-Z.; Pineda, E. M.; Helliwell, M.; Evangelisti, M.;Winpenny, R. E. P. Chem.Eur. J. 2012, 18, 4161. (e) Zheng, Y.-Z.;Evangelisti, M.; Tuna, F.; Winpenny, R. E. P. J. Am. Chem. Soc. 2012,134, 1057.(6) Pineda, E. M.; Tuna, F.; Pritchard, R. G.; Regan, A. C.;Winpenny, R. E. P.; McInnes, E. J. L. Chem. Commun. 2013, 49, 3522.(7) (a) Zheng, Y.-Z.; Evangelisti, M.; Winpenny, R. E. P. Angew.Chem., Int. Ed. 2011, 50, 3692. (b) Pineda, E. M.; Tuna, F.; Zheng, Y.-Z.; Winpenny, R. E. P.; McInnes, E. J. L. Inorg. Chem. 2013, 52, 13702.(8) An anion with a formula of X2M18O62

n−, where X = P, Si, and As,M = Mo and W, see Pope, M. T. Heteropoly and Isopoly Oxometalate;Springer: New York, 1983.(9) (a) Sharples, J. W.; Collison, D. Polyhedron 2013, 54, 91.(b) Sessoli, R. Angew. Chem., Int. Ed. 2012, 51, 43. (c) Evangelisti, M.;Brechin, E. K. Dalton Trans. 2010, 39, 4672. (d) Evangelisti, M.;Candini, A.; Ghirri, A.; Affronte, M.; Brechin, E. K.; McInnes, E. J. L.Appl. Phys. Lett. 2005, 87, 072504. (e) Garlatti, E.; Carretta, S.;Schnack, J.; Amoretti, G.; Santini, P. Appl. Phys. Lett. 2013, 103,202410.(10) Corradini, V.; Ghirri, A.; Candini, A.; Biagi, R.; del Pennino, U.;Dotti, G.; Otero, E.; Choueikani, F.; Blagg, R. J.; McInnes, E. J. L.;Affronte, M. Adv. Mater. 2013, 25, 2816.(11) (a) Gerbeleu, N. V.; Batsanov, A. S.; Timko, G. A.; Struchkov, Y.T.; Indrichan, K. M.; Popovich, G. A. Dokl. Akad. Nauk SSSR 1987,293, 364. (b) Tolis, E. I.; Helliwell, M.; Langley, S.; Raftery, J.;Winpenny, R. E. P. Angew. Chem., Int. Ed. 2003, 42, 3804.(12) (a) Fomina, I. G.; Kiskin, M. A.; Martynov, A. G.; Aleksandrov,G. G.; Dobrokhotova, Z. V.; Gorbunova, Y. G.; Shvedenkov, Y. G.;Tsivadze, A. Y.; Novotortsev, V. M.; Eremenko, I. L. Zh. Neorg. Khim.2004, 49, 1463. (b) Zoan, T. A.; Kuzmina, N. P.; Frolovskaya, S. N.;Rykov, A. N.; Mitrofanova, N. D.; Troyanov, S. I.; Pisarevsky, A. P.;Martynenko, L. I.; Korenev, Y. M. J. Alloys Compd. 1995, 225, 396.(13) Laye, R. H.; McInnes, E. J. L. Eur. J. Inorg. Chem. 2004, 14, 2811.(14) (a) Sheldrick, G. M. Acta Crystallogr. 2008, A64, 112.(b) Dolomanov, O. V.; Bourthis, L. J.; Gildea, R. L.; Howard, J. A.K.; Puschmann, H. J. Appl. Crystallogr. 2009, 42, 339.(15) X.Y1Y2Y3 where X is the total number of metal ions bound bythe ligand, and Y values refer to the number of metal ions attached tothe different donor atoms: Coxall, R. A.; Harris, S. G.; Henderson, D.K.; Parsons, S.; Tasker, P. A.; Winpenny, R. E. P. J. Chem. Soc., DaltonTrans. 2000, 2349.(16) For example: (a) Langley, S. K.; Moubaraki, B.; Murray, K. S.Inorg. Chem. 2012, 51, 3947. (b) Sakamoto, S.; Fujinami, T.; Nishi, K.;Matsumoto, N.; Mochida, N.; Ishida, T.; Sunatsuki, Y.; Re, N. Inorg.Chem. 2013, 52, 7218. (c) Bag, P.; Dutta, S.; Biswas, P.; Maji, S. K.;Florkec, U.; Nag, K. Dalton Trans. 2012, 41, 3414. (d) Barrett-Adams,D. M. Y.; Kahwa, I. A.; Mague, J. T. New J. Chem. 1998, 919.(17) (a) Jaklic, J.; Prelovsek, P. Phys. Rev. B: Condens. Matter Mater.Phys. 1994, 49, 5065. (b) Schnack, J.; Wendland, O. Eur. Phys. J. B2010, 78, 535−541.(18) Cannon, R. D.; White, R. P. Prog. Inorg. Chem. 1988, 36, 195.(19) (a) Mentrup, D.; Schmidt, H.-J.; Schnack, J.; Luban, M. Phys. A2000, 278, 214. (b) Barwinkel, K.; Hage, P.; Schmidt, H.-J.; Schnack, J.Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 054422.(20) Baker, M. L.; Timco, G. A.; Piligkos, S.; Mathieson, J.; Mutka,H.; Tuna, F.; Kozłowski, P.; Antkowiak, M.; Guidi, T.; Gupta, T.; Rath,H.; Woolfson, R. J.; Kamieniarz, G.; Pritchard, R. G.; Weihe, H.;Cronin, L.; Rajaraman, G.; Collison, D.; McInnes, E. J. L.; Winpenny,R. E. P. Proc. Natl. Acad. Sci. 2012, 109, 19113.





asas



S1


Iron lanthanide phosphonate clusters: {Fe6Ln6P6} Wells-‐Dawson like structures with D3d symmetry

Eufemio Moreno Pineda,a

Floriana Tuna,a

Yan-Zhen Zheng,a§

Simon J. Teat,b

Richard E. P. Winpenny,

a* Jürgen Schnack

c and Eric J. L. McInnes

a*

a. School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK.

b. Advanced Light Source, Lawrence Berkeley Laboratory, 1 Cyclotron Road, MS2-400, Berkeley CA 94720, USA.

c. Faculty of Physics, University of Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany.

§. Current address: Center for Applied Chemical Research, Frontier Institute of Science and Technology, Xi'an Jiaotong University, Xi'an 710054, China.

Experimental Details Synthesis of starting materials

Unless stated otherwise, all reagents and solvents were purchased from

Aldrich Chemicals and used without further purification. [Fe3(μ3-‐

O)(O2CtBu)6(HO2CtBu)3](HO2CtBu)9a 7 was prepared according to established

methods. [Ln2(O2CtBu)6(HO2CtBu)6]9b (Ln = Gd, 8; Tb, 9; Dy, 10 or Ho, 11) were

synthesized by refluxing Ln2O3 (3.62 g, 10 mmol) and excess pivalic acid (30 g, 300

mmol) at 160 ºC for 5 hrs to form a clear solution. Followed by cooling the solution

to room temperature and white precipitate came out. 50 ml toluene was added to

dissolve the access pivalic acid and filtered in vacuum and 50 ml n-hexane were used

to wash the product (yield ca. 13 g, 87 %).

Synthesis of compounds 1 to 6

All cluster were synthesized under similar conditions. Compound 1 to 6 were

obtained by mixing [Ln2(O2CtBu)6(HO2CtBu)6] (Ln = Gd, 8; Tb, 9; Dy, 10 or Ho, 11)

(0.1 mmol), 2 (0.1 g, 0.075 mmol), Et3N (0.1 ml, 1 mmol) and H2O3R (R = methyl,

phenyl or n-hexyl) (0.1 mmol) in MeCN (8 ml) and stirring at room temperature for a



S2

few minutes. The resulting slurry was transferred into a 10 mL Teflon-lined

autoclave, which was heated at 150 oC for 12 hrs and then cooled to room temperature

at a rate of 0.05 oC min-1. Reddish brown crystals were collected directly from the

autoclave. 1 IR (cm-1): 2959.3, 2927.9, 2902.8, 2867.8, 1553.2, 1478.0, 1423.2,

1360.7, 1230.7, 1088.8, 1003.6, 990.1; 2 IR (cm-1): 3055.0, 2973.6, 2960.9, 2928.7,

2904.2, 2866.7, 1550.0, 1480.3, 1424.1, 1356.8, 1228.6, 1089.1; 3 IR (cm-1): 2957.7,

2928.8, 2869.3, 2861.1, 1552.5, 1483.2, 1422.9, 1360.9, 1229.6, 1089.3, 993.7; 4 IR

(cm-1): 2959.9, 2927.3, 2903.1, 2869.2, 1552.2, 1481.7, 1426.4, 1357.6, 1230.2,

1082.6, 988.6; 5 IR (cm-1): 2961.1, 2927.5, 2905.4, 2870.1, 1554.9, 1482.1, 1427.5,

1360.5, 1230.0, 1081.2, 990.2; 6 IR (cm-1): 3053.7, 2961.7, 2927.3, 2902.8, 2868.4,

1550.2, 1483.6, 1425.0, 1358.4, 1231.5, 1088.7, 984.0.

Figure S1. IR spectra of {Fe6Ln6P6} clusters. a) 1; b) 2; c) 3; d) 4; e) 5 and f) 6.

b)a)

d)

e) f )

c)



S3

Unit cell collections for 4 and 5: for 4 [Fe6Dy6P6O59C96H180]: monoclinic, T = 100.0

K, a = 15.6404(6), b = 15.3450(2), c = 30.4378(9) Å, β = 99.820(2), V = 7197.9(2)

Å3; for 5 [Fe6Ho6P6O59C96H180]: monoclinic, T = 100.0 K, a = 15.6211(3), b =

15.3367(7), c = 30.3861(6) Å, β = 99.749(3), V = 7174.6(3) Å3.

Table S1. Elemental analysis and yield (%) for compounds 1 - 6

Formula Yielda Elemental analysis: Found (calculated) C H Fe Ln P

1 [Fe6Gd6(µ3-O)2(O3PMe)6(O2CtBu)18(CO3)] 52% 30.75 (30.81)

4.76 (4.85)

9.07 (8.95)

24.98 (25.21)

4.92 (4.96)

2 [Fe6Gd6(µ3-O)2(O3PPh)6(O2CtBu)18(CO3)] 41% 37.15 (36.96)

4.46 (4.50)

8.16 (8.12)

22.64 (22.86)

4.53 (4.50)

3 [Fe6Gd6(µ3-O)2(O3PHx)6(O2CtBu)18(CO3)] 48% 36.40 (36.53)

5.73 (5.79)

8.10 (8.02)

22.79 (22.6)

4.44 (4.45)

4 [Fe6Dy6(µ3-O)2(O3PMe)6(O2CtBu)18(CO3)] 46% 30.35 (30.55)

4.77 (4.81)

9.06 (8.88)

25.97 (25.83)

4.89 (4.92)

5 [Fe6Ho6(µ3-O)2(O3PMe)6(O2CtBu)18(CO3)] 43% 30.58 (30.43)

4.82 (4.79)

8.98 (8.84)

25.93 (26.12)

4.82 (4.90)

6 [Fe6Tb6(µ3-O)2(O3PPh)6(O2CtBu)18(CO3)] 40% 36.90 (36.87)

4.67 (4.68)

8.20 (8.10)

23.25 (23.05)

4.46 (4.49)

a. Calculated based on the lanthanide pivalate starting material.



S4

Figure S2. Crystal structures of 1 – 3: a) 1 (down the C3 axis); b) 2 (down the C3 axis); c) 3 (down the C3 axis); d) 1 (perpendicular the C3 axis); e) 2 (perpendicular the C3 axis) and f) 3 (perpendicular the C3 axis). Scheme: Gd, purple; Fe, blue; P, green; O, orange; C, grey; (H omitted for clarity).s

a)

d) e) f )

b) c)



S5

Figure S3. Comparison between Ni6Gd6P6 (a) and Fe6Gd6P6 (b) cluster; c) (from left to right) 5.222 and 5.221 coordination modes of phosphonates in {Ni6Gd6P6} and 5.222 in {Fe6Gd6P6}. Scheme: Gd, purple; Fe, blue; Ni, cyan; P, green; O, red; C, grey; H omitted for clarity.

a) b)

c)



S6

Figure S4. Magnetisation and magnetic entropy change calculated from isothermal magnetisations (left and right) for a) 1; b) 2; c) 3 for a ΔH = 0 - 7 T.

a)

b)

c)



S7

Figure S5. Theoretical χMT(T) and M(H,T) curves for 2 for various parameter sets. Since FTLM is numerically very demanding, χ2–fits are impossible. Thus a few reasonable parameter sets have been investigated. Parameters for (a) and (b) are provided in (a), those for (c) and (d) in (c). The red solid curves give the closest approximation to the experimental data (symbols), which can be clearly deduced from the magnetization versus field curves. χMT(T) was measured and calculated at µ0H=0.1 T, M(H,T) is displayed for T=2 K (upper curves) and T=4 K (lower curves).



asas



Chapter 5

Single Molecule Magnets

5.1 SMMs: ApplicationsThe physical realisation in the 1990’s that molecules can retain magnetisation at puremolecular level, entities called SMMs, led to extensive investigations of molecular ma-terials due to their potential use in technological applications[1]. SMMs are appealingmolecules since they combine large magnetic moments with a stable spin orientation,therefore showing magnetic properties as macroscopic bulk magnets[1]. Moreover,these milestone systems do not just display similar properties to their macroscopiccounterparts, but also exhibit interesting quantum phenomena, such as quantum phaseinterference[2] and quantum tunnelling of the magnetisation[3].

Other applications were envisaged, not just for SMMs, but also for MNMs, wheretheir collective magnetic behaviour led to fascinating physics, ranging from spintronics[4],molecular electronic[5], quantum computing[6] and molecular coolers[7,8]. The reasonsbehind such interest are not based solely on the enhanced properties observed in molec-ular systems, but also because these properties can be observed at a molecular level,opening a window to smaller devices, a clear trend observed in current device designs.Most importantly, these nano-entities can be synthesised so that each unit is identicalto the others and they also allow easy functionalisation through the variation of theligands, allowing their integration in devices through bottom-up approaches[9].

Despite the above-mentioned advantages and interesting facts of molecular materi-als the understanding of their physical properties still represents a great challenge. It isfor this reason that an in-depth understanding of the properties of molecular materialsis an active research area. A better understanding of their magnetic properties can givea handle to better development of molecular devices.

5.2 4f-SMMs: InteractionsIt is well known that at single ion level the magnetic behaviour of lanthanide ions isdue to the Ising anisotropy[11], which mainly depends on the geometry[15] and ligandfield in which the lanthanide is placed[15] (see Chapter 2 section 2.5). There are many

93

5.2. 4F-SMMS: INTERACTIONS

reports about the magnetic behaviour of single ion SMMs, where the main goal hasbeen to investigate the role of the ligand set surrounding the lanthanides and its ef-fect on the SMMs properties, such as Na[Dy(DOTA)(H2O)]·4H2O[16] where DOTA= 1,4,7,10-tetraazacyclododecane-N,N′,N′′,N′′′-tetra-acetate, [Dy(paaH∗)2(NO3)2][17]

where paaH = N-(2-Pyridyl)-ketoacetamide and [DyCp∗COT][18] where Cp* = pen-tamethylcyclopentadiene and COT = cyclooctatetraene (see Figure 5.1).

Figure 5.1: Structures of mononuclear lanthanide SMMs: (a) Na[Dy(DOTA)(H2O)]; (b)[Dy(paaH∗)2(NO3)2]; (c) [DyCp∗COT]. Colour code: Dy, purple; blue; N, cyan; O, red; Cgrey, Na, blue. Hydrogens omitted for clarity.

However, when two lanthanides are brought into close proximity, the magneticbehaviour is more complicated. For example, lanthanide-based SMMs usually ex-hibit energy barriers (Ueff) an order of magnitude larger than 3d-based counterparts;nonetheless despite such enhancement, they often show narrow hysteresis loops, dueto their fast quantum tunnelling (QTM).

In polymetallic systems the ligand and crystal field, exchange interactions, geom-etry and orientation of single sites are some of the factors that control the magneticbehaviour. Some groups have shown that introduction of some interactions betweenlanthanide pairs can yield bigger hysteresis loops[19,20]. For example, Long an co-workers have been able to achieve hysteresis loops up to 14 K[19,20], with the introduc-tion of radical bridging ligands between Dy(III) and Tb(III) lanthanide ions (Figure5.2).

Figure 5.2: (a) Radical-bridge dysprosium dimer SMM [[(Me3Si)2N]2Dy(THF)2(µ-η 2:η 2-N2)]−; (b) Magnetisation (M) vs. field (H) from 11 to 15 K for Dy-radical bridge compound.Colour code: Dy, purple; blue; N, cyan; O, red; C grey, Si, pink. Hydrogens omitted for clarity.


5.3. 3D/4F-SMMS: INTERACTIONS

However it has been observed that more often, magnetic interactions between lan-thanides increase the quantum tunnelling leading to smaller Ueff. An approach that hasbeen successful in the enhancement of Ueff has been magnetic dilution of the param-agnetic lanthanide ion into a diamagnetic isostructural host[13,21]. In such way, sev-eral authors have achieved better SMM performance with enhanced Ueff and it hasalso allowed better understanding of the role of the magnetic interactions between lan-thanides.

5.3 3d/4f-SMMs: InteractionsSimilarly, introduction of interactions using 3d transition metals has been intensivelyinvestigated. Regularly, due to the inner nature of the magnetic 4f orbitals of lanthanideions, the exchange interactions are quite small. In lanthanides the magnetic orbitals,4f, are situated below the 6s and 5d leading too poor overlap with the ligand orbitals.When 3d and 4f ions are brought into close proximity, the situation is slightly different.Gatteschi and co-workers in the 1980s showed that when a 3d and 4f metal are closeto each other, ferromagnetic interactions are achieved[22-24].

Figure 5.3: Structures of 3d/4f cages: (a) [(µ 3-C9H3O6){LCuDy(NO3)2}3]; (b)[Co2Dy2(L)4(NO3)2(THF)2]; (c) [Cr2Dy2(OMe)2(mdea)2(acac)4(NO3)2]; (d) [Cr4Dy4(µ3-OH)4(µ-N3)4(mdea)4(piv)4]. Colour code: Dy, purple; blue; N, cyan; O, red; C grey, Co,light purple; Cu, blue. Hydrogens omitted for clarity.



Due to the stronger exchange interactions observed in 3d/4f mixed metal systems,this has emerged as a common method to synthesise complexes with SMMs prop-erties. While stronger exchange interactions imposed for the 3d metal can lead tohigher spin ground states (S), the introduction of lanthanides, inherently having stronganisotropic character (D) when Tb(III), Dy(III), Ho(III) and Er(III) are the ions, canprompt better dynamic magnetic properties. For example, strong ferromagnetic inter-actions in a butterfly-like [Cr2Dy2(OMe)2(mdea)2(acac)4(NO3)2][25] (where mdea =N-methyldiethanolamine and acac = acetylacetonate), have led to hysteresis loops.

Similarly other 3d/4f SMMs have been obtained, such as: {LCuDy(NO3)2}3[28] (L

= 2-hydroxy-3-(hydroxymethyl)-methylbenzaldehyde), [Co2Dy2(L)4(NO3)2(THF)2][26]

(L = (2-(2-Hydroxy-3-methoxybenzylideneamino)phenol) and [Cr4Dy4(µ3-OH)4(µ-N3)4(mdea)4(piv)4][27] (mdea = N-methyldiethanolamine and piv = dimethylpropanoicacid) where interesting magnetic behaviour has been observed (Figure 5.3). Manyattractive 3d/4f molecules have been reported; nonetheless not much is understoodregarding the exchange interaction (J3d-4f) between the mixed-metal pair when thelanthanide centre is a highly anisotropic system.

References[1] D. Gatteschi, R. Sessoli and J. Villain, Molecular nanomagnets, Oxford Univer-

sity Press, Oxford, 2006.

[2] W. Wernsdorfer and R. Sessoli, Science, 1999, 284, 133.

[3] L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli and B. Barbara, Nature,1996, 383, 145.

[4] S. Sanvito, Chem. Soc. Rev., 2011, 40, 3336.

[5] R. Vincent, S. Klyatskaya, M. Ruben, W. Wernsdorfer and F. Balestro, Nature,2012, 488, 357.

[6] M. N. Leuenberger and D. Loss, Nature 2001, 410, 789.


[8] 8. F. Torres, J. M. Hernandez, X. Bohigas and J. Tejada, Appl. Phys. Lett., 2000,77, 3248.

[9] J. Bartolomé, F. Luis and J. F. Fernández, Molecular Magnets: Physics andApplications, Springer, London, 2014.

[10] R. Bagai and G. Christou, Chem. Soc. Rev., 2009, 38, 1011.

[11] O. Roubeau and R. Clérac, Eur. J. Inorg. Chem., 2008, 28, 4325.

[12] N. Ishikawa, M. Sugita, T. Ishikawa, S.-Y. Koshihara and Y. Kaizu, J. Am. Chem.Soc., 2003, 125, 8694.



[13] R. J. Blagg, L. Ungur, F. Tuna, J. Speak, P. Comar, D. Collison, W. Wernsdorfer,E. J. L. McInnes, L. F. Chibotaru and R. E. P. Winpenny, Nat. Chem., 2013, 5,673.

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[16] N. F. Chilton, S. K. Langley, B. Moubaraki, A. Soncini, S. R. Batten and K. S.Murray, Chem. Sci., 2013, 4, 1719.

[17] G. Cucinotta, M. Perfetti, J. Luzon, M. Etienne, P. Car, A. Caneschi, G. Calvez,K. Bernot and R. Sessoli, Angew. Chem., Int. Ed., 2012, 51, 1606.

[18] S.-D. Jiang, S.-S. Liu, L.-N. Zhou, B.-W. Wang, Z.-M. Wang and S. Gao, Inorg.Chem., 2012, 51, 3079

[19] J. D. Rinehart, M. Fang, W. J. Evans and J. R. Long, J. Am. Chem. Soc., 2011,133, 14236.

[20] J. M. Zadrozny, D. J. Xiao, M. Atanasov, G. J. Long, F. Grandjean, F. Neese andJ. R. Long, Nature, 2013, 4, 577.

[21] J. D. Rinehart, M. Fang, W. J. Evan and J. R. Long, Nat. Chem., 2011, 3, 538.


[23] C. Bencini, C. Benelli, A. Caneschi, A. Dei and D. Gatteschi, Inorg. Chem.,1986, 25, 572.


[25] S. K. Langley, D. P. Wielechowski, V. Vieru, N. F. Chilton, B. Moubaraki, L. F.Chibotaru and K. S. Murray, Chem. Sci., 2014, DOI: 10.1039/c4sc01239a.

[26] K. Chandra Mondal, A. Sundt, Y. Lan, G. E. Kostakis, O. Waldmann, L. Ungur,L. F. Chibotaru, C. E. Anson and A. K. Powell, Angew. Chem. Int. Ed., 2012,51, 7550.

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Chapter 6

4f and 3d/4f SMMs

6.1 4f-4f and 3d-4f interactionsBearing in mind that 4f and 3d/4f interactions are poorly understood and that a thor-ough understanding of their magnetic properties is a key requirement for a rationaldesign of molecular devices, we have explored two different SMM systems. In thefirst one, an asymmetric {Dy2} has been studied. The neat sample do not show SMMproperties, however when doped in a diamagnetic host, the SMM properties are clearlyrevealed, inferring that exchange interactions play a key role in their dynamic magneticproperties. We have developed a model to rationally explain the role of the exchangeinteraction upon the SMM behaviour using SQUID measurements, EPR spectroscopyand ab-initio calculations, amongst others techniques. We have subsequently studieda family of twenty-seven 3d/4f mixed metal isostructural molecules, where the SMMproperties are 3d metal dependent, allowing us to study the effect of the 3d/4f interac-tions and the SMM behaviour of the anisotropic lanthanide ions.

6.1.1 Direct measurement of DyIII· · ·DyIII interactions in a single-molecule magnet

Nature Communications, 2014, 5, doi:10.1038/ncomms6243

6.1.2 Systematic study of a family of butterfly-like {M2Ln2} molec-ular magnets

To be submitted to JACS

99

6.1. 4F-4F AND 3D-4F INTERACTIONS


ARTICLE

Received 11 Jul 2014 | Accepted 12 Sep 2014 | Published 13 Oct 2014

Direct measurement of dysprosium(III)???dysprosium(III) interactions in a single-moleculemagnetEufemio Moreno Pineda1, Nicholas F. Chilton1, Raphael Marx2, Marıa Dorfel2, Daniel O. Sells1, Petr Neugebauer2,

Shang-Da Jiang3, David Collison1, Joris van Slageren2, Eric J.L. McInnes1 & Richard E.P. Winpenny1

Lanthanide compounds show much higher energy barriers to magnetic relaxation than

3d-block compounds, and this has led to speculation that they could be used in molecular

spintronic devices. Prototype molecular spin valves and molecular transistors have been

reported, with remarkable experiments showing the influence of nuclear hyperfine coupling

on transport properties. Modelling magnetic data measured on lanthanides is always com-

plicated due to the strong spin–orbit coupling and subtle crystal field effects observed for the

4f-ions; this problem becomes still more challenging when interactions between lanthanide

ions are also important. Such interactions have been shown to hinder and enhance magnetic

relaxation in different examples, hence understanding their nature is vital. Here we are able to

measure directly the interaction between two dysprosium(III) ions through multi-frequency

electron paramagnetic resonance spectroscopy and other techniques, and explain how this

influences the dynamic magnetic behaviour of the system.

DOI: 10.1038/ncomms6243

1 School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, UK. 2 Institut fur Physikalische Chemie,Universitat Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany. 3 1. Physikalisches Institut, Universitat Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart,Germany. Correspondence and requests for materials should be addressed to E.J.L.M. (email: [email protected]) or to R.E.P.W.(email: [email protected]).

NATURE COMMUNICATIONS | 5:5243 | DOI: 10.1038/ncomms6243 | www.nature.com/naturecommunications 1

& 2014 Macmillan Publishers Limited. All rights reserved.



Fascinating physics has been observed in lanthanide-basedmolecules ranging from single nuclear spin detectionand manipulation1,2, blocking of magnetization at

unprecedentedly high temperatures for a molecule3,4, magneticmemory in chiral systems with a non-magnetic ground state5,6

and energy barriers for loss of magnetization, Ueff, an order ofmagnitude higher than observed for polymetallic d-block cages7,8.A diverse range of applications has been envisioned forlanthanide (Ln) containing molecules, including use as qubitsfor quantum information processing9,10 and prototype devicessuch as molecular spin valves11 and transistors1 have beenreported. These advances have been very rapid since the initialreport that a terbium phthalocyanine compound could functionas a single-molecule magnet (SMM)12.

The SMM behaviour observed for Ln complexes is due to thelarge magnetic anisotropy of the individual ions, caused by strongspin–orbit coupling and the crystal field (CF) effects due to theligand environment13,14. Other interactions, for exampleintermolecular effects, often favour efficient quantum tunnellingof magnetization at zero external field, and this factor can meanlittle magnetic hysteresis is seen even in compounds with verylarge Ueff

13. When considering polymetallic Ln complexes, thesituation becomes even more complicated. Radical bridgingligands can provide a strong magnetic exchange pathwaybetween two lanthanide ions, leading to magnetic hysteresis at14 K3,4. In other compounds weak Ln � � � Ln interactions canshift the zero-field quantum tunnelling step to a finite field,known as exchange biasing15, with different effects on cryogenicmagnetization curves depending on the sign of the exchange16,17

or even mask single-ion slow relaxation modes18. Morefrequently, however, Ln � � � Ln interactions increase quantumtunnelling rates, leading to apparently lower Ueff values whencompared with paramagnetic Ln ions doped into a diamagneticlattice8,17,19. Understanding how Ln � � � Ln interactions can havesuch different and seemingly contradictory influences isimportant for improving the performance of Ln SMMs.

Understanding such interactions in polymetallic molecular Lncomplexes is far from trivial. Part of this problem is that bulkmagnetic measurements provide only indirect evidence of weakLn � � � Ln interactions which can be difficult to distinguish fromother contributions to the low energy physics, for example, CFeffects, intermolecular interactions, impurities. In this work westudy a {Dy2} complex where we can spectroscopically measure aDy(III) � � �Dy(III) interaction that quenches SMM behaviour.We combine magnetic measurements, electron paramagneticresonance (EPR) spectroscopy, ab initio calculations and far-infrared (FIR) spectroscopy to develop a simple model to describethe magnetic interaction in a Dy � � �Dy pair, and provide designcriteria for when this interaction will lead to exchange biasing,and when it will lead to collapse of the SMM behaviour.

ResultsSynthesis and structure. Hydrated lanthanide nitrateLn(NO3)3 � nH2O and 8-hydroxyquinoline (hqH) were combinedin a 1:2.5 mole ratio and heated to reflux in MeOH for 3 h. Slowevaporation of this solution gave yellow block-shaped X-rayquality single crystals in a yield of 52–75%. Characterization bysingle crystal X-ray diffraction revealed an asymmetric lanthanidedimer with formula [hqH2][Ln2(hq)4(NO3)3] �MeOH (Ln¼YIII,1; TbIII, 2; DyIII, 3; HoIII, 4; ErIII, 5; YbIII, 6 and LuIII, 7; seeMethods, Supplementary Tables 1 and 2 and SupplementaryData 1–7). Compounds 1–7 are isostructural, crystallizing in themonoclinic space group P21/c (Fig. 1a; see Methods andSupplementary Tables 3–5). We focus on 3 as it has the mostinteresting magnetic properties. The dimer consists of two Dy(III)

ions, three nitrate anions and four 8-quinolinolate ligands, crys-tallizing with a protonated 8-hydroxyquinolinium counter-cationand a molecule of MeOH. Dy(1) is bound by three bridging8-quinolinolate ligands and a single chelating 8-quinolinolateligand, generating an N4O4 coordination environment with abicapped trigonal prism geometry, subsequently referred to as the‘hq pocket’ (Fig. 1a). The Dy(2) site binds to three chelatingnitrate anions and the O-atoms from three bridging quinolinateligands, yielding a highly distorted O9 environment subsequentlyreferred to as the ‘NO3 pocket’. The eight-coordinate hq pocket issignificantly smaller than the nine-coordinate NO3 pocket: thevolumes defined by the donor atoms are 130 and 140 Å3,respectively.

As the two coordination sites are different in compounds 1–7,we can take advantage of the lanthanide contraction to dopeparamagnetic ions into one or the other of the two pockets ofthe diamagnetic yttrium or lutetium compound, 1 and 7respectively20. Crystallographic studies on 1:1 heterobimetallicLn-Y compounds (see Methods, Supplementary Tables 6–8 andSupplementary Data 8–13) show that LuIII occupies the smallerhq pocket in Lu-Y, while for the Dy-Y compound there is adistribution between the two pockets as YIII and DyIII havesimilar ionic radii. Therefore for DyIII doped at a low level into 7,hereafter {Dy@Lu2}, DyIII is in the NO3 pocket, while for DyIII

doped at a low level into 1, hereafter {Dy@Y2}, DyIII is distributedevenly between the two pockets.

Magnetic measurements. The room temperature wMT value for 3(26.8 cm3 K mol� 1) is close to the expected value for two non-interacting DyIII ions and declines smoothly on cooling reachinga minimum at 5 K (Fig. 2a) due to the depopulation of the CFstates. Below 5 K wMT increases due to a weak ferromagneticinteraction between the paramagnetic centres. The lowtemperature magnetization versus applied magnetic field does notsaturate at 1.8 K in a field of 7 T, indicating strong magneticanisotropy (Fig. 2a inset).

The dynamic magnetic behaviour of 3 was investigatedthrough alternating current (AC) magnetic susceptibilitymeasurements, performed both with a zero and a 1 kG applied

Dy(1)

Dy(2)

Dy(1) 44°

J ⊥

J ||

Dy(2)

gz = 20

gz′ = 13.9x

z

y

Figure 1 | Structural analysis. (a) Crystal structure of 3. Scheme: Dy, blue;

N, light blue; O, red; C, grey; H, dark grey. Orientation of the principal

magnetic axes for Dy(1) and Dy(2) in the ground Kramers doublet from ab

initio calculations shown as orange arrows and that for Dy(1) from

electrostatic calculations as green arrow. (b) Schematic of the magnetic

model for the EPR simulation. Relative projection of the principal magnetic

axes for Dy(1) and Dy(2), along which gz¼ 20 and 13.9 for Dy(1) and

Dy(2), respectively, and the anisotropic exchange interaction between the

dysprosium pair.

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6243

2 NATURE COMMUNICATIONS | 5:5243 | DOI: 10.1038/ncomms6243 | www.nature.com/naturecommunications




direct current (DC) magnetic field. No frequency dependence wasobserved under zero DC field; whereas at 1 kG a small out-of-phase component is observed, but with no maximum in thetemperature range 1.8–24 K (Supplementary Fig. 1a–c). Bystudying doped materials, we can show that the lacklustredynamic behaviour observed in 3 is due to the effect ofinteractions between the Dy(III) ions.

AC measurements on {Dy@Lu2} revealed only a small out-of-phase component below 3 K (Supplementary Fig. 1d–f), similar tothat of the pure compound 3. However the {Dy@Y2} analogueshows pronounced slow relaxation with frequency-dependentpeaks in the out-of-phase susceptibility wM

00 to 12 K (Fig. 2b,c andSupplementary Figs 2 and 3), when we use an optimal DC field of1 kG (Supplementary Fig. 2a). Treating the highest temperatureAC data with the Arrhenius model gives Ueff¼ 41 cm� 1 andt0¼ 1.4� 10� 6 s (Fig. 2b inset); however, the lower temperaturedata is markedly nonlinear suggesting the onset of competingOrbach and Raman processes and this Ueff value should betreated with some caution. Fitting the AC susceptibility data to asingle Debye function reveals a single dominant relaxation path athigher temperatures (distribution parameter, a¼ 0.03(1) at 12 K),with other pathways becoming competitive at lower temperatures(a¼ 0.55(2) at 3.5 K; Fig. 2c and Supplementary Fig. 3). Fromthese observations we can determine that Dy(III) in the smallerhq pocket is an SMM, whereas Dy(III) in the larger NO3 pocket isnot. The SMM behaviour is quenched in the pure compound 3due to intramolecular Dy � � �Dy interactions, vide infra.

Ab initio calculations and FIR measurements. Multi-configurational complete active space self-consistent field(CASSCF) calculations are the most accurate ab initio methods torationalize the magnetic properties of lanthanide systems6,8,15,21,

but they are not perfect and often require scaling to matchabsolute experimental values: this has been shown to be a result ofneglected correlation energies and possible small structuralchanges at low temperatures22. We have performed suchcalculations on compound 3 with MOLCAS 7.8 (ref. 23; seeMethods and Supplementary Table 9). Dy(III) has a 6H15/2

ground term, separated from the excited 6H13/2 term by roughly4,000 cm� 1, and therefore we need only consider the groundmultiplet for the magnetic properties. The CF removes the16-fold degeneracy of the 6H15/2 multiplet giving eight Kramersdoublets, which are linear combinations of mJ¼±1/2 � � �±15/2,where mJ is the projection of J upon the axis of quantization.

CASSCF calculations predict markedly different properties forthe two Dy(III) sites in 3 (Supplementary Tables 10 and 11), asexpected given the different coordination environments. ForDy(III) in the hq pocket, the ground doublet is an almost puremJ¼±15/2, as characterized by the calculated gz-value approach-ing 20 and gx and gy values close to zero. Its main magnetic axislies along the Dy-O vector of the terminal 8-hydroxyquinolinolateligand, which happens to be co-parallel with the Dy � � �Dy vector(Fig. 1a). Electrostatic optimization of the oblate mJ¼±15/2

electron density24 provides the same result (8.6� difference toCASSCF) and confirms that this orientation is due to the shortterminal Dy-O bond of 2.248(3) Å (c.f. 2.349(3)–2.384(3) Å forthe bridging oxygen atoms), identical to the motif in the recentlydescribed homoleptic [Dy3(hq)9]25. The first excited doublet iswell separated from the ground state (B100 cm� 1) and hasdominant mJ¼±13/2 character with its main magnetic axis (gz)almost colinear with that of the ground doublet. This is consistentwith the observed SMM behaviour of {Dy@Y2}. For Dy(III) in theNO3 pocket, the ground doublet has g-values of gz¼ 16.42,gy¼ 1.54, gx¼ 0.05 (Supplementary Table 11) and hence is not apure mJ¼±15/2 doublet. The first excited doublet is at only

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2 4 6 8 10 12 14 16 18 20Temperature / K

1 Hz10 Hz70 Hz200 Hz451 Hz700 Hz957 Hz1,202 Hz

–9

–7

–5

–3

–1

0.1 0.2 0.3

Temperature–1 / K

18

20

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24

26

28

0 50 100 150 200 250 300Temperature / K

0

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0 1 2 3 4 5 6 7Field / T

1.8 K3 K4 K

0.0

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0.7

0.5 1.0 1.5 2.0 2.5 3.0 3.50.80

0.85

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1.05

1.10

10 20 30 40 50 60 70 80 90

Nor

mal

ized

tran

smis

sion

Energy / cm–1

0T/6T1T/6T2T/6T3T/6T4T/6T5T/6T

Calculation

Experiment

3.5 K

Ueff = 41 cm–1

�0 = 1.4 ×10–6 s0.03 > � > 0.55

χ″M

/ cm

3 m

ol–1

12 K

χ″M

/ cm

3 m

ol–1

χ′M / cm3 mol–1

Mag

netiz

atio

n / N

Aμ B

χ MT

/ cm

3 m

ol–1

K ln(τ

)

Figure 2 | Magnetic measurements. (a) Experimental wMT(T) and M(H,T) (inset) data (symbols) and best fits (red lines) for 3. (b) wM0 0 (T) measured

under a 1 kG HDC field (1.55 G AC field) and Arrhenius treatment of wM0 0 data for the high temperature process (inset) for {Dy@Y2}. (c) Cole-Cole plots

(wM0 0 versus wM

0) showing a single relaxation process above 3.5 K, solid lines are fits of the AC susceptibility data to a modified Debye function for

{Dy@Y2}. (d) Normalized FIR transmission spectra at 9 K for 3.

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6243 ARTICLE





B24 cm� 1, is strongly mixed and is misaligned with the grounddoublet. This is consistent with {Dy@Lu2} not behaving as anSMM. The angle between the principal magnetic axes (gz) of theground states for the two sites is calculated to be 44� by CASSCF(Fig. 1a).

As the calculated CF splittings of the ground multiplet ofDy(III) in the NO3 pocket lie squarely in the FIR region, we haveused magnetic field-dependent FIR absorption spectroscopy22 tomeasure them directly. Studies of compound 3 show two field-dependent bands at 39 and 59 cm� 1 (Fig. 2d and SupplementaryFig. 4) and therefore these are assigned as CF (as opposed tophonon) transitions. CASSCF predicts the first two CF transitionsto be at 24 and 39 cm� 1. The agreement is remarkably goodgiven that CF splittings for lanthanides can be several hundredwavenumbers. The ratio of the energy intervals is correct, and asimple scaling factor22 of 1.6 (see above) gives the experimentalenergies (Supplementary Table 12).

The CASSCF results can be recast in the form of a set of CFparameters26. We have applied the FIR scaling factor to theseparameters, and then used the scaled CF parameters(Supplementary Table 13) to calculate magnetic observables andthe magnetic transitions in the FIR spectra (Fig. 2d). This alonegives excellent agreement with experimental wMT(T) from5–300 K (c.f. using unscaled CF parameters, SupplementaryFig. 5), but to simulate the low temperature wMT(T) and M(H)data, we need to account for a weak exchange interaction.One way to simulate such thermodynamic data for orbitallydegenerate ions is the Lines model27, which employs an isotropicexchange between the spin component of the angular momenta(S¼ 5/2 for Dy(III); see Methods) and has been used previously tomodel interactions between lanthanides15,28. Employing thismodel with PHI29 we find JLines¼ þ 0.047(1) cm� 1, whichgives excellent fits to both wMT(T) and M(H) (Fig. 2a).

EPR studies. Weak exchange can be better defined by EPRspectroscopy, even between orbitally degenerate ions30,31, butsuch studies on lanthanide pairs are rare outside minerals, due tofast spin-lattice relaxation. Compound 3, {Dy@Y2} and {Dy@Lu2}all give rich EPR spectra; the spectra of {Dy@Y2} and {Dy@Lu2}are very similar since in both cases we only see resonances for theDy(III) ion in the NO3 pocket. This is because Dy(III) in the hqpocket has an essentially pure mJ¼±15/2 state, which is EPRsilent and hence no g¼ 20 resonance is observed.

At low microwave frequencies (9.7, 24 and 34 GHz), thespectra of {Dy@Y2} and {Dy@Lu2} are dominated by an intensefeature at geffE14, which broadens at higher frequencies4130 GHz (Fig. 3 and Supplementary Figs 6–8). There are otherweaker features that match features from spectra of the pure

compound 3 (Fig. 3 and Supplementary Fig. 6). We simulate allspectra of the doped species with EasySpin32, using the effectivespin formalism (Seff¼ 1/2) with gx¼ gy¼ 0.1, gz¼ 13.9. Thetransverse g-values of 0.1 are arbitrarily small numbers and notmeasurable. The measured gz-value is similar to that calculatedfor the ground doublet of the NO3 pocket by ab initio methods(Supplementary Table 11) and is indicative of a strongly mixedground state.

The Dy � � �Dy exchange significantly perturbs the EPR spectraof compound 3 measured at lower frequencies (3.9, 9.7, 24 and34 GHz) with multiple resonances observed (Fig. 3 andSupplementary Fig. 9). For example, the 24 GHz spectrum of 3has a resonance close to zero field; hence a splitting has beenintroduced equal to the microwave energy of B0.8 cm� 1. Thehigh-frequency EPR spectra are much broader, and therefore lesssensitive to weak exchange interactions (Supplementary Fig. 10).

As an initial approach to modelling the EPR spectra of thecoupled system, we can of course use the same approachemployed for the fitting of the thermodynamic magnetic data, viz.the Lines model with scaled ab initio CFPs. Simulations of thelow-frequency EPR spectra using the isotropic Lines exchangeparameter (extracted from fitting the magnetometry data) yieldsome features of the spectra (Supplementary Fig. 11), however, itis clear that the simulations are far from perfect. It is also clearfrom the spectra on doped samples that while the ab initio-calculated CFPs provide a decent approximation to the groundstates, they are not a perfect starting point for examining theexchange interaction (that is, we must get the description of theindividual sites correct before tackling the exchange interaction).Unfortunately due to the low symmetry of both pockets in thismolecule, no reduction in the number of allowed CFPs can bemade and therefore we are left with 27 parameters to describeeach pocket. Clearly this problem is over-parameterised and itwould not be feasible to find a unique solution.

Therefore, a much simpler approach to simulating thesespectra has been adopted, invoking a model of two effective spins,Seff¼ 1/2. For the hq pocket we have gx¼ gy¼ 0 and gz¼ 20 fromits EPR silent nature, SMM behaviour and ab initio calculations.For the NO3 pocket, we have gz¼ 13.9 from multi-frequency EPRspectroscopy on doped materials, and we take gx¼ gy¼ 0.1. Asboth sites are axial in this model, we need only consider therelative orientation of the local z axes, which we fix at the abinitio-calculated angle of 44� (Fig. 1b). We define the molecularcoordinate frame as that of the hq pocket (where z is along the gz

vector of Dy(1) in the hq pocket, coincident with the Dy � � �Dyvector, and the two gz vectors define the zx plane). We can thenuse the Hamiltonian [1] to simulate the EPR spectra, where theonly variables are the components of the anisotropic J-matrix.No agreement could be found for an isotropic J. The next simplest

{Dy2}{Dy2}{Dy2}

0

EP

R in

tens

ity /

a.u.

EP

R in

tens

ity /

a.u.

EP

R in

tens

ity /

a.u.

200 400 600

Field / mT Field / mT

800 0 200 400 600 800 1,000 1,200 1,400

Field / mT

0 200 400 600 800 1,000 1,200 1,400 1,600

X-band, 9.7 GHz K-band, 24 GHz Q-band, 34 GHz{Dy@Y2} {Dy@Y2} {Dy@Y2}

Figure 3 | EPR spectroscopy. X- (a), K- (b) and Q-band (c) experimental EPR spectra at 5 K (black traces) and simulated data for {Dy@Y2} (red traces)

and 3 (blue traces). See text for simulation parameters.






model has an axially symmetric J-matrix, where we set theprincipal component, J||, along the Dy � � �Dy vector (Fig. 1b).

H ¼ � 2 J? S1xS2x þ S1yS2y� �

þ JkS1zS2z� �

þ mBðS1 � g1þ S2 � g2Þ�B*:

ð1Þ

Using [1] we can model the EPR spectra of 3 with only two freevariables, and we find excellent fits with J>¼ þ 0.525 cm� 1 andJ||¼ þ 1.52 cm� 1 (Fig. 3 and Supplementary Figs 9 and 10). Thisis a ferromagnetic interaction, consistent with the low tempera-ture rise in wMT(T). The spectra are not reproduced by a simpledipolar model (Jdip

zz ¼ þ 1:48 cm� 1¼ , Jdipzx ¼ þ 1:41 cm� 1, all

other Jdipij ¼ 0cm� 1; Hdip ¼ � 2S1 � Jdip � S2) hence there is a

significant exchange contribution, although we note that J|| is verysimilar in magnitude to Jdip

zz .

DiscussionWith an accurate knowledge of the low energy eigenstates of oursystem, we are able to explain the lack of SMM behaviour incompound 3. From the coupled Seff¼ 1/2 model used to simulatethe EPR spectra, in zero field we have a ground doublet withwavefunctions c1¼ |mmS and c2¼ |kkS due to the ferromag-netic exchange. The two excited states are singlets at B1 andB2 cm� 1, which are the symmetric and antisymmetric linearcombinations c3 ¼ 1ffiffi

2p "#ij þ #"j ið Þ and c4 ¼ 1ffiffi

2p "#ij � #"ijð Þ,

respectively (Fig. 4). The average transition matrix elements(average of x, y and z magnetic transition probability) betweenthe ground doublet wavefunctions vanish in zero field and nodirect relaxation is possible. Even if we take into account theexperimental perturbations, such as intermolecular dipole andhyperfine fields, direct magnetic relaxation between the twocomponents of this doublet are unlikely due to this involving aflip of both moments. On the other hand, the average transitionmatrix elements between these doublet states and both the excitedsinglets are large, B4 mB

2, indicating that relaxation processesinvolving these excited states are readily available. Given the smallenergy gaps to these excited states, they present an extremelyefficient method for the reorientation of magnetization and thusexplain the lack of any significant out-of-phase component in theAC susceptibility of 3 in zero field.

In a non-zero magnetic field, the situation is more complicateddue to the anisotropic magnetic nature of the system. To illustrateour point we will discuss the case where the magnetic field iscoincident with the principal axis of Dy(1) (as in Fig. 4). As the

magnetic field is increased from zero, the component of thedoublet that is destabilized by the field begins to strongly mixwith the first singlet excited state. This mixing causes an avoidedcrossing between c1 or c2 and c3 between |B|¼ 100–150 mT andtherefore significantly increases the average transition matrixelements between the two components of the doublet to amaximum value of B2.4 mB

2 at |B|¼ 200 mT. Thus, in an appliedDC magnetic field further relaxation pathways become availablefor the magnetization vector, therefore meaning that the appliedfield does not quench fast relaxation modes. For low microwavefrequencies the EPR transition energies are on the scale of theexchange-induced splitting and even of the avoided crossing,hence these EPR experiments are directly measuring theprobabilities and energies associated with the magnetic relaxationprocesses (see allowed EPR transitions marked on Fig. 4).

The origin of these many efficient relaxation pathways is thenon-colinearity of the principal axes of the DyIII ions. If weconsider a scenario where the tilt angle of 44� between the two gz

vectors is removed, but the exchange remains unchanged, thesituation changes considerably. In zero field, while the averagetransition matrix elements between the ground doublet wave-functions remains zero, the average transition matrix elementsbetween these states and the excited singlets are now very small,on the order of 10� 3 mB

2, indicating that zero-field relaxation inthis case would be hindered. With the application of a magneticfield along the easy axis (Supplementary Fig. 12) the avoidedcrossings are no longer present, which implies that mixingbetween the ground doublet and the excited states does not occurand does not induce any transition matrix element between thecomponents of the ground doublet. Therefore this hypotheticalcompound would be expected to show slow magnetic relaxationin zero field.

Compound 3 shows very different physics from the exchangebias type of compounds, originally described by Wernsdorferet al.33, and also seen in {Dy2} complexes16, where a remnantmagnetization is present in the open hysteresis loops; a featurenot observed here because of rapid zero-field relaxation. Thehypothetical compound where the tilt angle is 0� may possiblyshow the characteristic QTM steps at the crossing points inSupplementary Fig. 12 once all perturbations are included andtherefore we conclude that it is also the non-colinearity in 3which distinguishes this compound from those of the exchangebias type.

With the nature of the anisotropic magnetic exchangedetermined exactly by EPR spectroscopy, we are in a uniqueposition to compare this with the magnetic exchange approxi-mated by the Lines approach. Comparing the lowest four statesobtained from EPR spectroscopy (Fig. 4) to those of the Linesmodel used for fitting the magnetic susceptibility (SupplementaryFig. 13), it is obvious that there are certain similarities. At zerofield, the ground pseudo-doublet of the EPR model has gzB34,which is identical to that of the Lines model of gzB34, and thegap to the first excited state for the EPR model is B1 cm� 1, alsosimilar to that of the Lines model (B0.7 cm� 1).

