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Manganese Complexes as Molecular Nanomagnets: Alcoholysis and Carboxylate Abstraction Routes to Nanoscale Magnetic Materials

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Manganese Complexes as Molecular Nanomagnets: Alcoholysis and Carboxylate Abstraction Routes to Nanoscale Magnetic Materials
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VINSLAVA, ALINA ( Author, Primary )
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2008

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Atoms ( jstor )
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Magnetic permeability ( jstor )
Magnetism ( jstor )
Magnetization ( jstor )
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University of Florida
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University of Florida
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Copyright Alina Vinslava. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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12/31/2011
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1 MANGANESE COMPLEXES AS MOLECULAR NANOMAGNETS: ALCOHOLYSIS AND CARBOXYLATE ABSTRACTION ROUTES TO NANOSCALE MAGNETIC MATERIALS By ALINA VINSLAVA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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2 Copyright 2006 by ALINA VINSLAVA

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3 To my parents and brother, for their love, c onstant encouragement a nd unconditional support of me as I pursue my career goals.

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4 ACKNOWLEDGMENTS It has been a long journey, and I have b een helped and supported by many along the way. It is now my great pleasure to take this opportunity to thank them. First of all, I would like to acknowledge and th ank my research advisor, Professor George Christou, for providing me with the opportunity of earning a docto ral degree in his research group. Without his help and guidance, as well as the constant encouragement and inspiration, this dissertation would not have been possible. I would also like to thank my other committee members, Dr. D. R. Talham, Dr. M. J. Scott, Dr. L. McElwee-White and Dr. S. Hill, for their helpful insights, comments and suggestions. My sincere thanks go to Dr. Anastasios Ta siopoulos, for introducing me to the [Mn84] project, for all his help, friendship and time he i nvested in guiding me in my initial years in the group. Additionally, I would like to thank Rashmi Bagai and Dr. Theocharis Stamatatos for reading this dissertation and help ful suggestions. I would like to express my appreciation to all research scientists with whom I have worked during my doctoral studies. I would like to thank Dr. K. A. Abboud and his staff at UFCXC for solving very ch allenging X-ray structures, Dr. Wolfgang Wernsdorfer, for the low temperature (below 1.8 K) single-crystal magnetism studies, and Dr. Stephen Hill and his research group for the HFEPR measurements. I owe my special thanks to my wonderful friends for the best of times. I want to thank the entire Christou group, past and present, for thei r companionship and support in my educational pursuits, and especially Abhu, Dolos, Rashmi a nd Antonio for their friendship and all the fun time we had together. In addition, I would like to thank Alina Munteanu for being my true best friend from day one in Gainesville.

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5 Last but not least, I would like to thank my parents and my brother Eugenijush. I fill most fortunate to have their unquestio ning love and support and dedicate this dissertation to them.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES................................................................................................................ .......11 ABSTRACT....................................................................................................................... ............15 CHAPTER 1 GENERAL INTRODUCTION..............................................................................................17 2 GIANT [Mn84] SINGLE-MOLECULE MAGNETS AS THE FIRST MEETING OF THE “BOTTOM-UP” AND “TOP-DOWN” APPROACHES TO NANOSCALE MAGNETIC MATERIALS...................................................................................................32 2.1 Introduction............................................................................................................... ........32 2.2 Results and Discussion.....................................................................................................35 2.2.1 Syntheses................................................................................................................35 2.2.2. X-ray crystal structures of [Mn84O72(O2CMe)78(MeO)24(MeOH)12(H2O)42(OH)6]( 3 )H2O12CHCl3 and [Mn84O72(O2CEt)81(MeO)24(MeOH)18(H2O)30(OH)3]( 4 )x solvents...........................37 2.2.3 Magnetochemistry of Complexes 3 and 4 ..............................................................41 2.2.3.1 Direct Current Magnetic Susceptibility Studies...........................................41 2.2.3.2 Alternating Current Magne tic Susceptibility Studies...................................43 2.2.3.3 Hysteresis Studies below 1.8 K....................................................................45 2.2.4 Electronic Absorption Spectra of complex 3 ..........................................................47 2.3 Conclusions................................................................................................................ .......49 2.4 Experimental Section....................................................................................................... .50 2.4.1 Syntheses................................................................................................................50 2.4.2 X-ray Crystallography............................................................................................51 3 A NEW FAMILY OF GIANT [Mn70] SINGLE-MOLECULE MAGNETS EXHIBITING QUANTUM TUNN ELING OF MAGNETIZATION...................................69 3.1 Introduction............................................................................................................... ........69 3.2 Results and Discussion.....................................................................................................70 3.2.1 Syntheses................................................................................................................70 3.2.2. X-ray Crystal Structures of [Mn70O60(O2CMe)70(OEt)20(EtOH)16(H2O)22]( 5 )MeCO2HC2H5OH32H2O, [Mn70O60(O2CMe)70(OC2H4Cl)20(ClC2H4OH)18(H2O)22]( 6 )60ClC2H4OHH2O....72 3.2.3 Magnetochemistry of Complexes 5 and 6 ..............................................................75 3.2.3.1 Direct Current Magnetic Susceptibility Studies...........................................75 3.2.3.2 Alternating Current Magne tic Susceptibility Studies...................................77

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7 3.2.3.3 Magnetism Studies below 1.8 K..................................................................78 3.3 Conclusions................................................................................................................ .......80 3.4 Experimental Section....................................................................................................... .82 3.4.1 Syntheses................................................................................................................82 3.4.2 X-ray Crystallography............................................................................................83 4 SINGLE-MOLECULE MAGNETS: STUDY OF DISTORTED CUBANE [MnIVMnIII 3O3X(O2CMe)3(dbm)3] (X = Cl, N3, NCO) COMPLEXES.............................98 4.1 Introduction............................................................................................................... ........98 4.2 Results and Discussion...................................................................................................104 4.2.1 Syntheses..............................................................................................................104 4.2.2 Single-Crystal High-Frequency Electr on Paramagnetic Resonance Studies of Complex 8 ..................................................................................................................106 4.2.3 Description of Structures of Complexes 8 10 ......................................................111 4.2.4 Magnetochemistry of Complexes 9 and 10 ..........................................................112 4.2.4.1 Direct Current Magnetic Suscep tibility Studies of Complexes 9 and 10 ...112 4.2.4.2 Magnetization versus Direct Cu rrent Magnetic Field Studies for Complexes 9 and 10 ............................................................................................114 4.2.4.3 Alternating Current Magnetic Sus ceptibility Studies of Complexes 9 and 10 ..................................................................................................................115 4.3 Conclusions................................................................................................................ .....116 4.4 Experimental Section......................................................................................................117 Syntheses...................................................................................................................... .117 5 INCORPORATION OF A FERROMAGNE TIC COUPLER VIA CARBOXYLATE ABSTRACTION: NEW [Mn 11], [Mn4] AND [Mn3] COMPLEXES WITH END-ON ISOCYANATES...................................................................................................................133 5.1 Introduction............................................................................................................... ......133 5.2 Results and Discussion...................................................................................................136 5.2.1 Syntheses..............................................................................................................136 5.2.2. Description of Structures.....................................................................................140 5.2.2.1 X-ray Crystal Structure of ( n -Bu 4N)2[Mn 11O10(NCO)6(O2CPh)11(H2O)4]( 12 ) 13Me2CO..........................140 5.2.2.2 X-ray Crystal Structure of ( n -Bu4N)3[Mn4O3(NCO)7(O2CPh)3]( 13 ).........141 5.2.2.3 X-ray Crystal Structure of ( n -Bu4N)2[Mn3O(NCO)6(O2CPh)3]( 14 )CH2Cl2................................................142 5.2.3 Magnetochemistry of Complexes 12 14 ..............................................................143 5.2.3.1 Direct Current Magnetic Susceptibility Studies.........................................143 5.2.3.2 Alternating Current Magnetic Su sceptibility Studies of Complex 12 ........149 5.2.3.3 Alternating Current Magnetic Sus ceptibility Studies of Complexes 13 and 14 ..................................................................................................................152 5.3 Conclusions................................................................................................................ .....153 5.4 Experimental Section......................................................................................................154 5.4.1 Syntheses..............................................................................................................154 5.4.2 X-ray Crystallography..........................................................................................155

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8 APPENDIX A BOND DISTANCES AND ANGLES..................................................................................178 B BOND VALENCE SUM CALCULATIONS......................................................................191 C VAN VLECK EQUATIONS...............................................................................................195 Distorted-cubane complex with a virtual C3v symmetry......................................................195 Trinuclear complex: 2J model.............................................................................................196 D PHYSICAL MEASUREMENTS.........................................................................................197 LIST OF REFERENCES.............................................................................................................199 BIOGRAPHICAL SKETCH.......................................................................................................216