It is also clear that the Lines approach yields two pseudo-doublets, whereas the excited states of the EPR model are singlets;this is a result of the anisotropic nature of the exchangeinteraction; such an interaction being excluded by the Linesapproach. The high field limits of the two models are very similar,as would be expected due to the field ‘decoupling’ the individualmoments in both cases (Paschen–Back effect). It is in theintermediate field regimes where the differences are mostapparent, where we observe a number of avoided crossings inthe EPR model and none in the Lines model.

Intramolecular magnetic interactions between lanthanides areknown to strongly influence magnetic relaxation. Here we can

–3

–2

–1

0

1

2

–400 –300 –200 –100 0 100 200 300 400

Ene

rgy

/ cm

–1

X K Q

Field / mT

Figure 4 | Lowest energy states. All states in the EPR model for 3,

calculated as a function of magnetic field coincident with the principal axis

of Dy(1). Blue line, c1; red line, c2; green line, c3; purple line, c4 (see text).

Arrows correspond to the EPR resonances observed for this orientation.






quantify this interaction, and demonstrate that it is the anglebetween the principal anisotropy axes and the associatedmagnetic exchange that has the effect of quenching the SMMbehaviour in this dimetallic compound. Although the ferromag-netic exchange interactions lead to a highly magnetic groundstate, the local transverse moment due to the asymmetric natureof the dimer makes relaxation very efficient. Many other {Dy2}complexes are reported to be SMMs14; in every {Dy2} SMMwhere the orientation of the anisotropy axes is known, eitherfrom symmetry or calculation, they are parallel. In these cases, theDy � � �Dy interaction is still present, but as it does not induce atransverse magnetic field at either Dy site, it does not destroy thebarrier to magnetization reversal. This gives the design criterionthat the magnetic moments of individual spins should be alignedparallel within polymetallic lanthanide SMMs to enhancemeasurable magnetization retention at zero field.

MethodsSynthetic methods. Compounds 1–6 were synthesized according to the followinggeneral method. To a solution of Ln(NO3)3 � nH2O (0.6 mmol), where Ln¼YIII,TbIII, DyIII, HoIII, ErIII, YbIII or LuIII, in MeOH (20 ml) was added 8-hyxdrox-yquinolinoline (hqH; 220 mg, 1.5 mmol). The solution was then refluxed for 3 hand subsequently filtered. Yellow block crystals were collected after 24 h of slowevaporation crystallization for Y (1), Tb (2), Dy (3), Ho (4), Er (5), Yb (6) and Lu(7) (Supplementary Table 1). The magnetically dilute samples, {Dy@Y2} and{Dy@Lu2}, were obtained by combining accurately measured amounts ofDy(NO3)3 � nH2O and Y(NO3)3 � nH2O or Lu(NO3)3 � nH2O in a 5:95 molar ratio,following the procedure above. The 1:1 mixed-metal systems were prepared byreacting Ln(NO3)3 � nH2O (where Ln¼TbIII, DyIII, HoIII, ErIII, YbIII and LuIII)with Y(NO3)3 � nH2O in a 1:1 molar ratio using the procedure described above.

Crystallography. The crystallographic data for 2 was collected on a BrukerProspector CCD diffractometer with CuKa radiation (l¼ 1.5418 Å). The crystal-lographic data for 3–5 were collected on an Oxford SMART CCD diffractometerwith MoKa radiation (l¼ 0.71073 Å). The data collection for 7 was carried out onAgilent SUPERNOVA diffractometer with MoKa radiation (l¼ 0.71073 Å). Thedata for 1 and 6 were collected on a Rigaku Saturn724þ diffractometer (syn-chrotron, l¼ 0.68890 Å) at the I19 beamline at the Diamond Light Source, UK.The structures were solved by direct methods and refined on F2 using SHELXTL.

Electron paramagnetic resonance. X-band (B9.7 GHz) and Q-band (B34 GHz)EPR spectra were recorded with a Bruker EMX580 spectrometer, while S-band(B3.9 GHz) and K-band (B24 GHz) EPR spectra were recorded with a BrukerElexsys580 spectrometer. The data were collected on polycrystalline powders in thetemperature range 5–30 K using liquid helium cooling. High-frequency EPRspectra (260–380 GHz) were recorded in Stuttgart on a home-built spectrometer.Its radiation source is a 0–20 GHz signal generator (Anritsu) in combination withan amplifier–multiplier chain (VDI) to obtain the required frequencies. It features aquasi-optical bridge (Thomas Keating) and induction mode detection. The detectoris a QMC magnetically tuned InSb hot electron bolometer. The sample is located inan Oxford Instruments 15/17T cryomagnet equipped with a variable temperatureinsert (1.5–300 K). Spectral simulations were performed using the EasySpin 4.5.5simulation software.

Magnetometry. The magnetic properties of polycrystalline samples of 2–6were investigated in the temperature range 1.8–300 K with a Quantum DesignMPMS-XL7 SQUID magnetometer equipped with a 7 T magnet. The samples wereground, placed in a gel capsule and fixed with a small amount of eicosane to avoidmovement during the measurement. The data were corrected for the diamagnetismfrom the gel capsule and the eicosane, with the diamagnetic contribution of thecomplexes calculated from Pascal’s constants. AC susceptibility measurementswere performed with an AC field of 1.55 G oscillating at frequencies between 1and 1,400 Hz.

Far infrared. FIR spectra were recorded using a Bruker 113v FTIR spectrometerequipped with a mercury light source. For the detection we used an InfraredLaboratories pumped Si bolometer (operating temperature 1.5 K). For sampleswe used 10 mm pressed powder pellets. The samples were placed in an OxfordInstruments Spectromag 4000 optical cryostat allowing fields up to 8 T andtemperatures down to 1.8 K. The sample holder permitted in situ change betweenan aperture and the sample, which allowed recording absolute transmissionspectra.

CASSCF calculations. The CASSCF calculations were performed with MOLCAS7.8 using the geometry as elucidated with X-ray crystallography. All calculations

considered the individual DyIII ions independently, where the ion not in focus wasreplaced by the diamagnetic LuIII. All calculations were of the complete activespace type where the 4f9 configuration of DyIII was modelled with nine electrons inseven orbitals CAS(9,7), using the RASSCF module. The basis sets for these cal-culations were taken from the ANO-RCC library, where the paramagnetic ion wasof VTZP quality, the first coordination sphere of VDZP quality and all other atomsof VDZ quality. Supplementary Table 9 details the states included in the RASSCFand RASSI modules. The RASSI module was used to calculate the g-tensors for the6H15/2 multiplet34 and SINGLE_ANISO was used to generate a complete set of CFparameters from the ab initio-calculated spin–orbit eigenstates35.

CF and lines models. The CF parameters (CFPs) were treated as explained in themain text, and the reference frame rotations were optimized to reproduce themutual orientations from the ab initio calculations (Supplementary Table 13).These were fixed while the exchange interaction was fitted to the magnetic data.The following Hamiltonian was used in the |J, mJS basis for each DyIII ion, wherethe exchange term acts on the true spins (S¼ 5/2) for each DyIII and the SDyð1Þ �SDyð2Þ term was evaluated using a Clebsch–Gordan decomposition. yk are theoperator equivalent factors for DyIII in the |J, mJS basis, gJ is the Lande g-factor forthe 6H15/2 term of DyIII and is equal to 4/3, I is the identity matrix and JLines is theexchange parameter. Note that the Oq

k DyðnÞoperators are expressed in the localcoordinate frame of each DyIII ion, using the given Euler angles.

H¼X

k¼2;4;6

Xk

q¼� kyk Bq

kDy 1ð ÞOqk Dyð1Þ þBq

kDy 2ð ÞOqk Dyð2Þ

� �� 2JLines SDy 1ð Þ � SDy 2ð Þ

� �

þmBgJ JDy 1ð Þ � Iþ JDy 2ð Þ � I� �

� B*

ð2Þ

EPR simulation with the Lines model. Using exactly the same Hamiltonian asabove, the EPR was simulated in a non-perturbative manner with PHI. The EPRabsorption spectrum was calculated at discrete field points using the followingequation, where HBx0 and HBy0 are the Zeeman Hamiltonians for the components ofthe perpendicular microwave magnetic field, Ei and Ej are the energies for the states|iS and |jS (eigenstates of the above Hamiltonian), respectively, Z is the partitionfunction and Z is the linewidth expressed in energy units.

A B*� �¼Xi;j2dim

ioj

ðjhjjHBx0 ij ij2 þ jhjjHBy0 ij ij2Þe�EikB T � e

� EjkB T

� �

Z8ffiffiffiffiffiffiffiln2p

Zffiffiffipp e

� Ei �Ej � EMWð Þ2

Z2 ln2

ð3Þ

As the linewidth is evaluated in frequency space, there is no need for thefrequency-field conversion factor. The absorption spectrum was summed overa large number of orientations on a hemisphere using the Zaremba–Conroy–Wolfsberg spherical integration scheme36. The first derivative of the absorptionspectrum was then obtained to yield the spectral simulations.

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AcknowledgementsE.M.P. thanks the Panamanian agency SENACYT-IFARHU for funding and COSTAction: CM1006 for funding for HF-EPR measurements. N.F.C. thanks The University ofManchester for a President’s Doctoral Scholarship. The work at Stuttgart was supportedby the DFG. R.E.P.W. thanks the Royal Society for a Wolfson Merit Award. We alsothank EPSRC (UK) for funding the National EPR Facility and Service, and for an X-raydiffractometer (grant number EP/K039547/1). S.-D.J. thanks the Humboldt foundationfor a postdoc fellowship. We thank Professor M. Dressel (Stuttgart) for access to thefar-infrared spectrometer. We thank Diamond Light Source for access to synchrotronX-ray facilities.

Author contributionsThe synthesis, crystallographic characterization and magnetic data collection andprocessing for all complexes was performed by E.M.P. Low-frequency EPR data wascollected jointly between D.O.S. and E.M.P. FIR and HF-EPR measurements wereperformed by R.M., M.D., P.N., S.-D.J. and J.v.S. N.F.C. performed ab initio calculationsand modelled the magnetic data. E.M.P. and N.F.C. jointly performed EPR simulationswith input from R.E.P.W., E.J.L.M. and D.C. The paper was written by E.M.P., N.F.C.,E.J.L.M. and R.E.P.W. with input from the other co-authors.

Additional informationAccession codes: The X-ray crystallographic coordinates for structures reported in thisstudy have been deposited at the Cambridge Crystallographic Data Centre (CCDC),under deposition numbers CCDC 1011262–1011274. These data can be obtained free ofcharge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif, (or from the Cambridge Crystallographic Data Centre, 12 Union Road,Cambridge CB21EZ, UK; fax: (þ 44)1223-336-033; or [email protected]).

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

Competing financial interests: The authors declare no competing financial interests.

Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/

How to cite this article: Pineda, E. M. et al. Direct measurement of dysprosiu-m(III) � � � dysprosium(III) interactions in a single-molecule magnet. Nat. Commun.5:5243 doi: 10.1038/ncomms6243 (2014).






asas



S1


Direct measurement of dysprosium(III)··· dysprosium(III) interactions in a single-molecule magnet Eufemio Moreno Pineda,a Nicholas F. Chilton,a Raphael Marx,b María Dörfel,b Daniel O. Sells,a Petr Neugebauer,b Shang-Da Jiang,c David Collison,a Joris van Slageren,b Eric J. L. McInnesa* and Richard E. P. Winpennya* a School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom. b Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany. c Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.

1. Supplementary figures

Magnetic measurements 1.1.

Supplementary Figure 1. In-phase χM’(T) (a), out-of-phase χM’’(T) (b) and χM’T(T) (c) behaviour for 3 measured under 1 kG DC field (HDC) and an oscillating magnetic field of 1.55 G. In-phase χM’(T) (d), out-of-phase χM’’(T) (e) and χM’T(T) (f) behaviour for {Dy@Lu2} measured under 1 kG dc field (HDC) and an oscillating magnetic field of 1.55 G.

Supplementary Figure 2. a) χM’’(H) for {Dy@Y2} measured at 7 K and applied DC fields from 0 to 3 kG; b) χM’(T) for {Dy@Y2} under 1 kG applied dc field; c) for {Dy@Y2} experimental data and fits (solid lines) for χM’(ν) (1 kG DC field); d) for {Dy@Y2} experimental data and fits (solid lines) for χM’’(ν) (1 kG DC field).

a) c)

e) f )d)

b)

a) b)

d)c)



S2

Supplementary Figure 3. (a) Frequency dependence χM’(ν); (b) Frequency dependence χM’’(ν); and (b) Cole-Cole plots (χM’’ vs. χM’) showing two relaxation process from 1.8 – 3.0 K for {Dy@Y2} under 1 kG applied DC field

Supplementary Figure 4. Comparison of CF calculations using the scaled (red) and non-scaled (blue) CFPs, using the exchange parameter JLines = +0.047(1) cm-1. The poor agreement of the calculation with the non-scaled CFPs to the experimental χMT values prevents any meaningful determination of JLines. The magnetization data is insensitive to JLines as the magnetic field quickly overcomes this small interaction.

Far Infrared 1.2.

Supplementary Figure 5. (a) Far-infrared transmission spectra recorded on a pressed powder pellet of 3 at various magnetic fields as indicated; (b) Normalized transmission spectra (all spectra divided by the 6T spectrum) of 3. All measurements were performed at 9 K.

b)a) c)

a) b)



S3

EPR 1.3.

Supplementary Figure 6. (a) X-, (b) K-band and (c) Q-band experimental (black trace) and simulated (blue and red trace) EPR spectra for {Dy@Lu2} at 5 K. Simulation of a single Dy(III) in NO3 pocket with gx = gy = 0.1, gz = 13.9 (red trace). Simulations of Dy in NO3 pocket and small fraction of 3 (blue trace) (see main text for simulation parameters). Statistically a small amount of 3 should be present in the doped material (i.e. 0.25% of the total is {Dy2}). Due to the low transition probability of Dy(III) in the NO3 pocket a small intensity would be expected compared with the transition probabilities for 3.

Supplementary Figure 7. Experimental (black trace) and simulated (blue trace) spectra for {Dy@Y2} at 5 K and (a) 260 GHz; (b) 320 GHz; (c) 350 GHz and (d) 380 GHz. Simulation obtained using Seff = ½ with gx = gy = 0.1, gz = 13.9.



S4

Supplementary Figure 8. Experimental (black trace) and simulated (blue trace) spectra for {Dy@Lu2} at 5 K and (a) 260 GHz; (b) 320 GHz; (c) 350 GHz and (d) 380 GHz. Simulation obtained using Seff = ½ with gx = gy = 0.1, gz = 13.9.

Supplementary Figure 9. Experimental (black trace) and simulated (blue trace) spectra for 3 at S-band and 5 K. Simulated as the exchange-coupled system, using the parameters and model described in the main text



S5

Supplementary Figure 10. (a) 260, (b) 320, (c) 350 and (d) 380 GHz experimental HF-EPR spectra of compound 3 at 5 K (black trace) and simulated EPR spectra (blue trace). Simulated as the exchange coupled system, using the parameters and model described in the main text.

Supplementary Figure 11. (a) S-, (b) X-, (c) K- and (d) Q-band experimental EPR spectra (black trace) and simulated (blue trace) EPR spectra for compound 3 at 5 K. Simulated using the Lines model with scaled ab-initio CFPs and the exchange parameter extracted from magnetometry measurements. The poor agreement indicates that the Lines model is inadequate in this case



S6

Zeeman diagrams 1.4.

Supplementary Figure 12. Four lowest lying states of 3 where the 44° tilt has been removed, calculated as a function of magnetic field coincident with the easy axis. This model uses the EPR exchange parameters determined for 3.

Supplementary Figure 13. Four lowest lying states of 3, calculated as a function of magnetic field coincident with the principal axis of Dy(1). This model uses the scaled ab-initio CFPs, ab-initio rotations and the Lines exchange parameter of JLines = +0.047(1) cm-1.



S7

2. Supplementary Tables

Elemental Analysis 2.1.

Supplementary Table 1. Elemental analysis and yield (%) for compounds 1–7 Formula Yielda % Elemental analysis: Found (calculated) C H N Ln

1 [hqH2][Y2(hq)4(NO3)3]·MeOH

75.4 49.39 (49.18)

3.24 (2.99)

10.02 (10.00)

15.9 (15.77)

2 [hqH2][Tb2(hq)4(NO3)3]·MeOH

51.9 43.89 (43.74)

2.88 (2.69)

8.90 (8.81)

25.25 (25.20)

3 [hqH2][Dy2(hq)4(NO3)3]·MeOH

74 43.65 (43.49)

2.87 (2.76)

8.85 (8.92)

25.67 (25.43)

4 [hqH2][Ho2(hq)4(NO3)3]·MeOH

58.7 43.48 (43.23)

2.86 (2.67)

8.82 (8.78)

25.96 (25.78)

5 [hqH2][Er2(hq)4(NO3)3]·MeOH

72.2 43.32 (43.16)

2.84 (2.62)

8.79 (8.69)

26.23 (26.05)

6 [hqH2][Yb2(hq)4(NO3)3]·MeOH

72.8 42.93 (42.95)

2.82 (2.87)

8.71 (8.88)

26.89 (27.03)

7 [hqH2][Lu2(hq)4(NO3)3]·MeOH

67.7 42.8 (42.93)

2.81 (2.78)

8.68 (8.56)

27.11 (27.13)

a. Calculated based on 8-hydroxyquinoline

Supplementary Table 2. Elemental analysis and yield (%) for doped compounds 8–13 Formula Elemental analysis: Found (calculateda) C H N Y Ln Lu

8 ca. 5% Tb@1 49.1 (48.92)

3.22 (3.13)

9.95 (9.84)

15.01 (15.07)

1.41 (1.06)

-

9 ca. 5% Dy@1 49.07 (48.97)

3.22 (3.18)

9.95 (10.10)

15.00 (14.70)

1.44 (1.87)

-

10 ca. 5% Ho@1 49.06 (49.02)

3.22 (3.04)

9.95 (9.79)

15.00 (14.85)

1.46 (1.64)

-

11 ca. 5% Er@1 49.05 (48.93)

3.22 (3.19)

9.95 (9.73)

15.00 (14.98)

1.48 (1.53)

-

12 ca. 5% Yb@1 49.02 (48.89)

3.22 (3.06)

9.94 (9.74)

14.99 (14.92)

1.53 (1.76)

-

13 ca. 5% Dy@7 42.85 (42.54)

2.81 (2.64)

8.69 (8.56)

- 1.26 (1.17)

25.78 (25.64)

a) Calculated based on 5% doping by molar ratio



S8

Crystallography 2.2.

Supplementary Table 3. Crystallographic information for dimers 1 – 4

Supplementary Table 4. Crystallographic information for dimers 5 – 7

1 2 3 4

Formula Y2N8O15H36C46 Tb2N8O15H36C46 Dy2N8O15H36C46 Ho2N8O15H36C46 Molecular Mass / g mol-1 1118.65 1258.67 1265.83 1270.69 Crystal System monoclinic monoclinic monoclinic monoclinic Space Group P21/c P21/c P21/c P21/c a / Å 20.9895(8) 21.0148(16) 20.9630(6) 20.8835(7) b / Å 11.6630(5) 11.6603(7) 11.5969(3) 11.5805(3) c / Å 20.4338(8) 20.3588(17) 20.3323(6) 20.2541(7) β / ° 114.458(5) 114.416(10) 114.349(3) 114.287(4) V / Å3 4553.3(4) 4542.5(7) 4503.2(2) 4464.8(3) Z 4 4 4 4 ρ calc. / g cm-3 1.632 1.840 1.867 1.890 T / K 100.15 100.15 106.5(1) 102.4(8) R1(I > 2σ)(I))a 0.0452 0.0408 0.0348 0.0351 wR2

a 0.1017 0.0840 0.0797 0.0646 aR1 = ||Fo| - |Fc||/|Fo|, wR2=[w(|Fo| - |Fc|)2/w|Fo|2]1/2

5 6 7

Formula Er2N8O15H36C46 Yb2N8O15H36C46 Lu2N8O15H35C46 Molecular Mass / g mol-1 1275.35 1286.91 1290.77 Crystal System monoclinic monoclinic monoclinic Space Group P21/c P21/c P21/c a / Å 20.8408(18) 20.9279(6) 20.8413(12) b / Å 11.5872(6) 11.6145(3) 11.5713(5) c / Å 20.2631(18) 20.4114(7) 20.2950(12) β / ° 114.303(11) 114.324(4) 114.204(7) V / Å3 4459.6(7) 4520.9(3) 4464.1(5) Z 4 4 4 ρ calc. / g cm-3 1.899 1.891 1.921 T / K 101.6(5) 100.15 164(2) R1(I > 2σ)(I))a 0.0678 0.0344 0.0557 wR2

a 0.1530 0.0965 0.0989 aR1 = ||Fo| - |Fc||/|Fo|, wR2=[w(|Fo| - |Fc|)2/w|Fo|2]1/2



S9

Supplementary Table 5. Selected bond lengths for dimers 1 – 7. (Å) Y Tb Dy Ho Er Yb Lu

Ln1—Ln2 3.4606(5) 3.5056(6) 3.4854(4) 3.4659(4) 3.4456(8) 3.4222(4) 3.4033(5)

Ln1—O1A 2.243(2) 2.260(4) 2.248(3) 2.241(3) 2.236(9) 2.212(3) 2.208(6)

Ln1—O1B 2.340(2) 2.361(4) 2.349(3) 2.337(3) 2.304(7) 2.313(2) 2.304(5)

Ln1—O1C 2.365(2) 2.372(5) 2.358(4) 2.341(4) 2.323(9) 2.344(2) 2.303(7)

Ln1—O1D 2.347(3) 2.390(4) 2.384(4) 2.372(3) 2.373(7) 2.318(3) 2.343(6)

Ln1—N1A 2.469(2) 2.496(3) 2.476(3) 2.462(3) 2.448(8) 2.438(3) 2.427(6)

Ln1—N1B 2.516(3) 2.539(4) 2.535(3) 2.525(3) 2.496(8) 2.497(3) 2.483(6)

Ln1—N1C 2.499(4) 2.573(5) 2.561(4) 2.537(4) 2.540(1) 2.520(4) 2.496(7)

Ln1—N1D 2.545(3) 2.530(5) 2.522(5) 2.500(5) 2.490(1) 2.474(4) 2.440(1)

Ln2—O1N 2.402(2) 2.428(5) 2.416(3) 2.399(3) 2.388(7) 2.369(3) 2.364(6)

Ln2—O1B 2.312(2) 2.328(5) 2.318(4) 2.298(3) 2.292(7) 2.280(3) 2.276(6)

Ln2—O1C 2.287(2) 2.308(3) 2.298(3) 2.286(3) 2.278(7) 2.253(3) 2.248(5)

Ln2—O1D 2.285(2) 2.312(4) 2.301(4) 2.280(4) 2.280(9) 2.247(2) 2.231(7)

Ln2—O2N 2.478(2) 2.495(4) 2.478(3) 2.471(3) 2.464(7) 2.460(3) 2.454(5)

Ln2—O4N 2.455(3) 2.498(5) 2.475(4) 2.458(4) 2.445(9) 2.444(4) 2.424(7)

Ln2—O6N 2.427(3) 2.511(5) 2.499(4) 2.487(4) 2.480(1) 2.401(3) 2.439(7)

Ln2—O7N 2.468(4) 2.468(4) 2.463(4) 2.443(4) 2.430(1) 2.452(4) 2.426(6)

Ln2—O8N 2.481(4) 2.463(3) 2.451(3) 2.436(3) 2.400(8) 2.459(4) 2.396(5)



S10

Supplementary Table 6. Crystallographic information for mixed-metal systems (1:1)

Y:Tb Y:Dy Y:Ho Formula YTbN8O15H36C46 YDyN8O15H36C46 YHoN8O15H36C46 Molecular Mass / g mol-1 1188.66 1192.24 1194.67 Crystal System monoclinic monoclinic monoclinic Space Group P21/c P21/c P21/c a / Å 20.9511(12) 20.9166(12) 20.9304(13) b / Å 11.6457(3) 11.6153(5) 11.6242(5) c / Å 20.3330(9) 20.330(2) 20.3448(10) β / ° 114.319(6) 114.331(9) 114.266(7) V / Å3 4520.9(4) 4500.6(6) 4512.5(4) Z 4 4 4 ρ calc. / g cm-3 1.746 1.760 1.758 T / K 100.15 139(1) 100.15 R1(I > 2σ)(I))a 0.0457 0.0625 0.0420 wR2


Supplementary Table 7. Crystallographic information for mixed-metal systems (1:1)

Y:Er Y:Yb Y:Lu Formula YErN8O15H36C46 YYbN8O15H36C46 YLuN8O15H36C46 Molecular Mass / g mol-1 1197.00 1202.78 1204.71 Crystal System monoclinic monoclinic monoclinic Space Group P21/c P21/c P21/c a / Å 20.8897(8) 20.8637(18) 20.926(3) b / Å 11.5976(3) 11.6041(7) 11.5849(9) c / Å 20.3126(8) 20.3299(16) 20.340(2) β / ° 114.304(5) 114.274(10) 114.245(13) V / Å3 4485.0(3) 4486.8(7) 4496.0(9) Z 4 4 4 ρ calc. / g cm-3 1.773 1.781 1.780 T / K 150.0(2) 100.15 150.0(2) R1(I > 2σ)(I))a 0.0426 0.0646 0.0701 wR2


Supplementary Table 8. Occupancy of Ln in 50% Ln@[Y2(hq)4(NO3)3][hqH2]·MeOH.

Y-Ln % hq pocket % NO3 pocket Tb 45 55 Dy 56 44 Ho 64 36 Er 69 31 Yb 71 29 Lu 84 16



S11

ab- initio calculations 2.3.

Supplementary Table 9. States included for Dy complex Spin RASSCF roots RASSI states

5/2 21 21 3/2 224 128 1/2 158 130

Supplementary Table 10. ab-initio results for Dy(1) (hq pocket)

E (cm-1) gx gy gz Angle/o a Dominant mJ states b 0.0 0.01 0.01 19.75 - 98% ± 15 2

106.0 0.15 0.16 16.91 1.9 96% ± 13 2 221.2 0.21 0.37 13.79 3.6 91% ± 11 2 311.1 3.83 4.92 9.54 4.9 69% ± 9 2 383.3 1.30 5.68 8.64 82.3 58% ± 7 2 + 21% ± 1 2 439.7 2.27 2.90 12.63 84.4 43% ± 5 2 + 18% ± 3 2 515.1 0.50 1.15 17.90 84.8 28% ± 1 2 + 21% ∓ 3 2 + 20% ± 3 2 598.1 0.14 0.36 19.20 75.5 20% ± 3 2 + 20% ± 1 2 + 17% ± 7 2 + 15% ± 5 2

a) Angle of gz with respect to gz of ground Kramers doublet b) Calculated using the CFPs in Supplementary Table S13 with PHI

Supplementary Table 11. ab-initio results for Dy(2) (NO3 pocket)

E (cm-1) gx gy gz Angle/o a Dominant mJ states b

0.0 0.05 1.54 16.42 - 40% ± 11 2 + 18% ± 15 2 + 18% ± 13 2 + 12% ± 9 2 23.9 1.29 7.72 10.71 72.7 30% ± 7 2 + 24% ± 13 2 + 10% ± 5 2 38.8 2.45 4.17 7.15 80.0 23% ± 9 2 + 20% ∓ 9 2 86.8 2.42 3.77 14.06 22.8 48% ± 15 2 + 21% ± 11 2

127.4 0.86 1.32 15.98 68.3 23% ± 15 2 + 36% ± 13 2 158.5 2.34 5.27 10.24 76.1 19% ± 3 2 + 17% ± 5 2 + 12% ∓ 9 2 222.2 0.61 3.62 6.01 61.3 36% ± 1 2 + 16% ± 7 2 + 16% ± 5 2 + 11% ± 3 2 265.5 1.33 7.79 12.68 49.9 29% ± 3 2 + 28% ± 1 2 + 15% ± 5 2

a) Angle of gz with respect to gz of ground Kramers doublet b) Calculated using the CFPs in Supplementary Table S13 with

Far Infrared measurements 2.4.

Supplementary Table 12. Comparison of the ab-initio calculation and FIR spectroscopy for 3. A scaling factor of 1.6 was used.

FIR (cm-1) ab-initio, NO3 pocket

scaled ab-initio, NO3 pocket

ab-initio, hq pocket

scaled ab-initio, hq pocket

39 23.9 38.2 106.0 169.6 59 38.8 62.1 221.2 353.9

86.8 139.9 311.1 497.8



S12

Crystal Field Parameters 2.5.

Supplementary Table 13. Ab initio Crystal Field Parameters (CFPs) for 3, scaled by factor of 1.6 derived from FIR results (see Table S12).

CFP Dy(1) hq pocket (cm-1) Dy(2) NO3 pocket (cm-1) 𝐵!!! 82 14 𝐵!!! 81 -16 𝐵!! 757 179 𝐵!! -287 -55 𝐵!! -162 -36 𝐵!!! 671 -63 𝐵!!! 1726 876 𝐵!!! 20 64 𝐵!!! -89 77 𝐵!! 21 -80 𝐵!! 155 649 𝐵!! -223 -35 𝐵!! -1175 1016 𝐵!! 82 -217 𝐵!!! 43 176 𝐵!!! -90 460 𝐵!!! -242 -130 𝐵!!! 298 443 𝐵!!! 61 174 𝐵!!! 19 135 𝐵!! 21 -15 𝐵!! -8 254 𝐵!! -59 -153 𝐵!! -664 -178 𝐵!! 126 157 𝐵!! 771 560 𝐵!! -121 518

Euler rotations (α, β, γ), in degrees, (using the PHI convention) to transform the above CFPs in the local reference frames defined by the magnetic axes of ground Kramers doublets of Dy(1) and Dy(2), to the molecular frame (see main text):

Dy(1) = (-126, -33, 86) Dy(2) = (-44, -78, 146)



1

Systematic study of a family of butterfly-like {M2Ln2} molecular magnets (M = MgII, MnIII, CoII, NiII and CuII; Ln = YIII, GdIII, TbIII, DyIII, HoIII and ErIII) Eufemio Moreno Pineda, Nicholas F. Chilton, Floriana Tuna, Richard E. P. Winpenny* and Eric J. L. McInnes*

School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom.

ABSTRACT: A family of 3d-4f [MII2LnIII

2(µ3-OH)2(O2CtBu)10]2- “butterflies” (where MII = Mg, Co, Ni and Cu; LnIII = Y, Gd, Tb, Dy, Ho and Er) and [MnIII

2LnIII2(µ3-O)2(O2CtBu)10]2-

molecules (where LnIII = Y, Gd, Tb, Dy, Ho and Er) have been synthesised and characterised through single crystal X-ray diffraction, SQUID magnetometry and ab-initio calculations. All dysprosium- and some erbium-containing tetramers showed a frequency dependent maxima in the out-of-phase component of the susceptibility associated with slow relaxation of magnetization and hence they are single molecule magnets (SMMs). AC susceptibility measurements have shown that the SMM behaviour is entirely intrinsic to the Dy and Er sites and the magnitude of the energy barrier is influenced by the interactions between the 4f and the 3d metal. A trend is observed between the strength of the 3d-4f exchange interaction between and the maximum observed in the χ"M(T).

INTRODUCTION

Continuous work towards the synthesis of molecular nanoclusters has taken place since it was

demonstrated that such systems could retain magnetisation purely at the molecular level.1

Molecules possessing these characteristics display hysteresis, and are considered potential

candidates for use in data storage, spintronics and quantum computing devices.2 Initially most of

the effort was concentrated on 3d-metal clusters with manganese, commonly displaying a

relatively big spin ground state (S) and high negative zero field splitting (D), by far the most

explored.3

Intensive investigation of the magnetism of lanthanide complexes arose from the

discovery that monometallic complexes of 4f-ions can also show slow relaxation of

magnetisation; the most studied compounds are the double-decker phthalocyaninato–lanthanide

complexes.4 These molecules opened up a new era for single molecule magnets (SMMs)5 where

the observed behaviour was due to the large magnetic moments and inherent anisotropy of

lanthanide ions.6 Lanthanides have shown higher energy barriers than observed for transition



2

metal ions; for example [TbIII(Pc)2], an SMM consisting of a single ion with a barrier of 938 K,7

whilst a value of 842 K was obtained for DyIII doped in [YIII4K2O(OtBu)12].8

The magnetic behaviour of lanthanide clusters is complex and poorly understood at

present. At a single ion level the Ising anisotropy is mainly dependent on the ligand field and

geometry, whereas in polymetallic systems the ligand field, exchange interactions, geometry and

relative orientation of single sites in the cluster are some of the factors that determine the

magnetic behaviour.6 Despite having large magnetic moments and anisotropy and showing slow

relaxation of magnetization, lanthanide complexes do not generally show wide hysteresis loops

due to their fast quantum tunnelling of the magnetisation (QTM) at zero external field. This can

be suppressed when other interactions are introduced. For example, suppression of the quantum

tunnelling process in Ln-based SMMs at zero field has been addressed by introducing radicals as

bridging ligands. Rinehart et al. have employed this approach in DyIII and TbIII dimers, obtaining

hysteresis up to 14 K, the highest observed for a molecule-based system.9 Ruben and co-workers

have also reported hysteresis, observed by XMCD measurements, on terbium phthalocyanine

complexes deposited on ferromagnetic nickel supports up to 100 K.10

Combining 3d metals with lanthanides was first studied by the Gatteschi group in the

1980s,11 and in the 1990s by ourselves.12 Recently it has re-emerged as a method to combine the

large anisotropic character imposed for lanthanides i.e. TbIII, DyIII, HoIII and ErIII, while strong

magnetic interactions can be promoted by 3d ions therefore improving the dynamic properties of

SMMs.13 Many interesting 3d-4f molecules have been reported, however little is known about

the exchange interaction (J3d-4f) between the mixed-metal pair when the lanthanide centre is a

highly anisotropic system, limiting most of the research to the isotropic GdIII analogues.11,12

Insight into the exchange interactions between 3d metals with anisotropic lanthanides has

become achievable through the use of multi-configurational ab-initio calculations of the

Complete Active Space Self Consistent Field (CASSCF) variety.8,13c,g Furthermore,

experimentally astonishing work by means of High Field Electron Paramagnetic Resonance (HF-

EPR) combined with pulsed-field magnetisation studies has shed some light into the direct

determination of the exchange interaction between 3d-4f systems, with LnIII = Tb, Dy, Ho and/or

Er.14



3

Many factors play a key role in the relaxation mechanism(s) in lanthanide-based systems,

ranging from ligand set and lanthanide geometry to exchange interactions; therefore a better

understanding of parameters that affect the magnetic behaviour of such systems is a key

requirement towards development of better SMMs and their potential exploitation. With this in

mind, herein we report the synthesis and magnetic properties of a family of hetero-tetrametallic

{M2Ln2} cage compounds, each comprising two 3d (M) and two 4f (Ln) centres, where M =

MnIII, CoII, NiII and CuII; and Ln = GdIII, TbIII, DyIII, HoIII and ErIII. In addition we also report the

{Mg2Ln2} and {M2Y2} analogues, where MgII and YIII are diamagnetic. By means of static and

dynamic magnetic measurements on this near-complete grid of 27 complexes (with only the

{Cu2Tb2} and {Cu2Y2} members missing; {Mg2Y2} is neglected as it is entirely diamagnetic) we

can systematically probe the interaction between the 3d and 4f ions and the effects on SMM

behaviour.

EXPERIMENTAL SECTION

Synthesis

Unless stated otherwise, all reagents and solvents were purchased and used without further

purification. Syntheses of inorganic starting materials, [MII2(µ2-OH2)(O2CtBu)4(HO2CtBu)4] (MII

= Mg, Co and Ni)15a-c, [MnII(O2CtBu)4EtOH]n15d, [Cu2

II(O2CtBu)4(HO2CtBu)2]15e and [Ln2III

(O2CtBu)6(HO2CtBu)6]15f,g (LnIII = Y, Gd, Tb, Dy, Ho and Er) were carried out by literature

methods (See Table S1).

A total of 27 mixed-metal tetramers were synthesised through two different methods,

described below.

Method A:

[MgII2LnIII

2(µ3-OH)2(O2CtBu)10][iPr2NH2]2: [MgII2(µ2-OH2)(O2CtBu)4(HO2CtBu)4] (0.1 g, 0.1

mmol), [LnIII2(O2CtBu)6(HO2CtBu)6] (LnIII = Gd (1), Tb (2), Dy (3), Ho (4) and Er (5)) (0.1

mmol) and diisopropylamine (iPr2NH) (0.1 mL, 0.7 mmol) in acetonitrile (MeCN) (8 mL) were

stirred at room temperature for 5 minutes. The resulting solution was transferred into a 10 mL

Teflon-lined autoclave, which was heated at 150 ºC for 12 hours and then cooled to room

temperature at a rate of 0.05 ºC min-1. Colourless X-ray quality crystals were obtained directly

from the autoclave.



4

[CoII2LnIII

2(µ3-OH)2(O2CtBu)10][iPr2NH2]2: [CoII2(µ2-OH2)(O2CtBu)4(HO2CtBu)4] (0.1 g, 0.1

mmol), [LnIII2(O2CtBu)6(HO2CtBu)6] (LnIII = Y (6), Gd (7), Tb (8), Dy (9), Ho (10) and Er (11))

(0.1 mmol) and iPr2NH (0.1 mL, 0.7 mmol) in MeCN (8 mL) were stirred at room temperature

for 5 minutes. The resulting solution was transferred into a 10 mL Teflon-lined autoclave, which

was heated at 150 ºC for 12 hours and then cooled to room temperature at a rate of 0.05 ºC min-1.

The resulting solution was then filtered and left undisturbed. Pink X-ray quality crystals were

obtained after 48 hours.

[MnIII2LnIII

2(µ3-O)2(O2CtBu)10][Et3NH]2: [MnII(O2CtBu)4EtOH]n (0.1 g, 0.5 mmol),

[LnIII2(O2CtBu)6(HO2CtBu)6] (LnIII = Y (12), Gd (13), Tb (14), Dy (15), Ho (16) and Er (17))

(0.1 mmol) and triethylamine (Et3N) (0.1 mL, 0.5 mmol) in MeCN (8 mL) were stirred at room

temperature for 5 minutes. The resulting solution was transferred into a 10 mL Teflon-lined

autoclave, which was heated at 150 ºC for 12 hours and then cooled to room temperature at a rate

of 0.05 ºC min-1. The resulting solution was then filtered and left undisturbed. Orange X-ray

quality crystals were obtained after 72 hours.

Method B:

[NiII2LnIII

2(µ3-OH)2(O2CtBu)10[Et3NH]2: To a stirred solution of [NiII2(µ2-

OH2)(O2CtBu)4(HO2CtBu)4] (0.2 g, 0.2 mmol) and [LnIII2(O2CtBu)6(HO2CtBu)6] (LnIII = Y (18),

Gd (19), Tb (20), Dy (21), Ho (22) and Er (23)) (0.2 mmol), in of MeCN (20 mL) was added

Et3N (0.2 mL, 1.4 mmol) after 15 minutes. The resulting solution was heated to reflux for a

period of 3 hours. The solution was then cooled to room temperature and filtered. Yellow-green

X-ray quality crystals were obtained directly from slow evaporation after 24 hours.

[CuII2LnIII

2(µ3-OH)2(O2CtBu)10][iPr2NH2]2: To a stirred solution of [CuII2(O2CtBu)4(HO2CtBu)2]

(0.15 g, 0.2 mmol) and [LnIII2(O2CtBu)6(HO2CtBu)6] (LnIII = Gd (24), Dy (25), Ho (26) and Er

(27)) (0.2 mmol), in of MeCN (20 mL) was added iPr2NH (0.2 mL, 1.4 mmol) after 15 minutes.

The resulting solution was heated to reflux for a period of 3 hours. The solution was cooled to

room temperature and then filtered. Blue X-ray quality crystals were obtained directly from slow

evaporation after 48 hours.



5

X-ray data collection and structure solution

Single crystal X-ray diffraction measurements for 7, 9, 15, 19, 21, 24 and 25 were carried out on

an Oxford Xcalibur CCD diffractometer with MoKα radiation (λ = 0.71073 Å). Data collection

of 1, 3, 5, 12, 13, 18 and 23 was carried out on an Agilent SUPERNOVA diffractometer with

MoKα radiation (λ = 0.71073 Å). Data reduction and unit cell refinement were performed with

CrysAlisPro software. The structures were solved by direct methods using SHELXS-9716a and

were refined by full-matrix least-squares methods using Olex2.16b In all cases the crystals were

mounted on a tip using crystallographic oil and placed in a cryostream. Data were collected using

ϕ and ω scans chosen to give a complete asymmetric unit. All non- hydrogen atoms were refined

anisotropically, while hydrogen atoms were calculated geometrically and refined in riding mode.

Crystal data and refinement parameters are given in Table S2-S4.


The magnetic properties of polycrystalline samples of 1–27 were measured with a Quantum

Design MPMS-XL7 SQUID magnetometer. The samples were ground, placed in a gel capsule

and fixed with a small amount of eicosane to avoid movement during the measurement. The data

were corrected for the diamagnetism of the gel capsule and the eicosane with the diamagnetic

contribution from the complexes calculated from Pascal constants.17 Alternating current (AC)

measurements were performed using a small oscillating magnetic field, 1.55 G, with and without

a direct current (DC) applied magnetic field of 1 kG.

Results and discussion

Synthetic description

Reaction of the 3d and 4f carboxylate precursors in the presence of a mild base in acetonitrile

gives a family of isostructural tetrametallic {M2Ln2} clusters. The molecules feature a butterfly-

like core, with an M2 body and Ln wing-tips, and consist of an anion [MII2LnIII

2(µ3-

OH)2(O2CtBu)10]2- (MII = Mg, Co, Ni and Cu) balanced by two diisopropylammonium

(iPr2NH2+) or triethylammonium (Et3NH+) cations. We were also able to synthesise the

manganese(III) analogue with isostructural metal core [MnIII2LnIII

2(µ3-O)2(O2CtBu)10][Et3NH]2

where the two µ3-OH are substituted by two µ3-O (See later for explanation).



6

The M2Ln2 family was obtained from two different methods. The yield in both cases

ranges between 30–92 %. The {Ni2Ln2} and {Cu2Ln2} clusters were obtained by refluxing

[NiII2(µ2-OH2)(O2CtBu)4(HO2CtBu)4] or [CuII

2(O2CtBu)4(HOCtBu)2], respectively, with

[LnIII2(O2CtBu)6(HOCtBu)6] in the presence of triethylamine or diisopropylamine, respectively.

The {Mg2Ln2}, {Mn2Ln2} and {Co2Ln2} clusters were prepared under solvothermal conditions

using [MgII2(µ2-OH2)(O2CtBu)4(HO2CtBu)4], [MnII(O2CtBu)4EtOH]n, or [CoII

2(µ2-

OH2)(O2CtBu)4(HO2CtBu)4], respectively, and the lanthanide source in the presence of

triethylamine or diisopropylamine (see supporting information for more details). Attempts to

synthesise {Cu2Y2} and {Cu2Tb2} were made, but we were not able to crystallise these materials.

Crystal Structures

The complexes crystallise in three different space groups, P-1, C2/c and P21/c, depending on the

lanthanide metal source. The molecular structures of the complex anions are very similar in all

cases, and always have centrosymmetric symmetry. The description of 3 is given as

representative (Figure 1). The anionic cluster is composed of two MgII, two DyIII, two µ3-OH

(µ3-O for the MnIII analogue) and ten pivalates. The cluster is charged-balanced by two

[iPr2NH2+] cations. In 3 the MgII ion has adopted a slightly distorted octahedral geometry with an

O6 donor set. The DyIII ion was systematically analysed using SHAPE 2.118 software, resulting in

a distorted square antiprism geometry (D4h, with a value of 2.323) with an O8 donor set (See

Table S5 for geometrical parameters for other {M2Dy2} analogues). The MgII ion is chelated by

four pivalates and two (cis) µ3-OH, while the DyIII ion is bridged by four pivalates, one µ3-OH

and a terminal pivalate. Hydrogen bonding is observed between the diisopropylammonium

cations and the unbound oxygen of the terminal pivalates.

Complexes containing copper or manganese show a Jahn-Teller distortion, along the O4-

M-O10’ axis, with an elongated octahedral environment typical for d4 and d9 metals (bond length

ranges: Cu–Oeq 1.945(3)–1.978(2) Å, Cu–Oax 2.397(2)–2.421(1) Å; bond angle ranges: cis at Cu

81.45(8)–96.09(8)°, trans at Cu 172.46(9)–174.98(8)°); while Mn–Oeq 1.866(2)–1.970(2) Å,

Mn–Oax 2.289(2)–2.349(2) Å; bond angle ranges: cis at Mn 82.88(8) – 98.38(8)°, trans at Mn

174.10(9)–177.29(8)°). (Table 1 and Figure S1)



7

Figure 1. Crystal structure of [MgII

2DyIII2(µ3-OH)2(O2CtBu)10]2-. Scheme: Dy, blue; Mg, cyan; O, red; C, grey; H

omitted for clarity.

Table 1. 3d metal-oxygen distances dysprosium-containing molecules.

{M2Dy2} {Mg2Dy2} {Mn2Dy2} {Co2Dy2} {Ni2Dy2} {Cu2Dy2} M...O11eq 2.084(3) 1.866(2) 2.078(2) 2.058(1) 1.978(2) M...O4ax 2.099(3) 2.289(2) 2.178(2) 2.102(2) 2.397(2) M...O10ax 2.070(3) 2.349(2) 2.171(2) 2.092(2) 2.421(2) M...O6eq 2.036(2) 1.975(3) 2.041(3) 2.029(1) 1.945(3) M...O8eq 2.038(3) 1.970(2) 2.038(2) 2.023(1) 1.954(3)

The equatorial sites of the 3d metal are occupied by two bridging hydroxides or oxides

and oxygen atoms from bridging pivalates, while oxygen atoms from the Dy-chelating pivalates

fill the axial sites. The oxidation state of all manganese-containing systems was determined by

consideration of its coordination geometry, bond lengths, coordination numbers, the presence of

Jahn–Teller elongation axes for the manganese sites and the magnetic properties (see later).

Selected bond lengths and angles for Dy-containing complexes are listed in Table 1.

A considerably shorter M···O11eq bond length was observed for all manganese containing

clusters compared to the other 3d analogues, e.g. Table 1. A search of the crystallographic

database shows the characteristic metal-oxygen bond lengths for µ3-OH– and µ3-O2– groups are

1.921–2.120 Å and 1.838–1.918 Å, respectively. This, in addition to the presence of two

triethylammonium cations, confirms that there are bridging oxides in the manganese analogues.

Dy1O1

O5

O3

O2

O9O7

O8

O10

µ3-O11

O4

O6



8

Magnetism

DC magnetic susceptibility studies

The magnetic properties of all clusters were probed on polycrystalline samples via variable-

temperature (2–300 K) susceptibility (applied DC magnetic field, H = 1 kG), and variable-field

(0–7 T) and temperature (2–4 K) magnetisation measurements (see below and Table S6).

In order to understand how the paramagnetic 3d-metal affects the magnetic behaviour of

the lanthanide in the {M2Ln2} clusters we first describe the {Mg2Ln2} and {M2Y2} examples,

allowing us to independently assess the 3d···3d interactions, the 4f ion electronic structure and

possible 4f···4f interactions. We then discuss the {M2Ln2} clusters where M and Ln are both

paramagnetic. When Ln is the spin-only GdIII (8S7/2) ion, we can directly model and determine

the 3d···4f interaction. Such exact modelling is not possible where Ln is an orbitally degenerate

ion. However, we can indirectly assess the 3d···4f interactions in these examples through

comparison of the χMT(T) behaviour of {M2Ln2} with the sum of those for the appropriate

{M2Y2} and {Mg2Ln2} systems: these would be identical in the case of nil interaction, with any

divergences depending on the sign and strength of interaction.

{M2Y2}: The magnetic behaviour for [MII2YIII

2(µ3-OH)2(O2CtBu)10](R3NH)2 (MII = Co

and Ni) and [MnIII2YIII

2(µ3-OH)2(O2CtBu)10][Et3N]2 is depicted in Figures 2 and S2. For

{Mn2Y2} (12), χMT(T) steadily decreases from 1.76 cm3 K mol-1 at 300 K (lower than the spin-

only value of 6.0 cm3 K mol-1 for two non-interacting S = 2 ions with g = 2.0) towards zero on

cooling (Figure 2a). This is characteristic of an antiferromagnetic interaction, consistent with the

lack of a low temperature Mβ(H) signal, suggesting an S = 0 ground state. We have modelled the

χMT(T) behaviour of {Mn2Y2} using a simple isotropic Heisenberg Hamiltonian for two S = 2

spins: 𝐻 = −2𝐽!"!!"𝑆!"! ∙ 𝑆!"! + 𝑔!"𝜇!𝐵 𝑆!"! + 𝑆!"! , where JMn-Mn is the exchange

interaction. Good agreement was found with JMn-Mn = –58 cm-1 with fixed gMn = 2.0, with a small

4% monomeric impurity of S = 2 (Figure 2a). This conclusion is not surprising since oxide

bridges are likely to lead to antiferromagnetic interactions.

The χMT(T) value for {Ni2Y2} (18) at room temperature is 2.62 cm3 K mol-1 (consistent

with two uncoupled S = 1 ions with g = 2.29; see Table S6 and Figure 2b), decreasing only

slowly down to about 100 K where it starts decreasing more rapidly. This could be due to

antiferromagnetic coupling or significant single ion anisotropy. An interesting Mβ(H) profile is



9

observed (inset in Figure 2b), with exponential-like behaviour and higher magnetisation values

observed at 4 than at 2 K, suggesting that paramagnetic excited states are close to an S = 0

ground state. Modelling the magnetic behaviour of {Ni2Y2} requires an additional term in the

Hamiltonian, because the zero-field splitting of the NiII ions (DNi) is likely to be of the same

order as the weak exchange interaction, therefore we adopt the Hamiltonian:

𝐻 = −2𝐽!"!!"𝑆!"! ∙ 𝑆!"! + 𝐷!" 𝑆!"!!! − 𝑆!"!

! 3+ 𝑆!"!!! − 𝑆!"!

! 3 + 𝑔!!𝜇!𝐻 𝑆!"! + 𝑆!"!

Simultaneous fitting20 of Mβ(H,T) and χMT(T) provides good agreement with JNi-Ni = –4.6 cm-1,

DNi = +10.3 cm-1 and gNi = 2.34.

For {Co2Y2} (6), χMT(T) decreases slowly from 5.6 cm3 K mol-1 at room temperature

until about 24 K, below which it quickly drops to 0.47 cm3 K mol-1 (Figure S2a). Such behaviour

is expected from the orbitally degenerate 4T1g ground term of six-coordinate CoII, with a well-

isolated spin-orbit doublet ground state. Mβ(H,T) shows a crossover feature at about 4 T (inset in

Figure S2a. Modelling this exchange (which is likely to be highly anisotropic) meaningfully

requires further information19 and we do not attempt this in the present work.

Figure 2. a) Experimental χMT(T) data and fits for {Mn2Y2}; b) experimental χMT(T) and Mβ(H,T) (inset) data and fits for {Ni2Y2}.

{Mg2Ln2}: At room temperature [MgII2GdIII

2(µ3-OH)2(O2CtBu)10][iPr2NH2]2 (1) has a

χMT(T) of 15.7 cm3 K mol-1, close to the value for two non interacting gadolinium ions (15.6 cm3

K mol-1), and is essentially temperature independent except at very low temperatures (Figure

S3a). Hence, any interactions between the GdIII ions are very weak, consistent with the Gd···Gd

distance of 6.2326(6) Å. The small downturn at low temperatures could be due to weak

antiferromagnetic interactions or small zero-field splitting of the S = 7/2 state of each GdIII ion.

a) b)



10

Figure 3. a) Experimental χMT(T) and Mβ(H,T)(b) data and fits for {Mg2Dy2}.

For all the {Mg2Ln2} analogues with orbitally degenerate Ln (TbIII, DyIII, HoIII and ErIII),

room temperature χMT(T) values are in good agreement with those for two uncoupled LnIII ions

(see Table S6 and Figure S3). For {Mg2Dy2} (3), χMT(T) decreases slowly on cooling down to

about 30 K, due to depopulation of Starks levels, below which it increases to 28.6 cm3 K mol-1 at

2 K (Figure 3). This upturn can be modelled simply by using the effective g-values of the ground

Kramers doublet obtained from ab-initio calculations (see later), and then considering the

anisotropic dipole interaction between two effective spins of Seff = 1/2. The resulting magnetic

axis has an angle of 2.0º to the vector between the DyIII ions and the ground doublets have

effective g-values of gxx = gyy = 0.01 and gz = 19.76 in the Seff = 1/2 formalism. Along with the

Dy···Dy distance of 6.1298(4) Å, the main component of the dipolar interaction gives Jzz = +0.72

cm-1 (for a –2J Hamiltonian). This value reproduces the low temperature χMT(T) (where only this

doublet is populated) and Mβ(H,T) well (Figure 3).

For {Mg2Tb2} (2), {Mg2Ho2} (4) and {Mg2Er2} (5), χMT(T) decreases only slowly to

about 100 K, below which it decreases more rapidly, dominated by depopulation of the excited

Stark levels (Figure S3b-d). We have not tried to model any very weak exchange interactions for

these complexes, since the data are insensitive to them, but the result for {Mg2Dy2} suggests that

the interactions are likely dipolar in nature.

Paramagnetic mixed-metal systems {M2Ln2}: In order to gain insight into the 3d···4f

interactions we first model the model χMT(T) and Mβ(H,T) data for the {M2Gd2} complexes,

using the JM-M parameters obtained from {M2Y2} where possible. The magnetic data of

a) b)



11

{Mn2Gd2} has been modelled using the isotropic Hamiltonian: 𝐻 = −2𝐽! 𝑆!"! ∙ 𝑆!"! −

2𝐽! 𝑆!"! + 𝑆!"! ∙ 𝑆!"! + 𝑆!"! + 𝜇!𝐵 𝑔!" 𝑆!"! + 𝑆!"! + 𝑔!" 𝑆!"! + 𝑆!"! . This

neglects the Gd···Gd interaction and any single ion anisotropy. For {Ni2Gd2} we allowed for the

zero-field splitting of NiII as in {Ni2Y2}, and a small Gd····Gd interaction, to reproduce the

upturn observed at low temperature, using the Hamiltonian:

𝐻 = −2𝐽! 𝑆!"! ∙ 𝑆!"! − 2𝐽! 𝑆!"! + 𝑆!"! ∙ 𝑆!"! + 𝑆!"! − 2𝐽! 𝑆!"! ∙ 𝑆!"!

+ 𝐷!" 𝑆!"!!! + 𝑆!"!!

! + 𝜇!𝐵 𝑔!" 𝑆!"! + 𝑆!"! + 𝑔!" 𝑆!"! + 𝑆!"!

For {Mn2Gd2} (13), good agreement between experiment and simulation was obtained

with J2 = +5.5 cm-1 where J1 was fixed from {Mn2Y2} (Figure 4c). Similarly for {Ni2Gd2} (19),

with J1 and DNi fixed from {Ni2Y2}. We find good agreement for J2 = +0.09 cm-1 and J3 =

+0.015 cm-1 (Figure 4a). We were unable to prepare {Cu2Y2}, hence we have refined J1 and J2 in

a simultaneous fit to χMT(T) and M(H,T) for {Cu2Gd2} (24) giving J1 = –178 and J2 = +13 cm-1

(Figure 3d). These values are in good agreement with related Cu···Cu21 and Cu···Gd11,21 pairs,

however care take must be taken with the Cu···Gd value, due to the strong Cu···Cu interaction.

Figure 4. Experimental χMT(T) and M(H,T) and simulations (red lines) for (a) {Ni2Gd2} and (c) {Mn2Gd2}. (b) Exchange scheme.

J1

J2

J2

J2J3

J2

b)a)

c) d)



12

For both {Mn2Gd2} and {Ni2Gd2}, the M···Gd exchange is at least an order of magnitude

smaller than the M···M exchange. While we cannot model the magnetic data for the Ln = TbIII,

DyIII, HoIII and ErIII analogues to obtain the 3d···4f interaction directly, some qualitative insight

can be gained from comparing the sum of the data for {Mg2Ln2} with {M2Y2} with those from

{M2Ln2} (See Figure 5 and S4-6). Despite not having the {Cu2Y2} analogue, some insight into

the behaviour of the {Cu2Ln2} has been achieved using the Cu···Cu exchange interaction

obtained for {Cu2Gd2} and simulating the χMT(T) for {Cu2Y2}.

In all cases the room temperature χMT(T) values are in good agreement between the

measured {M2Ln2} and composed {M2Y2}+{Mg2Ln2} data: this is expected as the effect of

rather weak JM-Ln exchange interactions will be “washed out” when kT >> J. Significant

deviations are observed, however, at lower temperatures (Figures 5 and S4-S6). For {M2Dy2} the

measured χMT values fall below the sum of the components at around 70 K for {Co2Dy2},

{Ni2Dy2} and {Cu2Dy2}, and at around 150 K for {Mn2Dy2}, implying antiferromagnetic JM-Dy

interactions. The deviation for the former three compounds continues to grow as temperature

falls, while for {Mn2Dy2} it remains small throughout the temperature range. It is worthy to note

that the low temperature upturn is maintained in {Mn2Dy2}, {Ni2Dy2} and {Cu2Dy2}, but not for

{Co2Dy2}.

Figure 5. Comparison of χMT(T) magnetic behaviour for {M2Dy2} and the summed value for {M2Y2} + {Mg2Dy2}; Where M is : a) Mn; b) Co; c) Ni and d) Cu.

a)

c) d)

b)



13

Similarly the nature and strength of the interaction observed at low temperatures can be

better observed through the ΔχMT function for {M2Ln2} – ({M2Y2} + {Mg2Ln2}); ferromagnetic

M···Ln behaviour is expected when this function is greater than zero and antiferromagnetic if it is

less than zero (Figure S7). Ferromagnetic interaction was observed for {Mn2Gd2}, {Ni2Gd2},

{Mn2Tb2}, {Ni2Tb2} and {Ni2Er2}, while antiferomagnetic interactions were observed for most

of the remaining systems. These findings are summarised in Table 2.

Table 2. 3d-4f exchange interaction obtained from simulation and qualitative analysis.

3d-4f Mn Co Ni Cu Gd F - F - Tb F - F - Dy AF AF AF AF Ho AF AF AF AF Er AF AF F AF (F) = ferromagnetic; (AF) = antiferromagnetic; (-) no observable difference

AC magnetic susceptibility

Frequency and temperature dependent magnetic susceptibility measurements (1.55 G

oscillating field) were obtained for all clusters at zero and/or 1 kG applied DC field. Frequency

dependent behaviour, typical of SMMs, was observed in all {M2Dy2} clusters and four of the

{M2Er2} analogues (M = MgII, MnII, NiII and CuII}. We first describe the behaviour of the

{M2Y2} and {Mg2Ln2} systems, and then what effect the JM-Ln interaction has on the dynamic

magnetic properties for the {M2Ln2} complexes.

{M2Y2}: No frequency dependent behaviour was observed in nil or 1 kG applied DC field.

Hence the {M2} units do not give rise to SMM behaviour, which is as expected due to small

magnetic anisotropy and the antiferromagnetic J1 interactions leading to S = 0 ground states.

{Mg2Ln2}: Clear peaks in the out-of-phase susceptibility (χ"M) as a function of

temperature and frequency were observed for {Mg2Dy2} (Figure 6) and {Mg2Er2} (Figure 7). No

out-of-phase component was observed for the Tb and Ho analogues, even with the application of

a small DC field.

For {Mg2Dy2} (Figure 6), χ"M(T) has a significant out-of-phase signal below 12 K at zero

DC field with a maximum at 7.5 K for the highest measurement frequency (ν) of 1.2 kHz. The

peaks in χ"M(ν) become temperature independent below 3 K, indicating a quantum regime. The



14

tunnelling frequency was found to be 2.2 Hz, resulting in a quantum tunnelling time of (τQTM) of

71 ms. At temperatures above 5 K the relaxation data is roughly linear and can be described

using the Arrhenius law, τ = τ0exp(Ueff/kT), revealing a thermal energy barrier to magnetization

relaxation of Ueff = 44 K and τ0 = 7.8 × 10-7 s (6c and d). Cole-Cole plots (χ'M vs. χ"M) for the

temperature range 1.8 – 9.5 K give temperature-dependent α parameters: at high temperatures α

= 0.05, characteristic of a single relaxation time and upon lowering the temperature α increases

to 0.30, indicating a wider distribution of relaxation times (Figure 6c).

Figure 6. (a) χ"M(T), (b) χ"M(ν), (c) Cole-Cole plot, and (d) Arrhenius analysis of {Mg2Dy2} at zero DC field.

For {Mg2Er2} (Figure 7), there is a frequency-dependent behaviour of the susceptibility

without applied field; this is enhanced with the application of a small DC field of 1 kG,

presumably due to the suppression of quantum tunnelling of the magnetization through the

anisotropy barrier. The maximum in χ"M(T) is observed at 4 K for ν = 1.2 kHz. No temperature

independent behaviour was observed in the χ"M(ν) susceptibility, hence we do not reach the pure

quantum regime consistent with the suppression of tunnelling. An Arrhenius fit to the high-

temperature, pseudo-linear region show Ueff = 23 K and τ0 = 6.6 × 10-7 s. Cole-Cole plots behave

similarly to those for {Mg2Dy2}, with α = 0.035 at higher temperatures increasing to α = 0.2 at

the lowest temperatures.

9.5 K 1.8 K

��_��

a) b)

d)c)



15

Figure 7. (a) χ"M(T), (b) χ"M(ν), (c) Cole-Cole plot, and (d) Arrhenius analysis of {Mg2Er2}, measured under 1 kG DC field.

Mixed paramagnetic metal complexes {M2Ln2}:

χ"M(T) for {Mn2Dy2} (Figure 8) peaks around 7 K at 1.2 kHz, before increasing again at

lower temperatures: the peaks are broader than those observed in {Mg2Dy2}. χ"M(ν) is frequency

independent below ca. 3 K. Analysis of the data gives Ueff = 29 K with K0 = 4.6 × 10-6 s, and the

distribution of relaxation processes varying from α = 0.2 to 0.3 from high to low temperature.

The high temperature α is noticeable larger than that found for {Mg2Dy2}. We have obtained the

tunnelling frequency 27.7 Hz, which corresponds to a τQTM of 5.7 ms, larger than the obtained in

{Mg2Dy2}.

a) b)

d)c)

��_��

1.8 K5 K



16

Figure 8. (a) χ"M(T), (b) χ"M(ν), (c) Cole-Cole plot, and (d) Arrhenius analysis of {Mn2Dy2} at zero DC field.

For {Ni2Dy2} the maximum in χ"M(T) is observed 3.5 K for 1.2 kHz (Figure 9), i.e. at a

lower temperature than {Mg2Dy2}. Analysis of χ"M(T,ν) gives Ueff = 20 K, τ0 = 6.0 × 10-7 s, with

α varying from 0.01 to 0.1 from high to low temperature, lower than those for {Mg2Dy2}.

Figure 9. (a) χ"M(T), (b) χ"M(ν), (c) Cole-Cole plot, and (d) Arrhenius analysis of {Ni2Dy2} at zero DC field.

a) b)

d)c)

��_��

1.8 K8.5 K

a) b)

d)c)

��_��

1.8 K4 K



17

Similar behaviour is observed for {Ni2Er2}, with a maximum in χ"M(T) at 2.4 K under 1

kG dc field. Arrhenius analysis gives Ueff = 18 K with τ0 = 3.9 × 10-6 s, and α = 0.1 at high

temperature, increasing to 0.2 at lower temperatures (Figure 10).

Figure 10. (a) Temperature-dependence χ"M(T); (b) Frequency-dependence χ"M(ν); (c) Cole-Cole plot ; (d) energy barrier of {Ni2Er2} under 1 kG applied magnetic field.

{M2Dy2} where M = CoII and CuII, and also {Cu2Er2}, exhibit out-of-phase components;

however no maxima are observed in χ"M(T) above 2 K, making it impossible to derive an energy

barrier (Figure S9).

ab-initio calculations

Many studies of dysprosium complexes have shown that slow relaxation of magnetisation (i.e.

SMM behaviour) occurs when the ground state is a well-defined mJ = ±15/2 Kramers doublet.

Such a state has a strongly axial effective g-tensor with principal values gxx = gyy ≈ 0 and gzz = 20.

To understand the origin of the slow magnetic relaxation in the DyIII clusters, we have performed

CASSCF (complete active space self-consistent field) ab-initio calculations using MOLCAS22-24

(see Supporting Information for details). These calculations have widely proven to be effective in

the prediction and understanding of the SMM behaviour. For all the present {M2Dy2} clusters,

the CASSCF calculations predict similar properties for the DyIII ions – strongly anisotropic

a) b)

d)c)

��_��

1.8 K2.5 K



18

ground doublets with gz approaching 20 while gx and gy are close to zero, with the first excited

state at ~ 60 – 140 cm-1 (Tables S7 – S11). In all cases the principal magnetic axis of the ground

doublet is almost co-parallel with the Dy···Dy vector and the principal axis of the first excited

state is not coincident with that of the ground state, with deviations of 12 – 29°. These results

suggest that the DyIII ions in the {M2Dy2} clusters would show some slow relaxation properties

with maximum energy barriers corresponding to the first excited state. However, it is likely that

the effective barriers will be much lower due to the low symmetry and lack of strong magnetic

uniaxiality.

Figure 11. Magnetic axis calculated CASSSCF calculations for: (a) {Mg2Dy2} lying 2.0º off the Dy···Dy vector.

The magnetic axes for the remaining {M2Dy2} clusters lies close to the observed for {Mg2Dy2} with small

deviations, i.e. 4.0, 3.6, 5.4 and 1.6º for {Mn2Dy2}, {Ni2Dy2}, {Cu2Dy2} and {Co2Dy2} respectively, from the

Dy···Dy vector. Colour code: Dy, blue; Mg, cyan; Mn, brown, Ni, green; O, red; C, grey; H omitted for clarity.

Discussion

As none of the {M2Y2} clusters show an out-of-phase component of the AC susceptibility, it is

clear that the SMM behaviour for the {M2Dy2} and some of the {M2Er2} compounds is due to

the lanthanide ions in the molecule. For the Dy-based systems, the maximum χ"M(T) value at 1.2

kHz is observed for {Mg2Dy2} at ~ 7.5 K, and is shifted to lower temperatures of 6.5 K and 3.5

K for {Mn2Dy2} and {Ni2Dy2}, respectively, with no maximum above 1.8 K for {Co2Dy2} or

{Cu2Dy2}. Detailed advanced multi-configurational ab-initio has allowed us to determine the

magnetic axis for all the systems, leading to basically all axes being collinear with the Dy···Dy

vector. A closer look at the electronic states obtained from ab-initio calculation (Table S7-S11)



19

show all Dy(III) sites show little deviation with respect to each other, implying that in all cases,

small differences should be observed between systems. If the electronic differences between the single Dy(III) sites are present as suggested by

ab-initio, then a plausible explanation of different dynamic behaviours is the strength of the 3d-

4f exchange interactions, Table 3. To estimate the M···Dy exchange interaction in the {M2Ln2}

pairs where Ln is anisotropic, we consider the difference between the observed χMT value and

that calculated for the sum of the appropriate {M2Y2} and {Mg2Ln2} compounds, at 2 K. We

observe that as the M···Dy interaction becomes stronger, the Ueff barrier decreases and becomes

unmeasurable for {Co2Dy2} and {Cu2Dy2} where the interactions seem to be the strongest. A

similar conclusion seems to be evident for the {M2Er2} complexes, where slow relaxation can

only be quantified for {Mg2Er2} (where there is no paramagnetic 3d co-metal) and {Ni2Er2},

where the magnetic interactions are negligible.

Table 3. 3d-4f exchange interaction obtained from simulation and qualitative analysis.

Ln = Gd Ln = Dya Ln = Erb

JGd-M/cm-1 (χMT)obs–

(χMT)calcc

Ueff/k /K τo /s-1 αd (χMT)obs–

(χMT)calcc

Ueff/k /K τo /s-1 αd

{Mg2Ln2} - - 44 7.8 x 10-7 0.05 - 23 6.6 x 10-7 0.035

{Mn2Ln2} +4.2 -4.4 29 4.6 x 10-6 0.2 -5.3 - - -

{Co2Ln2} - -8.5 - - - -1.5 - - -

{Ni2Ln2} +0.08 -5.2 20 6.0 x 10-7 0.01 +0.4 18 3.9 x 10-6 0.1

{Cu2Ln2} - -8.0 - - - -5.7 - - -

a. SMM behaviour measured in zero DC field

b. SMM behaviour measured in 1 kG DC field

c. Calculated at 2 K

d. Value at highest measured temperature

CONCLUSIONS

The successful synthesis of twenty-seven isostructural complexes has been achieved through two

methods in good yield. The stability presented for the metal core towards 3d- and 4f-metal

exchange allows us to study the magnetic behaviour of the mixed paramagnetic metal systems.

Dynamic magnetic susceptibility measurements show SMM behaviour for all Dy-based



20

tetramers and some Er-based molecules, in zero and 1 kG DC fields, respectively. Moreover, no

SMM behaviour was observed for any of the molecules when just the diamagnetic yttrium

analogue is present clearly revealing that the SMM behaviour observed in the Dy- and Er-based

systems is intrinsic to the lanthanide ion, further demonstrated by the behaviour observed in

{Mg2Dy2} and {Mg2Er2}. Ab-initio calculations studies performed on all Dy-containing

molecules reveal similar electronic structure for all systems, implying that small differences in

dynamic behaviour should be attained, however we have shown that this is not the case. In the

molecules here described it seems that the strength of the 3d-4f exchange interaction plays a key

role in the SMM properties observed.

AKNOWLEDGEMENTS

EMP thanks the Panamanian agency SENACYT-IFARHU for funding. REPW thanks the Royal

Society for a Wolfson Merit Award. We also thank EPSRC (UK) (grant number EP/K039547/1)

for funding for an X-ray diffractometer. NFC thanks The University of Manchester for a

President’s Doctoral Scholarship.

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asas



1


Systematic study of a family of butterfly-like {M2Ln2} molecular magnets (M = MgII, MnIII, CoII, NiII and CuII; Ln = YIII, GdIII, TbIII, DyIII, HoIII and ErIII) Eufemio Moreno Pineda, Nicholas F. Chilton, Floriana Tuna, Richard E. P. Winpenny* and Eric J. L. McInnes*

School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom.

Synthesis of starting materials

Unless stated otherwise, all reagents and solvents were purchased from Aldrich Chemicals and

used without further purification. [MII2(µ-OH2)(O2CtBu)4(HO2CtBu)4] (M = MgII, CoII and NiII),

[MnII(O2CtBu)4EtOH]n and [Cu2II(O2CtBu)4(HO2CtBu)2] were prepared according to described

procedures. [Ln2III(O2CtBu)6(HO2CtBu)6] (Ln = YIII, GdIII, TbIII, DyIII, HoIII and ErIII), were

synthesized by refluxing LnIII2O3 (10 mmol) and excess pivalic acid (30 g, 300 mmol) at 160 ºC

for 5 hrs to form a clear solution. Followed by cooling the solution to room temperature and

white or pink precipitate came out. 50 mL toluene was added to dissolve the excess pivalic acid

and filtered in vacuum and 50 ml n-hexane were used to wash the product (yield ca. 13 g, 87 %).

CASSCF method

CASSCF calculations were performed with MOLCAS 7.8. All calculations were on single

isolated molecules, excluding counter-ions, and employed the experimental crystal structure with

no optimization. Only one of the dysprosium sites was examined for each cluster, as the cluster

possesses inversion symmetry, therefore the other DyIII site was replaced with LuIII. For the cases

with paramagnetic 3d ions, these were replaced by the diamagnetic analogues ZnII (for CoII, NiII

and CuII) or GaIII (for MnIII). The basis sets were chosen from the ANO-RCC library, where the

Dy ion was treated with VTZP quality, the first coordination sphere with VDZP quality, all other

non-hydrogen atoms with VDZ quality and hydrogen atoms with MB quality. In the RASSCF

module, the sextets and quartets were state averaged with 21 and 224 roots, respectively. In the

RASSI module, all 21 sextets and 128 quartets were mixed by spin-orbit coupling. No doublets

were included in the calculation due to computational limitations.



2

Table S1. Elemental analysis and yield (%) for compounds 1 - 27 Formula Yielda % Elemental analysis: Found (calculated) C H N M Ln

1 [MgII2YIII

2(µ-OH3)(O2CtBu)4(HO2CtBu)4](iPr2NH2)2 90 50.31 (50.45)

8.38 (8.47)

1.94 (1.90)

3.19 (3.29)

12.00 (12.05)

2 [MgII2GdIII

2(µ-OH3)(O2CtBu)4(HO2CtBu)4](iPr2NH2)2�MeCN

79 45.96 (46.48)

7.82 (7.74)

2.84 (2.54)

2.92 (2.94)

19.08 (19.02)

3 [MgII2TbIII


7.74 (7.73)

1.72 (1.73)

2.99 (3.00)

19.46 (19.67)

4 [MgII2DyIII

2(µ-OH3)(O2CtBu)4(HO2CtBu)4](iPr2NH2)2

92 45.86 (45.87)

8.09 (7.70)

1.69 (1.73)

2.98 (2.99)

20.02 (20.02)

5 [MgII2HoIII

2(µ-OH3)(O2CtBu)4(HO2CtBu)4](iPr2NH2)2

87 46.14 (45.74)

7.88 (7.68)

1.68 (1.72)

2.93 (2.99)

20.10 (20.26)

6 [MgII2ErIII


7.88 (7.66)

1.70 (1.72)

2.78 (2.98)

20.19 (20.49)

7 [MnIII2YIII

2(µ-OH3)(O2CtBu)4(HO2CtBu)4](Et3N)2�MeCN

48 47.86 (48.76)

8.26 (7.99)

3.02 (2.67)

7.15 (6.97)

10.40 (11.28)

8 [MnIII2GdIII

2(µ-OH3)(O2CtBu)4(HO2CtBu)4](Et3N)2 44 43.64 (44.54)

7.56 (7.35)

1.64 (1.67)

6.56 (6.57)

16.24 (18.81)

9 [MnIII2TbIII


30 43.86 (44.78)

7.51 (7.34)

2.37 (2.45)

5.88 (6.40)

17.22 (18.52)

10 [MnIII2DyIII


74 44.15 (44.60)

7.27 (7.31)

2.65 (2.44)

6.12 (6.37)

18.43 (18.86)

11 [MnIII2HoIII


36 44.14 (44.47)

7.50 (7.29)

2.65 (2.43)

4.54 (6.36)

15.51 (19.08)

12 [MnIII2ErIII


42 43.74 (44.35)

7.64 (7.27)

2.31 (2.42)

5.86 (6.34)

18.39 (19.30)

13 [CoII2YIII


8.08 (8.09)

2.14 (1.81)

7.02 (7.63)

10.68 (11.51)

14 [CoII2GdIII

2(µ-OH3)(O2CtBu)4(HO2CtBu)4](iPr2NH2)2�MeCN

63 44.38 (44.61)

7.58 (7.42)

2.80 (2.44)

6.54 (6.84)

17.36 (18.25)

15 [CoII2TbIII


7.61 (7.39)

1.76 (1.66)

6.43 (6.96)

17.54 (19.20)

16 [CoII2DyIII


7.74 (7.38)

2.30 (2.42)

6.92 (6.80)

18.62 (18.75)

17 [CoII2HoIII


7.56 (7.36)

1.86 (1.65)

6.30 (6.94)

19.16 (19.43)

18 [CoII2ErIII


7.41 (7.34)

1.60 (1.65)

7.51 (6.92)

18.50 (19.65)

19 [NiII2YIII

2(µ-OH3)(O2CtBu)4(HO2CtBu)4](Et3NH)2 40 48.07 (48.20)

7.86 (8.09)

1.81 (1.81)

7.33 (7.60)

11.77 (11.51)

20 [NiII2GdIII


7.43 (7.43)

6.54 (2.44)

17.53 (6.81)

2.85 (18.26)

21 [NiII2TbIII


7.53 (7.42)

1.68 (1.66)

6.95 (6.97)

18.54 (18.86)



3

Table S1 continued. Elemental analysis and yield (%) for compounds 1 - 27

Formula Yielda % Elemental analysis: Found (calculated)

C H N M Ln

22 [Niv2DyIII2(µ-OH3)(O2CtBu)4(HO2CtBu)4](Et3NH)2 55 43.71

(44.01) 7.81 (.39)

1.63 (1.66)

6.72 (6.94)

19.30 (19.21)

23 [NiII2HoIII


7.50 (7.37)

1.65 (1.65)

6.96 (6.91)

19.68 (19.44)

24 [NiII2ErIII


7.47 (7.34)

1.64 (1.65)

6.86 (6.90)

19.70 (19.66)

25 [CuII2GdIII


7.31 (7.39)

3.21 (3.16)

6.56 (7.17)

17.98 (17.74)

26 [CuII2DyIII


7.54 (7.34)

3.24 (3.14)

7.08 (7.12)

18.77 (18.22)

27 [CuII2HoIII


7.78 (7.27)

2.30 (2.40)

6.95 (7.27)

18.61 (18.87)

28 [CuII2ErIII

2(µ-OH3)(O2CtBu)4(HO2CtBu)4](iPr2NH2)2 51 (43.87) (7.25) (2.40) (7.25) (19.09)

a. Calculated based on MgII and transition metal pivalate

Table S2. Crystallographic information for Dy-containing molecules.

3 15 9 21 25 chem formula Mg2Dy2N2O22C62C124 Mn2Dy2N2O22C62C122 Co2Dy2N2O22C62C124 Ni2Dy2N2O22C62C124 Cu2Dy2N2O22C62C124 fw 1623.24 1871.72 1638.06 1692.04 1735.72 cryst system monoclinic triclinic triclinic monoclinic triclinic space group P21/c P-1 P-1 C2/c P-1 a/Å 15.4531(3) 13.2219(2) 11.3913(4) 20.7072(4) 11.1732(4) b/Å 19.5753(4) 13.5495(3) 13.3809(5) 21.2970(3) 13.2788(4) c/Å 14.0907(3) 14.1560(2) 15.4188(5) 18.3086(3) 15.5030(6) α/° 90 71.5364(15) 103.070(3) 90 102.315(3) β/° 109.082(2) 64.2521(15) 98.378(3) 101.572(2) 97.228(3) γ/° 90 81.4352(15) 109.653(3) 90 110.072(3) V/Å3 4028.20(15) 2166.49(7) 2092.04(14) 7910.0(2) 2060.48(14) Z 2 1 1 4 1 ρ calcd/g cm-3 1.338 1.435 1.300 1.421 1.399 T/K 150.06(15) 106(6) 104.2(2) 102(1) µ (Mo Kα)/mm-1

1.920 2.963 2.215 2.401 2.367

R1(I>2σ)(I))[a] 0.0347 0.0311 0.0318 0.0219 0.0303 wR2

[a] 0.0662 0.0888 0.0727 0.0515 0.0688

a R1 = ||Fo| - |Fc||/|Fo|, wR2=[w(|Fo| - |Fc|)2/w|Fo|

2]

1/2



4

Table S3. Crystallographic information for Er-containing molecules. 5 17 11 23 27 chem formula Mg2Er2N2O22C62C124 Mn2Er2N2O22C62C122 Co2Er2N2O22C62C124 Ni2Er2N2O22C62C124 Cu2Er2N2O22C62C124 fw 1623.24 1871.72 1638.06 1692.04 1735.72 cryst system monoclinic triclinic triclinic monoclinic triclinic space group P21/c P-1 P-1 C2/c P-1 a/Å 15.4531(3) 13.2219(2) 11.3913(4) 20.7072(4) 11.1732(4) b/Å 19.5753(4) 13.5495(3) 13.3809(5) 21.2970(3) 13.2788(4) c/Å 14.0907(3) 14.1560(2) 15.4188(5) 18.3086(3) 15.5030(6) α/° 90 71.5364(15) 103.070(3) 90 102.315(3) β/° 109.082(2) 64.2521(15) 98.378(3) 101.572(2) 97.228(3) γ/° 90 81.4352(15) 109.653(3) 90 110.072(3) V/Å3 4028.20(15) 2166.49(7) 2092.04(14) 7910.0(2) 2060.48(14) Z 2 1 1 4 1 ρ calcd/g cm-3 1.338 1.435 1.300 1.421 1.399 T/K 150.06(15) 106(6) 104.2(2) 102(1) µ (Mo Kα)/mm-1

1.920 2.963 2.215 2.401 2.367

R1(I>2σ)(I))[a] 0.0347 0.0311 0.0318 0.0219 0.0303 wR2

[a] 0.0662 0.0888 0.0727 0.0515 0.0688

a R1 = ||Fo| - |Fc||/|Fo|, wR2=[w(|Fo| - |Fc|)2/w|Fo|

2]

1/2

Table S4. Unit Cells determination for remaining clusters chem formula {Mg2Y2} {Mg2Tb2} {Mg2Ho2} {Mn2Tb2} {Mn2Ho2} {Mn2Er2} {Co2Y2} a/Å 12.9400(11) 15.7443(5) 15.4985(4) 16.8219(4) 16.8346(3) 13.2163(7) 11.3596(3) b/Å 14.1629(12) 13.1628(4) 19.5983(5) 13.1584(2) 13.1278(3) 13.5584(5) 13.2938(4) c/Å 14.2789(10) 21.9247(9) 14.1128(3) 21.4410(5) 21.5476(3) 14.1537(7) 15.4073(4) α/° 98.793(7) 90 90 90 90 71.640(4) 102.961(3) β/° 108.203(7) 109.812(4) 109.120(3) 109.994(3) 109.766(3) 64.229(5) 98.742(2) γ/° 116.745(9) 90 90 90 90 81.467(4) 109.556(3) V/Å3 2082.94 4274.73 4050.2 4487.55 4481.47 2167.52 2070.26 chem formula {Co2Tb2} {Co2Ho2} {Co2Er2} {Cu2Ho2} {Cu2Er2} {Ni2Tb2} {Ni2Ho2} a/Å 15.7469(4) 15.8238(7) 10.5068(9) 11.2038(5) 11.2136(5) 15.9241(5) 20.7201(6) b/Å 13.0245(3) 13.0747(4) 14.4090(12) 13.3226(6) 13.3202(6) 12.9928(3) 21.3022(5) c/Å 21.9609(5) 22.0964(8) 14.7534(7) 15.5565(5) 15.5839(7) 21.7668(8) 18.2890(5) α/° 90 90 77.808(7) 102.642(3) 102.470(4) 90 90 β/° 110.893(3) 110.860(4) 69.522(8) 96.869(3) 97.202(4) 111.049(4) 101.679(3) γ/° 90 90 81.934(7) 110.014(4) 110.001(4) 90 90 V/Å3 4207.91 4171.91 2039.83 2080.42 2084.77 4203.02 7905.75



5

Table S5. Continuous shaped measures (CShM) for {M2Dy2} obtained using SHAPE. {Mg2Dy2} {Mn2Dy2} {Co2Dy2} {Ni2Dy2} {Cu2Dy2} OP-8 32.114 32.1761 32.110 32.319 32.677 HPY-8 21.838 21.497 21.619 21.638 21.178 HBPY-8 17.782 17.561 17.468 17.486 16.784 CU-8 11.719 10.960 11.654 11.391 11.660 SAPR-8 2.323 1.973 2.270 2.114 2.280 TDD-8 2.811 2.773 2.621 2.996 2.363 JGBF-8 15.664 15.959 15.818 15.396 15.001 JETBPY-8 28.249 27.552 28.570 27.732 28.331 JBTPR-8 4.373 3.702 4.041 3.847 3.839 BTPR-8 3.094 2.641 2.801 2.745 2.669 JSD-8 5.853 5.726 5.561 5.742 5.101 TT-8 12.521 11.620 12.402 12.114 12.285 ETBPY-8 23.152 23.022 23.469 22.515 24.112

OP-8 = (D8h) Octagon HPY-8 = (C7v) Heptagonal pyramid HBPY-8 = (D6h) Hexagonal bipyramid CU-8 = (Oh) Cube SAPR-8 = (D4d) Square antiprism TDD-8 = (D2d) Triangular dodecahedron JGBF-8 = (D2d) Johnson gyrobifastigium J26 JETBPY-8 = (D3h) Johnson elongated triangular bipyramid J14 JBTPR-8 = (C2v) Biaugmented trigonal prism J50 BTPR-8 = (C2v) Biaugmented trigonal pris JSD-8 = (D2d) Snub diphenoid J84 TT-8 = (Td) Triakis tetrahedron ETBPY-8 = (D3h) Elongated trigonal bipyramid



6

Table S6. Magnetic data for clusters {M2Ln2}.

Mg2Gd2 Mg2Tb2 Mg2Dy2 Mg2Ho2 Mn2Er2 Mn2Y2 Mn2Gd2 S (M2+/3+) - - - - - 2 2 S (Ln3+) 7/2 3 5 2 3/2 - 7/2 L (Ln3+) 0 3 5/2 6 6 - 0 J (Ln3+) 7/2 6 15/2 8 15/2 - 7/2 gJ (Ln3+) 1.99 3/2 4/3 5/4 6/5

- 1.99 g (M2+/3+) - - - - - 2.12 2.12 χMT/ (calcd)b 15.59 23.62 28.33 28.12 22.95

1

6.74 22.33 χMT (obs)a,b 15.70 23.26 27.80 27.84 22.35 1.76 19.62 χMT (at 2K)b 15.32 4.31 28.65 14.60 17.06 0.07 15.30 Mβ (obs at 1.8 K)c 13.74 9.53 10.78 10.19 9.67 0 13.97 S (total spin angular momentum), L (total orbital angular momentum) and J (total angular momentum), of the ground multiplet. gJ is the Landé factor. aRoom temperature χMT, bValues of χMT are given in emu mol-1 K, cValues of M are given in µB mol-1, value observed at 7 T. dMagnetisation measured at 2 K and 7 T.

Table S6 continued. Magnetic data for clusters {M2Ln2}.

Mn2Tb2 Mn2Dy2 Mn2Ho2 Mn2Er2 Co2Y2 Co2Gd2 S (M2+/3+) 2 2 2 2 3/2 3/2 S (Ln3+) 3 5 2 3/2 - 7/2 L (Ln3+) 3 5/2 6 6 - 0 J (Ln3+) 6 15/2 8 15/2 - 7/2 gJ (Ln3+) 3/2 4/3 5/4 6/5

- 1.99 g (M2+/3+) 2.12 2.12 2.12 2.12 χMT/ (calcd)b 30.36 35.07 34.86 29.69 χMT (obs)a,b 25.81 29.68 30.03 24.9 5.59 21.8 χMT (at 2K)b 13.62 24.28 12.79 11.79 0.47 15.75 Mβ (obs at 1.8 K)c 9.72 10.22 9.62 9.97 4.28d 17.76d S (total spin angular momentum), L (total orbital angular momentum) and J (total angular momentum), of the ground multiplet. gJ is the Landé factor. aRoom temperature χMT, bValues of χMT are given in emu mol-1 K, cValues of M are given in µB mol-1, value observed at 7 T. dMagnetisation measured at 2 K and 7 T.



7


Co2Tb2 Co2Dy2 Co2Ho2 Co2Er2 Ni2Y2 Ni2Gd2 Ni2Tb2 S (M2+/3+) 3/2 3/2 3/2 3/2 1 1 1 S (Ln3+) 3 5 2 3/2 - 7/2 3 L (Ln3+) 3 5/2 6 6 - 0 3 J (Ln3+) 6 15/2 8 15/2 - 7/2 6 gJ (Ln3+) 3/2 4/3 5/4 6/5

- 1.99 3/2 g (M2+/3+) 2.34 2.34 2.34 χMT/ (calcd)b 2.74 18.32 26.36 χMT (obs)a,b 29.09 33.39 33.43 28.60 2.62 18.39 26.76 χMT (at 2K)b 4.34 20.70 12.10 16.25 0.14 17.46 5.65 Mβ (obs at 1.8 K)c 13.74 14.45 14.74 14.15 0.61d 15.12 9.28 S (total spin angular momentum), L (total orbital angular momentum) and J (total angular momentum), of the ground multiplet. gJ is the Landé factor. aRoom temperature χMT, bValues of χMT are given in emu mol-1 K, cValues of M are given in µB mol-1, value observed at 7 T. dMagnetisation measured at 2 K and 7 T.


Ni2Dy2 Ni2Ho2 Ni2Er2 Cu2Gd2 Cu2Dy2 Cu2Ho2 Cu2Er2 S (M2+/3+) 1 1 1 1/2 1/2 1/2 1/2 S (Ln3+) 5 2 3/2 7/2 5 2 3/2 L (Ln3+) 5/2 6 6 0 5/2 6 6 J (Ln3+) 15/2 8 15/2 7/2 15/2 8 15/2 gJ (Ln3+) 4/3 5/4 6/5

1.99 4/3 5/4 6/5

g (M2+/3+) 2.34 2.33 2.34 2.05 2.05 2.05 2.05 χMT/ (calcd)b 31.07 30.86 25.69 16.38 29.11 28.90 23.74 χMT (obs)a,b 30.31 31.05 25.13 17.30 28.1 27.99 23.64 χMT (at 2K)b 23.69 10.07 17.59 15.40 20.62 7.37 11.39 Mβ (obs at 1.8 K)c 10.47 11.08d 11.29 13.71 10.51d 10.00 10.36 S (total spin angular momentum), L (total orbital angular momentum) and J (total angular momentum), of the ground multiplet. gJ is the Landé factor. aRoom temperature χMT, bValues of χMT are given in emu mol-1 K, cValues of M are given in µB mol-1, value observed at 7 T. dMagnetisation measured at 2 K and 7 T.



8

Table S7. CASSCF calculated magnetic states for {Mg2Dy2}

E (cm-1) gx gy gz Angle (°) 0.0 0.01 0.01 19.76 -

119.1 0.02 0.03 17.85 23.5 239.5 0.12 0.35 13.97 24.1 308.1 1.42 3.33 16.32 89.3 348.4 4.21 4.97 7.97 57.0 387.5 0.02 1.25 12.24 50.0 480.8 0.67 0.72 16.34 68.4 745.7 0.02 0.03 19.74 82.6

Table S8. CASSCF calculated magnetic states for {Mn2Dy2}

E (cm-1) gx gy gz Angle (°) 0.0 0.01 0.01 19.79 -

63.3 0.07 0.09 17.25 11.7 213.3 0.54 0.74 14.10 12.5 336.7 2.03 4.39 10.10 33.7 385.0 2.15 5.39 9.60 88.1 432.4 0.20 2.45 11.59 54.0 482.8 0.98 2.25 14.98 66.1 694.8 0.00 0.03 19.66 88.4

Table S9. CASSCF calculated magnetic states for {Co2Dy2}

E (cm-1) gx gy gz Angle (°) 0.0 0.01 0.02 19.68 -

124.8 0.05 0.07 17.93 24.8 221.8 0.23 0.44 14.14 27.2 283.5 0.47 0.95 17.27 89.5 323.5 4.24 5.85 8.82 79.4 357.8 1.03 2.52 13.27 61.3 440.0 0.78 0.80 16.42 68.1 713.4 0.02 0.03 19.77 82.3



9

Table S10. CASSCF calculated magnetic states for {Ni2Dy2}

E (cm-1) gx gy gz Angle (°) 0.0 0.01 0.02 19.60 -

140.9 0.03 0.05 17.83 23.4 219.2 0.38 0.96 14.51 32.2 262.0 0.37 1.92 17.54 82.7 297.9 3.06 4.75 12.26 53.6 336.0 0.88 3.18 11.99 58.5 407.1 0.93 1.86 15.81 67.4 689.4 0.01 0.02 19.79 81.9

Table S11. CASSCF calculated magnetic states for {Cu2Dy2}

E (cm-1) gx gy gz Angle (°) 0.0 0.03 0.06 19.31 -

126.4 0.29 0.34 17.68 28.6 169.0 0.75 1.16 14.75 37.0 218.3 2.16 3.36 15.60 85.7 269.5 0.56 4.37 6.38 60.3 295.1 0.67 5.93 12.83 84.3 339.9 1.28 2.34 14.73 62.3 614.3 0.01 0.03 19.77 78.0



10

Scheme 1. Synthetic procedures and photos of crystals obtained.

Figure S1. Geometry of 3d (left) and 4f (right) metals in the butterfly-like cluster. Colour code: Dy, blue; Mg, cyan; O, red; C, grey; H omitted for clarity.



11

Figure S2. (a) Experimental χMT(T) and Mβ(H,T) (inset) data for {Co2Y2}; (b) experimental χMT(T) (purple symbols) and Mβ(H,T) (inset) data for {Co2Gd2} [{Co2Y2} + {Mg2Gd2}] (red symbols).

Figure S3. Experimental χMT(T) and Mβ(H,T) (inset) data for: (a) {Mg2Gd2}; (b) {Mg2Tb2}; (c) {Mg2Ho2} and (d) {Mg2Er2}.

a) b)



12

Figure S4. Comparison χMT(T) magnetic behaviour for {M2Tb2} and [{M2Y2} + {Mg2Tb2}] were M = Mn (a); Co (b) and Ni (c); inset is the Mβ(H,T) behaviour for the pure {M2Tb2}, where M = Mn (a); Co (b) and Ni (c).

Figure S5. Comparison χMT(T) magnetic behaviour for {M2Ho2} and [{M2Y2} + {Mg2Ho2}] were M = Mn (a); Co (b); Ni (c) and Cu (d); inset is the Mβ(H,T) behaviour for the pure {M2Ho2}, where M = Mn (a); Co (b); Ni (c) and Cu (d).



13

Figure S6. Comparison χMT(T) magnetic behaviour for {M2Er2} and [{M2Y2} + {Mg2Er2}] were M = Mn (a); Co (b); Ni (c) and Cu (d); inset is the Mβ(H,T) behaviour for the pure {M2Er2}, where M = Mn (a); Co (b); Ni (c) and Cu (d).

Figure S7. Comparison χMT(T) magnetic behaviour for {M2Ln2} and [{M2Y2} - {Mg2Ln2}] were Ln = Tb, Dy, Ho and Er and M = Mn (a); Co (b); Ni (c) and Cu (d).

a)

a)



14

Figure S8. Temperature-dependence χ´´M(T) (a) and Frequency-dependence χ´´M(ν) (b) for {Cu2Dy2}; Temperature-dependence χ´´M(T) (c) and Frequency-dependence χ´´M(ν) (d) for {Co2Dy2}.

Figure S9 . χ´M(T) for: (a) {Mg2Dy2}; (b) {Mn2Dy2}; (c) {Ni2Dy2}; (d) {Co2Dy2}; and (e) {Cu2Dy2}.

a)

c) d)

b)



Chapter 7

Quantum Computing

7.1 BeginningsIn the early 1980’s Richard Feynman observed that certain properties of systems couldnot be simulated efficiently with classical computers, leading to the first speculationof the exploitation of quantum effects to solve these problems[1]. The tricky part ofthis conjecture was to develop algorithms and computers, "Quantum Computers", thatcould use quantum effects. Obviously the early developments of such machines wereslow. It was not until 1994, when a remarkable quantum polynomial algorithm tofactorise integers developed by Peter Shor, that quantum computing research field wasboosted[2]. Similarly Lov Grover demonstrated quadratic speedup in search queries if aquantum database was used[3]. Furthermore, Lloyd validated Feynman conjecture thata Quantum Computer was more suitable to simulated intractable quantum systems,where the probabilistic nature cannot be simulated in classical machines[4]. Theseadvantages suggest one conclusion; a quantum computer can outperform a classicalcomputer in tasks that even extremely powerful classical computer clusters, takingadvantage of parallelism, would not be able to perform.

Moreover continuous improvements of classical computers have also motivated theminiaturisation in the manufacturing process[5,6] leading the boundaries to the quan-tum regime. In the past two decades components that store and process information incomputers shrink every year to about half the size. Current electronic devices are in-organic based materials such as semiconductors, and magnetic systems (oxide based),built up by lithographic processes, usually a few tens of nanometres in size. If thecurrent miniaturisation trend continues a major problem will be reached for two majorreasons: (i) more demanding and expensive lithography steps will be needed and: (ii)efficient storage of information and speed are difficult to maintain at nanometre size[5].

The powerful computational advantages proposed for Quantum Computers overclassical, and the miniaturisation trend, are demanding from the scientific communitymore thorough understanding and development of such quantum systems. The realisa-tion of such enhanced properties and advantages of quantum computers over classicalones prompted a burst of interest from theoreticians, looking for new quantum al-gorithms, and experimentalists, trying to find the right components to built a quantum

159

7.2. QUBITS

computer. In this context many materials have been proposed as building blocks, basedon electron spins[5,9], nuclear spins[25], atoms[11] and superconducting systems[12]. Ex-amples of materials proposed as qubits are: defects in solids[7,8], quantum dots[10],molecular nanomagnets[5,9], ion traps[11] and Josephson junctions[12] amongst others.MNMs are appealing systems to perform, as qubits in a quantum computer becausethey can be systematically manipulated and assembled at will.

7.2 QubitsTo understand the way a qubit works, it is useful to understand its classical analogue,the bit. In a classical computer the operations are performed by a set of strings, zeros|0〉 and ones |1〉, called bits which are later converted to other string sets leading tospecific operations. In a computer each set of strings have a physical meaning, whichcan operate as ON/OFF depending on the state i.e. |1〉 or |0〉. In the quantum analogue,a qubit can perform the exact same operation as the classical bit with two defined states|1〉 or |0〉. However, besides these strings, a qubit also generates superposition statesnamely |Ψ〉 = a0|0〉 + a1|1〉 and |Ψ〉 = a0|0〉 − a1|1〉with no classical analogues, whichrepresent non-orthogonal configurations, giving 2N values, giving a quantum computerits potential.

7.3 Requirements for QubitsQuantum computers offer many advantages over classical computers, however a goodsystem has to meet some basic requirements to perform as qubits, stated by DiVincenzoand Loss, which soon after became known as the DiVincenzo criteria[14,15].

(i). Well-defined system and scalability: this implies that the qubit presents a welldefined two level system, i.e. |1〉 or |0〉. For example, electron and nuclear spinswith s = 1

2 or I = 12 respectively have been proposed. In electron spin based systems,

any system with a well-defined s = 12 well isolated from exited states is a plausible

candidates. The scalability refers to the ability to collect many qubits into a singledevices whilst still gathering a well defined two level system.

(i). Initialisation: at time τ = 0 all qubits must start from the same level, that isfrom level |0〉. In a molecular system this can be achieved through application of amagnetic field at low temperature.

(iii). Decoherence: Just as in classical computers logical operations are performedthrough a gate. Quantum gates are however extremely susceptible to interactionswith surroundings; therefore small physical interactions with the surroundings mustbe present. It is also necessary that the coherence time is longer than the gate opera-tion. Generally a τ d/τ g (where τ d stands for decoherence time and τ g stands for gatetime operation) lower than 10−4 is required.


7.4. MNMS IN QC

(iv). Universal quantum gates: selectively addressing the qubits to perform algo-rithms is a general requirement. Generally it is accepted that two qubit gates are suf-ficient to perform quantum algorithms. Two common quantum gate operations are theCNOT and

√SWAP gates. In both cases a condition has to be fulfilled. Entanglement

between the qubits, therefore communication between the two s = 12 has to be present.