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9 LIST OF TABLES Table page 2-1 Crystallographic data and structur e refinement details for complexes 3 and 4 .................54 2-2 Bond valence sum (BVS) calculationsa for the Mn Atoms in 3 ........................................54 2-3 Bond valence sum (BVS) calculationsa for selected oxygen atoms in 3 ...........................55 2-4 Selected interatomic distances () for 3 ............................................................................55 3-1 Crystallographic data and structur e refinement details for complexes 5 and 6 .................85 4-1 Comparison of the spin Ham iltonian parameters of complex 8 ......................................119 4-2 Comparison of selected inte ratomic distances () for [Mn4O3X(O2CMe)3(dbm)3] complexes (X = Cl ( 8 ), N3 ( 9 ) or NCO ( 10 ))..............................................................119 4-3 Comparison of selected bond angles () for [Mn4O3X(O2CMe)3(dbm)3] complexes (X = Cl ( 8 ), N3 ( 9 ) or NCO ( 10 )).................................................................................119 4-4 Comparison of exchange parameters, g -values and low-lying electronic states of [Mn4O3X(O2CR)3(dbm)3] complexes..............................................................................119 5-1 Crystallographic data and structur e refinement details for complexes 12 , 13 and 14 .....158 5-2 Bond valence sum (BVS) calculationsa for the Mn atoms in 12 .....................................158 5-3 BVS calculationsa for selected oxygen atoms in 12 ........................................................159 5-4 BVS calculationsa for the Mn atoms in 13 .......................................................................159 5-5 BVS calculationsa for selected oxygen atoms in 13 ........................................................159 5-6 BVS calculationsa , b for the Mn atoms and for selected oxygen atoms in 14 ...................159 5-7 Comparison of exchange parameters, g -values and low-lying electronic states of [Mn4O3X(O2CR)3(dbm)3] and ( n -Bu4N)3[Mn4O3(NCO)7(O2CPh)3]( 13 ) complexes with virtual C3v symmetry...............................................................................................160 A-1 Selected interatomic distances () and angles () for 3 ...................................................178 A-2 Selected interatomic distances () for 4 ..........................................................................179 A-3 Selected interatomic distances () and angles () for 5 ...................................................183 A-4 Selected interatomic distances () and angles () for 6 ...................................................184

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10 A-5 Selected interatomic distances () and angles () for 12 .................................................186 A-6 Selected interatomic distances () and angles () for 13 .................................................187 A-7 Selected interatomic distances () and angles () for 14 .................................................189 B-1 Bond valence sum (BVS) calculationsa for the Mn atoms in 4 .......................................191 B-2 BVScalculationsa for the Mn atoms in 5 ..........................................................................193 B-3 Bond valence sum (BVS) calculationsa for selected oxygen atoms in 5 .........................193

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11 LIST OF FIGURES Figure page 1-1 Types of magnetic materials depending on the nature of the interaction between spins.......................................................................................................................... .........29 1-2 Hysteresis curve of a magneton.........................................................................................29 1-3 Equivalent schematic representation s of the potential en ergy barrier of an S = 10 spin ground state, split by the negative zero-field splitting, D , in the absence of an applied magnetic field................................................................................................................. ....30 1-4 Magnetization vs magnetic field hysteresis loops for the [Mn12Ac] complex, measured at a constant field sweep rate of 0.004 T/s in the 1.3K to 3.6K temperature range.......................................................................................................................... .........31 1-5 Schematic representation of the pot ential energy diagram of an SMM with S = 10.........31 2-1 PovRay representations of complex 3 ................................................................................56 2-2 PovRay representation of the asymmetric unit of 3 ...........................................................57 2-3 Space-filling representations of 3 (including hydrogen atoms), showing the dimensions of the molecule and its central cavity.............................................................58 2-4 Space-filling representations of 3 , and its supramolecular aggregation into ordered nano-size tubes and sheets.................................................................................................59 2-5 PovRay representation of 4 , shown along the crystallographic a -axis..............................60 2-6 Space-filling representations of 4 (including hydrogen atoms), showing the dimensions of the molecule and its central cavity.............................................................61 2-7 Space-filling representations of 4 , and its supramolecular aggregation into ordered nano-size tubes................................................................................................................ ...62 2-8 Plot of mT vs T for a dried, microcrystalline sample of complex 3 ..................................63 2-9 Plot of mT vs T for a dried, microcrystalline sample of complex 4 ..................................63 2-10 AC magnetic susceptibility data for a dried, microcrystalline sample of complex 3 ........64 2-11 AC magnetic susceptibility data for a dried, microcrystalline sample of complex 4 ........65 2-12 The results of low temperature (< 1.8 K) magnetism studies performed on a singlecrystal of complex 3 ...........................................................................................................66 2-13 Electronic spectra of complex 3 in MeCN.........................................................................67

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12 2-14 Plot of absorbance vs concentration (Beer’s law plot) for complex 3 at 474 nm..............67 2-15 The position of [Mn84] complexes on a size scale spanning atomic to nanoscale dimensions..................................................................................................................... ....68 3-1 PovRay representations of the asym metric unit and the overall structure of 5 .................86 3-2 Space-filling representations of 5 ......................................................................................87 3-3 Space-filling representations, of the supramolecular aggregation of 5 into ordered nano-size tubes................................................................................................................ ...88 3-4 PovRay representation of 6 excluding hydrogen atoms....................................................89 3-5 PovRay representation of th e supramolecular aggregation of 6 emphasizing the ABAB packing mode of molecules in adjacent tubu lar chains...........................................90 3-6 Plots of mT vs T for complexes 5 and 6 in a 0.1T DC field.............................................90 3-7 AC magnetic susceptibility data for a dried, microcrystalline sample of complex 5 ........91 3-8 AC magnetic susceptibility data for a dried, microcrystalline sample of complex 6 ........92 3-9 Magnetization ( M ) vs applied DC magnetic field ( 0H ) hysteresis loops, measured at a constant sweep rate of 0.14 T/s for a si ngle crystal (wet with mother liquor) of complexes 5 and 6 at the indicated temperatures...............................................................93 3-10 Magnetization ( M ) vs applied DC magnetic field ( 0H ) hysteresis loops, measured at a constant temperature of 0.6 K for a singl e crystal (wet with mother liquor) of complexes 5 and 6 at the indicated field sweep rates........................................................94 3-11 Magnetization ( M ) vs time decay plots for a single crystal of complexes 5 and 6 ............95 3-12 Arrhenius plot of the relaxation time ( ) vs 1/ T for complexes 5 and 6 using data obtained from a single crystal DC magnetization decay measurements............................96 3-13 The position of [Mn70] molecules on a size scale sp anning atomic to nanoscale dimensions..................................................................................................................... ....97 4-1 Pov-Ray representation of the la beled central distorted-cubane [MnIVMnIII 3O3X]6+ core........................................................................................................................... ........120 4-2 Pov-Ray representation of the [Mn4O3Cl(O2CMe)3(dbm)3]( 8 ) complex with the labeled core................................................................................................................... ...120 4-3 Plot of the energy vs the external magnetic field ( H ) for the 10 zero-field split components of the S = 9/2 ground state and D 0..........................................................121

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13 4-4 Energy level diagram for the S = 9/2 ground state and D < 0 and HFEPR spectra recorded on a singlecrystal of complex 8 with the external magnetic field applied parallel to the easy ( z ) axis of the molecule.....................................................................122 4-5 Energy level diagram for the S = 9/2 ground state and D < 0 and HFEPR spectra recorded on a singlecrystal of complex 8 with the external magnetic field applied perpendicular to the easy ( z ) axis of the molecule...........................................................123 4-6 The frequency dependence of EPR tran sitions obtained with the magnetic field applied at = 10 angle away from the easy axis in the easy/hard plane of the sample..124 4-7 The frequency dependence of EPR tran sitions obtained with the magnetic field applied along the hard axis of the molecule.....................................................................124 4-8 PovRay representation of complex 9 with the labeled core.............................................125 4-9 PovRay representation of complex 10 with the labeled core...........................................126 4-10 Plot of mT vs T for dried, microcrystalline samples of complexes 9 and 10 ..................127 4-11 Plots of reduced magnetization ( M / N B) vs H / T for dried, microcrystalline samples of complexes 9 and 10 at the indicated applied fields.....................................................128 4-12 Representations of the error surface for the D vs g fit of reduced magnetization ( M / N B) vs H / T for complex 9 .........................................................................................129 4-13 Representations of the error surface for the D vs g fit of reduced magnetization ( M / N B) vs H / T for complex 10 .......................................................................................130 4-14 Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried mi crocrystalline sample of complex 9 at the indicated oscillation frequencies................................................................................131 5-1 PovRay representations of the anion of complex 12 and its labeled core (including terminal NCO groups)......................................................................................................161 5-2 PovRay representati ons of the packing of 12 , excluding tetrabutylammonium groups and solvent molecules......................................................................................................162 5-3 PovRay representations of the anion of complex 13 and its labeled core (including terminal NCO groups)......................................................................................................163 5-4 PovRay representati ons of the packing of 13 , excluding tetrabutylammonium groups..164 5-5 PovRay representations of the anion of complex 14 and its labeled core (including terminal NCO groups)......................................................................................................165