Despite CNOT and√

SWAP gate being the common gates, quantum algorithms withmore than two qubits are feasible. For example three qubit gates such TOFFOLI andFredkin (see Appendix C) are also feasible if the right materials and control betweenthe qubits is achieved13.

(v). Read out: Basically is the ability to read or measure the response of the qubitsafter the logical gate operation: that is, to obtain the result. Two other requirementswere later added by DiVincenzo in an article dedicated to quantum communicationcriteria, that is the transmission of qubits from place to place in its original form. Thesetwo are: (vi) Interconversion between stationary and "flying" (e.g. photonic) qubitsand (vii) Faithful transmission of flying qubits. These two extra requirements basicallystate that a "flying qubit" is an optimally designed qubit with enhanced characteristicsto be transmitted. These characteristics can be very different than those observed inlocal qubits. Qubits encoded in the polarisation or spatial wavefunction of the photonare one of the most proposed flying qubits.

7.4 MNMs in QCSeveral materials have been proposed as qubit candidates for quantum computing,however among them particularly appealing systems to fulfil this task are MNMs[9,5,16].MNMs represent viable candidates because of their interactions with other qubits (i.e.spatial distribution, important for the realisation of quantum gates) can be systemati-cally controlled, which is a major drawback observed in the defect in solids systemssuch as: Nitrogen Vacancy centred in diamond. Molecular nanomagnets are entitiesthat can be synthetically linked by desired distances (chelating ligands) due to system-atically developed chemical approaches, moreover they can be functionalised for theirdeposition on to surfaces.

Molecular spin clusters were proposed as plausible qubits in 2010 by Loss andLeuenberger[9]. One proposal to fulfil this task is spin clusters with antiferromagneticexchange interactions, with a well-defined s = 1

2 ground state. In order to perform alogical quantum gate these units must interact weakly so that the exchange interactionbetween the adjacent metal centres is smaller than the thermal energy (JA-B � kT,where JA-B is the exchange interaction between metal centres, k is the Boltzmannconstant and T the temperature).

Several spin cluster with an s = 12 ground state have been synthesised with the hope

of realisation of a quantum gate. Some examples are: {Na12[Sb2W18Cu3O66(H2O)]}[17],[Tb2Cl(HL)2(H2L)(Py)2][18] (L = (2-hydroxyphenyl)propionyl)-2-pyridinecarboxylicacid), [(CuTb)2L2(NO3)6(H2O)2][19] (L = bis-iminophenol) and {Gd(W5O18)}9[20] (Fig-ure 7.1).


7.4. MNMS IN QC

Figure 7.1: Structure of Molecular qubits candidates: (a) {Cu3W18}17; (b) {Tb2}18; (c){CuTb}19; (d) {GdW5}20. Colour code: Ln, purple; Cu, blue; N, cyan; O, red; C grey; Sb,pink. Hydrogens omitted for clarity.

Amongst these systems is the family of heterometallic antiferromagnetically cou-pled {Cr7M}[21] wheels (See Section 2.4), with chemical formula [NH2

nPr2][Cr7M(µ-F)8(O2CtBu)16] where M = Mg(II), Ca(II), Mn(II/III), Cu(II), Fe(II), Ni(II), Co(II) andZn(II). The antiferromagnetic {Cr7M} wheel draws special attention due to its physi-cal properties. This wheel has a well-defined spin S = 1

2 ground state relatively quiteisolated from exited states. Chemically, the molecules are robust toward carboxylatefunctionalisation, allowing the introduction of anchoring groups to further aggregationbetween wheels and also surfaces.

For example, due to the easy formation of the metal core with a variety of car-boxylate groups long decoherence times (τ d) have been observed through pulsed EPRtechniques[22]. The decoherence time represents the time in which the quantum in-formation can be stored before it is lost due to interaction with the surroundings[23].Furthermore, through functionalisation of {Cr7Ni}, it has been possible to bring to-gether two {Cr7Ni} wheels, leading to the observation of long distance interactionsbetween the spin qubits (See figure 7.2)[24,26].


7.4. MNMS IN QC

Figure 7.2: Crystal structures of antiferromagnetic wheels: (a) {[NH2nPr2][Cr7Ni(µ-

F)8(O2CtBu)15]}2(Cu(NO3)2)[24] known as green wheel and (b) {[Cr7Ni(µ-F)3(O2CtBu)15(Etglu)(L)]}[26], also known as purple wheel. Colour code: Cr, purpleand green; Cu, blue; N, cyan; O, red; C grey; Ni, grey-blue. Hydrogens omitted for clarity.

References[1] R. P. Feynman, Int. J. Theor. Phys., 1982, 21, 467.

[2] P. W. Shor, SIAM J. Comput., 1997, 26, 1484.

[3] L. Grover, Proceedings of 28th Annual ACM Symposium on Theory of Comput-ing (STOC), 1996, 212.

[4] S. Lloyd, Science 1996, 273, 1073.

[5] F. Troiani and M. Affronte, Chem. Soc. Rev., 2011, 40, 3119.

[6] G. E. Moore, Electronics 1965, 38, 114.

[7] G. Davie and M. F. Hamer, Proc. R. Soc. Lond Ser-A, 1976, 348, 285.

[8] A. Gali, E. Janzén, P. Deak, G. Kresse, E. Kaxiras, Phys. Rev. Lett., 2009, 103,186404.

[9] M. N. Leuenberger and D. Loss, Nature, 2001, 410, 789.

[10] H.L. Störmer, R. Dingle, A.C. Gossard, W. Wiegmann, M.D. Sturge, Solid StateComm., 1979, 29, 705.

[11] R. Blatt and D. J. Wineland, Nature, 2008, 453, 1008.

[12] T. Van Duzer, C. Turner, Principles of Superconducting Devices and Circuits,Prentice Hall, New Jersey, 1999.

[13] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Informa-tion, Cambridge University Press, New York, 2010.


7.4. MNMS IN QC

[14] D. P. DiVincenzo, D. Loss, Superlattices Microstruct., 1998, 223, 419.

[15] D. P. DiVincenzo, Fortshritte der Physik, 2000, 48, 771.

[16] P. Santini, S. Carretta, F. Troiani and G. Amoretti, Phys. Rev. Lett., 2011, 107,230502/1.

[17] K.-Y. Choi, Z. Wang, H. Nojiri, H. van Tol, P. Kumar, P. Lemmens, B.S. Bassil,U. Kortz, N.S. Dalal, Phys. Rev. Lett., 2011, 108, 067206/1.

[18] F. Luis, A. Repollés, M.J. Martonez-Pérez, D. Aguilá, O. Roubeau, D. Zueco,P.J. Alonso, M. Evangelisti, A. Camón, J. Sesé, L.A. Barrios, G. Aromí, Phys.Rev. Lett., 2011, 107, 117203/1.

[19] G. Novitchi,J.-P. Costes, J.-P. Tuchagues, L. Vendier and W. Wernsdorfer, NewJ. Chem., 2008, 32, 197.

[20] M. J. Martínez-Pérez, S. Cardona-Serra, C. Schlegel, F. Moro, P. J. Alonso, H.Prima-García, J. M. Clemente-Juan, M. Evangelisti, A. Gaita-Ariño, J. Sesé, J.van Slageren, E. Coronado and F. Luis, Phys. Rev. Lett., 2011, 107, 117203(1).

[21] F. K. Larsen, E. J. L. McInnes, H. E. Mkami, J. Overgaard, S. Piligkos, G. Ra-jaraman, E. Rentschler, A. A. Smith, G. M. Smith, V. Boote, M. Jennings, G. A.Timco and R. E. P. Winpenny, Angew. Chem. Int. Ed., 2003, 42, 101.

[22] C. J. Wedge, G. A. Timco, E. T. Spielberg, R. E. George, F. Tuna, S. Rigby, E. J.L. McInnes, R. E. P. Winpenny, S. J. Blundell and A. Ardavan, Phys. Rev. Lett.,2011, 108, 107204(1).

[23] M. Affronte, I. Casson, M. Evangelisti, A. Candini, S. Carretta, C. A. Muryn, S.J. Teat, G. A. Timco, W. Wernsdorfer and R. E. P. Winpenny, Angew. Chem. Int.Ed., 2005, 44, 6496.

[24] G. A. Timco, S. Carretta, F. Troiani, F. Tuna, R. J. Pritchard, C. A. Muryn, E. J.L. McInnes, A. Ghirri, A. Candini, P. Santini, G. Amoretti, M. Affronte and R.E. P. Winpenny, Nat. Nanotechnol., 2008, 4, 173.

[25] G. Burkard, D. Loss, and D. P. DiVincenzo, Phys. Rev., 1999, B59, 2070.

[26] T. B. Faust, V. Bellini, A. Candini, S. Carretta, G. Lorusso, D. R. Allan, L.Carthy, D. Collison, R. J. Docherty, J. Kenyon, J. Machin, E. J. L. McInnes, C.A. Muryn, H. Nowell, R. G. Pritchard, S. J. Teat, G. A. Timco, F. Tuna, G. F. S.Whitehead, W. Wernsdorfer, M. Affronte, and R. E. P. Winpenny, Chem. Eur. J.,2011, 17, 14020.


Chapter 8

QC using MNMs

8.1 QC using AF-WheelsChemical control of the {Cr7Ni} spin clusters, and the intrinsic magnetic propertiesassociated with the system, has led this interesting molecule to meet several of theDiVincenzo criteria. Controlled communication between qubits is a demanding butnecessary task for the operation of universal quantum gates. In the following workwe have investigated the entanglement between two {Cr7Ni} wheels, and the ability tosystematically switch the interaction between the qubits through a redox active cobalt-terpyridine linker. A full synthetic, crystallographic and spectroscopic EPR study isdescribed. Preliminary theoretical calculations conducted by Professors Stefano Car-retta and Paolo Santini have shown that the linked systems represent a plausible uni-versal

√SWAP gate candidate. Detailed theoretical investigation is still undergoing.

8.1.1 A supramolecular assembly for implementation of the√

SWAPgate

To be submitted to Nature Nanotechnology

165

8.1. QC USING AF-WHEELS


1

A supramolecular assembly for implementation of the √SWAP gate Eufemio Moreno Pineda,a Antonio Fernandez Mato,a James P. S. Walsh,a Stefano Carretta,b Paolo Santini,b Iñigo J. Vitorica-Yrezabal,a Grigore A. Timco,a Floriana Tuna,a Eric J. L. McInnesa & Richard E. P. Winpennya* a School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom, Tel: +44 (0)161 2751022; E-mail: [email protected] b Dipartimento di Fisica e Scienze della Terra, Università di Parma, viale delle Scienze 7/a, 43123 Parma, Italy

Electron spin qubits are often proposed as one means to implement quantum computers. Several such spin qubits – defect sites, semiconductor quantum dots – are excellent routes for making individual qubits, with long coherence times but they present a significant challenge in creating gate structures, where such qubits are linked to perform algorithms. As an alternative magnetic molecules have been proposed as qubits. Individually they do not perform as well as defect sites, but in supramolecular chemistry a methodology exists to link together molecular qubits into arrays that can act as switches. Here we show how supramolecular chemistry can bring together {Cr7Ni} molecules that have been studied as possible qubits, through a tunable and switchable redox active linker. Spectroscopic and theoretical work demonstrates that this new {Cr7Ni}àCoII/IIIß{Cr7Ni} supramolecule can perform as a √SWAP gate.

Quantum information processing (QIP) offers the possibility of performing some computational

tasks faster than is possible using conventional computers. Efficient quantum computation

requires at least single unitary quantum bits operations and two qubits quantum gates1,2. Two

important universal gates are the CNOT and the √SWAP gate, which employs exchange

interactions in its mechanism3. The √SWAP gate would play a crucial role for the

implementation of Shor algorithm4 and in reducing the number of qubits needed to perform

quantum computation, as the √SWAP gate requires at least three CNOT gates.

Molecular magnets were first proposed as possible qubits in the early part of this

century5-7, and have been shown to meet many of the criteria set for qubits, including reasonable

phase memory times,8 which have now been reported to reach 68 µS9. To this point studies have

focused largely on single qubit operations. The only experimental report of a two-qubit gate, is a

CNOT gate reported by Nakazawa et al10, while there are other molecular proposals for the

CNOT involving heterometallic lanthanide complexes11. A scheme has been proposed for the

√SWAP operation12 by Lehmann et al. This proposal is imaginative and intriguing as electrical



2

control is used via the tips of a scanning tunnelling microscope to switch-on and off the

interaction between two S = ½ centres at the peripheries of a polyoxometallate. There is no

experimental evidence that the “switch” in this √SWAP gate can be operated, especially as the

polyoxometallate proposed is electrochemically inactive on a glassy carbon electrode13.

Here we report introduction of a switch that can control the interaction between S = ½

states, switching on and off entanglement and hence producing a molecule that could be used for

the √SWAP gate; as the switch and qubits are from different molecular components we can

easily modify the size of the interaction involved, which we demonstrate. The measured

interaction in the on state does not fit the previous scheme12, hence we put forward an alternative

scheme which appears extremely promising. Our new scheme is based on a heterometallic

{Cr7Ni} ring14, which has been extensively studied as a potential qubit. It is characterised by

well-defined spin ground state (S = ½, > 99 %), long phase memory time (up to 15 µs)8 that can

be engineered by chemistry, and a robust metal core that allows synthetic functionalization of the

ring allowing the coupling of such {Cr7Ni} molecules to other molecules and grafting onto

surfaces15,16. We have previously demonstrated that through chemical modification two {Cr7Ni}

rings can be linked through an organic or metal-organic linker17,18 resulting in the

communication of the two S = ½ low-lying states of the {Cr7Ni} units.

Chemical Strategy

The fabrication of two qubits linked by a switch was achieved using as starting material the

heterometallic ring [NH2nPr2][Cr7Ni(µ2-F)8(O2CtBu)16] 1, which is our qubit and which can be

made in excellent yield. To include a switchable group between these qubits, 4-carboxy-

2,2’:6’,2”-terpyridine (HO2C-tpy) and 4’-(4-carboxyphenyl)-2,2’:6’,2”-terpyridine (HO2C-Ph-

tpy) were prepared by known methods19. These can then be reacted with 1 to give

[NH2nPr2][Cr7Ni(µ2-F)8(O2CtBu)15(O2C-terpy)] 2 and [NH2

nPr2][Cr7Ni(µ2-F)8(O2CtBu)15(O2C-

Ph-terpy)] 3 in good yields (full experimental details are given in the Supplementary

Information). Structural analysis shows that we can control conditions to replace only one

pivalate from the precursor (see Fig. S1). The structure contains eight metal sites arranged in an

octagon, with each edge of the metal octagon bridged by a fluoride and two carboxylates.

Divalent nickel sites are expected to be around 1010 times more reactive than trivalent chromium

sites,20 and hence the substitution must take place on a Cr…Ni edge of the ring, and not on a



3

Cr…Cr edge. Steric requirements lead to the bulky group terpyridyl group lying perpendicular to

the plane of the eight metals within the ring. This group is a tridentate N-donor.

A redox active metal centre can be simply introduced by reacting compounds 2 or 3 with

cobalt tetrafluoroborate in a mixture of Et2O/acetone leading to two complexes of formula

[{[NH2nPr2][Cr7Ni(µ2-F)8(O2CtBu)15(O2C-terpy)]}2Co](BF4)2 4 and [{[NH2

nPr2][Cr7Ni(µ2-

F)8(O2CtBu)15(O2C-Ph-terpy)]}2Co](BF4)2 5; the structure of the heterometallic di-cations are

shown in Figure 1.

Figure 1. Schematic showing operation of the switch in compounds 4 and 5. a Scheme of magnetic coupling between {Cr7Ni}–CoII–{Cr7Ni} allowing magnetic coupling (interaction) between two {Cr7Ni} (S = ½) and CoII (S = ½). b, Scheme off state (no-magnetic coupling) between {Cr7Ni}–CoIII–{Cr7Ni} between two {Cr7Ni} (S = ½) and CoIII (S = 0). c, structure of 4 in the crystal. d, structure of 5 in the crystal. Pivalate groups omitted for clarity. Colour code: Co, pale blue; Cr, green; Ni, purple; N, blue; O, red; C, grey; F, yellow; H omitted for clarity.

The compounds are closely related. In both cases the heterometallic rings are unchanged from 2

and 3. The CoII site is found at the centre of the ensemble, and is bound to two chelating

terpyridyl groups, thus linking the heterometallic rings into a dimer (Fig. 1). The six Co-N bonds

are found to be 1.90(2)–2.097(2) indicating low spin CoII, as has been previously found for

cobalt in this coordination environment; this is confirmed by EPR spectroscopy (see below).

There are differences between the two cations. The shortest Co…M(ring) contact in 4 is

8.738(1) Å while it is longer at 10.98(2) Å in 5; this is due to the additional phenyl-group in the

(a)

(c)

(b)

(d)

Sa = 1/2 Sc = 1/2Sb = 1/2

-��-�� -� �� -� ��Sa = 1/2 Sc = 1/2Sb = 0



4

carboxy-terpyridyl ligand in 5. The two {Cr7Ni} rings in 4 are arranged in a staggered fashion,

while in 5 the two rings are almost perfectly eclipsed; the structure could be described as an

elongated octagonal prism with the CoII site at the centre. These subtle differences mean that the

interaction between the CoII site and the spin centres within the rings are tunable, depending on

the precise derivative we are using.

Electrochemistry and EPR spectroscopy of 4 and 5

Both 4 and 5 show reversible one-electron oxidations, as expected for cobalt(II) complexes of

terpyridyl21, with E1/2 values of 0.20 and 0.22 V respectively (vs. FeCp2/FeCp2+) (Fig. S2). As

the electrochemistry is reversible then the one-electron oxidation is between low spin cobalt(II) –

which is an S = 1/2 ion – and low spin cobalt(III) – which is S = 0, i.e. diamagnetic. We have

therefore potentially created a switching mechanism between two non-interacting qubits in the

oxidised forms (4ox and 5ox respectively) and a tripartite system of three S = ½ groups in the

reduced form.

EPR spectroscopy allows small exchange interactions to be measured and is ideal for

studying 4 and 5. Firstly the EPR spectra of [Co(tpy-CO2H)2](BF4)2 6 and [Co(tpy-Ph-

CO2H)2](BF4)2 7 were measured to understand the CoII site ; at X-band cobalt hyperfine structure

is resolved for 6, but not for 7 (Figure S3). The spectra at both frequencies can be simulated with

a rhombic g-tensor: for 6 gx = 2.047; gy = 2.076; gz = 2.195 and for 7 gx = 2.022; gy = 2.111; gz =

2.215. At Q-band these g-values do not overlap with the known g-values of {Cr7Ni} rings14,

which is vital in allowing us to study the interaction in both states of the switch.

Q-band EPR spectra of frozen solutions of 4 and 5 were collected showing three resonances

between 1100 and 1500 mT (Fig. 2). The spectra can be simulated by considering a simple

Hamiltonian [1] where there is an interaction between the S = ½ centre on the CoII site and the

two S = 1/2 {Cr7Ni} rings:

𝐻 = −2𝐽 𝑆! ∙ 𝑆! + 𝑆! ∙ 𝑆! + µμ!(𝑆! ∙ 𝑔! + 𝑆! ∙ 𝑔! + 𝑆! ∙ 𝑔!) ∙ 𝐵 [1]

Where S1 and S3 are the spins on the {Cr7Ni} qubits and S2 is the spin on CoII.

This interaction will generate three spin states, which we can define in terms of an

intermediate spin, S*, which arises from coupling the two {Cr7Ni} rings, and which can therefore

have values of 1 or 0 (from S1 + S2 and S1 - S2 respectively), and a total spin ST, which arises



5

from coupling S* with the S = ½ on cobalt. The three states therefore have quantum numbers

0,½ , 1,½ and 1, 3/2 (represented as 𝑆∗, 𝑆! . The three resonances seen are therefore due

to transitions in each of these three states; the spectra can be simulated with the g-tensors for 6

and 7, and the known g-values of {Cr7Ni}24 which are gx = 1.830; gy = 1.830; gz = 1.790; the

only variable is the isotropic exchange interaction between the spin states, J. The simulations

(Fig. 2a and 2b) show a small but significant difference between the exchange in the two

compounds; in 4, J = –0.026 cm-1 while in 5, J = –0.024 cm-1. This subtle difference is

presumably due to the slightly longer super-exchange path through the additional phenyl-ring in

5. The interaction is therefore tunable, and could be modified further by other chemistry.

Figure 2. Q-band EPR studies of the switching mechanism at 5 K. a, Experimental frozen solution spectrum of 4 (black trace) and simulation of EPR spectrum with J = 0 (blue trace) and system with J = –0.026 cm-1(red trace). b, Experimental frozen solution spectrum of 5 (black trace) and simulation of EPR spectrum with J = 0 (blue trace) and system with J = –0.024 cm-1(red trace). c, EPR spectrum of 4 as synthesised (blue trace), 4ox after oxidation with AgBF4 (ca. 3 mM, 1:1) (red trace) and compound 4 after reducing using 4ox with cobaltocene (3 mM, 1:1) (black trace). d, EPR spectrum of 5 as synthesised (blue trace), 5ox after oxidation with AgBF4 (ca. 3 mM, 1:1) (red trace) and 5 after reducing 5ox with cobaltocene (3 mM, 1:1) (black trace). All simulations used g-values given in the text. The sharp peak marked * is a radical impurity. To demonstrate that the oxidation of the CoII switches off the magnetic interaction, we have

chemically oxidised both 4 and 5 (Fig. 2c and 2d). Addition of a mild oxidising agent, e.g.



6

AgBF4, generates a species where the EPR spectra of 4ox and 5ox which is essentially that of 1

(red traces, Fig 2c and 2d); the diamagnetic CoIII ion blocks communication of the spin

information between the two ends of the supramolecule. Reduction of the {Cr7Ni}2CoIII with

cobaltocene regenerates a species with the EPR spectra of 4 or 5 respectively.

Electrical control of a √SWAP gate

Electrical control of the Co valence can be exploited to perform the universal √SWAP gate on

the {Cr7Ni} qubits. The √SWAP gate is defined as |𝛼 𝛽 > → (|𝛼 𝛽 > +𝑖 |𝛽𝛼 >)/(1+ 𝑖) with

𝛼,𝛽 = 0,1. When Co is in the diamagnetic CoIII state, the two qubits are decoupled and only

single qubit operations could be performed. Conversely, when CoII is present the system behaves

as a trimer described by the Hamiltonian [1]. Loss and co-workers have theoretically postulated12

that two spins 1/2 connected by a redox-active unit can be exploited for the implementation of

the √SWAP gate by switching the redox unit with a scanning tunnelling microscope (STM) tip at

a suitable potential. In this way one electron can be added or removed from the redox unit very

quickly. It was demonstrated that appropriate parameters of the trimer Hamiltonian lead to a pure

√SWAP evolution of the two qubits (controlled by the third spin) after specific time intervals. In

particular, high fidelity for the gate is guaranteed only for specific ratios of the qubit-qubit

exchange (Jqq) to the qubit-redox unit exchange (Jqr). However, for the present values Jqr ≡ J and

Jqq = 0 the gate fidelity is low. The fidelity of a gate is defined by….

Here we propose a different scheme for the √SWAP gate, which works if the two qubits

have the same Zeeman energy but one different to the switch in the “on” state. This is the case

here where the g-values of the qubits and switches are so different; gaverage = 1.82 for 1 and

gaverage = 2.12 for 6 and 7. This difference in the g-values means that in magnetic fields of a few

T, the ring-CoII exchange J is small compared to the difference between the Zeeman energies of

CoII and of the {Cr7Ni} rings. The spin state of the central CoII site has only tiny virtual

fluctuations that lead to an effective interaction between the two {Cr7Ni} qubits given by

𝐻!! = Γ 𝑆!!𝑆!! + 𝑆!!𝑆!! + 𝜆 𝑆!! + 𝑆!! [2]

where the field is along z, where S1x is the component of the first {Cr7Ni} spin along the x-axis,

and

Γ = ! !!

! (!!!!!!!) 𝜆 = 𝐽 + !!

! (!!!!!!!) ,



7

Thus, when diamagnetic CoIII is present, the two {Cr7Ni} qubits are decoupled, whereas when

CoII is present the state of the two qubits evolves according to [2], with negligible entanglement

with the CoII spin. For specific times (see Figure 3 and Table I) this evolution coincides with the

√SWAP gate apart from trivial single-qubit rotations along z due to the second term in [2].

The perturbative picture is confirmed by the results of detailed calculations using the full

Hamiltonian [1] (Fig. 3 and Table I). Starting from the |10> logical state (i.e. the spin on one

{Cr7Ni} ring +1/2, representing 1, and on the second ring -1/2, representing 0), the time

evolution of the trimer wavefunction implements the √SWAP gate (Fig. 3). In a magnetic field of

3 T, after 4 ns the wavefunction has equal contributions from |10> and |01>, which is the

√SWAP gate, while after 8 ns the two spins are fully exchanged, i.e. we have the |01> state.

The full performance of the scheme is quantified by the so-called fidelity

𝐹 = | 𝜓! 𝜓(𝑡!) |. For any given starting logical state, |𝜓! > is the final state after an ideal

√SWAP gate, whereas | 𝜓 𝑡! > is the output of our calculation. Table I reports F averaged over

the four initial basis states |𝛼 𝛽 > for several values of the applied magnetic field. The

calculations have been performed for several magnetic fields ranging from 0.25 to 4 T. The time

needed to perform the √SWAP gate, 𝑡! , is found to be inversely proportional to Γ and of the

order of a few ns, and shows excellent fidelity. As Γ is proportional to J2 we can propose

chemically controlling the gate time as we have shown we can tune J (see EPR studies above).

By reducing the magnetic field B the gate time 𝑡! decreases, but the fidelity progressively

worsens because the validity of the perturbative picture of equation [2] gradually breaks down.

Figure 3. Simulation of the √SWAP gate. By choosing |10> ≡ |1/2,-1/2> ⊗|-1/2>Co as initial state, we calculate for 4 the time-dependence of the trimer wavefunction components on |10> and |01> ≡ |-1/2,1/2> ⊗|-1/2>Co with B = 3 T. Other components are negligible.



8

Table I. Average gate fidelity. F averaged over the four initial basis states.

Magnetic Field (T) Gate time (ns) Average fidelity

4 5.56 1

3 4.17 1

2 2.73 0.9995

0.5 0.66 0.9875

0.25 0.46 0.9306

Conclusions

In summary, the scheme proposed is entirely feasible. It requires the capability to inject or

remove an electron with a chosen spin (e.g., by a half-metal tip) on a timescale much shorter than

one nanosecond; typical timescales for such experiments are in the low femtosecond region22. In

addition, a small static magnetic field is needed, where the static field direction must be such that

the two Cr7Ni rings have equal Zeeman energy, which is the case in both compounds discussed

here. The gate time tf is estimated as around 1 to 6 ns while retaining a high fidelity. This

compares with measured coherence times for {Cr7Ni} rings that can be as high as 15 µS.8 This

set of parameters suggest that while any experiment will be extremely challenging, the

supramolecular assembly found in 4 and 5 is a feasible candidate for implementation of the

√SWAP gate.

Acknowledgements

This work was supported by the EPSRC(UK), by a Marie Curie Intra-European Fellowship to

A. F. (FP7-PEOPLE-2011-IEF-300402). E.M.P. thanks the Panamanian agency SENACYT-

IFARHU for funding. REPW thanks the Royal Society for a Wolfson Merit Award. We also

thank EPSRC (UK) for funding the National EPR Facility and Service, and for an X-ray

diffractometer (grant number EP/K039547/1). This work was also supported by the Italian FIRB

Project No. RBFR12RPD1 of the Italian MIUR “New Challenges in Molecular Nanomagnetism:

From Spin Dynamics to Quantum-Information Processing.” We thank Diamond Light Source for

access to synchrotron X-ray facilities.



9

Author Contributions

E. M. P., A. F. and G. A. T. carried out the chemical synthesis while E. M. P. and I. J. V.-Y.

performed the X-ray structural characterisation. E. M. P., J. W. and F. T. measured the EPR

spectra, and E. M. P. guided by E. J. L. M performed simulations of this data. The theoretical

simulations of the √SWAP were performed by S. C. and P. S. The research was overseen by R.

E. P. W. who also co-wrote the manuscript with E. M. P., S. C. and P. S., with input from other

authors.

Additional Information

Supplementary information is available in the online version of the paper. Reprints and

permissions information is available online at www.nature.com/reprints. Correspondence and

requests for materials should be addressed to R. E. P. W.

Competing Financial Interests

The authors declare no competing financial interests.

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computation. Phys. Rev. Lett. 94, 207208 (2005).



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8. Wedge, C. J., Timco, G. A., Spielberg, E. T., George, R. E., Tuna, F., Rigby, S.,

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6O40(VIVO)2]5-. Inorg. Chem. 35, 2403-2405 (1996).

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Rings: An Ideal System for Studying Magnetically-Coupled Systems. Chem. Soc. Rev.

42, 1796-1806 (2013).

15. Ghirri, A. et al. Self-Assembled Monolayer of Cr7Ni Molecular Nanomagnets by

Sublimation. ACS Nano 5, 7090-7099 (2011).

16. Rath, H et al. Studies of hybrid organic–inorganic [2] and [3]rotaxanes bound to Au

surfaces. Chem. Commun. 49, 3404–3406 (2013).

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11

21. Hayami, S., Komatsu, Y., Shimizu, T., Kamihata, H. and Lee, Y. H. Spin-crossover in

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asas



S3-‐1

Supplementary Information

A supramolecular assembly for implementation of the √SWAP gate Eufemio Moreno Pineda,a Antonio Fernandez,a James Walsh,a Stefano Carretta,b Paolo Santini,b Iñigo J. Vitorica-Yrezabal,a Grigore A. Timco,a Floriana Tuna,a Eric J. L. McInnesa & Richard E. P. Winpennya* a School of Chemistry and Photon Science Institute, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom, Tel: +44 (0)161 2751022; E-mail: [email protected] b Dipartimento di Fisica e Scienze della Terra, Universitàdi Parma, via G.P. Usberti 7/a, 43123 Parma, Italy

1. Experimental details .................................................................................................................... 3-1 1.1. Synthesis of ligands ............................................................................................................... 3-1

1.1.1. 4-carboxy-2,2’:6’,2”-terpyridine (O2C-tpy) .................................................................. 3-1 1.1.2. 4′-(4-carboxyphenyl)-2,2′:6′,2″-terpyridine (O2C-Ph(tpy)) ........................................... 3-3

1.2. Synthesis of ‘green wheels’ and functionalized derivatives ................................................. 3-3 1.2.1. Synthesis of ‘green wheels’ and functionalized derivatives ......................................... 3-3 1.2.2. [NH2

nPr2][Cr7Ni(µ2-F)8(O2CtBu)15(O2C-terpy)] (2) .................................................... 3-3 1.2.3. [NH2

nPr2][Cr7Ni(µ2-F)8(O2CtBu)15(O2C-Ph-terpy)] (3) ............................................... 3-4 1.3. Synthesis of cobalt-linked wheel dimers ............................................................................... 3-4

1.3.1. [{[NH2nPr2][Cr7Ni(µ2-F)8(O2CtBu)15(O2C-terpy)]}2Co](BF4)2 (4) .............................. 3-4

1.3.2. [{[NH2nPr2][Cr7Ni(µ2-F)8(O2CtBu)15(O2C-Ph-terpy)]}2Co](BF4)2 (5) ........................ 3-4

1.4. Synthesis of cobalt precursors ............................................................................................... 3-5 1.4.1. [Co(HO2C-tpy)](BF4)2 (6) ............................................................................................. 3-5 1.4.2. [Co(HO2C-Ph(tpy))](BF4)2 (s) ...................................................................................... 3-5

1.5. Crystallography ..................................................................................................................... 3-5 1.6. Electrochemistry .................................................................................................................... 3-5 1.7. Electron Paramagnetic Resonance ........................................................................................ 3-5

2. Supplementary Tables ................................................................................................................. 3-6 2.1. Crystallography ..................................................................................................................... 3-6

3. Supplementary Figures ............................................................................................................... 3-7 3.1. Crystal structures ................................................................................................................... 3-7 3.2. Electrochemistry .................................................................................................................... 3-8 3.3. Electron Paramagnetic Resonance ........................................................................................ 3-9 3.4. Precursor EPR ....................................................................................................................... 3-9

1. Experimental details

Unless stated otherwise, all reagents and solvents were purchased from Aldrich Chemicals and used without further purification.

Synthesis of ligands 1.1.

1.1.1. 4-carboxy-2,2’:6’,2”-terpyridine (O2C-tpy)

4-Furane-2,2’:6’,2”-terpyridine: 2-furaldehyde (1.92 g, 20 mmol) and 2-acetyl-pyridine (4.84 g, 40 mmol) were dissolved in EtOH (100 mL). To this was added KOH (3.08 g, 55 mmol) and aqueous ammonia solution (50 mL, 25%). The solution



S3-‐2

was then stirred at 60 °C for 24 h after which about half the solvent was removed under reduced pressure yielding an off-white product (5.30 g, 88%). 1H-NMR (400 MHz, CDCl3): δ 8.74 p.p.m. (d, J = 4.8 Hz, 2H), 8.72 (s, 2H), 8.64 (d, J = 8.0 Hz, 2H), 7.87 (dt, J = 1.9, 7.8 Hz, 2H), 7.59 (d, J = 1.2 Hz, 1H), 7.35 (ddd, J = 1.0, 4.8, 7.4 Hz 2H), 7.11 (d, J = 3.2 Hz, 1H), 6.57 (dd, J = 1.8, 3.4 Hz, 1H); ESI-MS (m/z): +300 [M + H]+ (100%); +32 [M + Na]+ (100%); −298 [M − H]- (10%); analysis (% calcd., % found for C19H13N3O): C (76.24, 76.44), H (4.38, 4.38), N (14.04, 13.94).

Supplementary Scheme 1. Reaction of 2-furaldehyde and 2-acetylpyridine to form 4-furane-terpyridine.

4-carboxy-2,2’:6’,2”-terpyridine To a solution of 4-furane-terpyridine (2.20 g, 7.3 mmol) in pyridine (30 mL) and H2O (15 mL) was added KMnO4 (7.10 g, 45 mmol) in stepwise portions and then stirred for 48 h. Residual KMnO4 was reduced by adding Na2S2O3 in H2O until the violet colour of the mixture disappeared. The solution was then made basic by the addition of NaOH (2 M) and the resultant MnO2 formed was filtered off. The solvent was removed from the filtrate in vacuo and then reconstituted in NaOH (pH ≈ 12). The resultant suspension was acidified with HCl (0.1 M) filtered and the white solid was collected (1.86 g, 92%). 1H-NMR (400 MHz, DMSO-d6): δ 7.51–7.55 p.p.m. (m, 2H, Py-H), 8.03 (dt, J = 7.7, 1.8 Hz, 2H, Py-H), 8.64 (dd, J = 8.1, 1.1 Hz, 2H, Py-H), 8.74–8.76 (m, 2H, Py-H), 8.85 (s, 2H, Py-H); ESI-MS (m/z): +300 [M + Na]+ (100%); +278 [M + H]+ (50%); −276 [M − H]- (100%); analysis (% calcd., % found for C16H11N3O2): C (69.31, 69.28), H (3.99, 4.02), N (15.15, 15.12).

Supplementary Scheme 2. Permanganate-mediated oxidation of the furan ring of 4-furane-terpyridine to yield 4-carboxyterpyridine.

OO

NO

KOH and NH4OH in EtOH60 ºC for 24 h

NN

N

O2-furaldehyde 2-acetylpyridine

4-furane-terpyridine

2

NN

N

O

4-furane-terpyridine

1. KMnO42. Na2S2O3

3. NaOH 2 M, pH ~ 124. HCl 0.1 M, pH ~ 5

NN

N

O OH

4-carboxyterpyridine



S3-‐3

1.1.2. 4′-(4-carboxyphenyl)-2,2′:6′,2″-terpyridine (O2C-Ph(tpy))

4-phenyl-(4-carboxyterpyridine): 2-acetyl-pyridine (2.90 g, 24 mmol) and 4-carboxybenzaldehyde (1.80 g, 12 mmol) were dissolved in MeOH (80 mL) by stirring for 5 min, followed by the addition of 15% KOH (72 mL) and concentrated NH4OH (8 mL). The mixture was allowed to stand at ambient temperature for 3 d. The emulsion that formed was filtered off and washed with CHCl3 (40 mL) and cold MeOH/H2O (1:1, 40 mL). The crude product was suspended in MeOH/H2O (80:20), and the mixture was stirred sonicated at 35 ºC until a clear solution was obtained. This was then acidified to pH = 2 by addition of HCl (1 M), resulting in the formation of a white precipitated that was collected by vacuum filtration and rinsed with cold water and then dried (6.70 g, 79%). 1H-NMR (400 MHz, [D]tfa/D2O): δ 7.90 p.p.m. (d, 2H), 8.13 (dd, 2H), 8.30 (d, 2H), 8.83 (d, 2H), 8.65 (dd, 2H), 8,74 (s, 2H), 9.04 (d, 2 H); ESI-MS (m/z): +353 [M + H]+ (100%); analysis (% calcd., % found for C22H15N3O2): C (74.78, 74.63), H (4.28, 4.33), N (11.89, 11.84).

Supplementary Scheme 3. Reaction of 4-carboxybenzaldehyde with 2-acetylpyridine to form 4-phenyl-(4-carboxyterpyridine).

1.2. Synthesis of ‘green wheels’ and functionalized derivatives

1.2.1. Synthesis of ‘green wheels’ and functionalized derivatives

[n-Pr2NH2][Cr7Ni(µ-F)8(O2CtBu)16] 1, was prepared using the method given in Larsen et al,2 but with [2NiCO3·3Ni(OH)2·4H2O] as the source of Ni(II) instead of the compound [Ni2(µ-OH2) (O2CtBu)4(HO2CtBu)4] used in the original method, and with a reaction time of 24 h at 160 ºC.

1.2.2. [NH2nPr2][Cr7Ni(µ-F)8(O2CtBu)15(O2C-terpy)] (2)

An excess of 4-carboxyterpyridine (1.30 g, 4 mmol) was reacted with 1 (3 g, 1.3 mmol) in toluene (25 mL) and 1,2-dichloro benzene (75 mL). The solution was heated with constant stirring at 160 ºC for 5 h in a round-bottomed flask. Toluene was removed under reduced pressure and the resulting solution was filtered. The solution was then separated by column chromatography using Toluene/EtOAc resulting in the mono substituted [NH2

nPr2][Cr7Ni(µ-F)8(O2CtBu)15(O2C-terpy)] wheel (1.2 g, 37 %).

NO

15% KOH and conc. NH4OHRT for 3 days

NN

N

2-acetylpyridineHO O

O

2

O OH

4-carboxybenzaldehyde

4-phenyl-(4-carboxyterpyridine)



S3-‐4

X-ray quality crystals were obtained from recrystallization from Et2O/MeCN. ESI-MS (m/z): +2493 [M + Na]+ (100%); +1258 [M + 2Na]+2 (60%); −2368 [M − NH2n-Pr2]- (100%); −2368 [M − NH2n-Pr2]- (100%); analysis (% calcd., % found for C97H161Cr7F8N4NiO32): C (47.17, 47.25), H (6.57, 6.58), Cr (14.17, 14.23), N (2.27, 2.30), Ni (2.38, 2.27).

1.2.3. [NH2nPr2][Cr7Ni(µ-F)8(O2CtBu)15(O2C-Ph-terpy)] (3)

An excess of 4-phenyl-(4-carboxyterpyridine) (1.40 g, 4 mmol) was reacted with 1 (3 g, 1.3 mmol) in toluene (25 mL), DMF (20 mL) and 1,2-dichloro benzene (75 mL). The solution was heated with constant stirring at 160 ºC for 5 h in a round-bottomed flask. Toluene and DMF were removed under reduced pressure and the resulting solution was filtered. The solution was then separated by column chromatography using toluene/EtOAc resulting the mono substituted [NH2

nPr2][Cr7Ni(µ2-F)8(O2CtBu)15(O2C-Ph-terpy)] wheel (0.68 g, 21%). ESI-MS (m/z): +2467 [M + Na − NH2n-Pr2]+ (40%); +1258 [M + 2Na − NH2n-Pr2]+2 (70%); −2368 [M − 2NH2n-Pr2 + Na]- (100%); analysis (% calcd., % found for C103H165Cr7F8N4NiO32): C (48.59, 48.71), H (6.53, 6.58), Cr (14.30, 14.14), N (2.20, 2.08), Ni (2.30, 2.34).

1.3. Synthesis of cobalt-linked wheel dimers

1.3.1. [{[NH2nPr2][Cr7Ni(µ-F)8(O2CtBu)15(O2C-terpy)]}2Co](BF4)2 (4)

To a solution of 2 (400 mg, 0.16 mmol) in Et2O/Acetone (15 mL, 3:1) was added a solution of Co(BF4)·6H2O (20 mg, 0.08 mmol) in acetone (5 mL). The resulting solution was then stirred for 1 hr at room temperature. The dark-red solution was then filtered and kept at room temperature undisturbed until brown crystals appeared (350 mg g, 84%). Analysis (% calcd., % found for C194H322B2CoCr14F24N8Ni2O64): C (45.05, 44.89), H (6.28, 6.48), B (0.42, 0.38), Co (1.14, 1.15), Cr (14.07, 13.74), N (2.17, 2.19), Ni (2.27, 2.32). Due to the difficulty crystallising this cluster, the counteranion was changed from BF4

- to ClO4-. X-ray diffraction quality crystals of 4 were obtained after two weeks

from slow evaporation of the solvent using this anion.

1.3.2. [{[NH2nPr2][Cr7Ni(µ-F)8(O2CtBu)15(O2C-Ph-terpy)]}2Co](BF4)2 (5)

To a solution of 3 (400 mg, 0.16 mmol) in Et2O/Acetone (15 mL, 3:1) was added a solution of Co(BF4)·H2O (20 mg, 0.08 mmol) in acetone (5 mL). The solution was then stirred for 1 hr at room temperature. The dark-red solution was then filtered and kept at room temperature undisturbed (370 mg, 87%). Analysis (% calcd., % found for C206H330B2CoCr14F24N8Ni2O64): C (46.47, 46.63), H (6.25, 6.32), B (0.41, 0.45), Co (1.11, 1.22), Cr (13.67, 13.46), N (2.10, 2.10), Ni (2.10, 2.15). The same method of anion substitution as used for 3 was performed to obtain X-ray quality crystals of 4.



S3-‐5

1.4. Synthesis of cobalt precursors

1.4.1. [Co(HO2C-tpy)](BF4)2 (6)

To a solution of 4-carboxyterpyridine (100 mg, 0.36 mmol) in MeOH/DCM (1:1) was added Co(BF4)·6H2O (45 mg, 0.18 mmol). The solution was then stirred for 1 hr. The dark-red solution was then filtered and kept at room temperature undisturbed. X-ray quality crystals were obtained after 24 hr from slow evaporation of the solvent (112 mg, 79%). ESI-MS (m/z): +613 [M − 2BF4 + H]+ (40%); +307 [M − 2BF4]+2 (100%); analysis (% calcd., % found for C35H28B2Cl6CoF8N6O4): C (40.46, 40.31), H (2.43, 2.62), B (2.08, 2.23), Co (5.67, 5.86), N (8.09, 8.22).

1.4.2. [Co(HO2C-Ph(tpy))](BF4)2 (7)

To a solution of b (100 mg, 0.28 mmol) in a solution of MeOH/DCM (1:1) was added Co(BF4)·H2O (38 g, 0.15 mmol). The solution was then stirred for 1 hr. The dark-red solution was then filtered and kept at room temperature undisturbed. X-ray quality crystals were obtained after 24 hr from slow evaporation of the solvent (107 mg, 82%). ESI-MS (m/z): +767 [M − 2BF4 + H]+ (20%); +383 [M − 2BF4]+2 (100%); analysis (% calcd., % found for C34H28B2Cl2CoF8N6O5): C (52.31, 51.87), H (3.44, 3.29), B (2.05, 1.96), Co (5.58, 5.69), N (7.96, 8.06).

1.5. Crystallography

The data of 2 was recorded on an Agilent SuperNova CCD diffractometer with MoKα radiation (λ = 0.71073 Å). The crystallographic data for 3, 6 and 7 were collected on a Bruker Prospector CCD diffractometer with CuKα radiation (λ = 1.5418 Å). The data for 4 and 5 were collected on a Rigaku Saturn724 þ diffractometer (synchrotron, λ = 0.68890 Å) at the I19 beamline at the Diamond Light Source, UK. The structure were solved by direct methods and refined against F2 using SHELXTL. CCDC 1029608-1029613 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/conts/retrieving.html (or from the Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB21EZ, UK; fax: (+44)1223-336-033; or [email protected]).

1.6. Electrochemistry

Cyclic voltammograms were recorded on a ca. 0.1 mM solution of [NBu4]PF6 in dried DCM using a three-electrode assembly equipped with a glassy carbon working electrode, Pt wire counter electrode, and a Ag/AgCl reference electrode. All of the potentials reported in this study were referenced against an internal standard ferrocene/ferrocenium couple (FeCp2/FeCp2

+ = 0.00 V).

1.7. Electron Paramagnetic Resonance

Q-band (ca. 34 GHz) and X-band (ca. 9.5 GHz) EPR spectra of polycrystalline powders and frozen solutions were recorded with a Bruker EMX580 spectrometer.



S3-‐6

The data was collected in the temperature range 5–30 K using liquid helium. Spectral simulations were performed using the EasySpin 4.5.5 simulation software.

2. Supplementary Tables

Crystallography 2.1.

Table S1. Crystallographic information for 2 – 4

Table S2. Crystallographic information for 5 – 7

2 3 4 Formula C97H161Cr7F8N4NiO32 C110H173Cr7F8N4NiO32 C216H347Cl2CoCr14F16N9Ni2O72 Molecular Mass / g mol-1 2469.73 2638.22 5501.25 Crystal System monoclinic monoclinic triclinic Space Group P21/c P21/c P-1 a / Å 16.7978(4) 30.5037(19) 19.3835(3) b / Å 31.2594(11) 16.5057(5) 27.6538(4) c / Å 24.9128(9) 32.2556(19) 29.1765(6) α / ° 90 90 76.8220(16) β / ° 103.209(3) 115.872(7) 84.5616(15) γ / ° 90 90 89.7001(13) V / Å3 12735.3(7) 14612.5(15) 15156.9(5) Z 4 4 2 ρ calc. / g cm-3 1.288 1.199 1.205 T / K 150 100 100 R1(I > 2σ)(I))a 0.0569 0.1191 0.1050 wR2


5 6 7 Formula C206H330Cl2CoCr14F16N8Ni2O72 C34H27B2CoF8N6O7 C44.5H29B2ClCoF8N6O4 Molecular Mass / g mol-1 5350.01 864.16 979.74 Crystal System monoclinic monoclinic triclinic Space Group C2/c C2/c P-1 a / Å 56.308(3) 40.103(2) 9.2332(6) b / Å 16.4647(3) 9.0797(4) 12.2853(9) c / Å 30.7417(9) 21.8936(12) 19.3386(11) α / ° 90 90 85.098(5) β / ° 93.238(3) 106.060(6) 76.757(5) γ / ° 90 90 88.790(5) V / Å3 28454.9(16) 7660.9(7) 2127.5(2) Z 4 8 2 ρ calc. / g cm-3 1.249 1.499 1.522 T / K 100 100 100 R1(I > 2σ)(I))a 0.1272 0.0831 0.1045 wR2




S3-‐7

3. Supplementary Figures

3.1. Crystal structures

Supplementary Figure 1. Crystal structure of 2 (right) and 3 (left). Colour code: Cr, green; Ni, purple; N, cyan; O, red; C, grey; F, pale green; H omitted for clarity.

Supplementary Figure 2. Crystal structure of 4. Colour code: Co, blue; Cr, green; Ni, purple; N, cyan; O, red; C, grey; F, pale green; H omitted for clarity.



S3-‐8

Supplementary Figure 3. Crystal structure of 5. Colour code: Co, blue; Cr, green; Ni, purple; N, cyan; O, red; C, grey; F, pale green; H omitted for clarity.

Supplementary Figure 4. Crystal structure of 6 (right) and 7 (left). Colour code: Co, blue; N, cyan; O, red; C, grey; B, dark green; F, pale green; H omitted for clarity.

3.2. Electrochemistry

Supplementary Figure 5. Cyclic voltammograms of compound 4 (right) and 5 (left) against internal standard ferrocene/ferrocenium couple (FeCp2/FeCp2

+ = 0.00 V).



S3-‐9

3.3. Electron Paramagnetic Resonance

3.4. Precursor EPR

Supplementary Figure 6. (Left) Experimental and simulated frozen solution spectrum of 6 (X-band, parameters: S = 1/2; gx = 2.047; gy = 2.076; gz = 2.195; Axx = 48; Ayy = 201; Azz = 279 MHz). (Right) Experimental and simulated powder spectrum of 7 (Q-band, parameters: S = 1/2; gx = 2.022; gy = 2.111; gz = 2.215; Axx = 14; Ayy = 183; Azz = 278 MHz).



asas



Chapter 9

Conclusions

9.1 ConclusionsNovel applications have been envisioned for molecule-based magnetic materials sincethe discovery of the bulk-like magnetic properties observed in molecular spin clustersand later in single ion 4f systems. At a synthetic level a lot has been achieved throughserendipitous approaches and more rational design of molecules. Exploring in detailthe physical behaviour of such systems has led to the proposal of MNMs as build-ing blocks in cooling, data storage and quantum computing devices amongst others.However, despite the possible uses of molecules in such applications a lot more hasto be done to obtain systems that can fulfil the minimum requirements for practicalimplementation.