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14 5-6 PovRay rep6resentations of the packing of 14 , excluding tetrabutylammonium groups and solvent molecules..........................................................................................166 5-7 Plot of mT vs T for a dried, microcrystalline sample of complex 12a ............................167 5-8 Plot of mT vs T for a dried, microcrystalline sample of complex 12b ...........................167 5-9 Plot of mT vs T for a dried, microcrystalline sample of complex 13 ..............................168 5-10 Plots of reduced magnetization ( M / N B) vs H / T for dried, microcrystalline samples of complex 13 ..................................................................................................................168 5-11 Representations of the error surface for the D vs g fit of reduced magnetization ( M / N B) vs H / T for complex 13 .......................................................................................169 5-12 Plot of mT vs T for a dried, microcrystalline sample of complex 14 ..............................170 5-13 Schematic representation of th e pairwise exchange interactions J and J between MnIII ions of complex 14 ..................................................................................................170 5-14 Plots of reduced magnetization ( M / N B) vs H / T for dried, microcrystalline samples of complex 14 ..................................................................................................................171 5-15 Representations of the error surface for the D vs g fit of reduced magnetization ( M / N B) vs H / T for complex 14 .......................................................................................172 5-16 Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried microcrystalline sample of 12a ....................173 5-17 Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried microcrystalline sample of 12b ...................174 5-18 Plot of the out-of-phase ( Mm") AC magnetic susceptibility signals vs temperature for a fully solvated sample of 12a .........................................................................................175 5-19 Plot of the out-of-phase ( Mm") AC magnetic susceptibility signals vs temperature for a fully solvated sample of 12b .........................................................................................175 5-20 Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried mi crocrystalline sample of complex 13 .......176 5-21 Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried mi crocrystalline sample of complex 14 .......177

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15 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MANGANESE COMPLEXES AS MOLECULAR NANOMAGNETS: ALCOHOLYSIS AND CARBOXYLATE ABSTRACTION ROUTES TO NANOSCALE MAGNETIC MATERIALS By Alina Vinslava December 2006 Chair: George Christou Major Department: Chemistry Single-molecule magnets (SMMs) offer a molecular approach to nanoscale magnetic materials. These molecules, below their bl ocking temperature, f unction as single-domain magnetic particles and exhibit th e classical macroscale property of a magnet — magnetization hysteresis. In addition, they straddle the classi cal/quantum interface in also displaying quantum tunnelling of magnetization (QTM) and quantum phase interference. Potential appl ications of SMMs include high-density information storage and qubits for quantum computing. One of the biggest challenges in this field lies in the development of new synthetic procedures that could lead to a breakthrough in terms of operating temperatures of SMMs. To meet this goal, different synthe tic strategies have been develo ped: (i) the synthesis of highnuclearity clusters, with the aim of obtaining molecules composed of a very large number of magnetic centers and sizes in the mesoscopic re gime; (ii) the incorporation of ferromagnetic couplers, such as isocyanate and azide, in manganese clusters to promote ferromagnetic exchange interactions between the metal centers. Alcoholysis of [Mn12] complexes under acidic conditions has been identified as a successful synthetic route for the formation of giant [Mn84] and [Mn70] SMMs. These clusters