9.1.1 Molecular CoolersIn this work, advantages of serendipitous and rational design of molecular systemshave been taken in order to obtain molecular materials that could be used in coolingdevices. As shown in Chapter 4, thanks to the chemical knowledge of the chelatingproperties of phosphonates, the advantages of solvothermal synthesis to obtain highnuclearity cages alongside the knowledge of behaviour of 3d/4f mixed metal systems,we have been able to obtain a range of 3d/4f phosphonates systems which could po-tentially be used in MCE applications. Structural characterisation of such systemsthrough X-ray single crystal diffraction yielded three families of cages, {Co4Ln10P8},{Co6Ln4P6}, {Fe6Ln6P6} and {Ni6Gd6P6}, whilst magnetic characterisation was ob-tained through SQUID measurements. They have also allowed us to obtain some un-derstanding of the role of the magnetic interaction in clusters, to better rationally designmolecular coolers.

189

9.1. CONCLUSIONS

9.1.2 Single Molecule MagnetsAn emerging trend in the synthesis of single molecule magnets is the use of lanthanideions due to their inherent strong anisotropic character, leading to Ueff an order of mag-nitude higher than observed in 3d polymetallic cages. Through the understanding ofthe magnetic properties of an asymmetric lanthanide dimer we have been able to obtainsome insight of the magnetic behaviour when the two Dy(III) are brought into closeproximity. As described in Chapter 6, in the asymmetric {Dy2} when the two dys-prosium ions are interacting the slow magnetic relaxation behaviour is quenched, dueto the new relaxation pathways induced by the exchange interaction. However, a clearmagnetic behaviour is fully revealed when the interaction is switched off through mag-netic dilution in the yttrium analogue. In this study, modelling of the EPR data alongwith X-ray structural analysis, SQUID magnetometry, ab-initio calculations and farinfrared data, have allowed us to develop a simple yet useful model to characterise andunderstand the role of the exchange interaction in the SMM behaviour of the system.

Finally the magnetic behaviour of a family of 27 isostructural butterfly complexeswas investigated through single crystal X-ray diffraction and SQUID measurements.In all dysprosium-containing molecules an out of phase susceptibility was observed,intrinsic to the dysprosium sites as demonstrated by SQUID measurement and ab-initio calculations. A trend is observed. Whilst when no paramagnetic 3d interactionis present the Ueff reaches the highest value, subsequent introduction of interactionsthrough paramagnetic 3d metal ions renders the U eff and SMM behaviour diminished.Meticulous analysis of the DC and AC SQUID data reveals a trend where the SMMbehaviour varies inversely with the strength of the interaction, without taking into ac-count its origin, i.e. ferromagnetic or antiferromagnetic.

Understanding of the interactions in 4f· · ·4f and 3d· · ·4f SMMs allows us to ratio-nally design better performing SMM, therefore generating more plausible candidatesfor futuristic applications.

9.1.3 Quantum ComputingThe implementation of molecular nanomagnets in quantum computing requires thesystem to fulfil the DiVincenzo criteria. Several of these criteria have been success-fully satisfied by the archetypal {Cr7Ni} antiferromagnetic wheels, proposing them assuitable molecular systems to perform as qubits. Following the previously describedfunctionalised {Cr7Ni} wheels, in Chapter 8 we have introduced a new functionality ofsuch systems, allowing further binding modes to the wheel. This was achieved throughbasic synthetic procedures and rational design. Furthermore, the use of a redox activetransition metal ion, such as Co(II), allows us to bring together two {Cr7Ni} and mag-netically couple them in an interaction that can be controlled using redox chemistry.The switch ON/OFF ability of this system has led to its proposal as a

√SWAP candi-

date, and its implementation in QC as a logic gate.


Appendices

191


Appendix A

Magnetism

Any atom with unpaired electrons moving around the nucleus or nuclear spin can giverise to magnetic fields. The movement of the charge leads to the fundamental object inmagnetism, the magnetic moment.

A.1 Atoms in a Magnetic FieldAn atom in a magnetic field (H) in the z-direction has an energy equal to:

E = gµBHms (A.1)

where g is the free electron g-value (2.0023), ms is the multiplicity of the spin (ms= 2S+1), H the applied magnetic field and µ B is the Bohr magneton µ B = eh/2me,being e the charge of the electron, me the mass of a electron and h = h/2π , where h isPlanck’s constant.

Additionally to spin orbital angular momentum, atoms also posses orbital angularmomentum which can be taken into account through the total angular momentum hL= ∑iri×pi, where pi is the momentum of the electron at the ith position of ri sum-ming over all the electrons in the atoms. The Hamiltonian of such systems under theinfluence of a magnetic field takes the form:

H = H0 +µB(L+gS)+e2

8me∑

i(H× ri)

2 (A.2)

where L is the orbital contribution. The major perturbation to the initial Hamilto-nian is usually the second term known as the paramagnetic term; whilst the third termis due to diamagnetic moments.

When a substance is subjected to an external magnetic field it generates a magneticmoment in response to the external magnetic field. This effect is known as magneticsusceptibility (χ) and is related to the magnetisation and the magnetic field through:

χ =δMδH

(A.3)

193

A.1. ATOMS IN A MAGNETIC FIELD

In weak magnetic fields the magnetic susceptibility is independent of the externalmagnetic field yielding,

χ =MH

(A.4)

The resultant magnetic susceptibility of a paramagnetic material is the addition ofthe diamagnetic and paramagnetic responses to the applied magnetic field.

χ = χD +χ

P (A.5)

where χ D and χ P represent the diamagnetic and paramagnetic susceptibility re-spectively. Diamagnetism is intrinsic to any material and is caused due to close shellelectrons rotating against the applied magnetic field (negative response). The diamag-netism is a temperature and field independent additive term, (χ D = −N

Ve2µ06me

∑Zi=1 〈r2

i 〉),which can be calculated through the Pascal’s constants. Being in this equation N andV the Avogadro’s number and the volume of the substance respectively.

χ P on the other hand represents the positive response to the external magnetic field.In classical models the randomly oriented spin vectors acquire a minimum energy ori-entation upon application of an external magnetic field. Due to the intrinsic quantisedangular momentum behaviour the total spin angular momentum S splits in a new setof quantum numbers ms with multiplicity equal to 2S+1. In the absence of the exter-nal magnetic field all these levels are degenerate, unless other effects are present (Seesection A.3). The application of a magnetic field leads to a Zeeman splitting of thesublevels, with the energy of each level given by the equation (A.1). The energy of amolecule under the influence of a magnetic field can be expressed as power series.

En = E(0)n +E(1)

n H +E(2)n H2 + . . . (A.6)

where the first term is the energy of the object at zero field, the second term is theenergy of the system under applied field and the third term is the energy resulting ofthe interaction of the ground and excited states. The variation of the energy levels in amolecule with energies En (n = 1, 2,. . . ) upon application of an external magnetic fieldquantum-mechanically is related to,

µn =−δEn/δH (A.7)

Introducing equation (A.6) in (A.7) yields µn = − E(1)n − E(2)

n H + . . . . Furthersimplification yields the so-called Van Vleck formula.

χ =N ∑n(

E(1)n

2

kT −2E(2)n

2)exp(−E(1)

n2

kT )

∑n exp(E(0)n

2

kT )

(A.8)

Where k is the Boltzmann constant and T the temperature. Application of themagnetic field induces mixing of the ground and excited states through the secondorder Zeeman interaction H2 (Scheme A.1).


A.1. ATOMS IN A MAGNETIC FIELD

ψ1

E1

E2

o

ψ2o

o

o

Unperturbedstates

Perturbation toThe first order

Perturbation toThe second order

ψ1o +

I21·ψ2o

E1o -E2

o

(1)

ψ2o +

I12·ψ1o

E2o -E1

o

(1)

E1o -I11

(1)

E2o -I22

(1)

E1o I11

(1)+I12

E1o -E2

o

(1) I21· (1)

+

E2o I22

(1)+I21

E2o -E1

o

(1) I12· (1)

+

Scheme A.1: Mixing of states under the application of a magnetic field.

If the separation between the ground state and any excited state is large, no mixingof these two is expected therefore En(2) could be neglected. Secondly if the H/kT issmall then En(0) = 0 and introduction of En(1) in the Van Vleck formula yields:

χ =N ∑n(

E(1)n

2

kT )

∑n exp(E(0)n

2

kT )

(A.9)

where En(1) = MSgµB,MS =−S,−S+1, ....,S−1,S, then:

χ =Ng2µ2

BkT

+S

∑mS=−S

m2s/(2S+1) (A.10)

which takes the form,

χ =Ng2µ2

B3kT

S(S+1) (A.11)

Equation (A.11) is known as the Curie law and is valid just for small H/kT regimes.Some degree of understanding of the interactions can be observed in the variation ofχMT , or χM, with temperature. A Constant behaviour would be expected for a sys-tem behaving according to the Curie law due to non-interacting spins. When interac-tions are present the nature of the interactions can be rationalised through the Weissconstant, θ of the Curie-Weiss law. A negative Weiss constant usually indicates anantiferromagnetic interactions and a positive one indicates ferromagnetic interactions.

χ =CT

(A.12)

χ =C

T −θ(A.13)


A.2. MAGNETISATION

A.2 MagnetisationWhen H/kT is large the magnetic moment tends to the saturation value (M), whichcorresponds to the alignment of all magnetic dipoles with the external magnetic field.

M is calculated from the partition function Z,

Z =+S

∑mS=−S

exp(−MSµBH/kT ) (A.14)

and can be re-written as

Z = sinh[(2S+1)gµBH/2kT ]/sinh(gµBH/2kT ) (A.15)

using δ lnZ/δH as,

δ lnZ/δH = (gµB/2kT )(2S+1)coth[(2S+1)y/2S)]− coth(y/2S) (A.16)

where y = gµBSH/kT . The molar magnetisation (M) is then,

MSat = NgµBSBS(y) (A.17)

where BS(y) is the Brillouin function defined by

BS(y) =2S+1

2Scoth

2S+12S

y− 12S

coth1

2Sy (A.18)

For small H/kT the BS(y) tends to unity leading to A.19 (Figure A.1)

MSat = NgµBS (A.19)

(a) (b)+5/2(gµBH)

+3/2(gµBH)

+1/2(gµBH)

–1/2(gµBH)

–3/2(gµBH)

–5/2(gµBH)

Figure A.1: (a) Saturation of the magnetisation for S = 12 , 3

2 , 52 and 7

2 for a g = 2.0; (b) Zeemansplitting for S = 5

2 under application of a magnetic field.


A.3. MAGNETIC ANISOTROPY

A.3 Magnetic AnisotropyThe SMM behaviour observed in {Mn12} is largely due to the negative zero field split-ting (D), which combined with the large spin ground state (S) introduces an anisotropicenergy barrier to the relaxation of the magnetisation. The Hamiltonian of a system withn unpaired electron is characterised by S = n

2 , with 2S+1 spin levels in a crystal field,which follows the form,

HCF = S ·D ·S (A.20)

which can be expanded as,

HCF = D[S2z +

13

S(S+1)]+E(S2x−S2

y) (A.21)

where D = Dzz−(Dxx+Dyy)/2 and E = (Dyy−Dxx)/2. In (A.21) E is the rhombicparameter and can take values −1

3 ≤ E/D≤+13 . If an axial system is considered then

the energy of the spin microstates are given by (A.16),

En = D[S2z +

13

S(S+1)] (A.22)

The effect of D in a free ion is to remove the degeneracy of the spin microstatewithout an external magnetic field. For example, an ion with S = 5

2 and D 6= 0, willsplit the degeneracy zero applied magnetic field. Furthermore, the effect of D in an ionhas two effects due to its magnitude and sign dependence (Figure of D > 0 and D < 0)(Figure A.2).

ms = –5⁄2

ms = +5⁄2

ms = –3⁄2ms = +3⁄2

ms = +½ms = –½

S = 5⁄2

2D

2D

4D

4D

Hz HzD > 0 D < 0Free Ion

ms = –5⁄2

ms = +5⁄2

ms = –3⁄2

ms = +3⁄2

ms = +½ms = –½

Figure A.2: (a) Behaviour of S = 52 state. The degeneracy is partially removed before the

application of the applied magnetic field.


A.4. EXCHANGE COUPLING

A.4 Exchange couplingInteractions between the magnetic moments (spins) of individual metal ions is com-monly observed when they are brought into close proximity. Commonly the exchangeinteraction is obtained through the overlap of the orbitals of the metal centres and theorbitals of the bridging ligands. The resultant low temperature magnetic behaviour ofthese systems deviates considerably from the Curie and Curie Weiss laws. Inspectionof the χMT (T ) behaviour is a usual procedure to verify if the magnetic interactions areantiferromagnetic or ferromagnetic.

If for example two S = 12 are brought into close proximity, the application of an

external magnetic field will align the spins in two different fashions, parallel and an-tiparallel. In a ferromagnetically-coupled system, the individual spins tend to align ina parallel fashion upon application of an external magnetic field. Conversely, if thealignment were antiparallel it would lead to an antiferromagnetic interaction (FigureA.3).

Ferromagnetic

FerromagneticInteraction

AntiferromagneticInteraction

Paramagnetic

Antiferromagnetic

-2J

S = 0

S = 1 S = 0

S = 1

-2J

(a) (b) (c)

Figure A.3: (a) χMT vs. T graphs for ferromagnetic, antiferromagnetic and non-interacting(paramagnetic) coupled spins; (b) Ground and excited state representation for two s = 1

2 spinswith ferromagnetic and antiferromagnetic interactions using a −2J formalism.

The states generated in the afore mentioned hypothetical case, will generate statesseparated by J, where J is the so-called isotropic exchange constant. If anisotropy ispresent, then J can be decomposed in Jxx, Jyy and Jzz. In a −2J Hamiltonian a negativeJ signifies antiferromagnetic coupling, and a positive J ferromagnetic coupling, withunits typically in cm–1 or K.

For isotropic systems the magnetic behaviour of the coupled system is often de-scribed by the Heisenberg-Dirac-Van Vleck (HDVV) Hamiltonian, which takes theform:

H =−2∑i j

SiJi jS j +µBSgi j−→H (A.23)

When magnetic anisotropy is encountered, then the zero field splitting is intro-duced, leading to:


A.5. ALTERNATING CURRENT MAGNETIC SUSCEPTIBILITY

H =−2∑i j

SiJi jS j +µBSgi j−→H +∑

iSiDS j (A.24)

A.5 Alternating Current Magnetic SusceptibilityA typical indication of the SMM property is the observation of a frequency-dependentout-of-phase magnetic susceptibility at zero dc field. In the ac susceptibility experi-ment, an oscillatory ac magnetic field is applied at a particular frequency. An out-of-phase ac susceptibility signal is observed when the rate of the operating frequency ofthe ac field is close to the flipping rate of the magnetic moment of the molecule. Ifan SMM is kept at a certain temperature and the frequency of the ac field is varied,a maximum will be observed once the rate of the ac signal equals the rate at whichthe molecule interconverts between the halves of the potential-energy double well (seeFigure A.4).

-40

-30

-20

-10

0 0

10

9

-1 012

3456

7

8

-10

-9

-8

-7

-6

-5-4

-3-2

Ener

gy (c

m–1

)

Magnetisation Direction

Figure A.4: Representation of the potential energy vs. the magnetisation direction for a singlemolecule with an S = 10 spin ground state ion, {Mn12}, split by axial zero field splitting.

The energy barrier of the relaxation of the magnetisation U eff in an SMM can beobtained through fitting of the in-phase (χ ′) and out-of-phase (χ ′′) susceptibility data.χ ′ and χ ′′ for a single relaxation process are given by (A.25) and (A.26) respectively.

χ′(ω) = χS +

(χT −χS)

1+ω2τ2 (A.25)

χ′′(ω) =

(χT −χS)ωτ

1+ω2τ2 (A.26)

where χS and χT are the adiabatic and isothermal susceptibility respectively, ω =2πν is the angular frequency and τ is the relaxation time. A distribution of singlerelaxation processes is given by:



χ′(ω) = χS +

(χT −χS)[1+(ωτ)1−αsinαπ

2 ]

1+2(ωτ)1−αsinαπ

2 +(ωτ)(2−2α)(A.27)

χ′′(ω) =

(χT −χS)[1+(ωτ)1−αcosαπ

2 ]

1+2(ωτ)1−αsinαπ

2 +(ωτ)(2−2α)(A.28)

In (A.27) and (A.28) α is a measure of the distribution width for relaxation pro-cesses between 0 and 1. The smaller α the narrower the distribution of relaxationprocesses. When α = 0, (A.27) and (A.28) become (A.25) and (A.26) respectively,indicating a single relaxation process.

A useful way of identifying relaxation processes from ac data is through the useof Cole-Cole plots. The symmetry of the graphs obtained from χ ′ vs. χ ′′ indicateswhether one or more relaxation processes are present (Figure A.5).

χT

χT

χ’’

χ’

χSχS

π(1–α)

(a) (b)

Figure A.5: (a) Frequency dependence of the real and imaginary component of the magneticsusceptibility. χT and χS are the isothermal and adiabatic susceptibility respectively; (b) Ar-gand plot (or Cole-Cole) χ ′′ vs. χ ′ at a given temperature.

τ can be obtained through ωτ = 1 at the maxima of χ ′′(ν). Plots of ln(τ) vs. 1/Tfollows an Arrhenius behaviour, 1/τ=1τ0exp(−U eff/kT ), characteristic for thermallyactivated Orbach process, giving the effective anisotropy energy barrier.

References[1] D. Gatteschi, R. Sessoli and J. Villain, Molecular nanomagnets, Oxford Univer-

sity Press, United Kingdom, 2006.

[2] O. Kahn, Molecular Magnetism, VCH Publishers, USA, 1993.

[3] S. Blundel, Magnetism in Condensed Matter, Oxford University Press, UnitedKingdom, 2001.

[4] R. L. Carlin, Magnetochemistry, Springer-Verlag, Berling Heidelberg, 1986.



[5] F. E. Mabbs and D. J. Machin, Magnetism and Transition Metal Complexes,Dover Publications, New York, 2008.




Appendix B

EPR Spectroscopy

B.1 EPR BasicsElectron paramagnetic resonance (EPR) is a spectroscopic technique that measuresthe energy difference between electronic states with different orientation of spins. Asingle electron s = 1

2 in zero applied magnetic field has two-fold degenerate levels,however application of a magnetic field removes the degeneracy of the state into ms =±1

2 , according to (2S+1), due to the Zeeman effect. The difference in energy betweenthe two states is related to:

∆E = gµBHms (B.1)

where g is the Landé g-factor (For a free electron ge = 2.0023), µB is the Bohr mag-neton and H is the applied field. Once the Zeeman splitting matches the microwaveenergy, more electrons are typically in the lower state, due to the Maxwell-Boltzmanndistribution, a net absorption is obtained. The first derivative of the absorption spec-trum is recorded (Figure B.1).

hν = gµBH

E = –½ gµBH

E = +½ gµBH

S = ½

H = 0 Increasing µ0H

I = –½

I = +½

I = +½

I = –½

S = ½

H = 0 Increasing µ0H

Ener

gy

Ener

gy

(a) (b)

Figure B.1: (a) Zeeman splitting of S = 12 separated by gµBH; (b) Zeeman splitting for S = 1

2interacting with I = 1

2 .

EPR is a very sensitive technique where interactions between the nuclear spin (I)

203

B.2. ANISOTROPY

and electron spin (S) can be observed through the hyperfine interaction. Analogous tothe electron magnetic moments are associated to the nuclear spin momentum. Theycan generate small local magnetic fields, which depending on their relative orientationwith respect to the external magnetic field, i.e. I =+1

2 or −12 for I = 1

2 , that is (2I+1),can split the spectrum of an S = +1

2 in two lines. The energy of the interaction betweena nuclear spin and an electron is give by En = gSµBSz(H +HI), where H is the appliedfield and HI is the magnetic field due to the nuclear spin (Figure A.2.1b).

B.2 AnisotropyFor isotropic systems, no orientation dependence is observed in the spectrum, i.e. ap-plication of the magnetic field in any of the three directions (Hx, Hy, Hz) would give thesame spectrum. This is the case for many radical systems where the orbital momentum(L) is rather small or nil. The EPR transition in metal ions and lanthanides are howeverlargely influenced by the orbital angular momentum leading to anisotropy in the g-factor and zero field splitting (D). In such cases, the direction of the external magneticfield and the molecule results in different behaviour depending on their orientation.

B.3 Zero Field SplittingAs mentioned in section A.1.2 the magnetic properties for S >1

2 are slightly differentthan expected due to the removal of the degeneracy at zero field by D. Similarly,EPR spectroscopy is a sensitive technique where the magnitude and sign of D canbe determined. The Hamiltonian describing a system with more than one unpairedelectron is given by equation A.20.

hν = gµBHΔε

Δε

E = –gµBH + ⅓ D

E = +gµBH + ⅓ D

E = – ⅔ DS = 1D > 0S = 0

H = 0

Ener

gy

hν = gµBH

Δε

Δε

E = –gµBH – ⅓ D

E = +gµBH – ⅓ D

E = + ⅔ D

S = 1

S = 0

H = 0

Ener

gy

(a) (b)

Increasing µ0Hz Increasing µ0Hz

D < 0

Figure B.2: (a) Zeeman splitting for an S = 1, with a zero-field splitting D > 0 and (b) D > 0.

If an external field is applied along the z-axis of a hypothetical S = 1 system, twotransitions would be observed (See Figure B.2). D splits the single expected transition,


B.4. SPIN EFFECTIVE FORMALISM

for an S = 1 state when D = 0, into two transitions. If the magnetic field is applied alongx- or y-axis it leads to different transitions and intensities. In non-axial symmetry,E 6= 0, the EPR spectrum renders more complicated, with higher number of transitionsobserved. The EPR spectrum of powdered samples is the result of the addition differenttransitions at different orientation of magnetic field.

EPR have also proven to be very useful to determine the sign of D, due to the inten-sity of the transitions involved. The determination of the sign of D however requiresmulti-frequency High-Field High-frequency studies.

B.4 Spin Effective formalismIn the solid state a metal ion is by no means isolated due to its interaction with thelattice, i.e. ligands, neighbouring ions, molecules, etc. Moreover, if an ion with S > 1

2 isinvolved LS-coupling introduces more inhomogeneity to the metal ion in consideration.The result of such an interaction is the splitting of the levels of the ion, leaving littledegeneracy. In metal ions with an odd number of electrons the degeneracy of the ms= ±n/2 is not removed in zero field due to the Kramers theorem. Such examplez areoften encountered in high spin Co(II) in octahedral environments and in Dy(III).

A method to represent the energy level under the application of a magnetic field inone of these ions is the Spin Effective formalism. This is a fictitious spin momentumthat sets the degeneracy of the levels involved equal to (2S +1), where S = 1

2 . The spineffective Hamiltonian taking into account the Anisotropy along the principal axis is,

H = µB{gxxHxSx +gyyHySy +gzzHzSz} (B.2)

In axial symmetry, gxx = gyy = g⊥; gzz = g‖ leading to g2 = g2‖cos2θ + g2

⊥sin2θ ,where θ is the angle between the applied field and z-axis.

The consequence of the introduction of the spin effective formalism is that theg-values deviate appreciably from the free electron g-value.

B.5 Exchange interactionWhen two ions are brought together two types of magnetic interactions are encoun-tered, antiferromagnetic or ferromagnetic interactions. The EPR spectrum in suchcases is rendered more complicated due to the new states created due to the interactionsbetween the spins. For example, for two s = 1 spins, magnetic interactions create twonew quantum numbers, S = 2, 1 and 0, where ferromagnetic interactions would lead toan S = 2 ground state and S = 1 and 0 first and second excited state respectively. An-tiferromagnetic interactions would lead to the reverse order of the ground and excitedstates (Figure B.3).


B.5. EXCHANGE INTERACTION

µ0Hz µ0Hz

100

100

50

50

0

Ener

gy /

GH

z

100

100

50

50

0

Ener

gy /

GH

z

µ0Hz

100

100

50

50

0

Ener

gy /

GH

zµ0Hz

100

100

50

50

0

Ener

gy /

GH

z

(a) (b) (c) (d)

Figure B.3: EPR simulation and Zeeman diagram along the z-axis for two coupled S = 1 inaxial crystal field and an isotropic exchange interaction: (a) J = +1 cm-1 and D = 0; (b) J = −1cm-1 and D = 0; (c) ) J = +1 cm-1 and D = +1 cm-1; (d) J = −1 cm-1.

References[1] A. Bencini and D. Gatteschi, EPR of Exchange Coupled Systems, Dover Pub-

lisher, New York, 2012.

[2] A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of TransitionIons, Oxford University Press, United Kingdom, 2012.

[3] J. A. Weil and J. R. Bolton, Electron Paramagnetic Resonance, Wiley-Interscience,New Jersey, 2007.


Appendix C

Quantum Gates

C.1 BasicsIn Clasical computers logical operations are performed by Boolean logic gates basedon string sets of 1 and 0. Logic gates transform the imput bits into one or more outputbits according to the definition of the logic gate. Similarly, Quantum Computers opera-tions are performed by logic quantum gates (QGs). The simplest logic gates are singlequbit unitary rotations which, starting from a basis set, i.e. |1〉 or |0〉, can produce asuperposition states α|0〉 + β |1〉 and α|0〉 − β |1〉, therefore in principle any algorithmcan be realized as a sequence of such unitary rotations.

Several universal QGs have been proposed, where the most commond two qubitgates are the controlled-NOT (CNOT) and the

√SWAP gates, whereas TOFFOLI and

FREDKIN are two examples of three qubit gates.

C.2 Two Qubit GatesUnwanted heat can be suppressed through the use of reversible logic gates. In a re-versible logic gate a unique input is always associated with a unique output and viceversa. Therefore, reversible gates do not erase information when performing a logicoperation, thus a computation based on reversible logic can be run forward to obtainan answer, copy the result, and finally the whole computation undone to recover all theenergy consumed apart from the small amount used to copy the answer at the mid-waypoint.

An important logic gate in quantum computing is the 2-bit controlled-not gate(CNOT). The effect of the "controlled"-NOT gate is to invert the bit value of the secondqubit if and only if the first qubit is in the |1〉 state.

207

C.3. THREE QUBIT GATES

Table C.1: Truth table of CNOT gate

a b a′ b′

0 0 0 00 1 0 11 0 1 11 1 1 0

CNOT =

00 01 10 11

00 1 0 0 001 0 1 0 010 0 0 1 011 0 0 0 1

(C.1)

A slightly more convoluted 2-qubit gate (2-input/2-output) is the√

SWAP gate.This change a two-qubit state |a,b〉 (with a and b being 0 or 1, and different) into asuperposition (|a,b〉 + i |a,b〉)/(1 + i) states. i.e. The qubits are change if and justif the superposition |0,1〉 and/or |1,0〉 are presnet. This gate employs the "exchangeinteraction" and arises inherently in spintronic quantum computing.

Table C.2: Truth table of SWAP gate

a b a′ b′

0 0 0 00 1 1 01 0 0 11 1 1 0

√SWAP =

00 01 10 11

00 1 0 0 001 0 1

2 +i2

12 −

i2 0

10 0 12 −

i2

12 +

i2 0

11 0 0 0 1

(C.2)

C.3 Three Qubit GatesGates that are both reversible and universal require three inputs and three outputs. Twowell-known examples are the FREDKIN (controlled-SWAP) gate and the TOFFOLI(controlled-CNOT) gate.

The TOFFOLI gate, also called controlled-controlled-NOT gate, can be understoodas flipping the third input qubit if, and only if, the first two input qubits are both |1〉.



Basically, the values of the first two input qubits control whether the third input qubitis changed.

Table C.3: Truth table of TOFFOLI gate

a b c a′ b′ c′

0 0 0 0 0 00 0 1 0 0 10 1 0 0 1 00 1 1 0 1 11 0 0 1 0 01 0 1 1 0 11 1 0 1 1 11 1 1 1 1 0

TOFFOLI =

000 001 010 011 100 101 110 111000 1 0 0 0 0 0 0 0001 0 1 0 0 0 0 0 0010 0 0 1 0 0 0 0 0011 0 0 0 1 0 0 0 0100 0 0 0 0 1 0 0 0101 0 0 0 0 0 1 0 0110 0 0 0 0 0 0 1 0111 0 0 0 0 0 0 0 1

(C.3)

A famous reversible gate is the FREDKIN (controlled-SWAP) gate. The FRED-KIN gate can be seen as a controlled-SWAP gate in that it swaps the values of thesecond and third bits, if, and only if, the first bit is set to |1〉.

Table C.4: Truth table of FREDKIN gate

a b c a′ b′ c′

0 0 0 0 0 00 0 1 0 0 10 1 0 0 1 00 1 1 0 1 11 0 0 1 0 01 0 1 1 1 01 1 0 1 0 11 1 1 1 1 1



FREDKIN =

000 001 010 011 100 101 110 111000 1 0 0 0 0 0 0 0001 0 1 0 0 0 0 0 0010 0 0 1 0 0 0 0 0011 0 0 0 1 0 0 0 0100 0 0 0 0 0 0 0 1101 0 0 0 0 0 1 0 0110 0 0 0 0 0 0 1 0111 0 0 0 0 1 0 0 0

(C.4)

References[1] Colin P. Williams, Explorations in Quantum Computing, Springer-Verlag, Lon-

don, 2011.

[2] N. David Mermin, Quantum Computer Science, Cambridge University Press,New York, 2007.


Appendix D

Contribution to other Projects

D.1 Contribution to other Projects

211

D.1. CONTRIBUTION TO OTHER PROJECTS


DaltonTransactions

PAPER

Cite this: DOI: 10.1039/c4dt02630f

Received 28th August 2014,Accepted 25th September 2014

DOI: 10.1039/c4dt02630f

www.rsc.org/dalton

Tetrametallic lanthanide(III) phosphonate cages:synthetic, structural and magnetic studies†

Karzan H. Zangana, Eufemio Moreno Pineda and Richard E. P. Winpenny*

The synthesis, structures and magnetic properties of a family of lanthanide complexes containing phos-

phonate ligands are reported. Reaction of hydrated lanthanide nitrate and tbutylphosphonic acid under

reflux conditions in iso-butanol, in the presence of pivalic acid as a co-ligand produced five new lantha-

nide complexes; pyridine (py) was present as a base. The compounds formed are tetrametallic, with the

general formula [pyH]4[Ln4(µ3-OH)(O3PtBu)3(HO3P

tBu)(O2CtBu)2(NO3)6] where Ln = GdIII, 1; TbIII, 2; DyIII,

3; HoIII, 4 and ErIII, 5. The metal sites within the complexes lie on the vertices of a triangle-based pyramid,

with phosphonate ligands on the triangular faces linking the apical Ln site to the Ln sites in the base. Each

lanthanide(III) site is eight-coordinate. Magnetic studies of the compounds show a decline in the product

χMT with T; modelling the behaviour of 1 shows anti-ferromagnetic exchange between GdIII centres

within the triangle with a negligible interaction to the fourth GdIII centre at the apex of the trigonal

pyramid.

IntroductionDuring the past two decades, the synthesis and characteris-ation of metal phosphonate cages has been an attractive fieldof synthetic chemistry and molecular magnetism for theiraesthetically pleasant structures with interesting magnetic pro-perties,1 including some examples of single molecule magnets(SMMs).2 Other metal phosphonate cages have been studied aspossible magnetic refrigerants.3 Phosphonate moieties areinteresting functional groups for the construction of molecularcages, as the three tetrahedral oxygen atoms mimic well thezeolite building blocks, providing suitable anchoring sites fora large variety of metal ion centres (including both transitionmetals and lanthanides).4 It is also possible to influencethe reactivity of compounds using the steric bulk of the phos-phonate ligands.5

Many research groups, notably those of Clearfield andZubieta have used phosphonate ligands to synthesise a largenumber of metal phosphonates that possess mainly extendedstructures 1D-coordination polymer, 2D-layered structured and3D-pillared structures.6 As a result of these studies a widerange of 3d-phosphonate and 3d–4f phosphonate cages have

been synthesised.7 In contrast to transition metal phospho-nates, reported molecular assemblies of purely 4f-phospho-nates are rare. The first reported lanthanide phosphonateswhere prepared in 1990 by Mallouk and coworkers;7 ceriumand lanthanum phenylphosphonates with composition[Ln(O3PC6H5)(HO3PC6H5)] and a series of alkylphosphonatessuch as [Ln(O3PMe)(HO3PMe)] were reported. Recently, wehave been synthesising molecular cages of lanthanide metalions with phosphonate ligands with the aim of preparing newcages, optimistically with interesting physical properties.8

Lanthanide phosphonate complexes normally have lowsolubility and poor crystallinity in water and organic solvents,hence it is generally difficult to obtain single crystals suitablefor X-ray structural analysis.9 One of the major reasons for thisis that the multisite coordination ability of the phosphonateligands leads to the formation of insoluble compounds. Weand others have proved that synthetically, this problem can beovercome for 3d-metal ions by different strategies, the firstexample arises from an initial report by Chandrasekhar andKingsley,10 where a second ligand is added alongside the phos-phonate. The co-ligand occupies certain number of coordi-nation sites on the metal ion as a result of which the numberof coordination sites that are accessible for the phosphonateligands decrease and soluble products can be isolated inthe form of single crystals. This methodology has been usedwith a co-ligand to synthesise molecular cages containingmanganese,11 iron,12 cobalt,13 nickel,14 copper,15 vanadium.16

A second method for introducing a phosphonate or ligandwithout causing an immediate precipitate is to react the ligandwith a preformed metal carboxylate cage, which was originally

†Electronic supplementary information (ESI) available: Cif files, further syn-thetic details, structural and magnetic plots. CCDC 1021470–1021474. ForESI and crystallographic data in CIF or other electronic format see DOI:10.1039/c4dt02630f

School of Chemistry and Photon Science Institute, The University of Manchester,Oxford Road, Manchester M13 9PL, UK.E-mail: [email protected]

This journal is © The Royal Society of Chemistry 2014 Dalton Trans.

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reported for iron and manganese and has since been extendedby our group and others.17,18

In this work, we extend the co-ligand approach to 4f-ions,reacting simple lanthanide salts LnIII(NO3)3·nH2O (LnIII = Gd,Tb, Dy, Ho and Er) with t-butylphosphonic acid (H2O3PtBu) inthe presence of pivalic acid (HO2CtBu) as a co-ligand, givingtetrametallic lanthanide phosphonate cages.

Experimental sectionStarting material

All reagents, metal salts, solvents and ligands were used aspurchased without any further purification. Analytical datawere obtained by the microanalytical service of the Universityof Manchester, the data and yields are given in Table 1.

Synthetic method

Pivalic acid (0.8 g, 7.83 mmol), Gd(NO3)3·6H2O (0.55 mmol),t-butyl phosphonic acid (0.07 g, 0.50 mmol) and pyridine (py)(0.5 mL, 6.15 mmol) were dissolved in ibutanol (HOiBu)(15 mL) and the solution was refluxed at 120 °C for 3 hours.The solution was filtered and then allowed to stand un-disturbed at room temperature for nine days. Colourless plate-like crystals suitable for single crystal X-ray diffractionof [pyH]4[Gd4III(µ3-OH)(O3PtBu)3(HO3PtBu)(O2CtBu)2(NO3)6] 1were formed. Similar reactions with LnIII(NO3)3·nH2O, (whereLnIII = Tb, Dy, Er and Ho) gave analogous metal cages(Table 1).


X-ray crystallographic measurements for compounds 1–5 werecollected on an Agilent SUPERNOVA diffractometer with MoKα

radiation (λ = 0.71073 Å). In all cases the selected single crys-tals were mounted on a tip of a glass pin using Paraton-N oiland placed in a cold nitrogen flow. Structure solution andrefinement was performed with the SHELXS-97 package,19a thestructures were solved by direct method and completed byiterative cycles of ΔF synthesis and full-matrix least-squaresrefinement against F2 using program Olex2.19b Crystal dataand refinement parameters are given in Table 2. Completehemispheres data were collected using ϕ and ω scans chosento give a complete asymmetric unit. All atoms excluding hydro-

gen were refined anisotropically. Hydrogen atoms were locatedon the basis of geometrical consideration and treated accord-ing to the riding model during refinement with isotropic dis-placement corresponding to the heavy atom they are linked to.Full crystallographic details can be found in CIF format: CCDCfor 1–5, 1021470–1021474.


Magnetic measurements were performed in temperatureranges 2–300 K, using a Quantum Design MPMS-XL7 SQUIDmagnetometer equipped with a 7 T magnet. The samples weregrounded and placed in a gel capsule. A small amount of eico-sane was used to avoid movement of the sample during themeasurement. Diamagnetic corrections for the compoundswere estimated using Pascal’s constants, and the magneticdata were corrected for diamagnetic contribution of the gelcapsule, the eicosane and the sample holder. Magnetic datawere fitted using the program PHI.20

Results and discussionSynthetic description

To date, just a few examples of lanthanide phosphonates cageshave been reported due to the tendency of these systems toform polymeric materials.9 However we, and others, haverecently proved that introducing of co-ligands along with ali-phatic R groups on the phosphonate can render better solubi-lity allowing their characterisation. This has led to families of{Ln8P6}8a cages and {Ln10P6}8b centred-rings. To illustrate howvariation of other reaction conditions influence the productformed, herein we report the synthesis of five new lanthanidephosphonate clusters {Ln4P4}, using the same general pro-cedure as used for synthesising {Ln8P6}, but replacing the baseiPrNH2 with pyridine. Using an aromatic base produces a com-pound of lower nuclearity, containing four Ln(III) metal ionsand four phosphonates. Three of the Ln(III) metal ions in thecluster form a µ3-OH centred triangle with the fourth Ln sitecapping this triangle.

Crystal structures

Compounds 1–5 crystallise in the monoclinic space group C2/cand have the same molecular structures (Fig. 1); we describe

Table 1 Elemental analysis and yield (%) for compounds 1–5

Formula Yielda

Elemental analysis: calculated (found)

C H Ln P N

1 [pyH]4[Gd4(µ3-OH)(O3PtBu)3(HO3PtBu)(O2CtBu)2(NO3)6] 45% 26.48 (26.22) 3.86 (3.55) 30.15 (30.10) 5.93 (5.89) 6.71 (6.66)2 [pyH]4[Tb4(µ3-OH)(O3PtBu)3(HO3PtBu)(O2CtBu)2(NO3)6] 39% 26.40 (26.18) 3.85 (3.71) 30.37 (30.25) 5.92 (5.88) 6.69 (6.63)3 [pyH]4[Dy4(µ3-OH)(O3PtBu)3(HO3PtBu)(O2CtBu)2(NO3)6] 30% 26.22 (26.11) 3.82 (3.79) 30.84 (30.77) 5.88 (5.73) 6.67 (6.61)4 [pyH]4[Ho4(µ3-OH)(O3PtBu)3(HO3PtBu)(O2CtBu)2(NO3)6] 35% 26.10 (25.98) 3.80 (3.75) 31.11 (30.97) 5.85 (5.80) 6.61 (6.59)5 [pyH]4[Er4(µ3-OH)(O3PtBu)3(HO3PtBu)(O2CtBu)2(NO3)6] 44% 25.98 (25.66) 3.79 (3.71) 31.46 (31.33) 5.82 (5.78) 6.58 (6.51)

a Calculated based on the lanthanide pivalate starting material.

Paper Dalton Transactions

Dalton Trans. This journal is © The Royal Society of Chemistry 2014

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the structure of [pyH]4[Gd4III(µ3-OH)(O3PtBu)3(HO3PtBu)-(O2CtBu)2(NO3)6] 1 as representative. Overall the molecularcage contains four lanthanide metal ions, four phosphonates,six nitrates, one µ3-OH and two pivalates. The metallic core of1 can be described as a triangular pyramid; the four Gd(III)ions (Gd1, Gd2, Gd3, and Gd4) lie on the vertexes of a triangu-lar pyramid. The three phosphonate ligands sit above the tri-angular faces linking the base to the apex, and adopt the 3.111

bonding mode (Harris notation).21 The fourth phosphonate islocated below the base of a triangular pyramid and bridges the(Gd1⋯Gd3) edge using the 2.11 bonding mode. There are sixchelating nitrate ligands in the structure; one nitrate coordi-nates to each of the vertices in the triangular base and thereare three nitrate ligands coordinated to the apex of the triangu-lar pyramid (Gd4). Two of the Gd⋯Gd edges within the tri-angular base are bridged by 2.11 pivalates.

Table 2 Crystallographic information for clusters 1–5

1 2 3 4 5

Chem formula C51H85O35N11Gd4P4 C51H85 O35N11Tb4P4 C46H80O35N10Dy4P4 C46H80O35N10Ho4P4 C46H80O35N10Er4P4fw 2123.10 2129.79 2065.01 2074.73 2084.05Temp. (K) 150.01(11) 150.04(13) 150.01(10) 150.02(19) 150.03(18)Cryst system Monoclinic Monoclinic Monoclinic Monoclinic Monoclinicspace group C2/c C2/c C2/c C2/c C2/ca/Å 44.8769(7) 44.8792(6) 44.8591(11) 44.7075(5) 44.7348(10)b/Å 19.0562(4) 19.1254(3) 19.1273(5) 19.0970(2) 19.1138(4)c/Å 24.0257(4) 24.0145(3) 23.9486(5) 23.9771(2) 23.8851(4)α/° 90 90 90 90 90β/° 91.0776(16) 91.0749(14) 91.090(2) 91.2548(9) 91.3155(18)γ/° 90 90 90 90 90V/Å3 20542.7(7) 20608.8(5) 20545.1(8) 20466.1(4) 20417.6(7)Z 8 8 8 8 8ρ calcd/g cm−3 1.373 1.373 1.335 1.347 1.356μ (Mo Kα)/mm−1 2.679 2.841 3.003 3.186 3.382R1 (I > 2σ)(I)a 0.0319 0.0389 0.0430 0.0361 0.0370wR2

a 0.0745 0.0846 0.0841 0.0816 0.0854

a R1 = ||Fo| − |Fc||/|Fo|, wR2 = [w(|Fo| − |Fc|)2/w|Fo|2]1/2.

Fig. 1 (a) and (b) side and top view of Crystal structure of the {Gd4P4} cluster. Scheme: Ln, purple; P, green; O, red; C, grey; N, cyan; (H omitted forclarity); (c) and (d) top and side view of metal and phosphonate core of the crystal structure of {Gd4P4} cluster.

Dalton Transactions Paper


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The distances between Gd1⋯Gd2, Gd2⋯Gd3 andGd1⋯Gd3 that are forming the edges of the base of thetriangular pyramid are 3.8104(6), 3.8151(8) and 3.8642(6) Årespectively. The µ3-OH group is displaced about 0.8230(1) Åout of the plane of the gadolinium metal ions. The Gd–O–Gdangles range from 108.34(11) to 109.19(10)°; these angles areconsistent with a µ3-hydroxide and not with a bridging oxide.The distances between the plane of base (Gd1, Gd2 and Gd3)and the apex (Gd4) within the triangular pyramid are exactly5.1150(1) Å.

Two different geometries are adopted by the GdIII ionsin the cluster: whilst Gd2, Gd3 and Gd4 exhibit a biaugmentedtrigonal prism geometry (C2v) and a ContinuousShape Measure value (CShM) of 2.494, 2.573 and 2.434respectively; Gd4 adopts a less regular coordination (muffin,Cs, with a CShM value of 2.345).22 There are no significantintermolecular interactions between clusters within the lattice.

Magnetic description

The magnetic properties of 1–5 were investigated by solid-statemagnetic susceptibility (where χM stands for molar magneticsusceptibility) measurements in the 2–300 K range in a 0.1Tesla (T) DC field. The resulting data for complexes 1–5 areshown as χMT versus T plot in Fig. 2 and 3, respectively. In eachcase the room temperature value for χMT is equivalent to that

for four non-interacting metal ions of the appropriate type. Forcompounds 2–5 χMT decreases steadily upon cooling down toca. 90 K (Fig. 2), below which they drop at 2 K, respectively.Such behaviour is typical for the individual metal ions con-cerned, and is probably due to depopulation of Stark levelswithin the individual metal sites. While magnetic exchangebetween the Ln sites in these compounds cannot be ruled out,there is certainly no evidence for such exchange from thesemeasurements. Magnetisation (M) versus applied magneticfield were performed at temperatures of 2 and 3 K in the fieldrange of 0–7 T. For 1 M saturates at 27.7 emu K mol−1 at 7 T at2 K, as expected for four non-interacting GdIII metal ions withS = 7/2 and gGd = 1.99 (Fig. 3). For compounds 2–5, there is agradual increase in M vs. H curve with increasing field, whichreach 20.8, 22.7, 23.7, 21.5 μB at 7 T at 2 K without reachingsaturation.

As GdIII is an isotropic metal ion this allowed us to simulatethe magnetic data of complex 1. Structurally there is littledifference between the Gd⋯Gd edges of the triangles (seeabove); however the Gd⋯Gd contacts between the apical Gdand those in the base are between 5.544(1)–5.604(1) Å. Further-more, any intermolecular interaction between would be rathersmall since the closest Gd⋯Gd intercluster distance is 9.8665(6)Å. Based on this structure, we have fitted simultaneouslyχMT (T ) and M(H), using the program PHI,20 using as a model

Fig. 2 Molar magnetic susceptibility (χMT ) vs. T plot for 2–5 under 1 kG dc field and molar magnetization (M) as a function of applied magnetic field(H) at 2 and 3 K (inset) for (a) 2, (b) 3, (c) 4 and (d) 5.



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an equilateral Gd3, with no exchange interaction to the fourthGd, using the Hamiltonian (1).

H ¼ "2J S1S2 þ S2S3 þ S1S3! "

þ gμBHX4

i¼1

Si ð1Þ

where the first term is the isotropic exchange interaction betweenGd(1)⋯Gd(2), Gd(2)⋯Gd(3) and Gd(1)⋯Gd(3) and the second termis the Zeeman term of each Gd centre. This gives an antiferro-magnetic exchange interaction J = −0.01 cm−1 between the Gd ions,where g = 1.99 (Fig. 3). Clearly with such a small interaction othermodels would also fit; we prefer this model as it has the minimumnumber of parameters and fits the crystallography (see above).

AC magnetic susceptibility measurements are a suitablemethod to judge whether a molecule exhibits a slow magneti-sation relaxation rate, which is an essential property of a mole-cules that might be a single-molecule magnet (SMM). Suchmeasurements were carried out between 10 and 1.8 K with andwithout applied DC field, however no out-of-phase componentwas obtained for any of the clusters.

DiscussionThe core of compounds 1–5 is related to those found in 3d-metal phosphonate cages (Fig. 4).12a,b An Fe(III) phosphonate

Fig. 3 (a) Molar magnetic susceptibility (χMT ) vs. T and simulation plots for 1 under 1 kG dc field; (b) Molar magnetization (M) as a function ofapplied magnetic field (H) at 2 and 3 K for 1.

Fig. 4 (a) and (d) side and top view of crystal structure of the {Fe4P4} cluster; (b) and (e) side and top view of Crystal structure of the {Ln4P4} cluster;(c) and (f ) side and top view of Crystal structure of the {Mn4P4} cluster; Scheme: Ln, purple; Fe, brown; Mn, cyan; P, green; O, red; C, grey; N, cyan;(H omitted for clarity).



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cage {Fe4P4} has been reported which contains a μ3-O centredtriangle of Fe(III) sites capped by a fourth FeIII ion. The μ3-OFe(III) triangle is clearly related to the oxo-centred {Fe3} carboxy-late triangle precursor. As in 1–5 three phosphonate units siton the faces of the trigonal pyramid that link the base to theapex. All Fe(III) metal ion centres are six coordinated. The dis-tance between the plane of base (Fe1, Fe2 and Fe3) and theapex (Fe4) is 4.25(1) Å while the Fe⋯Fe distances within the tri-angular base of the tetrahedron are between 3.34 and 3.37 Å.A similar manganese phosphonate cage {Mn4P4} involves thebulky tritylphosphonic acid (TPA) as ligand; this manganesecage is a mixed valent with two MnII and two MnIII sites. Inthis compound all four faces of the triangle pyramid are occu-pied by TPA ligands and the oxo-centred Mn triangle is muchmore distorted with Mn⋯Mn distances within of 3.19 and3.61 Å; the Mn⋯Mn distances to the apical Mn site remainlonger at 3.88(1) Å. In these 3d-cages, the phosphonatespresent 3.111 coordination mode and each metal ion centre iscoordinated to a pyridine molecule to complete its coordi-nation sphere. In the 4f-phosphonate compounds 1–5 reportedhere there is a μ3-OH centred triangle, not oxide centred, andthe phosphonates show two diverse binding modes. There isno pyridine binding to 4f metals, with the coordination of the4f-centres completed by chelating nitrates.

ConclusionsA new group of 4f-phosphonate tetranuclear clusters have beensynthesised from the reactions of a simple Ln(III) salt witht-butyl phosphonic acid. These products represent newadditions to what is still a very small family of such molecular4f-phosphonate species. We have previously reported that reac-tion of lanthanide nitrates with phosphonates in the presenceof aliphatic base like isopropylamine produce a series of {Ln8}clusters.20 Herein, our original goal of synthetic program wasto explore whether same strategy with aromatic base could beused to assemble Ln(III) ions into large combinations with newstructures and magnetic properties. It was observed that thereaction progress well in the presence of aromatic base, as thebase promotes the reaction by deprotonation of the phospho-nic acid ligand. So, in the present reaction system the identityof the cluster isolated is controlled by the nature of the baseused, each single component of the reaction matrix has astrong effect on the final product, and hence on the magneticbehaviour. The magnetic susceptibility data for all complexesdisplay dominant antiferromagnetic interactions. Hopefullyfurther efforts in this area will lead to more magnetically inter-esting compounds.

AcknowledgementsKZ thanks the KRG-Scholarship program in “Human CapacityDevelopment (HCDP)”. EMP thanks the Panamanian agencySENACYT-IFARHU. REPW thanks the Royal Society for a

Wolfson Merit Award. We thank the EPSRC (UK) for fundingfor an X-ray diffractometer (grant number EP/K039547/1).

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W. Wernsdorfer and R. E. P. Winpenny, Chem. Commun.,2005, 5029; (b) E. I. Tolis, L. P. Engelhardt, P. V. Mason,G. Rajaraman, K. Kindo, M. Luban, A. Matsuo, H. Nojiri,J. Raftery, C. Schroder, G. A. Timco, F. Tuna,W. Wernsdorfer and R. E. P. Winpenny, Chem. – Eur. J.,2006, 12, 8961; (c) S. K. Langley, M. Helliwell, R. Sessoli,S. J. Teat and R. E. P. Winpenny, Inorg. Chem., 2008, 47,497; (d) J.-T. Li, Y.-S. Ma, S.-G. Li, D.-K. Cao, Y.-Z. Li,Y. Song and L.-M. Zheng, Dalton Trans., 2009, 5029;(e) M. Wang, C. Ma, H. Wen and C. Chen, Dalton Trans.,2009, 994.

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16 (a) S. Khanra, M. Kloth, H. Mansaray, C. A. Muryn, F. Tuna,E. C. Sañudo, M. Helliwell, E. J. L. McInnes andR. E. P. Winpenny, Angew. Chem., Int. Ed., 2007, 46, 5568;(b) S. Khanra, L. Batchelor, M. Helliwell, F. Tuna,E. J. L. McInnes and R. E. P. Winpenny, J. Mol. Struct.,

2008, 890, 157; (c) S. Khanra, R. Shaw, M. Helliwell,F. Tuna, C. A. Muryn, E. J. L. McInnes andR. E. P. Winpenny, Materials, 2010, 3, 232.

17 (a) K. Brechin, R. A. Coxall, A. Parkin, S. Parsons,P. A. Tasker and R. E. P. Winpenny, Angew. Chem., Int. Ed.,2001, 40, 2700; (b) E. I. Tolis, M. Helliwell, S. Langley,J. Raftery and R. E. P. Winpenny, Angew. Chem., Int. Ed.,2003, 42, 3804; (c) E. I. Tolis, L. P. Engelhardt, P. V. Mason,G. Rajaraman, K. Kindo, M. Luban, A. Matsuo, H. Nojiri,J. Raftery, C. Schroder, G. A. Timco, F. Tuna,W. Wernsdorfer and R. E. P. Winpenny, Chem. – Eur. J.,2006, 12, 8961; (d) M. Maheswaran, G. Chastanet, S. J. Teat,T. Mallah, R. Sessoli, W. Wernsdorfer andR. E. P. Winpenny, Angew. Chem., Int. Ed., 2005, 44, 5044;(e) M. Shanmugam, G. Chastanet, T. Mallah, R. Sessoli,S. J. Teat, G. A. Timco and R. E. P. Winpenny, Chem. – Eur.J., 2006, 12, 8777.

18 (a) I. G. Fomina, M. A. Kiskin, A. G. Martynov,G. G. Aleksandrov, Z. V. Dobrokhotova, Y. G. Gorbunova,Y. G. Shvedenkov, A. Y. Tsivadze and V. M. Novotortsev, Zh.Neorg. Khim., 2004, 49, 1463; (b) T. A. Zoan, N. P. Kuzmina,S. N. Frolovskaya, A. N. Rykov, N. D. Mitrofanova,S. I. Troyanov, S. I. Pisarevsky, A. P. Martynenko andL. I. Korenev, J. Alloys Compd., 1995, 225, 396.

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21 Harris notation describes the binding mode as [X.Y1Y2...Yn] where X is the overall number of metal bond by thewhole ligand, and each value of Y refers to the number ofmetal atoms attached to the different donor atoms. SeeESI† and R. A. Coxall, S. G. Harris, D. K. Henderson,S. Parsons, P. A. Tasker and R. E. P. Winpenny, DaltonTrans., 2000, 14, 2349.

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asas



DaltonTransactions

PAPER

Cite this: DOI: 10.1039/c4dt01264j

Received 29th April 2014,Accepted 18th July 2014

DOI: 10.1039/c4dt01264j

www.rsc.org/dalton

Linking Cr3 triangles through phosphonates andlanthanides: synthetic, structural, magnetic andEPR studies†

Karzan H. Zangana, Eufemio Moreno Pineda, Iñigo J. Vitorica-Yrezabal,Eric J. L. McInnes and Richard E. P. Winpenny*

The preparation and structural characterisation of five 3d–4f mixed metal phosphonate cages with

general formula [CrIII6LnIII2(µ3-O)2(H2O)2(O3P

tBu)4(O2CtBu)12(HOiBu)2(

iPrNH2)2] where LnIII = La, 1; Tb, 3;

Dy, 4; Ho, 5 and [CrIII6GdIII2(µ3-O)2(H2O)2(O3P

tBu)4(O2CtBu)12(HOiBu)4] (2) are reported. The structure

contains two oxo-centred {Cr3} triangles, bridged by phosphonates and lanthanides. The magnetic be-

haviour of 1 has been modelled as two non-interacting isosceles triangles, involving two antiferro-

magnetic interactions (J1 = −8.8 cm−1) with a smaller ferromagnetic interaction for the unique edge of

the triangle (J2 = +1.3 cm−1) giving an isolated S = 3/2 ground state per triangle. The quartet ground state

has been proven through simulation of electron paramagnetic resonance (EPR) spectra obtained at the

X- and Q-band. EPR simulations have also resulted in the introduction of small single-ion Zero Field Split-

ting (ZFS) parameters D = ±0.19 cm−1 and rhombic term E = ±0.02 cm−1, which are consistent with

strong exchange limit calculations for an isolated S = 3/2 (D = ±0.22 and E = ±0.018 cm−1).

Introduction

The synthesis of paramagnetic polymetallic complexes hasbeen an area of significant interest since the discovery of thesingle molecule magnet (SMM), [Mn12O12(O2CMe)16(H2O)4].

1

One area of current interest is in making 3d–4f cage com-pounds, hoping that the combination of strong exchange fromthe 3d-ions will combine with the large anisotropy of the 4f-ions to produce interesting SMMs. The earliest studies of such3d–4f heterometallic compounds were by Gatteschi and col-leagues, who used designed Schiff-base ligands to bind toboth types of metal selectively.2 There was also considerablework involving use of anions of 2-hydroxypyridine and itsderivatives.3 More recently there has been a huge expansion inthis area, with many beautiful new compounds reported.4,5

Phosphonates are multidentate ligands that in their monoor dianionic form can adopt many different coordinationmodes, with a range of structures and nuclearities containingcopper,6 iron,7 manganese,8 nickel,9 cobalt9c,10 andvanadium.11 More recently phosphonates have been used for3d–4f-complexes,4n,5a,c,e,m and for 4f-compounds.12

One of our first forays into this area involved reactions ofoxo-centred tri-iron carboxylates with phosphonates,7a wherewe found that the phosphonate could displace a carboxylateand link triangles together. Frequently we found thatadditional reactions occurred, with an iron centre extractedfrom a triangle to bind to the phosphonate separately. Thisproduced compounds containing four (one triangle plus oneiron) and seven (two triangles bridged by one iron) metals.7a

We reasoned that if we used more stable oxo-centred triangles,and deliberately added a source of a second metal we couldmake similar arrays, but heterometallic. Therefore we haveundertaken the reaction of oxo-centred chromium(III) carboxy-lates with phosphonates in the presence of lanthanide ions.

In this paper we report the synthesis, structural characteris-ation, and magnetic properties of a series of octanuclearCrIII–LnIII phosphonate cages (LnIII = La, 1; Gd, 2; Tb, 3; Dy, 4;Ho, 5) using tbutyl phosphonic acid as ligand. We were able tosingle out the contribution of LnIII by comparing 2, 3, 4 and 5with the lanthanum analogue 1; this family of cages provides agood opportunity to systematically study the magneticexchange between 3d and 4f metal ions.

Experimental sectionMaterial and physical measurements

[CrIII3(µ3-O)(O2CtBu)6(H2O)3][O2C

tBu]·3H2O was synthesisedaccording to reported methods.13 All reagents, metal salts,

†Electronic supplementary information (ESI) available: Further crystallographicdetails. CCDC 999505–999509. For ESI and crystallographic data in CIF or otherelectronic format see DOI: 10.1039/c4dt01264j

School of Chemistry and Photon Science Institute, The University of Manchester,

Oxford Road, Manchester M13 9PL, UK.

E-mail: [email protected]; Fax: +44-161-275-1001


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solvents and ligands were used as purchased without anyfurther purification. Analytical data were obtained by themicroanalytical service of the University of Manchester. Thedata and yields are given in Table 1.

Synthesis

[CrIII3(µ3-O)(O2CtBu)6(H2O)3][O2C

tBu] (1 g, 1.225 mmol), Gd-(NO3)3·6H2O (0.554 mmol), t-butyl phosphonic acid (0.07 g,0.507 mmol) and isopropylamine (iPrNH2) (0.1 mL,1.164 mmol) in isobutanol (HOiBu)(15 mL) were refluxed at120 °C for 24 hours to form a dark green solution. The solu-tion was filtered and then allowed to stand undisturbed atroom temperature. Green plate-like crystals suitable for singlecrystal X-ray diffraction of [CrIII6Gd

III(µ3-O)2(H2O)2(O3PtBu)4-

(O2CtBu)12(HOiBu)4] (2) were collected after 10 days. Similar

reactions with LnIII(NO3)3·nH2O, where LnIII = La(1), Tb(3),Dy(4) and Ho(5) gave crystals of [CrIII6Ln

III2(µ3-O)2(H2O)2-

(O3PtBu)4(O2C

tBu)12(HOiBu)2(iPrNH2)2] (Table 1).


Data collection was carried out on Agilent SUPERNOVA diffracto-meter with MoKα radiation (λ = 0.71073 Å), data reduction andunit cell refinement were performed with CrysAlisPro software.The structures were solved by direct method usingSHELXS-9714a and were refined by full-matrix least-squarescalculations on F2 using the program Olex2.14b Suitable crystalsof 1–5 were mounted on a tip using crystallographic oil andplaced in a cryostream and used for data collection. Data werecollected using ϕ and ω scans chosen to give a complete asym-metric unit. All non-hydrogen atoms were refined anisotropi-cally. Hydrogen atoms were calculated geometrically and wereriding on their respective atoms. Hydrogens corresponding todisorder water molecules and hydroxyl groups form solvatedisobutanol molecules were omitted but included in theformula. Some degree of disorder was found in all cages. ThetBu groups of the pivalates, tBu groups of the phosphonates,the coordinated and uncoordinated (only compound 2) iso-butanol and isopropylamine are found to be disordered overtwo sites. These disordered groups were modelled splittingtheir occupancy into two parts. The isobutanol solvent mole-cules were found to be disordered over three sites for com-pound 1, 3–5. These disordered molecules were modelledsplitting their occupancy into three parts and restraining theirvalue to add to 1 using the SUMP command. The amount of

uncoordinated solvent was determined using SQUEEZE. Thenumber of electrons calculated agrees with two isobutanol andtwo water molecules per unit cell for compounds 1, 3–5. Forcompound 2, it was found to have four isobutanol and eightwater molecules per unit cell. The C–C distances of the tBugroups of the pivalates and the phosphonates were restrainedto be equal using SADI command. The C–C, C–O and C–N dis-tances for both the isopropylamine and the isobutanol wererestrained using DFIX command. The atomic displacementparameters of the disorder moieties were restrained usingRIGU command. Full crystallographic details can be found inCIF format: CCDC for 1–5, 999505–999509. Crystal data andrefinement parameters are given in Table 2.


The magnetic properties of polycrystalline samples of 1–5 weremeasured in the temperature range 1.8 K–300 K with aQuantum Design MPMS-XL7 SQUID magnetometer armedwith a 7 T magnet. The samples were ground, placed in a gelcapsule, and fixed with a small amount of eicosane to avoidmovement during the measurement. The data were correctedfor the diamagnetism from the gel capsule and the eicosanewith the diamagnetic contribution from the complexes calcu-lated from Pascal constants. Magnetic data were fitted usingthe program PHI.15

Electron paramagnetic resonance

X-band (ca. 9.5 GHz) and Q-band (ca. 34 GHz) EPR spectra ofpolycrystalline powders were recorded with a Bruker EMX580spectrometer. The data was collected in the temperature range5–30 K using liquid helium. Spectral simulations were per-formed using the EasySpin 4.5.516 simulation software.

Results and discussionSynthetic description

Many synthetic procedures rely on the reaction of oxo-centredmetal triangles,7,8,17 however fewer reactions use chromiumoxo-centered triangles [CrIII3(µ3-O)(RCO2)6(L)3]X (R = Me, Ph,tBu; X = Cl, NO3) and in many of those reactions the triangle isnot found in the final product.18 However here we find thatrefluxing a mixture of chromium pivalate oxo-centred triangle[CrIII3(µ3-O)(O2C

tBu)6(H2O)3][O2CtBu]·3H2O, hydrated lantha-

Table 1 Elemental analysis and yield (%) for compounds 1–5

Cage Yielda

Elemental analysis: found (calculated)

C H Cr Ln P N

1b 40% 41.33 (41.06) 7.32 (7.38) 10.58 (10.88) 9.41 (9.69) 4.19 (4.32) 0.94 (0.98)2b 31% 41.15 (40.95) 7.16 (7.28) 10.97 (10.64) 10.80 (10.72) 4.33 (4.21) — (—)3c 30% 41.09 (40.75) 7.38 (7.26) 10.48 (10.80) 11.21 (11.00) 4.10 (4.27) 0.93 (0.97)4c 29% 40.48 (40.65) 7.43 (7.24) 10.42 (10.77) 11.35 (11.22) 4.11 (4.28) 0.90 (0.97)5d 22% 40.89 (40.84) 6.79 (7.20) 10.53 (10.82) 10.97 (11.44) 4.07 (4.30) 0.93 (0.97)

a Based on phosphonate source. Calculated EA and crystallisation solvents. b 2(HOiBu)·2(H2O).c 2(HOiBu)·(H2O).

d 2(HOiBu).



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nide nitrate, LnIII(NO3)3·nH2O, phosphonic acid, H2O3PtBu,

and a mild base, iPrNH2, in iBuOH in the mole ratios1.2 : 0.50 : 0.50 : 1.2 gives reasonable yields of a family of{Cr6Ln2} cages Ln = La 1, Gd 2, Tb 3, Dy 4 and Ho 5.

Crystallography

The cages 1–5 crystallise in two different space groups mono-clinic P21/n (2) and triclinic P1 (1, 3, 4 and 5) (Fig. 1), howeverthe molecular structures are very similar and we describe thestructure of 1 as representative. Overall the structure containssix CrIII and two LaIII ions, which are held together by two

µ3-oxide and four phosphonates beside ten bridging pivalates.The octanuclear cage consists of two equivalent oxo-centeredchromium triangles {CrIII3(µ3-O)}.

In each triangle two edges are bridged by 2.11 pivalates(Harris notation)19 (ESI, Fig. S1†), as in the starting material,but on the third edge both pivalates have been displaced byphosphonates. These phosphonates bridge the Cr⋯Cr edge,but use their third oxygen atom to bind to a LaIII site; in onephosphonate (and its symmetry equivalent) the oxygen bridgesbetween two LaIII sites, given it a 4.211 binding mode. In theother pair of symmetry equivalent phosphonates the thirdO-atom is terminal to a LaIII, giving it the 3.111 binding mode.A 2.11 bridging pivalate also bridges between one Cr site, occu-pying the position trans to the μ3-oxide, and a lanthanum. Thissite is occupied by a terminal iBuOH for the other four Cr sites(Fig. 1).

The distance between the two µ3-oxides and the three CrIII

ions within triangles fall in the range 1.8924(1)–1.94955(8) Å,the Cr–O–Cr angles are very close to 120° and sum to 360°(ESI, Table S1 and Fig. S4†).

The Cr–Cr distances within the triangles fall in the range3.2351(2)–3.4275(5) Å, while the La–La′ distance within thecage is 4.192(8) Å. In 2, all CrIII centres have an O6 coordi-nation sphere, with octahedral coordination geometry; whilstin the remaining analogues a terminal amine fill the coordi-nation sphere of Cr1 and Cr(1)′, leading to a O5N set, and a O6

coordination sphere for Cr(2), Cr(3), Cr(2)′ and Cr(3)′. The LnIII

ion centres have an LnO8 coordination sphere, consisting offour oxygen atoms from the phosphonate bridging groups,three oxygens belonging to two pivalates and one water oxygenatom (ESI, Fig. S2 and S3†).

Magnetic description

We have studied the magnetic behaviour of complexes 1–5using polycrystalline samples in the temperature range2–300 K under 1000 Oe applied magnetic field. Similarly we

Fig. 1 Crystal structure of the {Cr6Gd2P4} cage 1. (a) Top left: top viewof cage. (b) Metal core of cage 1 without carbons. Scheme: La, purple;Cr, dark green; P, light green; O, red; C, grey; N, cyan; H omitted forclarity.

Table 2 Crystallographic information for cages 1–5

1·2iBuOH·2H2O 2·2iBuOH·4H2O 3·2iBuOH·2H2O 4·2iBuOH·2H2O 5·2iBuOH·2H2O

Chem formula C98H210Cr6La2N2O46P4 C100H210Cr6Gd2O50P4 C98H210Cr6N2O46P4Tb2 C98H210Cr6Dy2N2O46P4 C98H210Cr6Ho2N2O46P4fw 2866.37 2957.00 2906.39 2913.55 2916.83Cryst system Triclinic Monoclinic Triclinic Triclinic TriclinicSpace group P1 P21/n P1 P1 P1a/Å 13.7609(5) 13.8020(7) 13.918(1) 13.7094(6) 13.7501(4)b/Å 13.9671(5) 27.527(2) 14.0369(7) 14.0352(5) 14.0220(5)c/Å 23.3521(8) 19.718(2) 23.346(2) 23.1626(9) 23.1827(8)α/° 100.081(3) 90 99.776(5) 100.096(3) 100.079(3)β/° 100.916(3) 95.817(7) 101.128(6) 100.639(3) 100.637(3)γ/° 107.940(3) 90 108.202(5) 108.186(4) 108.254(3)V/Å3 4059.8(3) 7453(1) 4119.7(5) 4029.8(3) 4040.0(2)Z 1 2 1 1 1ρcalcd/g cm−3 1.172 1.295 1.171 1.201 1.199T/K 150(1) 150.0(2) 210.1(2) 150.0(1) 150.0(1)μ (Mo Kα)/mm−1 1.003 1.412 1.328 1.407 1.458R1 (I > 2σ)(I))a 0.0753 0.0777 0.0664 0.0661 0.0637wR2

a (all data) 0.2342 0.2048 0.2045 0.2052 0.2055

a R1 = ||Fo| − |Fc||/|Fo|, wR2 = [w(|Fo| − |Fc|)2/w|Fo|

2]1/2.



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have investigated the magnetisation as function of appliedmagnetic field (H) at 2 and 4 K in the range of 0–7 T. Thetemperature dependence of the χMT (T ) (where χM is the molarmagnetic susceptibility) for all polycrystalline samplesshow values lower than expected for the single ion contri-bution of six CrIII S = 3/2 and the paramagnetic lanthanidecontribution e.g. the contribution from GdIII, TbIII, DyIII orHoIII for 2–5 respectively. Complex 1 shows a χMT at roomtemperature of 9.6 cm3 K mol−1 considerably lowerthan expected (calcd 11.1 cm3 K mol−1 for six CrIII: gCr = 1.99,S = 3/2). For complex 1 χMT (T ) decreases with loweringtemperature reaching a value of 3.6 cm3 K mol−1 at 2 Ksuggesting, along with the χMT (T ) value at room temperature,antiferromagnetic interactions between the Cr sites in thecage. Complexes 2 to 5 exhibit similar behaviour: for 2 the χMTroom temperature value is 23.3 cm3 K mol−1 (calcd 26.7 cm3 Kmol−1 for six CrIII: gCr = 1.99, S = 3/2 and two GdIII: gGd = 1.99;S = 7/2) which gradually decreases to 20 K where it sharplydecreases to 15.9 cm3 K mol−1 at 2 K indicating that at thistemperature paramagnetic states are still populated; 3 to 5reveal room temperature χMT values of 33.2 cm3 K mol−1 (calcd34.8 cm3 K mol−1 for six CrIII: gCr = 1.99, S = 3/2 and two TbIII:gJ = 3/2; J = 6), 38.1 cm3 K mol−1 (calcd 39.5 cm3 K mol−1

for six CrIII: gCr = 1.99, S = 3/2 and two DyIII: gJ = 4/3; J = 15/2)and 37.6 cm3 K mol−1 (calcd 39.3 cm3 K mol−1 for six CrIII:

gCr = 1.99, S = 3/2 and two HoIII: gJ = 5/4; J = 8) mol−1 respecti-vely (Fig. 2).

The temperature dependent susceptibility graduallydecreases upon lowering temperature for all complexes,however at low temperature two different behaviours areobserved. For complex 3 a small plateau is observed fromca. 13 to 5 K, before dropping to 21.6 cm3 K mol−1 at 2 K. Inthe case of complex 4 the gradual decrease in χMT (T ) uponlowering temperature stops at about 8 K where it starts gradu-ally to increase up to 27.2 cm3 K mol−1 at 2 K. The behaviourexhibited by 3 and 4 suggest some ferromagnetic interactions,probably between the 3d–4f system.1–4 Complex 5 decreasesgradually up to ca. 40 K where it drops sharply to 12.9 cm3 Kmol−1 indicating antiferromagnetic interactions and/ordepopulation of the Stark sublevels (see Fig. 2).

The molar magnetisation (M) as function of applied mag-netic field at 2 K in the field range of 0–7 T shows a saturationvalue at 7 T for compounds 1 and 2 of 5.9 and 20.2 μB.Complex 3 to 5 show M(H) values of 14.7 for the 3 and 16.4 μBfor the other two. No conclusion can be drawn from the fielddependence for 3 to 5 due to the high anisotropy presented forthese lanthanide-containing cages.

The magnetic behaviour of 1 was modelled using PHIpackage,15 fitting χMT (T ) and M(H) simultaneously. As 1 con-tains LaIII, study of this compound allows the determination of

Fig. 2 Molar magnetic susceptibility (χMT ) vs. T plot for 2–5 under 1 kG dc field and molar magnetization (M) as a function of applied magnetic field(H) at 2 and 4 K (inset) for (a) 2, (b) 3, (c) 4 and (d) 5.



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the exchange interaction within the two {Cr3} moieties. Asimple model has been used based on the sum of two non-interacting {Cr3} triangles (based on the crystallographic data,the nearest Cr3⋯Cr3 distance from each triangle is 9.289(1) Å).Each {Cr3} triangle has been modelled using a Hamiltonian ofthe form (1):

H ¼ �2J1 S1S2 þ S1S3� �� 2J2 S2S3

� �þ gμBHX3

i¼1

Si ð1Þ

where the first term is the isotropic exchange interactionbetween Cr(1)⋯Cr(2) and Cr(2)⋯Cr(3), and the second termthat between Cr(1)⋯Cr(3), the chemically unique edge (Fig. 3).The fourth term is the Zeeman term of each Cr centre.

Good agreement between experiment and simulation forχMT vs. T and M vs. H is also obtained including a small ZFS(see below). Simultaneous fitting of χMT (T ) and M(H) yieldagreement between experimental data and simulation with anantiferromagnetic exchange interaction J1 = −8.8 cm−1, and aferromagnetic interaction of J2 = +1.3 cm−1 between the Crions in the unique edge of the triangle, giving a total spinground state for each individual {Cr3} fragment of S = 3/2 (seeFig. 3), with the first excited state, S = 1/2, at 33 cm−1 above it.The field dependence of the magnetisation can be reproducedusing the Brillouin function for two S = 3/2 states, which

suggests there is very little communication between the two{Cr3} triangles in the {Cr6La2} cage (Fig. 4).

Attempts to investigate the magnetic behaviour of 2 weremade, however due to the huge Hilbert space ((2Si + 1)n ×(2Sj + 1)n = 262 144) for the six CrIII (S = 3/2) and two GdIII (S =7/2), the system is rendered quite difficult for the evaluation ofits Hamiltonian. To overcome this issue the magnetic data of 2was modelled assuming two {Cr3} with S = 3/2, obtainedfrom the magnetic behaviour of 1 and the EPR data (seebelow) and two GdIII. We have used a simple Hamiltonian (2)considering a linear combination of Cr⋯Gd⋯Gd⋯Cr (seeinset Fig. 2a).

H ¼ �2J1 S1S2 þ S3S4� �� 2J2 S2S3

� �þ gμBHX4

i¼1

Si ð2Þ

Simultaneous fitting of M(H) at 2 and 4 K resulted in ferro-magnetic interactions between each {Cr3} and the neighbourGdIII J1 = +0.19 cm−1, whilst a small antiferromagnetic inter-action was obtained for the Gd⋯Gd pair J2 = −0.08 cm−1.

Electron paramagnetic resonance

EPR spectroscopy has generally been an important tool inprobing the spin ground states of molecular complexes.20 TheEPR spectroscopy of 1 was studied in the temperature range of5–30 K using X- and Q-band frequencies, ca. 9.5 GHz and 34.5GHz respectively. Several features are observed in X-band EPRat 5 K (Fig. 5). Broad intense transitions are observed at 60,160 and 440 mT resonance fields, whilst a less intense signalis observed at about 350 mT (g ∼ 2). Upon raising the tempera-ture the intense signals decrease while the minor signal atg ∼ 2 sharply increases, suggesting the population of anexcited state, probably S = 1/2 (see below). The Q-band EPRdata shows similar behaviour, with several features at 5 K,which broaden upon raising the temperature, whilst the signalat g ∼ 2 sharply increases.

We have simulated the X- and Q-band EPR data usingthe parameters obtained from fitting the magnetic data (see

Fig. 3 (a) Molar magnetic susceptibility (χMT ) vs. T and simulation plotsfor 1 under 1 kG dc field. (b) Molar magnetization (M) as a function ofapplied magnetic field (H) at 2 and 4 K for 1.

Fig. 4 Magnetisation of complex 1 and Brillouin function (red line) fortwo S = 3/2 states at 2 and 4 K.



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above), with inclusion of axial (D) and rhombic (E) ZFS terms,giving Hamiltonian (3):

H ¼ �2J1 S1S2 þ S2S3� �� 2J2 S1S3

� �þ DX3

i¼1

Siz2

þ EX3

i¼1

ðSix2 � Siy2Þ þ gμBHX3

i¼1

Si ð3Þ

Agreement between experimental data was achieved usingthe parameters above with DCr = ±0.19 cm−1 and ECr =±0.02 cm−1 (Fig. 6a and b). Inclusion of these small ZFS termsin the fit of magnetic data makes little difference to the qualityof the fit.

The EPR behaviour can also be modelled in the strongexchange limit as an isolated S = 3/2 state with D3/2 =±0.22 cm−1 and E3/2 = ±0.018 cm−1 revealing an isolatedquartet state with nearly no contribution from excited statespresent at 5 K (see Fig. 6c and d). If the strong exchange limitis valid here, the vector coupling method of Bencini andGatteschi21 would give D3/2 = 29DCr/25. Our two values for thezero-field splitting are entirely consistent with one another,demonstrating that use of the strong exchange limit isreasonable.

Conclusions

To summarise, by using an oxo-centered chromium pivalatetriangles complex as a starting material reacted with a range ofdifferent lanthanide starting materials and using t-butyl-phosphonate as a ligand we have obtained a range of 3d–4fmixed metal octanuclear complexes. The precursor {Cr3} tri-angles can be recognized in all the resulting cages, and thereis a relation to the {Fe7} cages we have reported previously,7a

where a single FeIII ion bound to the phosphonates, linking tri-angles. At present we cannot control or predict how the phos-phonates assemble the 4f-ions in order to form larger cages,but it appears this is a valuable strategy for synthesizing mod-erately large polymetallic cages.

Acknowledgements

KZ thanks the KRG-Scholarship program in “Human CapacityDevelopment (HCDP)”. EMP thanks the Panamanian agencySENACYT-IFARHU. REPW thanks the Royal Society for aWolfson Merit Award. We thank the EPSRC(UK) for fundingfor an X-ray diffractometer (grant number EP/K039547/1) andthe National EPR Facility.

References

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Fig. 5 (a) X-band spectrum for compound 1 in the temperature rangeof 5–30 K; (b) Q-band spectrum for compound 1 in the temperaturerange of 5–20 K.

Fig. 6 (a) X-band and (b) Q-band spectra (black trace) and simulation(red trace) for compound 1 modelled as exchange coupled system at5 K: gCr = 1.99, DCr = ±0.19, ECr = ±0.02, J1 = +1.8, J2 = −8.8 cm−1;(c) X-band and (d) Q-band spectra (black trace) and simulation (redtrace) for compound 1 at 5 K modelled as S = 3/2, g = 1.99, D = ±0.22,E = ±0.018 cm−1.



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19 Harris notation describes the binding mode as[X·Y1Y2⋯Yn] where X is the overall number of metal bondby the whole ligand, and each value of Y refers to thenumber of metal atoms attached to the different donoratoms. See ESI† and R. A. Coxall, S. G. Harris,D. K. Henderson, S. Parsons, P. A. Tasker andR. E. P. Winpenny, Dalton Trans., 2000, 14, 2349.

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Addition of pnictogen atoms to chromium(II):synthesis, structure and magnetic properties of achromium(IV) phosphide and a chromium(III)arsenide†‡

Sabine Reisinger,a Michael Bodensteiner,a Eufemio Moreno Pineda,bc

Joseph J. W. McDouall,b Manfred Scheer*a and Richard A. Layfield*b

Chromium(II) chloride reacts with lithium pentamethylcyclopentadienide (LiCp*, Cp* ¼ C5Me5) and

LiE(SiMe3)2 (E ¼ P or As) to give the heterocubane chromium phosphide [(h5-Cp*Cr)(m3-P)]4 (1) or the

chromium arsenide cage [(h5-Cp*Cr)3(m3-As)2] (2), respectively. The crystal and molecular structures of

both compounds have been determined by X-ray crystallography. The reactions represent unusual

oxidative additions of pnictogen atoms to chromium(II), which in the case of 1 results in the formation of

the unusual chromium(IV) formal oxidation state, and in the case of 2 provides access to chromium(III).

Compound 1 is also a rare example of a transition metal m3-phosphide-ligated cubane. Magnetic

susceptibility and magnetization measurements, with support from DFT calculations, indicate S ¼ 2 and S

¼ 9/2 ground states for 1 and 2, respectively, which can be rationalized by considering the electronic

structure in terms of chromium–chromium bonding.

IntroductionCluster compounds containing unsubstituted group 15 elementligands of the type [En] (E ¼ P or As, n $ 1), or so-called ‘naked’pnictogen ligands, continue to attract considerable interest dueto their remarkable structural diversity, and also because of theopportunities for using the clusters themselves as novel ligandsand in supramolecular chemistry.1 Synthetic routes to [En]-containing coordination compounds are well developed,particularly in the case of phosphorus, with activation reactionsof white phosphorus, P4, proving to be a particularly successfulsource of [Pn] complexes, including complexes of P4 itself.2

Although somewhat less extensive owing to greater technicalchallenges, analogous chemistry with yellow arsenic, As4,leading to complexes of [Asn] ligands, has also been reported.3

Recently, Cummins et al. have also developed a series of

transition metal complexes based on the naked mixed-pnic-togen starting material P3As.4

One branch of coordination chemistry in which the potentialof [En] ligands has been underexploited is molecular magne-tism. Indeed, there is a general paucity of studies addressing themagnetic properties of compounds containing P- and As-donorligands of the type [RxE]y", where x ¼ 2 and y ¼ 1, x ¼ 1 and y ¼2, or x ¼ 0 and y¼ 3.5 We recently reported studies of the P- andAs-mediated exchange coupling in the phosphide- and arse-nide-bridged dimers [(h5-Cp)M{m-E(SiMe3)2}]2, with M ¼ Cr(II)6

or Mn(II),7 and determined the exchange coupling constants viaphenomenological spin Hamiltonians. In the case of the chro-mium(II) dimers, the antiferromagnetic super-exchangecoupling between the high-spin S ¼ 2 ions was found to bestrong and also pnictogen-dependent, with exchange couplingconstants of J¼"166 cm"1 for E¼ P and J¼"77.5 cm"1 for E¼As (2J formalism). The antiferromagnetic exchange in themanganese(II) analogues is more than an order of magnitudeweaker, but these compounds are more noteworthy because oftheir S ¼ 5/2 to S ¼ 3/2 spin crossover properties. In the case ofthe arsenide-bridged manganese(II) dimer, the spin crossover isa two-step process that shows hysteresis at 96–105 K in thetemperature dependence of the magnetic susceptibility.

The spin congurations of rst-row transition metal Cpcomplexes can be very sensitive to the ligand substituents,particularly in the case of manganese(II)8 and, to a lesser extent,chromium(II).9 Chromocene itself has a low-spin, S ¼ 1 cong-uration,10 but substituting a [Cp]" ligand by [(Me3Si)2E]" to give

aInstitute fur Anorganische Chemie, Universitat Regensburg, 93040 Regensburg,Germany. E-mail: [email protected] of Chemistry, The University of Manchester, Oxford Road, Manchester, M139PL, UK. E-mail: [email protected] Science Institute, The University of Manchester, Oxford Road, Manchester,M13 9PL, UK

† Electronic supplementary information (ESI) available: Details of the synthesis,crystallography, magnetic property measurements and DFT calculations. CCDC984791 and 984792. For ESI and crystallographic data in CIF or other electronicformat see DOI: 10.1039/c4sc00666f

‡ This paper is dedicated to the memory of Professor Michael F. Lappert FRS.

Cite this: Chem. Sci., 2014, 5, 2443

Received 4th March 2014Accepted 27th March 2014

DOI: 10.1039/c4sc00666f

www.rsc.org/chemicalscience

This journal is © The Royal Society of Chemistry 2014 Chem. Sci., 2014, 5, 2443–2448 | 2443

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[CpCr{m-E(SiMe3)2}]2 (E ¼ P or As) evidently weakens the ligandeld sufficiently to give high-spin S ¼ 2 chromium(II).6 In anattempt to induce thermal spin crossover in [CpCr{m-E(SiMe3)2}]2 by forcing the ground state of the metal to switchfrom S ¼ 2 to S ¼ 1 with the aid of a stronger ligand eld, wehave targeted the analogous pentamethyl-cyclopentadienyl(Cp*) dimers [(Cp*)Cr{m-E(SiMe3)2}]2.

Results and discussionThe method used to synthesize [CpCr{m-E(SiMe3)2}]2, in whichCp2Cr is transmetallated by [(Me3Si)2ELi] with concomitantelimination of LiCp, was initially used to target [Cp*Cr{m-E(SiMe3)2}]2, but only starting materials were recovered.An alternative, two-step approach was then attempted,in which chromium(II) chloride and lithium pentam-ethylcyclopentadienide (LiCp*) were combined as solids in a1 : 1 stoichiometry, cooled to "78 #C, and then thf was added.The reactionmixtures were slowly warmed to room temperature,which resulted in the formation of a blue solution. The solutionwas cooled to "78 #C, and [(Me3Si)2PLi] or [(Me3Si)2AsLi] (1stoichiometric equivalent) in thf was added. Once again, thereactions were warmed to room temperature and stirred over-night. In the case of the phosphorus-containing reaction, the thfwas evaporated and replaced with toluene, and the resultingsolution was ltered, concentrated and stored at "30 #C forseveral days, which resulted in the formation of dark browncrystals of the heterocubane chromium phosphide [(h5-Cp*Cr)(m3-P)]4 (1), which was isolated in a yield of 33% based onthe chromium starting material. For the arsenic-containingreaction, the sameprocedure led to the formationof large, browncrystals of the arsenide-bridged trimetallic cage [(h5-Cp*Cr)3(m3-As)2] (2) in 42% yield based on the chromium starting material(Scheme 1). Themoderate yields of 1 and 2 are a consequence oftheir high solubility, even in hydrocarbon solvents, at thetemperature used for the recrystallizations. Although both 1 and2 are very air-sensitive, both compounds can be heated to reuxin toluene for brief periods with obvious signs of decomposition,and they appear to be stable indenitely at room temperatureunder an inert atmosphere of nitrogen or argon.

Compound 1 (Fig. 1) crystallizes in the tetragonal spacegroup I!4, and the molecular structure consists of four

symmetry-related chromium centres arranged in a tetrahedron,with Cr/Cr distances of 2.931(2) A and 2.935(1) A, and a P/Pseparation of 3.431(1) A (Fig. 1). The Cr–Cr–Cr and P–P–P anglesare all 60.0# within standard deviations. Each chromium iscoordinated by an h5-Cp* ligand, with Cr–C distances in therange 2.235(3)–2.248(4) A. The chromium atoms are bridged bythree m3-phosphide ligands, which produce very similar Cr–Pdistances of 2.2609(9), 2.2646(8) and 2.2610(9) A, and P–Cr–Pangles of 98.59(3), 98.32(3) and 98.59(3)#. Thus each chromiumresides in a classical {Cp*CrP3} piano stool coordination envi-ronment and formally exists as chromium(IV) (see below fordiscussion of electronic structure).

Compound 2 crystallizes in the orthorhombic space groupPbca, and the molecular structure consists of a triangle of {(h5-Cp*)Cr} units capped by two m3-arsenide ligands (Fig. 2).Although the three chromium atoms are not related by crys-tallographic symmetry, the close approximation to molecularD3h symmetry (regarding the Cp* ligands as undergoing ringwhizzing) is reected in the Cr(1)–Cr(2), Cr(1)–Cr(3) and Cr(2)–Cr(3) distances of 2.7658(5), 2.7869(4) and 2.7677(4) A, respec-tively, and the Cr(3)–Cr(1)–Cr(2), Cr(1)–Cr(2)–Cr(3) and Cr(2)–Cr(3)–Cr(1) angles of 59.79(1), 60.48(1) and 59.73(1)#. Withineach {(h5-Cp*)Cr} unit, the Cr–C distances are in the range2.227(2)–2.238(2) A for Cr(1), 2.224(2)–2.238(2) A for Cr(2), and2.226(2)–2.240(2) A for Cr(3). The D3h symmetry of molecules of2 is underscored by the similarity of the lengths of the Cr–As

Scheme 1

Fig. 1 Ball-and-stick representation of themolecular structure of 1. Cr¼ green; P ¼ purple; C ¼ grey (hydrogen atoms not shown).

Fig. 2 Ball-and-stick representation of the molecular structure of 2.Cr ¼ green; As ¼ yellow; C ¼ grey (hydrogen atoms not shown).

2444 | Chem. Sci., 2014, 5, 2443–2448 This journal is © The Royal Society of Chemistry 2014

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bonds, which are 2.4304(4)–2.4381(4) A to As(1) and 2.4258(4)–2.4316(4) A to As(2). The As(1)–Cr(1)–As(2), As(1)–Cr(2)–As(2)and As(1)–Cr(3)–As(2) angles are 97.85(1), 97.59(1) and97.48(1)#, respectively. In contrast to 1, the chromium centres in2 are present formally as Cr(III).

Several examples of ve-vertex coordination cages contain-ing {M3E2} cores are known for M ¼ Fe with E ¼ P or As,11 andfor M ¼ Co with E ¼ P, including the closely related[(Cp0 0Co)3(m3-P)2] (Cp0 0 ¼ C5H3

tBu2).12 However, compound 2 isthe rst example of such a cluster to contain chromium. Theformation of 1 is even more remarkable, for four reasons.Firstly, whereas clusters containing the {M4S4} (E ¼ O, S) unitare extremely well known,13 only two molecular compoundscontaining {M4P4} heterocubane units have been structurallycharacterized, both of which have M ¼ Co and were formedeither in low yield14 or as part of a mixture resulting from thethermolysis of [CpRCo(CO)2] with [Cp*Fe(P5)].12a The ironphosphide [(CpFe)4(P2)2] is reminiscent of 1, however its struc-ture differs in that the triangulated dodecahedral corecomprises {P2} ligands with a P–P bond distance of ca. 2.30 A,which is more than 1.1 A longer than the P/P separation in 1.15

The nickel phosphide [(CpNi)3(m3-P)(P4)], which contains abranched {P4} ligand,16 and the vanadium phosphorus cluster[(CpV)4(P3)2], which contains triphosphaallyl ligands,17 alsobear some structural similarities to 1. The synthesis of thecubane [(PhSn)(m3-P)]4 was reported in 1968, and although thestructural properties were not characterized in detail the tin(IV)phosphide is thought to be essentially isostructural to 1.18

Secondly, the chromium(II) starting material has been formallyoxidized to chromium(IV) in 1, which is an uncommon oxidationstate for this metal19 and, indeed, is also an unusual reaction forchromium(II), which tends to be oxidized to chromium(III) orchromium(VI),20 or to engage in metal–metal (multiple)bonding.21 Furthermore, although chromium heterocubanes ofthe type [CpCr(m3-E)]4 are known with E ¼ O, S or Se,22 thesespecies feature the formal chromium(III) oxidation state, ratherthan chromium(IV) as proposed for 1. Thirdly, the majority ofchromium(IV) complexes feature hard oxygen- or nitrogen-donor ligands,23 rather than so ligands such as phosphide orcyclopentadienide, and organometallic chromium(IV) is partic-ularly rare.24 Fourthly, to the best of our knowledge, compound1 is the rst polymetallic chromium(IV) compound.

The mechanism(s) through which 1 and 2 form are currentlyunclear, with NMR studies being hampered by the para-magnetism of both compounds. A reasonable assumption isthat salt metathesis occurs in the initial step, generating‘[Cp*CrCl]’ followed by [Cp*Cr{E(SiMe3)2}], with lithium chlo-ride as the by-product. Our previously reported chromium(II)compounds [(h5-Cp)Cr{m-E(SiMe3)2}]2 can therefore be regardedas models for the proposed intermediates, although thesestable complexes were synthesized using a different routeinvolving transmetallation of Cp2Cr by LiE(SiMe3)2.6 Generationof the naked pnictogen ligands may then occur by nucleophilicattack of LiE(SiMe3)2 on the E–Si bonds in [(h5-Cp*)Cr{m-E(SiMe3)2}]2, liberating E(SiMe3)3 as the by-product. However,analysis of the crude reaction mixture accompanying theformation 1 by the 31P NMR spectroscopy did not produce any

denitive information for the formation of P(SiMe3)3 owing tothe poor signal-to-noise ratio arising from the paramagnetismof 1 (Fig. S2†). Indeed, assignment of the NMR spectra of 1 and2 cannot be made with any certainty owing to the effects of theunpaired spin density.

Precedent for the reactivity proposed to account for theformation of 1 and 2 stems from our work on the synthesis oftris(phosphino)phosphines of the type P(PR2)3 (R ¼ variousalkyl, Ph),25 in which the P–Si bonds in intermediates speciessuch as R2P–P(SiMe3)2 are sequentially cleaved by [LiP(SiMe3)2].The formation of chromium(IV) in the presence of phosphorus,and the formation of chromium(III) in the presence of arsenic, isintriguing feature of the chemistry depicted in Scheme 1. Thedifferent chromium oxidation states in 1 and 2 can be explainedby considering that the energies of the valence orbitals ofchromium(IV) should be lower than those of chromium(III), andtherefore closer in energy to those of phosphorus. In contrast,the higher energy of the arsenic valence orbitals may be bettermatched to those of chromium(III).

An important consideration in 1 and 2 is the possibility ofchromium–chromium bonding. A search of the CambridgeStructural Database (CSD) reveals that the range of chromium–chromium single bonds is 1.858–3.471 A, with a mean value of2.755 A,26 suggesting that such interactions are at least possiblein 1 and 2. Studies on the bonding in related chalcogen-bridgedheterocubanes of general formula [(CpM)4(m3-E)4]n+ (M ¼ Ti, V,Cr, Mo, Fe, Ru, Co, Ir; E ¼ O or S; n ¼ 0, +1, +2) have consideredtwo limiting possibilities, one in which the unpaired spindensity is delocalized into metal–metal bonds, and one inwhich the spin density is localized in themetal d-orbitals, whichcan lead to magnetic exchange coupling via the ligands. To gaininsight into the electronic structure in 1 and 2, the temperaturedependence of the molar magnetic susceptibility (cM), and theeld (H) dependence of the magnetization (M) of polycrystallinesamples of both compounds were measured.

In an applied eld ofHdc¼ 1000 Oe, cMT for 1 at 300 K is 2.85cm3 K mol"1, and remains essentially constant down to about10 K, when a sharp decrease is observed, and then a value of2.05 cm3 K mol"1 is reached at 2 K (Fig. 3). The isothermalmagnetization of 1 at T ¼ 2 K shows a steep increase to reachM¼ 2.46 NmB at H ¼ 2.0 T, and then increases at a slower rate athigher elds, reaching M ¼ 3.67 mB at H ¼ 7.0 T, but withoutsaturation (Fig. 3). The cMT value of 1 in the range 10–300 K isless than the upper limit of 4.00 cm3 K mol"1 predicted for fourCr(IV) ions with S ¼ 1,27 and the magnetization at 7 T and 2 K issignicantly less than the value of 8 NmB predicted for thissystem (assuming g ¼ 2.00). Because cMT is essentiallytemperature-independent down to 10 K, any antiferromagneticexchange is likely to be extremely weak, therefore an alternativeexplanation involving metal–metal bonding should be consid-ered in order to account for the susceptibility and the magne-tization in 1.

A molecular orbital (MO) energy-level scheme to describe thebonding in cubanes of the type [(CpM)4E4] (E ¼ O, S) has beenproposed by Dahl et al., and developed by others for cubaneswith a range of d-electron counts.28 The metal–metal clusterbonding MOs consist of the dz2 orbitals oriented towards the


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centre of the cubane, with the dxy and dx2"y2 orbitals overlappingaround the cluster periphery. These interactions produce asimplied energy-level diagram with low-lying a1, e and t2bonding MOs, and t1 and t2 antibonding orbitals (Fig. S6†). Inthe case of 1, populating the frontier MOs with eight electronscan produce two congurations, either (a1)2 (e)3 (t2)3 with a totalspin of S ¼ 2, or (a1)2 (e)4 (t2)2 with a total spin of S ¼ 1. Theexpected value of cMT for a cluster with S ¼ 2 and g ¼ 2.00 is3.00 cm3 K mol"1,27 which agrees well with the values measuredfor 1 down to 10 K. Furthermore, the value of the magnetizationatH¼ 7 T is also close to the expected value of 4 NmB for an S¼ 2system. The magnetic susceptibility and magnetizationmeasurements therefore indicate that 1 occupies an S ¼ 2, spinquintet ground state.

To obtain further support for the assignment of themagneticground states of 1 and 2, we performed density functionalcalculations using the Gaussian suite of programs.29 Stabilityanalysiswasapplied to ensure that a trueminimumwasobtainedin the Kohn–Sham solutions. Calculations were attemptedwithin the generalized gradient approximation using the PBEexchange–correlation functional,30 and its derivative PBE0.31 Thehybrid DFT calculations were plagued by the presence of insta-bilities: in the case of 2, removing the instabilities was straight-forward, 1 proved very difficult to treat using PBE0 (calculationsusing the B3LYP hybrid functional were also unsuccessful).Consequently, for 1 we report calculations only at the PBE/TZVP

level.32 For 2, it was possible to obtain stable solutions at bothPBE/TZVP and PBE0/TZVP levels, with both levels producing thesame ordering of spin state energies. PBE has previously beenshown to be successful in describing metal–metal bonds,33 andwe accordingly have condence in its use here.

In the case of 1, the spin quintet was indeed found to be theground state, with the other spin multiplicities lying above theground state by: singlet (S ¼ 0) +25 kJ mol"1; triplet (S ¼ 1) +20kJ mol"1; septet (S ¼ 3) +99 kJ mol"1; nonet (S ¼ 4) +179 kJmol"1 (Table S2†). The spin density plot for the ground state of1 (Fig. 4) reveals that the unpaired spin resides almost entirelyon the chromium(IV) centres. The presence of chromium–chromium bonding in 1 is also substantiated by the calculatedCr–Cr Mayer bond orders for the ground-state quintet, which, at0.22–0.24, are non-negligible (Table S4†).

The magnetic properties of 2 are more straightforward tointerpret. Under the same experimental conditions as for 1, thecMT product for 2 at 300 K is 5.85 cm3 K mol"1, with this valuedecreasing slightly down to about 10 K, when a sharper decreaseis observed, reaching 4.65 cm3 K mol"1 at 2 K. The 2 Kmagnetization of 2 reachesM ¼ 4.96 NmB at H ¼ 7.0 T. A systemcontaining three Cr(III) ions, each with S ¼ 3/2, would beexpected to show a maximum of cMT¼ 5.63 cm3 K mol"1 at 300K, andM¼ 4.5 at 2 K;22 the similarity of the theoretical values tothose observed experimentally suggests that 2 occupies an S ¼9/2 ground state, i.e. a spin decet. DFT calculations are in goodagreement with the experimental data, with the excited spinstates being destabilized relative to the ground state as follows(PBE/TZVP): doublet (S¼ 1/2) +82 kJ mol"1; quartet (S¼ 3/2) +55kJ mol"1; sextet (S ¼ 5/2) +74 kJ mol"1; octet (S ¼ 7/2) +66 kJmol"1 (Table S3†). The same spin state ordering was found atthe PBE0/TZVP level. The Cr–Cr Mayer bond orders for 2 are inthe range 0.07–0.10, and hence much smaller than those in 1(Table S5†).

ConclusionsIn summary, we have discovered a new route to chromiumcomplexes of naked phosphide and arsenide ligands, whichinvolves formal oxidative addition of the pnictogen atom tochromium(II) using simple starting materials. Of particular noteis that the synthetic route provides convenient access to a rareexample of a phosphide-ligated heterocubane (1), which

Fig. 3 Temperature dependence of cMT in an applied field of 1 kG(upper), and magnetization (M) versusmagnetic field (H) at 2 K (lower),for 1 (shaded circles) and 2 (unshaded circles).

Fig. 4 PBE/TZVP spin density plot for the ground state of 1 (left) and 2(right) (isosurface value ¼ 0.004 a.u.).



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contains chromium in the unusual formal +4 oxidation state.Magnetic susceptibility and magnetization measurementsconrm that the spin ground state of 1 can be described by an S¼ 2 system with chromium–chromium bonding. The spinground state of 2 was determined experimentally to be S ¼ 9/2,and support for the assignment of the spin ground states wasprovided by DFT calculations. The general implication of thecurrent study is that the synthetic method may represent ageneral route to transition metal complexes of naked pnictogenligands, potentially with the metals present in uncommonoxidation states and unusual coordination environments. Ourongoing work will explore this possibility.

AcknowledgementsThe authors thank Prof. D. Collison (Manchester) and Dr S.Sproules (Glasgow) for insightful discussions. RAL thanks theAlexander von Humboldt Foundation for the award of aFellowship for Experienced Researchers.

Notes and references1 (a) C. Schwarzmaier, A. Schindler, C. Heindl,S. Scheuermayer, E. V. Peresypkina, A. V. Virovets,M. Neumeier, R. Gschwind and M. Scheer, Angew. Chem.,Int. Ed., 2013, 52, 10896.

2 (a) P. Dapporto, S. Midollini and L. Sacconi, Angew. Chem.,Int. Ed., 1979, 18, 469; (b) I. de los Rios, J.-R. Hamon,P. Hamon, C. Lapinte, L. Toupet, A. Romerosa andM. Peruzzini, Angew. Chem., Int. Ed., 2001, 40, 3910; (c)P. Barbaro, V. M. Di, M. Peruzzini, S. S. Costantini andP. Stoppioni, Chem.–Eur. J., 2007, 13, 6682; (d) V. Mirabello,M. Caporali, V. Gallo, L. Gonsalvi, D. Gudat, W. Frey,A. Ienco, M. Latronico, P. Mastrorilli and M. Peruzzini,Chem.–Eur. J., 2012, 18, 11238; (e) S. Heinl,E. V. Peresypkina, A. Y. Timoshkin, P. Mastrorilli, V. Galloand M. Scheer, Angew. Chem., Int. Ed., 2013, 52, 10887; (f)M. Scheer, G. Balazs and A. Seitz, Chem. Rev., 2010, 110,4236; (g) M. Scheer, Dalton Trans., 2008, 4372; (h)B. Cossairt, N. A. Piro and C. C. Cummins, Chem. Rev.,2010, 110, 4164; (i) M. Caporali, L. Gonsalvi, A. Rossin andM. Perruzini, Chem. Rev., 2010, 110, 4178.

3 For recent examples, see: (a) C. Schwarzmaier,M. Bodensteiner, A. Y. Timoshkin and M. Scheer, Angew.Chem., Int. Ed., 2013, 52, 290; (b) C. Schwarzmaier,A. Y. Timoshkin and M. Scheer, Angew. Chem., Int. Ed.,2013, 52, 7600.

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22 (a) L.-H. Song, H.-W. Cheng, X. Chen and Q.-M. Hu,Organometallics, 2004, 23, 1072; (b) L.-H. Song,H.-W. Cheng, X. Chen and Q.-M. Hu, Eur. J. Inorg. Chem.,


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2004, 3147; (c) L. Y. Goh, Z. Weng, W. K. Leong andP. H. Leung, Angew. Chem., Int. Ed., 2001, 40, 3236; (d)L. Y. Goh, Z. Weng, W. K. Leong and P. H. Leung,Organometallics, 2002, 21, 4398; (e) D. P. Allen,F. Bottomley, R. W. Day, A. Decken, V. Sanchez,D. A. Summers and R. C. Thompson, Organometallics,2001, 20, 1840; (f) F. Bottomley, D. E. Paez, L. Suti,P. S. White, F. H. Kohler, R. C. Thompson andN. P. C. Westwood, Organometallics, 1990, 9, 2443; (g)F. Bottomley, D. E. Paez and P. S. White, J. Am. Chem. Soc.,1981, 103, 5581.

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26 C. R. Groom and F. H. Allen, Angew. Chem., Int. Ed., 2014, 53,662.

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1438 | Chem. Commun., 2014, 50, 1438--1440 This journal is©The Royal Society of Chemistry 2014

Cite this:Chem. Commun., 2014,

50, 1438

Centred nine-metal rings of lanthanides†

Karzan H. Zangana,a Eufemio Moreno Pineda,a Eric J. L. McInnes,a Jurgen Schnackb

and Richard E. P. Winpenny*a

Two {Ln10} cages are reported (Ln = Dy or Gd) which feature a nine-

metal ring surrounding a central metal site. Magnetic studies show

weak anti-ferromagnetic exchange around the nine-metal ring,

which should create spin frustration.

Cyclic metal cages fall into two broad families. In one familythe metal sites are confined to the rim of the cage forming ametal ring, where the metals can be single metal sites1 or metalcages.2 In the second family there is a metal at the centre of thecage, and these are called either metallocrowns3 or metallo-coronands.4 Both classes have been studied, the former largelybecause of they can act as model compounds for studyingphysical phenomena, especially in magnetic molecules.1 Formetallocrowns studies extend to selective ion binding, as wellas studies of interesting magnetic behaviour.5 For both familiesmost examples involve 3d-metal ions, although there areremarkable polymolybdate2a and palladium phosphonaterings.2c Several metal rings have been reported for the 4f-metals,6

and for 3d–4f cages,7 but many fewer centred cyclic structures.8

Most rings and metallocrowns contain an even-number of metalsites in the cyclic portion, although metallocrowns are known withthree9 or five10 metals in the backbone. Few large odd-numberedrings have been reported.11 Here we report two cyclic {Ln10} cages(Ln = Dy, 1 or Gd, 2), where there is a nine-metal ring centred by atenth metal site.

To synthesise 4f-phosphonate cages we have used pivalate asa co-ligand,12 and we have reported a number of Co-4f cages.13

We were intending to extend this work by reacting [Ln2(O2CtBu)6-(HO2CtBu)6] (Ln = Dy and Gd) with [Co3(m3-O)(O2CtBu)6(py)3]-(O2CtBu), H2O3PtBu and pyridine; the CoIII cage was used to try to

control reactivity by using an inert 3d-metal and hence achieve amore predictable cage than using CoII substrates.13 After heating forseven hours, light-brown crystals form over two weeks at roomtemperature in yields of 10–20% based on lanthanide pivalate. X-raystudies show formation of [Co3(m3-O)(O2CtBu)6(py)3][Ln10(O2CtBu)18-(O3PtBu)6(OH)(H2O)4] (Ln = Dy 1, Gd 2) (Fig. 1).‡ The compoundsare isostructural, and contain an anionic {Ln10} cage co-crystallisedwith a [Co3(m3-O)(O2CtBu)6(py)3]+ cation (Fig. S1, ESI†). We describecompound 1 as crystals of 2 do not diffract sufficiently well to allowa full structure determination.

The anion of 1 contains nine DyIII metal ions in a ring and atenth DyIII metal ion at the centre of the structure (Fig. 1). Oxygendonors occupy all the coordination sites on these ten metals. Theten metal sites are almost co-planar; the mean deviation from theplane is 0.23 Å, with the maximum deviation of 0.43 Å found forthe central metal site. The nine DyIII metal ions in the ring arearranged at the vertices of an approximately regular nonagon (orenneagon). The distances from the central Dy (Dy10) to the rim fallinto two groups; there are longer contacts to Dy2, Dy5 and Dy8,

Fig. 1 Crystal structure of 1. Colours: Dy, purple; P, green; O, red; C, grey.H-atoms and Me groups omitted for clarity.

a School of Chemistry and Photon Science Institute, The University of Manchester,


E-mail: [email protected]; Fax: +44 (0)161-275-1001b Department of Physics, The University of Bielefeld, Bielefeld, Germany

† Electronic supplementary information (ESI) available: Synthetic method, crys-tallographic details, crystallographic figures and magnetic information. CCDC972030. For ESI and crystallographic data in CIF or other electronic format seeDOI: 10.1039/c3cc48708c

Received 14th November 2013,Accepted 12th December 2013

DOI: 10.1039/c3cc48708c

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This journal is©The Royal Society of Chemistry 2014 Chem. Commun., 2014, 50, 1438--1440 | 1439

averaging 5.92 � 0.13 Å, while the remaining six contacts average5.47 � 0.12 Å. Eight of the distances between neighbouring Dycentres around the ring average 3.83 � 0.13 Å; the ninth contact(Dy1� � �Dy9) is longer at 4.1496(2) Å.

Three of the six phosphonates lie below the plane of the{Dy10} disc (P2, P4, P6) and adopt the 4.221 binding mode(Harris notation14); it is noticeable that these phosphonateschelate to the Dy sites that have the long contacts to the centraldysprosium. The remaining three phosphonates are above theplane of metal centres; two (P3 and P5) adopt the 3.111 bindingmode, while the third (P1) adopts 3.211 mode. This phosphonateremoves the three-fold symmetry of the cage, and it is the Dy1–Dy9edge bridged by a m2-oxygen from this phosphonate that is the longDy� � �Dy contact in the ring (see above). Each edge is also bridged bytwo pivalates, one with a 2.21 mode and the other with the 2.11mode. The Dy3� � �Dy4 edge is bridged by a m-hydroxide (Dy–Odistances of 2.308(12) and 2.294(11) Å) while the Dy6� � �Dy7 isbridged by a m-water (Dy–O distances 2.537(12) and 2.635(12) Å).

The central Dy10 site is six-coordinate, with a geometryapproaching octahedral. The Dy–O distances range from2.207(10) to 2.338(10) Å, with cis O–Dy–O angles between84.3(4) and 98.4(4)1 while trans O–Dy–O angles like between171.6(4) and 178.0(4)1. Dy1 is also six-coordinate, bound to twoO-donors from phosphonates and four from carboxylates. Dy2 toDy8 are eight coordinate, bound to two phosphonate oxygens, fiveO-atoms from pivalates, and a further oxygen either from aterminal water, a bridging water or a bridging hydroxide. Dy9 isalso eight coordinate bound to three phosphonate oxygens and fivecarboxylate oxygens. The oxo-centred [Co3(m3-O)(O2CtBu)6(py)3]+

cationic triangle features CoIII sites around a central m3-oxide(Fig. S1, ESI†). Each cobalt is bound to five O-donors, from thecentral oxide and 2.11 bridging pivalates (av. Co–O distance =1.89 Å), with a terminal pyridine (av. Co–N distance = 2.24 Å).

Direct-current magnetic susceptibility studies of polycrystal-line samples 1 and 2 were carried out in the temperature range2–300 K (Fig. 2). At room temperature the value of the productwMT (where wM is the molar magnetic susceptibility) is 135.0and 78.5 emu K mol�1 for 1 and 2 respectively. The value for 1 isclose to that calculated for ten non-interacting ions, while thatfor 2 is slightly lower than that calculated for ten independentGdIII sites (calc. wMT = 141.2 emu K mol�1 for ten DyIII ions,6H15/2, g = 4/3; calc. wMT = 77.9 emu K mol�1 for ten GdIII ions,8S7/2, g = 1.99). For 1 the wMT product gradually decreases untilaround 35 K and then decreases more rapidly. This behaviour istypical of DyIII complexes and is due to depopulation of the Starksub-levels.15 1 does not show slow relaxation of magnetisation.For 2, wMT remains fairly constant to 20 K before falling. The Mversus H/T data for 2 at low temperature show a rapid increase ofmagnetisation, reaching 69.6 mB at 7 T at 2 K, which is close tothe saturation value for ten S = 7/2 centres with g = 2.00 (69.8 mB,inset Fig. 2b). For 1, the M versus H/T curve increases graduallywith increasing field, reaching 52.2 mB at 7 T at 2 K withoutreaching saturation (Fig. S3, ESI†).

While it is presently impossible to model data for a {Dy10}cage, for the isotropic {Gd10} cage modern quasi approximatemethods allow us to model the magnetic data, despite the

enormous Hilbert space of (2S + 1)n where n = 10 is the numberof Gd centres; this yields 576650390625. We employ the Finite-Temperature Lanczos Method, which is a Krylov-space methodand has proven to be very accurate.16 We have chosen aHamiltonian with one exchange interaction around the ring( J1), and a second between the central Gd ion and those in thering ( J2), i.e. assuming an approximate C9 symmetry:

H ¼ �2J1X8i¼1

si � siþ1 þ s1 � s9

!� 2J2

X9i¼1

si � s10 þ gmBBSz;

where si denote individual spin operators at site i and Sz

denotes the z-component of the total spin operator. An excellentfit of the wMT vs. T and M vs. H data could be obtainedwith several parameter sets, all with both J1 and J2 very small(see Fig. S2, ESI,† for further simulations). The best parametersare J1 = �0.02, J2 = +0.01 cm�1. These numbers are barelydistinguishable from zero, however they would generate ahighly frustrated magnetic system, with the nine GdIII ionsaround the ring unable to align mutually anti-parallel with theirnearest neighbours. Unfortunately the extremely small exchangeinteractions mean that any interesting physics arising fromfrustration17 could only be seen at temperatures below 100 mK.

The large magnetisation value obtained for 2 and negligibleanisotropy of GdIII (8S7/2) makes this cluster a good candidatefor MCE applications (Fig. S3, ESI†). The magnetic entropychanges of 2 for changing applied field can be calculated by theMaxwell equation for magnetic entropy (qSm/dH)T = (qM(T,M)/qT)H where the integration for an isothermal process yieldsDS =

Ð[qM(T,H)/qT]H dH.18 This equation gives magnetic entropy

Fig. 2 (a) Variation of wMT with T for 1 and 2 in a magnetic field of 1000 Oein the temperature range 2 to 300 K; (b) magnetisation against field for 2from 0–7 T at 2 and 4 K, simulation and Brillouin function for 10 non-interacting GdIII ions.

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1440 | Chem. Commun., 2014, 50, 1438--1440 This journal is©The Royal Society of Chemistry 2014

change for 2 at 3 K and for a field changes DH = 0.5–7 T whichcorresponds to 28.5 J kg�1 K�1. Much higher values have beenreported for pure Gd-cages, for example 46.1 J kg�1 K�1 for a{Gd24} cage,19 and for 3D Gd-frameworks, e.g. 59 J kg�1 K�1 for[Gd(O2CH)3]n.20 The smaller value observed here must be due tothe weak antiferromagnetic interactions between the paramag-netic centres.

KZ thanks the KRG-Scholarship program in ‘‘Human CapacityDevelopment (HCDP)’’. EMP thanks the Panamanian agencySENACYT-IFARHU. J.S. thanks the Deutsche Forschungsgemein-schaft (SCHN/615-15) for continuous support. Supercomputing timeat the LRZ Garching is gratefully acknowledged. REPW thanks theRoyal Society for a Wolfson Merit Award.

Notes and references‡ Crystal data for 1 [C159H291Dy10Co3O72P6N3]: Mr = 5384.52, triclinic,space group P%1, T = 150.1(8) K, a = 20.7198(8) Å, b = 23.4541(9) Å, c =26.0799(15) Å, a = 105.194(4)1, b = 93.035(4)1, g = 103.129(3)1, V =11825.6(10) Å3, Z = 2, r = 1.512 g cm�3, total data = 65 089, independentreflections 41 489 (Rint = 0.0429), m = 3.432 mm�1, 2169 parameters, R1 =0.0903 for I Z 2s(I) and wR2 = 0.2570. Unit cell parameters for 2[C159H291Gd10Co3O72P6N3]: triclinic, a = 20.6870(4) Å, b = 23.3983(6) Å,c = 25.9194(7) Å, a = 104.844(2)1, b = 93.166(18)1, g = 103.3427(18)1, V =11716.4(5) Å3. The data were recorded on an Agilent SuperNova CCDdiffractometer with MoKa radiation (l = 0.71073 Å) The structure of 1was solved by direct methods and refined on F 2 using SHELXTL.

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14 Harris notation describes the binding mode as [X�Y1Y2Y3. . .Yn],where X is the overall number of metals bound by the whole ligand,and each value of Y refers to the number of metal atoms attached tothe different donor atoms. See ESI† and R. A. Coxall, S. G. Harris,D. K. Henderson, S. Parsons, P. A. Tasker and R. E. P. Winpenny,J. Chem. Soc., Dalton Trans., 2000, 2349.

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Cite this: Dalton Trans., 2013, 42, 14045

Received 1st August 2013,Accepted 16th August 2013

DOI: 10.1039/c3dt52086b

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Octametallic 4f-phosphonate horseshoes†

Karzan H. Zangana,a Eufemio Moreno Pineda,a Jürgen Schnackb andRichard E. P. Winpenny*a

Three octanuclear phosphonate clusters, formulated as

[Ln8(O3PtBu)6(µ3-OH)2(H2O)2(HO

iBu)(O2CtBu)12](NH3

iPr)2 (Ln =

Gd, Dy and Tb), were synthesised by refluxing a mixture of pivalic

acid (HO2CtBu), Ln(NO3)3·6H2O, tert-Butyl phosphonic acid

(H2O3PtBu) and isopropylamine (iPrNH2) in isobutyl alcohol

iBuOH.

There has been considerable recent interest in the synthesis ofmolecular complexes of phosphonates.1 This work has beendriven by the optimistic opinion that the tendency of phospho-nates to generate 2D-lattices2 could be used to produce mole-cular cage complexes with anisotropic structures. In turn, thismight produce compounds with highly anisotropic magneticproperties and hence produce new “single moleculemagnets”,3 i.e. paramagnets that show slow relaxation of mag-netisation. Some interesting compounds have appeared as aresult,4 and a wide range of metal cage compounds has beenreported, covering 3d-metal ions from vanadium(III)5 to copper(II).6

More recently, 3d–4f phosphonates have appeared,7 and havebeen studied as potential molecular magnetic refrigerantsusing the magnetocaloric effect (MCE).

Reports on homometallic 4f-phosphonates are morelimited, as lanthanide phosphonates have poor solubility inmost solvents, therefore it is difficult to obtain single crystalsappropriate for X-ray structural analysis. The first reportedlanthanide phosphonates where prepared by Mallouk and co-workers,8 who prepared a series of layered lanthanidealkylphosphonates.

Several routes are used to produce molecular 3d-metalphosphonates;1 all involve increasing solubility. Some routes

involve a co-ligand that binds competitively with the phospho-nate. For the co-ligand approach to work with lanthanides, wereasoned a simple oxygen donor would be ideal. Here wereport synthesis of three lanthanide phosphonates usingt-butylphosphonate combined with an excess of pivalic acid(HO2C

tBu), choosing both ligands to enhance solubility. Thenew compounds have been characterised by single-crystal X-raydiffraction and SQUID magnetometry.

A simple lanthanide salt, LnIII(NO3)3·6H2O (Ln = Gd, Tb,and Dy) was mixed with HO2C

tBu, H2O3PtBu and a mild base

iPrNH2 iniBuOH in the mole ratios 1 : 14 : 0.8 : 1 and the solu-

tion refluxed for three hours, i.e. the pivalate is in excess overthe phosphonate. After cooling to room temperature, crystalsformed from the reaction after four days in yields of 50–60%.X-ray structure determination shows the formation of com-pounds with the formula (NH3

iPr)2[Ln8(O3PtBu)6(µ3-OH)2(O2C

tBu)12-(H2O)2(HO

iBu)], where Ln = Gd 1, Tb 2, and Dy 3 (Fig. 1).Compounds 1–3‡ are isomorphous and crystallize in the tri-

clinic space group P1; we describe the structure of 3 as rep-resentative. The molecule contains eight lanthanides, sixphosphonates and twelve pivalates. The metal ion and phos-phonate core can best be described as consisting of a centraldistorted octahedron sharing two vertexes with two differentdistorted pyramids (Fig. 1c). The four DyIII atoms (Dy1, Dy2,Dy3, and Dy4) and the two phosphorous atoms (P1, P2) are inthe asymmetric unit and form the central octahedron. The twodistorted pyramids are linked to the central octahedron by twovertexes (Dy3, Dy4). One of the pyramids that connected to thecentral octahedron contains Dy4, Dy5, Dy6, P3 and P4, whilethe other pyramid is constructed from Dy3, Dy7, Dy8, P5 andP6. There are two µ3-hydroxide centred dysprosium trianglesformed by (Dy2, Dy4, Dy6) and (Dy1, Dy3, Dy7); each triangle issharing an edge with the distorted central octahedron andanother edge with the distorted pyramid.

The Dy⋯Dy distance in the edges of the triangles is ca.3.8 Å and the two µ3-OH groups are displaced about 0.82 Å outof the plane of the metal ions. The Dy⋯Dy distances withinthe central octahedron {Dy4P2} are in the range 3.6–4.9 Å,whereas the distances between dysprosium ions inside the two

†Electronic supplementary information (ESI) available: Synthetic method, crys-tallographic details and magnetic information. CCDC 953479–953481. For ESIand crystallographic data in CIF or other electronic format see DOI: 10.1039/c3dt52086b

aSchool of Chemistry and Photon Science Institute, The University of Manchester,


E-mail: [email protected]; Fax: +44-(0)161-275-1001bFaculty of Physics, University of Bielefeld, Universitätsstr. 25, D-33615 Bielefeld,

Germany

This journal is © The Royal Society of Chemistry 2013 Dalton Trans., 2013, 42, 14045–14048 | 14045

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distorted pyramids {Dy3P2} are in the range 3.9–5.3 Å. All DyIII

are eight-coordinate with a dodecahedral geometry.The phosphonates present two different coordination

modes, P1 and P2 binds four Dy with a 4.221 coordinationmode, whilst P3, P4, P5 and P6 adopt the 3.211 mode.9 Thereare twelve pivalates with 2.21, 2.11 and 1.11 binding modes,and they bridge the edges of the distorted pyramids andcentral octahedron. Two terminal water and one iBuOH mole-cules complete the coordination spheres for Dy3, Dy4 and Dy7respectively.

The magnetic behaviour of 1 to 3 has been studied on poly-crystalline samples (Fig. 2 and 3, and Fig. S1†). At room temp-erature in each case, the χMT (where χM is the molar magneticsusceptibility) value is smaller than the calculated value: for 1,observed 61.9 emu K mol−1 (calc. 63 emu K mol−1 for eight S =7/2, g = 2); for 2, observed 89.3 emu K mol−1 (calc. 94.5 emu Kmol−1 for eight J = 6, gJ = 3/2); for 3, observed 107.7 emu Kmol−1 (calc. 113 emu K mol−1 for eight J = 15/2, gJ = 4/3centres). Upon cooling, for 2 and 3 the product χMT plotdecreases with decreasing temperature until approximately

25 K. Below 25 K the product falls more rapidly; this indicatesdepopulation of the LnIII excited Stark sub-levels, and possiblyweak antiferromagnetic interactions between the Ln sites. For1, χMT remains constant to around 20 K (Fig. 2) before fallingrapidly to 42.2 emu K mol−1 at 2 K, indicating a paramagneticstate. A.c. susceptibility studies on the three compoundsshowed no significant frequency dependence of the out-of-phase susceptibility, χM″; therefore none of these compoundsare single molecule magnets.3

Magnetization (M) against field (H) measurements on 1 atlow temperatures (2 to 9 K) were also performed (Fig. 3). Themagnetization (M) reaches 53.7µB at 7 T at 2 K, this valueapproaches a saturation value for eight S = 7/2, g = 2 centres.This value is close to the saturation value for eight non-inter-acting GdIII ions, calculated from the Brillouin function(Fig. 3). For 2, there is a gradual increase in M vs. H curve withincreasing field, which reaches 35.7 emu K mol−1 at 7 T at 2 Kwithout reaching saturation (Fig. S2a†). For 3, the M vs. T plotrises progressively with rising H reaching 42.2 µB at 7 T at 2 Kwithout reaching saturation (Fig. S2b†).

Fig. 1 (a) The structure of compound 3 in the crystal (H-atoms omitted forclarity); (b) the core of 3 showing the phosphonate binding modes; (c) thelinked polyhedral representation of 3. Colours: Dy, purple; P, green; O, orange;C, grey.

Fig. 2 The product χT vs. T for 1–3 under 1 kG DC field. The red line is the fitusing parameters given in the text.

Fig. 3 M vs. H of 1 at the temperatures indication. Measured data are given assymbols, with the fit as solid lines. The Brillouin function for eight GdIII ions isshown by the five-pointed stars.

Communication Dalton Transactions

14046 | Dalton Trans., 2013, 42, 14045–14048 This journal is © The Royal Society of Chemistry 2013

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Due to the high magnetisation value obtained in 1 and asGdIII is an isotropic 8S7/2 ion, the magnetic entropy change wasstudied to examine whether 1 could be used for magneticcooling.10 The magnetic entropy changes of 1 for changingapplied field are calculated indirectly from the magnetizationbehaviour as a function of applied field and temperatures(Fig. S2†) by using the Maxwell relationship ΔS =

Ð[∂M(T,H)/

∂T]H dH. This equation gives the magnetic entropy change for1 at 3 K and for field changes ΔH = 0–7 T which correspondsto 32.3 J kg−1 K−1. To date, no magnetic entropy studies havebeen reported for 4f-phosphonate clusters. However, higherΔSm values have been reported previously for other lanthanideclusters.11

The maximum entropy value per mole can be calculatedusing equation nR ln(2S + 1) [n = 8 GdIII spins S = 7/2], by repla-cing n, S and R (gas constant) values in the equation the ΔSmvalue, equivalent to 16.64R which corresponds to 45.9 J kg−1 K−1.This value is much higher that the observed through magneticmeasurements. The difference between the theoretical and theexperimental value could be attributed to antiferromagneticinteractions.

As Gd(III) is an isotropic ion we can simulate the magneticdata. The Hilbert space for the problem has a challengingdimension of (2S + 1)n where n = 8 is the number of Gdcentres; this yields 16 777 216, but modern quasi exact approxi-mations allow us to examine the problem. We employ theFinite-Temperature Lanczos Method, which is a Krylov-spacemethod and has proven to be very accurate.12

In principle there are multiple exchange paths, but giventhe likelihood that all exchange interactions are small we haveset all nearest neighbour interactions as equivalent (Fig. 4)and fit the data with the Hamiltonian:

H ¼ �2X

i,j

Jij Si �Sj þ gμβBSz;

where Ŝi denote individual spin operators at site i and Ŝzdenotes the z-component of the total spin operator.

A very good overall representation of the data, compare Fig. 2and 3, is achieved when an exchange interaction of J =−0.03 cm−1 is assumed. This small value is typical of Gd⋯Gdexchange interactions.7f,13 The exchange interaction and the topo-logy of the cage means that the ground state is S = 0 albeit witha large number of paramagnetic excited states close in energy.

In conclusion, by using phosphonate as ligands threehorseshoe-shaped isostructural octametallic clusters have

been synthesised. The magnetic studies of the Gd8 clustershow that even small values for anti-ferromagnetic exchangecan have a large adverse effect on the MCE if the topology ofthe compound avoids spin frustration. Further work is in pro-gress to investigate new lanthanide-phosphonate cages usingdifferent phosphonates, including functionalised phosphonateligands.

Acknowledgements

KZ thanks the KRG-Scholarship program in “Human CapacityDevelopment (HCDP)”. EMP thanks the Panamanian agencySENACYT-IFARHU. JS thanks the Deutsche Forschungsgemein-schaft (SCHN/615-15) for continuous support. Supercomputingtime at the LRZ Garching is gratefully acknowledged. REPWthanks the Royal Society for a Wolfson Merit Award.

Notes and references

‡Crystal data for 1 [C94H195Gd8N2O47P6]: Mr = 3549.33, triclinic, space group P1,T = 150.01 K, a = 14.0956(4), b = 24.0968(7), c = 26.5567(8) Å, α = 76.758(2), β =74.883(2), γ = 82.741(2)°, V = 8455.2(4) Å3, Z = 2, ρ = 1.393 g cm−3, total data =47 337, independent reflections 34 034 [R(int) = 0.0380], µ = 3.208 mm−1, 1284parameters, R1 = 0.0640 for I ≥ 2σ(I) and wR2 = 0.1717. Crystal data for 2[C94H195Tb8N2O47P6]: Mr = 3562.79, triclinic, space group P1, T = 150.05 K, a =14.0342(7), b = 24.0928(11), c = 26.4594(12) Å, α = 76.727(4), β = 75.084(4), γ =82.955(4)°, V = 8394.9(7) Å3, Z = 2, ρ = 1.409 g cm−3, total data = 46 176, indepen-dent reflections 33 802 [R(int) = 0.0899), µ = 3.441 mm−1, 1206 parameters, R1 =0.0782 for I ≥ 2σ(I) and wR2 = 0.2034. Crystal data for 3 [C94H196Dy8N2O47P6]: Mr

= 3592.34, triclinic, space group P1, T = 128.35 K, a = 14.0658(3), b = 24.0994(6),c = 26.4957(6) Å, α = 76.637(2), β = 75.300(2), γ = 83.1827(19)°, V = 8435.1(4) Å3,Z = 2, ρ = 1.414 g cm−3, total data = 67 875, independent reflections 34 418 [R(int) =0.0407), µ = 3.614 mm−1, 1253 parameters, R1 = 0.0499 for I ≥ 2σ(I) and wR2 =0.1293. All three compounds crystallise with large solvent voids and the electrondensity in these voids has been handled using SQUEEZE.14

The magnetic properties in the temperature range 1.8 K–300 K were performedon polycrystalline samples either constrained in eicosane or powdered, using aQuantum Design MPMS-XL7 SQUID magnetometer armed with a 7 T magnet (seeESI† for more details).

1 K. Gopal, S. Ali and R. E. P. Winpenny, in Metal Phospho-nate Chemistry: From Synthesis to Applications, ed. A. Clear-field and K. Demadis, Royal Society of Chemistry,Cambridge, 2012, pp. 364–419.

2 A. Clearfield and K. D. Karlin, Prog. Inorg. Chem., 1998, 47,371.

3 G. Christou, D. Gatteschi, D. N. Hendrickson andR. Sessoli, MRS Bull., 2000, 25, 66.

4 (a) J. Wang, L.-P. Zhang, L. Huang and J. Chen, J. Coord.Chem., 2012, 65, 3274; (b) X. H. Bu, M. L. Tong,H. C. Chang, S. Kitagawa and S. R. Batten, Angew. Chem.,Int. Ed., 2004, 43, 192; (c) H. J. Park, D. W. Lim, W. S. Yang,T. R. Oh and M. P. Suh, Chem.–Eur. J., 2011, 17, 7251;(d) Y. F. Zeng, X. Hu, F. C. Liu and X. H. Bu, Chem. Soc.Rev., 2009, 38, 469; (e) M. G. O’Brien, A. M. Beale andB. M. Weckhuysen, Chem. Soc. Rev., 2010, 39, 4767;(f ) J. J. Perry, J. A. Perman and M. J. Zaworotko, Chem. Soc.Rev., 2009, 38, 1400; (g) X. L. Wang, C. Qin, S. X. Wu,

Fig. 4 Schematic sketch of the magnetic core of 1, lines denote exchangeinteractions, which for simplicity are assumed to be identical; the numbers corres-pond to the spin centres numbers as in Fig. 1.

Dalton Transactions Communication


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K. Z. Shao, Y. Q. Lan, S. Wang, D. X. Zhu, Z. M. Su andE. B. Wang, Angew. Chem., Int. Ed., 2009, 48, 5291;(h) X. L. Tong, T. L. Hu, J. P. Zhao, Y. K. Wang, H. Zhangand X. H. Bu, Chem. Commun., 2010, 46, 8543.

5 S. Khanra, M. Kloth, H. Mansaray, C. A. Muryn, F. Tuna,E. C. Sañudo, M. Helliwell, E. J. L. McInnes andR. E. P. Winpenny, Angew. Chem., Int. Ed., 2007, 46, 5568.

6 (a) V. Chandrasekhar and S. Kingsley, Angew. Chem., Int.Ed., 2000, 39, 2320; (b) V. Chandrasekhar, D. Sahoo,R. S. Narayanan, R. J. Butcher, F. Lloret and E. Pardo,Dalton Trans., 2013, 42, 8192; (c) V. Baskar,M. Shanmugam, E. C. Sanudo, M. Shanmugam,D. Collison, E. J. L. McInnes, Q. Wei andR. E. P. Winpenny, Chem. Commun., 2007, 37.

7 (a) V. Baskar, K. Gopal, M. Helliwell, F. Tuna,W. Wernsdorfer and R. E. P. Winpenny, Dalton Trans., 2010,39, 4747; (b) Y.-Z. Zheng, M. Evangelisti andR. E. P. Winpenny, Angew. Chem., Int. Ed., 2011, 50, 3692;(c) Y.-Z. Zheng, E. Moreno Pineda, M. Helliwell andR. E. P. Winpenny, Chem.–Eur. J., 2012, 18, 4161;(d) Y.-Z. Zheng, M. Evangelisti, F. Tuna andR. E. P. Winpenny, J. Am. Chem. Soc., 2012, 134, 1057;(e) E. M. Pineda, F. Tuna, R. G. Pritchard, A. C. Regan,Y.-Z. Zheng, R. E. P. Winpenny and E. J. L. Mclnnes, Chem.Commun., 2013, 49, 3522; (f ) T. N. Hooper, J. Schnack,S. Piligkos, M. Evangelisti and E. K. Brechin, Angew. Chem.,Int. Ed., 2012, 51, 4633.

8 G. Cao, V. M. Lynch, J. S. Swinnea and T. E. Mallouk, Inorg.Chem., 1990, 29, 2112.

9 Harris notation describes the binding mode as [XY1Y2…Yn]where X is the overall number of metal bound to the wholeligand, and each value of Y refers to the number of metalatoms attached to the different donor atoms. See:R. A. Coxall, S. G. Harris, D. K. Henderson, S. Parsons,P. A. Tasker and R. E. P. Winpenny, Dalton Trans., 2000,2349.

10 M. Evangelisti, F. Luis, L. J. Jongh and M. Affronte,J. Mater. Chem., 2006, 16, 2534.

11 (a) J. W. Sharples, Y.-Z. Zheng, F. Tuna, E. J. L. McInnesand D. Collison, Chem. Commun., 2011, 47, 7650;(b) R. J. Blagg, F. Tuna, E. J. McInnes andR. E. P. Winpenny, Chem. Commun., 2011, 50, 3692;(c) M. Evangelisti, O. Roubeau, E. Palacios, A. Camon,T. N. Hooper, E. K. Brechin and J. J. Alonso, Angew. Chem.,Int. Ed., 2011, 50, 6606; (d) F.-S. Guo, J.-D. Leng, J.-L. Liu,Z.-S. Meng and M.-L. Tong, Inorg. Chem., 2012, 51, 405.

12 (a) J. Jaklič and P. Prelovšek, Phys. Rev. B: Condens. Matter,1994, 49, 5065; (b) J. Schnack and O. Wendland, Eur.Phys. J. B, 2010, 78, 535.

13 Y. Zheng, Q.-C. Zhang, L.-S. Long, R.-B. Huang, A. Müller,J. Schnack, L.-S. Zheng and Z. Zheng, Chem. Commun.,2013, 49, 36.

14 P. van der Sluis and A. L. Spek, Acta Crystallogr., Sect. A:Fundam. Crystallogr., 1990, 46, 194.



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DaltonTransactions

COMMUNICATION

Cite this: Dalton Trans., 2014, 43,3035

Received 26th August 2013,Accepted 30th September 2013

DOI: 10.1039/c3dt52337c

www.rsc.org/dalton

Fast magnetic relaxation in an octahedraldysprosium tetramethyl-aluminate complex†

Sonja N. König,a Nicholas F. Chilton,b Cäcilia Maichle-Mössmer,a

Eufemio Moreno Pineda,b Thomas Pugh,b Reiner Anwander*a andRichard A. Layfield*b

Ab initio calculations on the octahedral dysprosium aluminate

complex [Dy(AlMe4)3] (1) predict weak SMM properties. Dynamic

magnetic susceptibility measurements on 1 confirm the theoretical

predictions, revealing fast relaxation of the magnetization via

quantum tunnelling.

Complexes of dysprosium have attracted considerable interestin the last decade owing to their potential single-moleculemagnet (SMM) properties.1 Notwithstanding the fundamentalinterest in the dynamic magnetic properties of lanthanide (Ln)SMMs, these materials are also being developed for elegantapplications as spin-based devices.2 Whereas the literature isreplete with experimental studies of Ln-SMMs,3 detailedunderstanding of the underlying theory has evolved at a some-what slower rate, largely due to the complexity of the electronicstructure of the lanthanides.4 Factors, such as the nature ofthe crystal field, intra- and inter-molecular exchange, andhyperfine interactions are believed to play important rolesin determining the effective energy barrier to reversal of themagnetization (the anisotropy barrier, Ueff ) and the magneticblocking temperature.

Significant effort has been invested into understanding theinfluence of crystal field symmetry on the magnitude of theanisotropy barrier in Ln-SMMs. Monometallic Ln-SMMs (orsingle-ion magnets, SIMs), particularly the large family ofphthalocyanine-ligated SMMs,5 have furnished considerableinsight into this phenomenon. In SIMs based on terbium(III)and dysprosium(III), ligands that produce strong axial poten-tials with high-order principal molecular symmetry axes(n ≥ 4) are thought to increase the separation between theground-state and first-excited mJ sub-levels, which is

significant because this energy gap can be correlated withUeff.

6 The appeal of this symmetry-based approach is itssimplicity, however detailed theoretical studies have suggestedthat the orientation of the magnetic anisotropy does notnecessarily coincide with the principal molecular symmetryaxis.7 Key finding such as this have important implications forthe design and synthesis of Ln-SMMs.

We now investigate the electronic structure of an octahedralorgano-dysprosium complex, [Dy(AlMe4)3] (1), using ab initiocalculations and dynamic magnetic susceptibility measure-ments. Our study provides further insight into the potentialconflicts between the orientation of the molecular symmetryaxis and that of the anisotropy axis, and into the impact ofoctahedral crystal fields on SMM properties.

Complex 1 was synthesized according to a previouslyreported method (Scheme 1),8 and single crystals suitablefor X-ray diffraction were obtained by storing a concentratedhexane solution at −30 °C overnight. Complex 1 crystallizes inthe space group P21/c and has two unique molecules in theasymmetric unit, 1a and 1b, which are essentially isostruc-tural. In the case of 1a (Fig. 1), the coordination geometry ofDy(1) is slightly distorted octahedral, with Dy–C bond dis-tances of 2.512(3)–2.540(3) Å (average 2.526 Å). Complex 1apossesses two types of cis C–Dy–C angles, those within eachtetramethylaluminate ligand and those between each pair ofligands. The former type of cis angles are 84.28(9)–84.75(9)°,and the latter are slightly wider at 90.40(9)–93.14(10)° (average91.9°). The trans C–Dy–C angles are in the range 173.23(10)–175.45(10)°. The bond lengths and angles in 1b are verysimilar to those in 1a (Table S2, Fig. S1†). The metric para-meters in 1a and 1b indicate that the coordination geometry of

Scheme 1

†Electronic supplementary information (ESI) available: Synthetic, computationaland magnetic measurement details. Crystallographic details in .cif format.CCDC 954825. For ESI and crystallographic data in CIF or other electronicformat see DOI: 10.1039/c3dt52337c

aInstitut für Anorganische Chemie, Universität Tübingen, Auf der Morgenstelle 18,

D-72076 Tübingen, Germany. E-mail: [email protected] of Chemistry, The University of Manchester, Oxford Road, Manchester, UK.

E-mail: [email protected]


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each dysprosium ion deviates from ideal octahedral. The devi-ations take the form of slight compressions along the mole-cular three-fold symmetry axis, which is defined as beingperpendicular to the plane of the aluminium atoms andpassing through dysprosium. The deviation from octahedralgeometry can be quantified by calculating a continuous shapemeasure for 1a and 1b, which produced values of 0.267 and0.241, respectively, indicating small deviations from octahedralsymmetry.9 The shortest intermolecular Dy⋯Dy distanceis 8.64 Å.

Ab initio calculations on 1a and 1b were carried out to deter-mine the g-tensors and the relative energies of the Kramers’doublets in the 6H15/2 ground state of Dy(III) (Fig. 2 and S3, andTables S3 and S4†). Ultimately, the information derived fromthe calculations can be used as a tool to assess the likely per-formance of 1 as an SMM. The calculations used the crystallo-graphically determined atomic coordinates and wereperformed using the CASSCF/CASSI approach in MOLCAS7.8.†10

The results of the calculations for 1a and 1b are similar,with the energy spectrum for the electronic ground term of 1aspanning 359 cm−1 and that of 1b spanning 336 cm−1

(Tables S3 and S4†). The individual g-tensors of the lowesteight Kramers’ doublets are also broadly in agreement, aswould be expected on the basis of the similar molecular struc-tures. The g-tensors in the ground doublets in 1a (gx = 0.10,gy = 3.04, gz = 15.73) and 1b (gx = 0.03, gy = 0.55, gz = 18.41) arestrongly axial, but they both depart significantly from the Isinglimit of gz = 20 with gx = gy = 0, by displaying significant trans-verse anisotropies, particularly for 1a. Significantly, the orien-tation of the magnetic moment in each complex does not

coincide with the molecular three-fold axis, but is almost per-pendicular to it. This result is similar to that reported recentlyfor [Na{Dy(DOTA)}] (H4DOTA = 1,4,7,10-tetraazacyclododecane-N,N′,N″,N′′′-tetraacetic acid), for which the anisotropy axis wasdetermined by ab initio calculations and by magnetic measure-ments on oriented single crystals.7 Furthermore, the principalaxes of the first excited doublets of 1a and 1b are oriented atangles of 38.7 and 63.1° relative to their respective ground-state axes. The lack of uniaxiality, the significant transverseanisotropies and the small energy gaps to the first excited stateof only 10.9 and 19.9 cm−1 for 1a and 1b, respectively, suggestthat complex 1 is unlikely to be an SMM.

To test the hypothesis developed with the aid of ab initiocalculations, magnetic susceptibility measurements werecarried out on polycrystalline samples of 1. The susceptibilitymeasurements in a static (dc) field are unremarkable. At 300 Kin an applied field of Hdc = 1000 Oe, χMT = 13.8 cm3 K mol−1

(χM is the molar magnetic susceptibility), and the value of χMTvaries only slightly with decreasing temperature until about25 K, when a more rapid decrease occurs and a value of7.6 cm3 K mol−1 is reached at 1.8 K (Fig. S5†). The rapiddecrease at low temperatures is likely to be due to thermaldepopulation of the mJ sub-levels within the ground multiplet.The absence of SMM behaviour in 1 was confirmed bydynamic (ac) susceptibility measurements in zero applied field(Hdc = 0) and a small oscillating field of Hac = 1.55 Oe, atvarious ac frequencies in the range ν = 1–1202 Hz (Fig. S6–S9†). The in-phase susceptibility (χ′) as a function of tempera-ture does not vary with varying ac frequency. The out-of-phase(χ″) susceptibility as a function of temperature does show aslight frequency dependence below about 15 K, however nomaxima were observed. In an attempt to reduce the quantumtunnelling of the magnetization (QTM) in 1, a static field of1000 Oe was applied and the temperature dependence of χ′

and χ″ were re-examined. The effects of the applied field wereto change the χ′(T ) and χ″(T ) profiles, but once again χ′(T )shows no significant frequency dependence.

Whereas the χ″(T ) plots do show maxima in the appliedfield, these data are also frequency independent. Furthermore,in an applied field, the maxima in the plots of χ″(ν) at varioustemperatures are positioned at the same frequency (Fig. 3),suggesting a resonant QTM process. The lack of temperature-and frequency dependent ac susceptibility indicate that the

Fig. 1 Molecular structure of 1a with thermal ellipsoids at 50%. Hydro-gen atoms not shown.

Fig. 2 Calculated orientation of the magnetic moments of the ground(blue rod) and the first-excited (red rod) Kramers’ doublets in 1a.

Fig. 3 χ’’(ν) for undiluted 1 at various temperatures with Hdc = 1000 Oe.



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magnetic blocking in 1 is inefficient, and that the QTM israpid.

To investigate the possibility that local dipolar fieldsinduced by neighbouring Dy(III) centres might provide apathway for relaxation of the magnetization in 1, magneticmeasurements of 1 doped into the isostructural diamagnetichost lattice of [Y(AlMe4)3] (Dy : Y of 1 : 20) were also conducted(Fig. S10–S12†). With Hdc = 1000 Oe, slow relaxation wasobserved below 3 K over a narrow temperature range, and theχ″(ν) data feature maxima that shift to higher frequenciesas the temperature is increased from 1.8 to 2.3 K (Fig. 4).These data allow an estimate of the anisotropy barrier usingthe Arrhenius relationship τ = τ0 exp(Ueff/kBT ), which producedUeff ≈ 10 cm−1 with τ0 ≈ 2.9 × 10−7 s (Fig. S13†). The value ofUeff should be treated with caution owing to the limitednumber of data points available for the calculation, althougheven allowing for error the actual anisotropy barrier is certainlyvery small. However, the key conclusion from the dilutionexperiments is that dipolar interactions do contribute tothe QTM in 1. The anisotropy barrier determined for 1 issimilar to the calculated energy gaps between the groundand first-excited Kramers’ doublets for 1a and 1b, howeverthe single relaxation process can be cautiously assigned to1b because of the smaller transverse g values. The magnitudeof the Ueff value may indicate that the magnetization of1 relaxes via an Orbach mechanism involving the groundand first excited states, although the wide range of α

parameters derived from the Cole–Cole plots of χ′ vs. χ″ (0.2 <α < 0.33) imply a broad distribution of relaxation times(Fig. S14†).

Six-coordinate lanthanide complexes for which SMM behav-iour and/or field-induced slow relaxation have been observedare known yet uncommon.11 Small anisotropy barriers, similarto that of 1, have also been reported for dysprosium complexeswith other coordination numbers.12 An elegant explanation forthe apparent unsuitability of Oh crystal field symmetry for Ln-SMM applications has recently been developed by Chibotaruet al., who studied a model complex with idealized octahedralgeometry and strict Oh symmetry.13 Unsurprisingly, the calcu-lations produce completely isotropic g-tensors, i.e. gx = gy = gz =6.57, and the non-axial crystal field parameters are similar to,or even larger than, the axial parameters. High symmetry and

a lack of anisotropy are therefore thought to enable efficientQTM in strictly octahedral lanthanide complexes.

Extending this rationale to 1, although there is a significantaxial component to the g-tensor, the symmetry of the crystalfield generated by the three [AlMe4]

− ligands is evidently closeenough to octahedral to introduce an appreciable transversecomponent, and thus enable QTM.

Conclusions

Dynamic magnetic susceptibility measurements on the slightlydistorted octahedral complex [Dy(AlMe4)3] (1) reveal no temp-erature- or frequency-dependence. Magnetic dilution studiesreveal that intermolecular Dy⋯Dy interactions make a con-tribution to the QTM, but also that the QTM is a prominentfundamental property of individual molecules of 1. The ac sus-ceptibility data also confirmed the reliability of the predictionsmade by ab initio calculations on 1. The calculations showthat, although 1a and 1b possess significant axial anisotropy,the transverse components are non-negligible. The calculatedenergy gaps between ground and first-excited mJ sub-levelsare small, and indeed these energies are consistent withthe anisotropy barrier estimated from magnetic dilutionexperiments.

Acknowledgements

The authors acknowledge the EU COST Action ‘Europeanf-Element Network’ for funding a Short-Term ScientificMission. We also acknowledge financial support from theEPSRC.

The authors acknowledge the EPSRC UK National Service forComputational Chemistry Software (NSCCS) at ImperialCollege London. NFC thanks The University of Manchester fora President’s Doctoral Scholarship.

Notes and references

1 (a) P. Zhang, Y. N. Guo and J. Tang, Coord. Chem. Rev.,2013, 257, 1728; (b) D. N. Woodruff, R. E. P. Winpenny andR. A. Layfield, Chem. Rev., 2013, 113, 5110; (c) F. Habib andM. Murugesu, Chem. Soc. Rev., 2013, 42, 3278; (d) J. Luzonand R. Sessoli, Dalton Trans., 2012, 41, 13556.

2 (a) M. Ganzhorn, S. Klyatskaya, M. Ruben andW. Wernsdorfer, ACS Nano, 2013, 7, 6225; (b) R. Vincent,S. Klyatskaya, M. Ruben and W. Wernsdorfer, Nature, 2012,488, 357; (c) T. Komeda, H. Isshiki, J. Liu, K. Katoh,M. Shirakata, B. K. Breedlove and M. Yamashita, ACS Nano,2013, 7, 1092.

3 (a) J. D. Rinehart, M. Fang, W. J. Evans and J. R. Long,J. Am. Chem. Soc., 2011, 133, 14236; (b) J. D. Rinehart,M. Fang, W. J. Evans and J. R. Long, Nat. Chem., 2011, 3,538; (c) F. Tuna, C. A. Smith, M. Bodensteiner, L. Ungur,L. F. Chibotaru, E. J. L. McInnes, R. E. P. Winpenny,

Fig. 4 χ’’(ν) for magnetically dilute 1 (Dy : Y = 1 : 20), at various tempera-tures and with Hdc = 1000 Oe.

Dalton Transactions Communication


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D. Collison and R. A. Layfield, Angew. Chem., Int. Ed., 2012,52, 6976; (d) S. A. Sulway, R. A. Layfield, F. Tuna,W. Wernsdorfer and R. E. P. Winpenny, Chem. Commun.,2012, 48, 1508; (e) R. J. Blagg, L. Ungur, F. Tuna, J. Speak,P. Comar, D. Collison, W. Wernsdorfer, E. J. L. McInnes,L. F. Chibotaru and R. E. P. Winpenny, Nat. Chem., 2013, 5,673; (f ) S. K. Langley, N. F. Chilton, B. Moubaraki andK. S. Murray, Chem. Commun., 2013, 49, 6965;(g) R. A. Layfield, J. J. W. McDouall, S. A. Sulway, F. Tuna,D. Collison and R. E. P. Winpenny, Chem.–Eur. J., 2012, 16,4442; (h) A. Venugopal, F. Tuna, T. P. Spaniol, L. Ungur,L. F. Chibotaru, J. Okuda and R. A. Layfield, Chem.Commun., 2013, 49, 901.

4 (a) L. Sorace, C. Benelli and D. Gatteschi, Chem. Soc. Rev.,2011, 40, 3092; (b) L. Ungur, S. K. Langley, T. N. Hooper,B. Moubaraki, E. K. Brechin, K. S. Murray andL. F. Chibotaru, J. Am. Chem. Soc., 2012, 134, 18554.

5 (a) N. Ishikawa, M. Sugita, T. Ishikawa, S. Koshihara andY. Kaize, J. Am. Chem. Soc., 2003, 125, 8694; (b) N. Ishikawa,Struct. Bonding (Berlin), 2010, 135, 211; (c) C. R. Ganivet,B. Ballesteros, G. de la Torre, J. M. Clemente-Juan,E. Coronado and T. Torres, Chem.–Eur. J., 2013, 19, 1457.

6 J. D. Rinehart and J. R. Long, Chem. Sci., 2011, 2, 2078.7 (a) G. Cucinotta, M. Perfetti, J. Luzon, M. Etienne,

P. E. Car, A. Caneschi, G. Calvez, K. Bernot and R. Sessoli,Angew. Chem., Int. Ed., 2012, 51, 1606; (b) M. E. Boulon,G. Cucinotta, J. Luzon, C. Degl’Innocenti, M. Perfetti,K. Bernot, G. Calvez, A. Caneschi and R. Sessoli, Angew.Chem., Int. Ed., 2013, 52, 350.

8 (a) W. J. Evans, R. Anwander and J. W. Ziller, Organometal-lics, 1995, 14, 1107; (b) G. Occhipinti, C. Meermann,H. M. Dietrich, R. Litlabø, F. Auras, K. W. Törnroos,C. Maichle-Mössmer, V. R. Jensen and R. Anwander, J. Am.Chem. Soc., 2011, 133, 6323.

9 S. Alvarez, P. Alemany, D. Casanova, J. Cirera, M. Llunelland D. Avnir, Coord. Chem. Rev., 2005, 249, 1693.

10 (a) G. Karlström, R. Lindh, P. Å. Malmqvist, B. O. Roos,U. Ryde, V. Veryazov, P. O. Widmark, M. Cossi,B. Schimmelpfennig, P. Neogrady and L. Seijo, Comput.Mater. Sci., 2003, 28, 222; (b) V. Veryazov, P. Widmark,L. Serrano-Andrés, R. Lindh and B. O. Roos, Int. J. QuantumChem., 2004, 100, 626; (c) F. Aquilante, L. De Vico, N. Ferré,G. Ghigo, P. Malmqvist, P. Neogrády, T. B. Pederson,M. Pitoňák, M. Reiher, B. O. Roos, L. Serrano-Andrés,M. Urban, V. Veryazov and R. Lindh, J. Comput. Chem.,2010, 31, 224.

11 (a) D. N. Woodruff, F. Tuna, M. Bodensteiner,R. E. P. Winpenny and R. A. Layfield, Organometallics, 2013,32, 1224; (b) J. L. Liu, K. Yuan, J. D. Leng, L. Ungur,W. Wernsdorfer, F. S. Guo, L. F. Chibotaru and M. L. Tong,Inorg. Chem., 2012, 51, 8538.

12 (a) M. Menelaou, F. Ouharrou, L. Rodríguez, O. Roubeau,S. J. Teat and N. Aliaga-Alcade, Chem.–Eur. J., 2012, 18,11545; (b) D. Li, X. Zhang, T. Wang, B. Ma, C. Li, Y. Li andX. You, Chem. Commun., 2011, 47, 6867.

13 J. L. Liu, Y. C. Chen, Y. Z. Zheng, W. Q. Lin, L. Ungur,W. Wernsdorfer, L. F. Chibotaru and M. L. Tong, Chem.Sci., 2013, 4, 3310.



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Transmetalation of Chromocene by Lithium-Amide, -Phosphide, and-Arsenide NucleophilesSabine Scheuermayer,† Floriana Tuna,‡,§ Eufemio Moreno Pineda,‡,§ Michael Bodensteiner,†

Manfred Scheer,*,† and Richard A. Layfield*,†,‡

†Institute of Inorganic Chemistry, University of Regensburg, Germany D-93040‡School of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, U.K.§EPSRC U.K. National EPR Facility, Photon Science Institute, The University of Manchester, Oxford Road, Manchester, M13 9PL,U.K.


ABSTRACT: The pnictogen-centered nucleophiles LiE-(SiMe3)2 (E = N, P, or As) substitute a cyclopentadienideligand of chromocene (Cp2Cr), with elimination of lithiumcyclopentadienide, to give the series of pnictogen-bridgedcompounds [(μ:η2:η5-Cp)Cr{μ-N(SiMe3)2}2Li] (1) and [(η5-Cp)Cr{μ-E(SiMe3)2}]2, with E = P (2) or E = As (3). Whereas 1 is a heterobimetallic coordination polymer, 2 and 3 arehomometallic dimers, with the differences being due to a structure-directing influence of the hard or soft character of the bridginggroup 15 atoms. For compound 1, the experimental magnetic susceptibility data were accurately reproduced by a single-ionmodel based on high-spin chromium(II) (S = 2), which gave a g-value of 1.93 and an axial zero-field splitting parameter of D =−1.83 cm−1. Determinations of phosphorus- and arsenic-mediated magnetic exchange coupling constants, J, are rare: in thedimers 2 and 3, variable-temperature magnetic susceptibility measurements identified strong antiferromagnetic exchange betweenthe chromium(II) centers, which was modeled using the spin Hamiltonian H = −2J(SCrA·SCrB), and produced large couplingconstants of J = −166 cm−1 for 2 and −77.5 cm−1 for 3.

■ INTRODUCTION

Exchange coupling interactions between transition metal ionsare of fundamental importance in molecular magnetism.1 Suchinteractions have been studied extensively for over half acentury following the pioneering work of Bleaney and Bowerson copper(II) acetate dimers,2 and they have recently taken onadditional significance with the development of transition metalsingle-molecule magnets.3 With the notable exception ofthiolate ligands,4 the use of ligands with soft donor atoms inmolecular magnetism is uncommon, and exchange couplingmediated by phosphorus- and, particularly, arsenic-donorligands has not been investigated to any significant extent.The potential benefits of exploring the influence of, forexample, phosphide and arsenide ligands (R2E

−, E = P or As)on the magnetic properties of transition metal ions washighlighted by our study of the manganese(II) dimers[CpMn{μ-E(SiMe3)2}]2 (E = P or As, Cp = cyclopentadienyl),in which spin-crossover (SCO) and simultaneous antiferro-magnetic coupling were identified.5 In the case of the arsenic-bridged compound [CpMn{μ-E(SiMe3)2}]2, the magneticsusceptibility measurements revealed a two-step SCO fromthe S = 5/2 to the S = 3/2 spin states of the two manganese(II)ions, and the first SCO step around 96−105 K even showedhysteresis. Also noteworthy was that the antiferromagneticexchange coupling in the P-bridged dimer, although weak with J= −13.5 cm−1, was almost an order of magnitude stronger thanin the As-bridged analogue, with J = −1.5 cm−1. A recent study

by Wright and co-workers on the reaction of manganocenewith t-butylphosphine observed formation of the dimer[CpMn(PtBuH2)(μ-P

tBuH)]2, in which the introduction ofstronger-field primary phosphine and μ-phosphido ligands ledto a high-spin to low-spin switch of the manganese(II) ions,with concomitant formation of an unusual Mn−Mn bond.6

Thus, there is growing evidence that soft group 15 donoratoms can influence the electronic structure of transition metalions in unusual ways. To develop our understanding ofmagnetic exchange between transition metal ions mediated bynitrogen and, in particular, by phosphorus and arsenic, we nowturn our attention to chromium(II). Chromium(II) wastargeted because chromocene, Cp2Cr, shows similar reactivityto manganocene with respect to Cp ligand substitution bystrong nucleophiles; hence a series of isostructural andtherefore comparable compounds could be accessible. Anadditional reason for selecting chromium(II) is that studies ofexchange-coupled compounds based on this ion are surprisinglyrare. Thus, we report the synthesis, structures, and magneticproperties of the chromium−lithium amido coordinationpolymer [CpCr{μ-N(SiMe3)2}2Li]∞ (1), and the phosphorus-and arsenic-bridged chromium(II) dimers [CpCr{μ-E-(SiMe3)2}]2, with E = P (2) and E = As (3). The chromium(II)ions in the dimers 2 and 3 are coupled by strong

Received: November 26, 2012Published: March 11, 2013

Article

pubs.acs.org/IC

© 2013 American Chemical Society 3878 dx.doi.org/10.1021/ic3025815 | Inorg. Chem. 2013, 52, 3878−3883



antiferromagnetism, and modeling of the magnetic suscepti-bility data enabled J coupling constants for phosphorus- andarsenic-mediated exchange to be determined for only thesecond time.

■ SYNTHESIS AND STRUCTURES OF 1−3Compounds 1−3 were synthesized by exploiting the tendencyof cyclopentadienyl ligands in “electron deficient” metallocenesto be substituted by strong nucleophiles. Thus, 16-electronCp2Cr reacts with the lithium complexes of bis(trimethylsilyl)-amide, -phosphide, and -arsenide, LiE(SiMe3)2 (E = N, P, As),with elimination of CpLi, according to Scheme 1. Thestructures of 1−3 were determined by X-ray diffraction.

The outcome of the reaction that results in the formation of1 is the same when the ratio of Cp2Cr to LiN(SiMe3)2 is 1:2 or1:1. Two unique molecules of [(μ:η2:η5-Cp)Cr{μ-N-(SiMe3)2}2Li] are found in the unit cell (1a and 1b), whichassemble into coordination polymers, that is, [1a]∞ and [1b]∞,through μ:η2:η5-bridging modes of the Cp ligand (Figure 1 and

Supporting Information, Figure S1). In 1a, the η5-coordinationof the Cp ligand to Cr(1) produces Cr−C bond distances inthe range 2.359(5)−2.401(4) Å (average 2.381 Å), and theCr(1)−N(1) and Cr(1)−N(2) bond lengths are 2.0926(17)and 2.1025(19) Å, respectively (Table 1). Assuming that an η5-Cp ligand occupies three coordination sites, the chromium(II)centers in 1 are five-coordinate and have formal valenceelectron counts of 14. The Li(1)−N(1) and Li(1)−N(2) bondslengths are 2.079(4) and 2.065(4) Å, respectively, and therhombic shape of the CrN2Li ring is reflected in the N−Cr−N,N−Li−N, Cr−N(1)−Li, and Cr−N(2)−Li angles of 96.28(7),97.9(2), 82.86(13), and 82.96(13)°. Molecules of 1a (and 1b)therefore have approximate C2v point symmetry, although theslight differences in bond lengths show that the two “halves” ofthe molecule are not strictly symmetry-related. The tworelatively short Li−C distances of 2.592(6) and 2.655(6) Å,compared to three much longer distances in the range3.399(4)−3.769(6) Å, are within the upper limit of Li−Cdistances recorded in the Cambridge Structural Database(CSD) for lithium cyclopentadienides,7 suggesting that thebridging interaction between nearest neighbor molecules of 1a(and 1b) can be described as μ:η2-Cp. The 1H NMR spectrumof 1 recorded in toluene-D8 confirms the presence of the Cpligand (δ = 23.41 ppm); however, a sharp resonance at δ = 1.55ppm and a broad resonance at 2.85 ppm, likely due to thetrimethylsilyl groups, were also observed (Supporting Informa-tion, Figure S2). The 7Li NMR spectrum of 1 in toluene-D8(Supporting Information, Figure S3) features a weak, broadresonance with a chemical shift of δ = 140.3 ppm: this issubstantially downfield relative to the 7Li chemical shiftsreported for [Li{N(SiMe3)2}] in various solvents and at variousconcentrations, which are typically in the range of δ ≈ ± 1ppm.8 The position and appearance of 7Li resonance inparticular suggests that a paramagnetic lithium-containingcomplex is present in solution, although there is no directevidence to suggest that the solid-state structure of 1 ispreserved in toluene solution.As with compound 1, the syntheses of 2 and 3 were achieved

using chromium:pnictogen ratios of 1:1 or 1:2. X-raycrystallography revealed that the molecular structures of 2and 3 are very similar, each consisting of pnictogen-bridgeddimers with the general formula [(η5-Cp)Cr{μ-E(SiMe3)2}]2(E = P or As). The dimers have molecular D2h symmetry, andthe {CpCrE2} coordination environments have approximateC2v symmetry (Figures 2, Supporting Information, Figures S4,S6), and each chromium(II) in 2 and 3 is formally five-coordinate and has a valence electron of 14, as in 1.The phosphide-bridged dichromium compound [CpCr{μ-

P(SiMe3)2}]2 (2) crystallizes with two independent moleculesin the unit cell, 2a and 2b, which are iso-structural (Figures 2,Supporting Information, Figure S4). The structure of 2a is adimer in which the two Cr(II) atoms are bridged by two μ-[(Me3Si)2P]

− ligands. The resulting Cr(1)−P(1) and Cr(1)−P(1A) bond lengths are 2.3814(9) and 2.3864(9) Å,respectively, and the P−Cr−P and Cr−P−Cr bond angles are99.98(3) and 80.02(3)° (Table 1). A search of the CSD formolecular structures containing cyclic {Cr2(μ-P2)} structuralunits reveals Cr−P bond distances in the range 2.254−2.763 Å,with the mean average of 2.407 Å being similar to the Cr−Pdistances in 2a and 2b.7 The cyclopentadienyl ligands in 2a areη5-coordinated to the chromium atoms, with Cr−C distances inthe range 2.276(17)−2.33(2) Å (average 2.292 Å). TheCr(1)···Cr(1A) separation in 2a is 3.066(1) Å (3.086 Å in 2b).

Scheme 1. Synthesis of 1−3 (R = SiMe3)

Figure 1. Thermal ellipsoid plot (30% probability) of the molecularstructure of 1a, and a segment of the coordination polymer structureof [1a]∞. Unlabeled atoms are carbon (black) and silicon (gray).


dx.doi.org/10.1021/ic3025815 | Inorg. Chem. 2013, 52, 3878−38833879



The arsenide-bridged dichromium compound [CpCr{μ-As(SiMe3)2}]2 (3) also crystallizes with two iso-structuralmolecules in the unit cell, 3a and 3b, (Figure 2, SupportingInformation, Figure S6). The Cr(1)−As(1) and Cr(1)−As(1A)distances in 3a are 2.4963(5) and 2.4992(5) Å, which result in amuch longer Cr(1)···Cr(1A) separation of 3.394(1) Å(3.419(1) Å in 3b) compared to 2a/2b. The Cr−C bondlengths in 3a are 2.270(11)−2.327(11) Å (average 2.295 Å),and As−Cr−As and Cr−As−Cr bond angles of 94.41(2)° and85.59(1)°, respectively, were found in 3a. Surprisingly, very fewarsenide-bridged dichromium compounds have been structur-ally characterized: the example most closely related to 3 is themetal−metal bonded dichromium(I) compound [Cr(μ-AsMe2)(CO)4]2, which features a Cr−As distance of 2.421(2)Å.9 The Cr(1)···Cr(1A) distances of 3.066(1) Å and 3.394(1)Å in 2a and 3a, respectively, (and the analogous distances in 2band 3b, Table 1) lie within the range of chromium−chromiumbond distances according to the CSD: range 1.858−3.471 Å,average 2.761 Å, standard deviation 0.218 Å.7 However,whereas the Cr···Cr distances in 2a and 2b are considerablyless than the upper limit of a chromium−chromium bond, thedistances in 3a and 3b are close to the upper limit. Althoughthe possibility of Cr−Cr bonding in 2a and 2b in particularcannot be completely discounted based on X-ray crystallog-raphy, the magnetic susceptibility measurements on bulksamples of 2 suggest that the chromium(II) centers areexchange coupled via the phosphide bridge and are not directlybonded to each other (see below). The solution-phase 1HNMR spectra of 2 and 3 in benzene-D6 are consistent with theempirical formula [CpCr{E(SiMe3)2}], with broad resonancesfor the Cp environment being observed at 98.81 ppm in 2 and34.01 ppm in 3, and the trimethylsilyl environments occurringwith chemical shifts of 3.35 ppm and 2.38 ppm in 2 and 3,respectively (Supporting Information, Figures S5 and S7).The only variable in the reactions that produce 1−3, and

hence results in the structure of 1 being different to that of theisostructural dimers 2 and 3, is the group 15 element. The mostlikely explanation for the contrasting outcomes is therefore the

varying hard/soft character of the amide, phosphide, andarsenide donor atoms: rather than eliminate the hard lithiumcations as CpLi, the harder N-donor ligands in 1 remaincoordinated to lithium as well as chromium. In contrast, thesofter P- and As-donors in 2 and 3 preferentially coordinate tothe softer chromium(II) centers, and CpLi is precipitated fromthe reaction. This hypothesis points to a general pnictogen-based structure-directing influence in systems of this type.

■ MAGNETIC SUSCEPTIBILITY MEASUREMENTS

Variable-temperature magnetic susceptibility measurements andisothermal magnetization versus field measurements wereconducted on polycrystalline samples of 1−3. In the case of1, the molar magnetic susceptibility was determined in thetemperature range 2−300 K in fields of Hdc = 1000 and 5000G; however, the outcome was the same irrespective of the fieldstrength. The value of χMT at 300 K is 2.80 cm3 K mol−1, and isessentially independent of temperature down to about 10 K,when a small decrease to 2.35 cm3 K mol−1 was observed, mostlikely due to the effects of zero-field splitting (SupportingInformation, Figure S8). The isothermal magnetization (M)versus field data were collected at 1.8 and 4 K, with fieldstrengths in the range H = 0−7 T, and for each isotherm theM(H) curves reach saturation approximately at M = 3.5 μB(Supporting Information, Figure S9), in agreement with thepresence of four unpaired electrons on the Cr(II) centers. TheχMT(T) data and the M(H) curves were accurately reproducedby a spin Hamiltonian (see Supporting Information) that useda chromium(II) ion with S = 2, a g-value of 1.93, and an axialzero-field splitting parameter of D = −1.8 cm−1. The resultsobtained on 1 are similar to those previously reported g- and D-values for chromium(II) complexes.10

For 2 and 3, the graphs of χMT against T (Figure 3) showthat χMT at the high-temperature limit of the experiment is 0.60cm3 K mol−1 for 2 and is 1.24 cm3 K mol−1 for 3, both of whichare significantly less than the spin-only value of 6.0 cm3 Kmol−1 expected for two noninteracting high-spin Cr(II) ions

Table 1. Selected Interatomic Distances and Bond Angles for 1−3

1a/1b 2a/2b 3a/3b

Cr−E 2.0926(17), 2.1025(19)/2.1001(19), 2.0841(17) 2.3814(9), 2.3864(9)/2.3858(9), 2.3869(9) 2.4963(5), 2.4992(5)/2.5011(5), 2.5010(4)Cr−C 2.382(5)−2.401(4)/2.357(3)−2.397(3) 2.276(17)−2.33(2)/2.244(9)−2.297(13) 2.270(11)−2.327(11)/2.281(9)−2.325(11)Li−N 2.079(4), 2.065(4)/2.055(4), 2.078(4)Li−C 2.592(6), 2.655(6) 2.584(5), 2.677(5)Cr···Ma 2.761(4)/2.755(4) 3.066(1)/3.086(1) 3.394(1)/3.419(1)E−Cr−E 96.28(7)/96.22(7) 99.98(3)/99.43(3) 94.41(2)/93.79(2)Cr−E−Ma 82.86(13), 82.96(13)/83.05(13), 82.90(13) 80.02(3)/80.57(3) 85.59(1)/86.21(1)

aM = Li in 1, M = Cr in 2 and 3

Figure 2. Thermal ellipsoid plots (30% probability) of the molecular structures of 2a and 3a. Hydrogen atoms not shown.





(assuming g = 2). Upon cooling, χMT for 2 and 3 decreasescontinuously to reach a value of almost zero at 2 K, whichindicates strong antiferromagnetic coupling between thechromium centers, and leads to a diamagnetic (S = 0) spinground state. The nonzero value of χMT at 2 K is likely to bedue to the presence of small amounts of a paramagneticimpurity in samples of 2 and 3.To quantify the strength of the antiferromagnetic exchange

in 2 and 3, the experimental susceptibility data were fitted withthe Heisenberg−Dirac−Van Vleck (HDVV) model,1 adaptedfor dimers consisting of two S = 2 metal ions. To account forintermolecular magnetic exchange, a (T − θ) term, where θ isthe Weiss constant, was included. The spin Hamiltonianformalism H = −2J(SCrA·SCrB), where J is the exchange couplingconstant and SCrA and SCrB refer to the spin of the two Cr(II)ions in each dimer, was used.11 Very good fits to experimentwere obtained for both dichromium compounds, using g = 2and SCr = 2, and the following parameters: for 2, J = −166cm−1, θ = −0.7 K, and ρ = 0.022; and for 3, g = 2; J = −77.5cm−1, θ = −0.4 K, and ρ = 0.014. The parameter ρ representsthe proportion of the paramagnetic impurity in each sample,which was modeled as a monomeric Cr(II) species. The originof the minor paramagnetic impurity is not immediatelyobvious; however, the same parameters that were employedto model the susceptibility data produced good fits of theisothermal magnetization versus field plots for 3 (SupportingInformation, Figure S10), hence the impurity is unlikely to bean oxidized species.The temperature dependence of the magnetic susceptibilities

in 2 and 3 are qualitatively similar, the major difference beingthat the antiferromagnetic exchange in 2 is very strong, andmore than twice as strong as that in 3. Given that orbitaloverlap plays an important role in magnetic exchange, thedifference in the two J-values is most likely because the Cr−Asbonds in 3 are approximately 0.11 Å longer than the Cr−Pbonds in 2. This is also reflected in the Cr···Cr separations in 3being on average 0.33 Å longer than those in 2. In 2, the Cr−P−Cr bridging angles are also approximately 5−6° more acutethan the Cr−As−Cr angles in 3, and this small structuraldifference may also contribute to the different magnitude of theexchange coupling constants. The stronger exchange couplingin 2 relative to 3 is also consistent with our observations on themanganese(II) analogues [CpMn{E(SiMe3)2}]2, where cou-

pling constants of J = −13.5 cm−1 and −1.5 cm−1 weredetermined for E = P or As, respectively.5 The much smallercouplings in the manganese analogues is presumably due to thegreater ionic character of the Mn−E bonds.12

Diamagnetic, polymetallic compounds of chromium in whichthe metal centers are bridged by P- or As-donor ligands arewell-known. The range of bridging heavy-pnictogen ligands isquite broad, and includes poly pnictogen ligands [En]

x− andligands of the type [R2E]

−.13,14 Such compounds have typicallybeen studied for their intrinsically interesting coordinationchemistry and, in some cases, their applications in alkenepolymerization catalysis.14c Studies of the magnetism inparamagnetic analogues are limited to very few examples, andno exchange coupling constants have been disclosed. Althoughexperimental studies of exchange coupling between transitionmetals involving phosphorus- or arsenic-containing ligands arewell-known, for example, phosphonates and arsonates,15 to thebest of our knowledge the exchange coupling constants incompounds 2 and 3 are only the second examples to bedetermined with phosphorus or arsenic as the bridging atom. Inthe context of magnetic exchange, by far the most extensivelystudied chromium compounds are oxygen-bridged cages ofchromium(III), in which the metal ions can either coupleferromagnetically or, more commonly, antiferromagnetically.16

The exchange coupling in 2 and 3 is considerably stronger thanthe coupling in oxygen-bridged chromium(III) compounds,where coupling constants are typically only several wave-numbers. Studies of exchange-coupled chromium(II) com-pounds are much less common, presumably because of atendency to form chromium−chromium bonds, and measure-ments of exchange coupling constants involving this ion aretherefore rare.17 The chromium(II) centers in the 26-valence-electron triple-decker complex [{(η5-Cp*)Cr}2(μ:η

5:η5-P5)]+,

which contains the cyclo-[P5]− ligand, are thought to be coupled

antiferromagnetically; however, it was not possible todetermine a J-value for this compound owing to thesimultaneous occurrence of a spin crossover at lowertemperatures.18 Fryzuk et al. reported five-coordinatedichromium(II) compounds with chloride or hydride bridgesin which the metals couple antiferromagnetically; in the case ofthe chloride bridge an exchange coupling constant of J = −12.4cm−1 was determined, however for the hydride bridge verystrong coupling with J = −139 cm−1 was observed.19 In thehydr ide -br idged , mixed-va lence compound [(η 5 -C5Me4Et)4(Cr

III)3(CrII)(μ-H)5(μ3-H)2] reported by Heintz et

al., the effective magnetic moment is temperature-independent,which implies that the J-value is in excess of several hundredwavenumbers.20 The propensity of the hydride ligand forpromoting very strong exchange is well-known; hence, it isnoteworthy that the phosphorus-mediated exchange couplingbetween the chromium(II) centers in 2 can be stronger eventhan in some hydride-bridged chromium(II) compounds.

■ CONCLUSIONThe pnictogen-centered nucleophiles LiE(SiMe3)2 (E = N, P,As) displace a Cp ligand from chromocene, giving theheterodimetal l ic compound [(μ :η2 :η5-Cp)Cr{μ -N-(SiMe3)2}2Li] (1) and the homometallic dimers [(η5-Cp)M-{μ-E(SiMe3)2}]2 with E = P (2) or As (3). The inclusion oflithium into the coordination polymer structure of 1 is due tothe hard−hard lithium−nitrogen interactions, whereas thesofter phosphorus and arsenic donors in 2 and 3 preferentiallycoordinate only to chromium. The magnetic properties of 1

Figure 3. Temperature dependence of χMT for compounds 2(triangles) and 3 (squares). The red lines represent a theoretical fitof the experimental data (see text for parameters).





were interpreted in terms of a single-ion chromium(II) system,and simulation of the susceptibility and magnetization dataproduced a zero-field splitting parameter of D = −1.8 cm−1 witha g-value of 1.93. Compounds 2 and 3 display strongantiferromagnetic coupling between their chromium(II)centers, with exchange coupling constants of J = −166 and−77.5 cm−1, respectively. The coupling in 2 is particularlystrong, and highlights that phosphorus-mediated exchange canbe stronger than the exchange mediated by ligands that arewell-known for promoting very strong exchange, such ashydride.

■ EXPERIMENTAL SECTIONGeneral Considerations. Toluene was dried by refluxing under

nitrogen for several hours over sodium−potassium alloy. Benzene-d6was distilled from sodium−potassium alloy and stored over activated 4Å molecular sieves. Solids were manipulated using an MBraunLabMaster glovebox under an argon atmosphere, and solutions weretransferred using a Schlenk line under argon that had been passedthrough several columns of various drying agents and a heated coppercatalyst. Chromocene,21 lithium bis(trimethylsilyl)phosphide22 andlithium bis(trimethylsilyl)arsenide23 were synthesized according toliterature procedures. Compounds 1−3 are pyrophoric when dry andin the case of 2 and 3 a most unsupportable odor is produced.Paramagnetic 1H NMR spectra were acquired using a Bruker AvanceIII spectrometer across a chemical shift range of ±250 ppm. NMRspectra were acquired using a Bruker Avance III spectrometeroperating at 400.13 MHz (1H), 100.61 MHz (13C), and 155.51MHz (7Li). 1H and 13C chemical shifts are reported relative to SiMe4,and 7Li chemical shifts are reported relative to an external standard ofaqueous LiCl.Compound 1. A solution of Cp2Cr (0.10 g, 0.55 mmol) in toluene

(10 mL) was cooled to −78 °C, and a solution of [(Me3Si)2NLi] (0.34g, 1.10 mmol) in toluene (20 mL) was added dropwise. The blue-black

reaction mixture was warmed to room temperature and stirredovernight. The resulting very dark blue solution was filtered (porosity3) to remove a gelatinous precipitate of CpLi. The volume of thefiltrate was reduced until appreciable amounts of precipitate hadformed on the walls of the reaction vessel, and then the mixture wasgently heated until a homogeneous solution was obtained. Storage at−28 °C produced a crop of dark blue block-like crystals (0.05 g, 21%based on chromium). Analysis calculated for C17H41N2Si4LiCr: C45.90, H 9.29, N 6.30; found C 45.62, H 8.99, N 6.11. 1H NMR(benzene-D6, 400.13 MHz, 298 K, δ/ppm): 23.41, Cp, fwhm 1073 Hz;2.85, SiMe3, fwhm 149 Hz; 1.55, SiMe3, fwhm 40 Hz. 7Li NMR(pyridine-D5, 155.51 MHz, 298 K, δ/ppm): −5.11.

Compound 2. A solution of Cp2Cr (0.10 g, 0.55 mmol) in toluene(10 mL) was cooled to −78 °C, and a solution of[(Me3Si)2PLi·(thf)1.8] (0.17 g, 0.55 mmol) in toluene (10 mL) wasadded dropwise. The dark red reaction mixture was warmed to roomtemperature and stirred overnight. The resulting solution was filtered(porosity 3) to remove a gelatinous precipitate of CpLi. The volume ofthe filtrate was reduced until appreciable amounts of precipitate hadformed on the walls of the reaction vessel, and then the mixture wasgently heated until a homogeneous solution was obtained. Storage at−28 °C produced a crop of dark red block-like crystals (0.08 g, 50%based on chromium). Analysis calculated for C22H46P2Si4Cr2: C 44.87,H 7.87, P 10.52; found C 44.23, H 7.83, P 10.36. 1H NMR (benzene-d6, 400.13 MHz, 298 K, δ/ppm): 98.82, low intensity; 3.35, fwhm219.5 Hz, Cp; 0.28, fwhm 5.2 Hz, singlet, SiMe3. No signal wasobserved in the 31P NMR spectrum.

Compound 3. A solution of Cp2Cr (0.10 g, 0.55 mmol) in toluene(10 mL) was cooled to −78 °C, and a solution of[(Me3Si)2AsLi·(thf)2] (0.20 g, 0.55 mmol) in toluene (10 mL) wasadded dropwise. The dark red reaction mixture was warmed to roomtemperature and stirred overnight. The resulting solution was filtered(porosity 3) to remove a gelatinous precipitate of CpLi. The volume ofthe filtrate was reduced until appreciable amounts of precipitate hadformed on the walls of the reaction vessel, and then the mixture wasgently heated until a homogeneous solution was obtained. Storage at

Table 2. Crystal Data and Structure Refinement for Compounds 1−3

1 2 3

empirical formula C17H41CrLiN2Si4 C22H46Cr2P2Si4 C22H46As2Cr2Si4formula weight 444.82 588.89 676.79T/K 123(1) 123(1) 123(1)λ/Å 1.54178 1.54178 1.54178crystal system monoclinic triclinic triclinicspace group P21/n P1 P1a/Å 16.7360(2) 9.0064(10) 9.1939(3)b/Å 14.8988(2) 10.8050(13) 10.9303(4)c/Å 21.2558(3) 17.1383(18) 17.3201(7)α/deg 90.468(9) 91.042(3)β/deg 106.434(2) 90.944(9) 90.828(3)γ/deg 105.076(10) 106.057(3)V/Å3 5083.53(13) 1610.0(3) 1672.01(11)Z 8 2 2density (calcd.)/Mg m−3 1.162 1.215 1.344crystal size/mm3 0.32 × 0.19 × 0.07 0.15 × 0.03 × 0.02 0.13 × 0.09 × 0.05θ range /deg 2.96−66.60 4.24−67.5 4.21 to 76.39reflections collected 28031 11022 13531independent reflections 8792 [R(int) = 0.0344] 6372 [R(int) = 0.0399] 6764 [R(int) = 0.0210]completeness/% 97.6 99.6 96.3data/restraints/parameters 8792/0/442 6372/308/529 6764/500/373goodness-of-fit on F2 0.919 1.009 1.136final R indices [I > 2σ(I)] R1 = 0.0400 R1 = 0.0409 R1 = 0.0245

wR2 = 0.1053 wR2 = 0.0919 wR2 = 0.0738R indices (all data) R1 = 0.0448 R1 = 0.0603 R1 = 0.0291

wR2 = 0.1074 wR2 = 0.1017 wR2 = 0.0773largest diff. peak and hole/e Å−3 0.696, −0.446 0.366, −0.524 0.364, −0.416





−28 °C produced a crop of dark red block-like crystals (0.08 g, 43%based on chromium). Analysis calculated for C22H46As2Si4Cr2: C39.04, H 6.85; found C 39.20, H 6.72. 1H NMR (benzene-d6, 400.13MHz, 298 K, δ/ppm): 34.02, very low intensity, fwhm 466.7 Hz; 2.38,fwhm 82.1 Hz, Cp; 0.28, fwhm 5.3 Hz, singlet, SiMe3.X-ray Crystallography. The experiments were carried out using

an Agilent Gemini R Ultra (1) or an Agilent SuperNova (2, 3), andeither a multiscan24 (2) or an analytical25 (3) absorption correctionwas applied to the data (Table 2). The structures of 2 and 3 weresolved with SuperFlip,26 and SHELXL27 was used for the refinement(Table 2). Disorder is present in all of the structures. The affectedSiMe3 and Cp groups were refined employing SAME, SIMU, DELU,and ISOR restraints. The hydrogen atoms were constrained to thecorresponding carbon atom and refined according to the riding model.

■ ASSOCIATED CONTENT*S Supporting InformationX-ray crystallographic data on 1−3 in CIF format. Illustrationsof molecular structures of 1a, 1b, 2a, 2b, 3a, and 3b. 1H NMRspectra and details of magnetic susceptibility measurements.This material is available free of charge via the Internet athttp://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected] (M.S.),[email protected] (R.A.L.).Author ContributionsThe manuscript was written through contributions of allauthors. All authors have given approval to the final version ofthe manuscript.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSR.A.L. thanks the Alexander von Humboldt Foundation for theaward of a Fellowship for Experienced Researchers. Theauthors acknowledge the support of the EPSRC (U.K.). Theauthors thank Dr. S. Sproules (Manchester) for helpfuldiscussions.

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DOI: 10.1002/chem.201200152

MnII–GdIII Phosphonate Cages with a Large Magnetocaloric Effect

Yan-Zhen Zheng,*[a, b] Eufemio Moreno Pineda,[a] Madeleine Helliwell,[a] andRichard E. P. Winpenny*[a, c]

The magnetocaloric effect (MCE) was discovered morethan one hundred years ago.[1] Recently use of the MCEwithin molecular nanomagnets has been proposed to replacethe expensive and rare helium-3 in some ultra-low tempera-ture cooling applications such as hydrogen and natural gasliquefaction. This blue-print has been first envisaged by thevery famous single-molecule magnets, {Mn12} and {Fe8}.

[2]

However, as large magnetic anisotropy is adverse for MCEsa range of magnetic molecules with low magnetic anisotropyhas been studied, including 3d cages such as {Fe14}, {Mn10},{Mn14}, {Mn32}, {Mn17}, and {Mn19}; 3d–4f cages such as{Mn4Gd4}, {Cu5Gd4}, {Ni6Gd6}, {Ni12Gd36}, {CoxGdy}, andpure 4f cages, such as {Gd2} and {Gd7}.

[3–11]

Gadolinium ACHTUNGTRENNUNG(III) (s= 7/2) is the ideal spin center for MCEas it has a high isotropic spin; however, the internal natureof the 4f electrons hampers the magnetic communicationbetween them. A mixed-metal 3d–4f approach should havethe advantage of a better magnetic interaction and thus,a larger ground spin in the preferred ferromagnetic case. Wehave used this approach to make cobalt(II) (s= 3/2) andnickel(II) (s=1) gadolinium phosphonate complexes withlarge MCEs.[10] However, both these divalent 3d-metal ionshave some anisotropy, and we thought it worth investigatingsimilar molecules with the more isotropic and higher spinsof manganese(II) (s=5/2) ion.

Two precursors, namely [MnII ACHTUNGTRENNUNG(O2CtBu)4ACHTUNGTRENNUNG(EtOH)]n and[Ln2 ACHTUNGTRENNUNG(O2CtBu)6ACHTUNGTRENNUNG(HO2CtBu)6] (Ln= Gd and Dy)[12,13] were al-lowed to react with phosphonic acids. With methylphos-phonic acid (H2O3PMe), we isolated 1, in which L= (m3-

OH)1.5 ACHTUNGTRENNUNG(O2CtBu)1.5, and with benzylphosphonic acid we iso-lated 2 and 3. Compounds 1 and 3 show brand-new type ofcores in 3d–4f coordination chemistry, namely, for 1,a highly symmetric trigonal-bipyramidal {MnII

9GdIII9} core,

and for 3, a truncated-ball shaped {MnII6DyIII

6} core. Thelatter has a grid-type structure that resembles a previouslyreported {Co4Gd6} complex.[10a]

½MnII9GdIII

9ðO3PMeÞ12ðO2CtBuÞ18ðLÞ� 1

½MnII4GdIII

6ðO3PCH2PhÞ6ðHO2CtBuÞ13ðO2CMeÞðHO2CtBuÞðOH2Þ2ðMeCNÞ2�ðMeCNÞ3 2

[a] Prof. Dr. Y.-Z. Zheng, E. M. Pineda, Dr. M. Helliwell,Prof. Dr. R. E. P. WinpennySchool of ChemistryThe University of ManchesterOxford Road, M13 9PL, Manchester (UK)Fax: (+44) 161-275-4616E-mail : [email protected]

[b] Prof. Dr. Y.-Z. ZhengCenter for Applied Chemical ResearchFrontier Institute of Science and TechnologyXi’an Jiaotong University, Xi’an 710054 (P. R. China)E-mail : [email protected]

[c] Prof. Dr. R. E. P. WinpennyPhoton Science InstituteThe University of ManchesterOxford Road, M13 9PL, Manchester (UK)

Supporting information for this article (including experimental de-tails) is available on the WWW under http://dx.doi.org/10.1002/chem.201200152.

Figure 1. a) The structure of 1 in the crystal. b) Side view of of the trigo-nal-bipyramid {Mn9Gd9} core (left) and the top view (right) along the C3

axis. Two-fold disordered central Gd and peripheral Mn are shown in justone position. Color codes (the same as the following): Ln, purple; Mn,tan; P, green; O, red; N, blue; C, grey.

Chem. Eur. J. 2012, 18, 4161 – 4165 � 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 4161

COMMUNICATION



½MnII6DyIII

6ðm3-OHÞ2ðO3PCH2PhÞ6ðO2CtBuÞ16�ðMeCNÞ5 3

The use of the smallest organophosphonate leads to theformation of the highly symmetric complex 1 (Figure 1),which crystallizes in the hexagonal space group R3c, and thecage has D3h symmetry (allowing for disorder).[19] ThreeMnII sites lie near the trigonal plane of a trigonal bipyramid(Figure 1 b), with the remaining six manganese centers form-ing two triangles near the apical positions: the nine sitesform a trigonal bipyramid that is truncated on the trigonalaxis (Figure 1 b). Six of the GdIII centers lie on the non-equatorial edges of the trigonal bipyramid, while the finalthree GdIII sites form a triangle that lies between the twoMnII triangles (Figure 1 b and 1 c). Six MePO3

2� ligandsshow the 5.222 bonding mode (Harris notation[14]), bindingto two Mn sites from a triangle, two Gd sites from the cen-tral triangle, and one Gd on an edge. The other six phospho-nates show the 4.221 mode, binding to a single Gd site fromthe central triangle, a Mn site within the trigonal plane, andtwo Gd sites on the edges of the polyhedron.

There is disorder in the structure of 1. The six metalions—three Gd and three Mn—that lie near the centralplane do not lie on the crystallographic mirror plane but aredisordered over two sites related by this mirror plane. TheGd is approximately 0.15 � out of the plane, and the Mn ap-proximately 0.56 � out of the plane. There is also disorderin the ligands attached to the top and bottom Mn triangles;

these have been modeled with an equal mixture of m3-hy-droxide and a pivalate that bridges the edges of this triangle.Both Mn sites in the structure are five-coordinate, with a dis-torted square-pyramidal geometry in all disorder models.Both Gd sites are eight-coordinate.

The remaining three crystallographically unique pivalatesin the structure bridge Gd–Mn edges. One shows the 2.11mode, bridging from the Mn site in the central plane to theGd ion on the edge of the trigonal bipyramid. The othertwo unique pivalates bridge the edge from this Gd to theMn site within the Mn triangles. One shows the 2.11 mode,while the second shows the 2.21 mode, chelating to the Gdsite.

By replacing the methylphosphonate with benzylphospho-nate, we obtained the manganese(II)–gadolinium ACHTUNGTRENNUNG(III) com-plex 2. The crystal structure of 2 features a distorted [3 �3]{Mn4Gd6} grid as its core, if a pair of manganese ions isviewed as a node (Figure 2).[10a, 19] There are six phospho-nates, which bind in three different ways to the adjacentmetal ions. As shown in Figure 2 b, the first type of phospho-nate sitting on the top part of the core in an unusual 5.322

Figure 2. a) The structure of 2 in the crystal. b) A comparison of thecores of 2 (left) and the [3 � 3] {Mn4Gd6} grid (right) by taking the man-ganese dimer as a node.

Figure 3. a) The structure of 3 in the crystal. b) Side view of the truncatedball-shaped {Mn6Dy6} core. The yellow spheres are just to show the spacewithin the core.

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mode binds three gadolinium and two manganese atoms.Below this, three outward-facing phosphonates are bound tothe remaining gadolinium and manganese atoms in a 4.221mode. The other two back-side phosphonates bind only totwo gadolinium and one manganese atoms in a 3.211 mode.Evidently, there is no inversion center in this core. As a con-sequence, 2 crystallized in a chiral space group Cc. Howev-er, we estimated the whole batch of sample must be racemicas we observed a partial twinning in the measured crystal.Thirteen deprotonated pivalates are surrounded in the pe-riphery in either 2.11 or 2.21 mode. There also exists a pro-tonated pivalic acid that forms strong hydrogen bonding(O···O 2.42 �) with the adjacent oxygen atom from a 2.11pivalate; two additional aqua ligands that coordinate to twogadolinium ions and an in situ formed acetate from the hy-drolysis of the acetonitrile, which has been observedbefore.[11,15] The two isolated corner manganese ions arefive-coordinate with a geometry closer to a square pyramid(t= 0.33),[16] whereas the two linked manganese dimers aresix-coordinate with a Mn···Mn separation of 3.59 �.

If gadolinium is replaced by dysprosium a new truncated-sphere structure results (Figure 3). The core atoms of thestructure—namely six phosphorus, manganese, and gadolini-um atoms—form a hexagonal bipyramid, with a cap on eachof the square faces of the polyhedron. Looking down on thestructure (Figure 3 a) the top hexagon consists of P-Mn-Gd-P-Mn-Gd, with each edge bridged by an oxygen.[19] Thebottom hexagon has the same composition, with a Mnbelow each Gd from the top hexagon, and a Gd below eachMn from the top (Figure 3 b). The central caps also form

a hexagon, with a P atom the cap on each square face thatcontains two Mn and two Gd (Figure 3 b). There is a watermolecule at the center of the ball, and it seems other guestmolecules could be included in the structure.

There are two types of phosphonates in the structure. Thefour that form part of the hexagonal prism show the 4.211mode, while the two that act as caps show the 6.222 mode.The two manganese ions of the upper hexagon are onlyfour-coordinate with oxygen atoms from either phospho-nates or pivalates, whereas the remaining MnII ions are six-coordinate. All the dysprosium ions in 2 are seven-coordi-nate, with geometries related to a compressed pentagonal-bipyramidal. It is noticeable that the exterior of the cageconsists of phenyl or tert-butyl groups from the ligand, lead-ing to a hydrophobic exterior. The nearest Dy···Mn separa-tions in this core range from 3.47 to 3.93 �.

The magnetic behavior of 1–3 was studied on polycrystal-line samples (Figure 4). At room temperature except for 1,the cMT value is consistent with the expected value: for 2,observed 64.9 emu K mol�1 (calcd 64.8 emu K mol�1 for fours=5/2 and six s=7/2 spin-only (g= 2) centers); for 3, ob-served 111.6 emuK mol�1 (calcd 110.3 emu K mol�1 for sixs=5/2, g=2 and six s=7/2, L =5, g= 4/3, centers). For 1,the observed 104.2 emu K mol�1 is less than the spin-onlyvalue (calcd 110.3 emu K mol�1 for nine s= 5/2 and nine s=

7/2 spin-only centers); which indicates significant antiferro-magnetic interactions within 1.[17,18]

Upon cooling, for 1 and 3 the cT versus T curve decreasessignificantly with decreasing temperature.[15] For 1, the cTversus T curve reaches a value around 64.3 emu K mol�1 at

Figure 4. Top: The cT versus T plots of 1–3 under a 5 kG dc field. Inset: the field-dependent experimental magnetization plots at indicated temperatures.Bottom: Experimental magnetic entropy changes DSm for 1–3, obtained from the magnetization data, at various fields and temperatures. Lines areguides to the eye.

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COMMUNICATIONMnII–GdIII Phosphonate Cages



2 K. The M versus H plots from 2 to 9 K (insert of Figure 4)show a steady increase that reaches 80.9 mB at 7 T at 2 K.This value does not correspond to the saturated value(108 mB) for nine paramagnetic s= 5/2 and nine s=7/2 metalcenters. Instead, it corresponds to a value (78 mB) with threeparamagnetic s= 5/2 and nine s=7/2 metal centers. This cor-responds to a strong antiferromagnetic within the {Mn3} tri-angles that cancelled the magnetic moments from these sixmanganese centers. For 3, the cT versus T curve reachesa value around 63.2 emu K mol�1 at 2 K. The M versus Hplots from 2 to 9 K (insert of Figure 4) show a linear in-crease after 3 T that reaches 46.8 mB at 7 T at 2 K, but not sa-turated. This is the typical shape of a M versus H plot thatindicates significant magnetic anisotropy. The continuing fallof cT at all temperatures for 3 suggests an effect from thecombined action of the crystal-field effect of the dysprosiumand the predominantly antiferromagnetic exchange interac-tion between the metal centers.

For compound 2, cT remains nearly unchanged down to50 K; this reflects a very weak magnetic interaction betweenthe metal centers. Upon cooling, cT decreases sharply to43.0 emu K mol�1 at 2 K, indicating a paramagnetic state.The magnetization reaches a value of 60.8 mB at 2 K (insertof Figure 4), and the magnetization appears to be muchcloser to saturation (62 mB for four isolated s=5/2 and sixs= /2 metal centers) than in compounds 1 and 3. This obser-vation is consistent with the conclusion that the magnetic in-teractions in 2 are fairly weak.

Studies of the entropy changes from the magnetizationdata suggest the gadolinium-containing candidates could besuitable for low-temperature magnetic cooling, as the MCEcan be described as DS(T)DH = s[@M ACHTUNGTRENNUNG(T,H)/@T]HdH.[1,2] Cal-culated plots (Figure 4) give peak values for a field changeDH= 70 kG of 3 K of 28.0, 33.7, and 13.0 J kg�1 K�1 for 1–3,respectively. The entropy change of 2 is much larger thanthe value reported (25 J kg�1 K�1) for the 3d compounds at4 K,[5] and even slightly higher than the highest value report-ed (31 J kg�1 K�1 for a field change DH=90 kG) ofa {Cu5Gd4} cage.[9] It is noticeable that a smaller MCE isfound for 1 and 3, which indicates that the much larger anti-ferromagnetic interactions and magnetic anisotropy herereduce the entropy changes in 1 and 3.[7,8]

The maximum entropy value per mole, given by DSm =

SRln ACHTUNGTRENNUNG(2 s+1), corresponding to the sum of the individualcontributions from the MnII, GdIII, or DyIII spins, is 57.0,41.8, and 42.5 J kg�1 K�1, for 1, 2, and 3, respectively. Thesevalues are not reached experimentally mainly because of theantiferromagnetic interactions between the metal centers in1 and 2, and the magnetic anisotropy of DyIII in 3.[8] More-over, the larger MCE in 2 compared to that in 1 is presuma-bly proportional to the density of the gadolinium—a conclu-sion that is consistent with the previously reported resultsfor the cobalt lanthanide[10e] and the pure gadolinium sys-tem.[11c]

In summary, by using different phosphonate ligands, wehave not only obtained a series of structurally beautifulmanganese(II)–lanthanide ACHTUNGTRENNUNG(III) heterometallic cages but also

successfully introduced the magnetic isotropy into these mo-lecular coolants.

Acknowledgements

Y.Z.Z. is grateful for the support of a Marie Curie International Incom-ing Fellowship (EC Contract No: PIIF-GA-2008–219588) and the Start-ing Fund of Xi’an Jiaotong University. R.E.P.W. is supported by a RoyalSociety Wolfson Merit Award. We thank Dr. Marco Evangelisti for help-ful discussions.

Keywords: cage compounds · magnetic properties ·lanthanides · P ligands · phosphonate ligands · refrigerant

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Received: January 14, 2012Published online: March 12, 2012

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COMMUNICATIONMnII–GdIII Phosphonate Cages



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“New f-Block and Mixed d,f-Block Molecular Nanomagnets”

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