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16 possess ~ 4 nm diameter torus structures, exhibi ts both magnetization hy steresis and QTM, and crystallize as supramolecular nanotubes. The carboxylate abstraction appr oach has been employed for th e incorporation of azide and isocyanate ligands in manganese comp lexes. Magnetic characterization of [Mn4O3(N3)(O2CMe)3(dbm)3] and [Mn4O3(NCO)(O2CMe)3(dbm)3] clusters revealed that the primary pathway for the magnetic exchange inter actions between Mn centers is controlled by the oxide bridges rather than by the ligand framework. Carboxyl ate abstraction from the ( n -Bu 4N)[Mn4O2(O2CPh)9(H2O)] precursor complex has trigge red the formation of three new clusters: ( n -Bu 4N)2[Mn 11O10(NCO)6(O2CPh)11(H2O)4], ( n -Bu 4N)3[Mn 4O3(NCO)7(O2CPh)3] and ( n -Bu4N)2[Mn3O(NCO)6(O2CPh)3]. Magnetic susceptibility studies revealed the presence of predominant ferromagnetic exchange interactions in al l three compounds, thus , justifying the use of isocyanate ligands as effective ferromagnetic couplers. All complexes exhibit slow relaxation of the magnetization, indi cative of SMM behavior. As part of the ongoing study of the fundament al aspects that could provide important insights of the quantum tunneling process, a very accurate determination of the spin Hamiltonian parameters of the [Mn4O3Cl(O2CMe)3(dbm)3] complex has been achi eved by the use of highfrequency electron paramagne tic resonance technique.

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17 CHAPTER 1 GENERAL INTRODUCTION The phenomenon of magnetism has captivated mankind’s imagination since the earliest times. The first accounts of magnets date back to the ancient Greeks who also gave magnetism its name. It derives from Magne sia, a Greek town province in Asia Minor, where it was first discovered that a certain type of iron-rich ore, when stuck by lighting, possessed the ability to attract other iron object “in a magical way”. 1 Such naturally occurr ing iron mineral (Fe3O4) was named magnetite or “the stone fr om Magnesia”. The first practical application of magnetite was realized by the early Chinese, who noticed that magnetite not only attracted objects made from iron, but when made into the shape of a needle and floated on water, it always pointed in a northsouth direction – a simple observa tion that led to the discovery of the first magnetic compass. The invention soon spread worldwide, becomi ng an indispensable to ol in navigation. The magnetite also acquired an alternative name, that of lodestone or “leading stone”, originating from the word “lode”, in archaic English meaning “course” or “way”.2 Although the concept of magnetism is centuries old, it was not until the 19th century that the scientific understanding of this natural phenomenon began to take shape.2 The most pivotal contributions were provided by Coulomb, Oerste d, Ampere and Faraday, all of whom did the early work with electricity and magnetism. Maxw ell predicted the existence of electromagnetic waves and provided the theoretical foundation to the physics of electromagnetism. Imperative contributions to the development of the classica l description of magnetism were made by Weiss, who gave insight to the existence of magnetic dom ains and internal molecular magnetic fields, as well as by Nel, the Nobel prize winner for his theory of antiferromagnetism and ferrimagnetism. The 1900’s also represent the advent of quantum m echanics, which played a crucial role in the development of the quantitativ e understanding of magnetism. The work of Uhlenbeck and

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18 Goldsmiths, followed by Dirac and Heisenberg, pr ovided a quantum mechanical explanation that magnetic behavior is due to the electron spin.2 Over the course of technological advancement, extensive research efforts have been committed towards expanding the knowledge of magnetism and its prospective applications, developing into a broad range of technologically advanced devices we use today in our everyday life. A small number of app lications of magnetic material s include magnetic separators, loudspeakers, microphones, switches, sensors, data storage devices, frictionless bearings, medical devices, etc Traditional magnetic materials that are used in modern technological applications consist of 3D lattices of metals or ions possessing unpair ed electrons, the spins of which interact in a specific manner. Depending on the nature of these multi-dimensional long range interactions, several types of magnetic materials can be identified (Figure 1-1). If the nature of the interaction between the individual spins of the unpaired electrons aligns th em in a parallel fashion, the material is called a ferromagnet, while antiparallel alignment results in an antiferromagnet. If the individual spins interacting in antiparallel fash ion are of different magnitudes, a ferrimagnet results. When no interactions between spins are present, the material is called paramagnet and this causes a random orientation of the spin s in the material. Sin ce antiferromagnets and paramagnets give a total net spin of zero, magnets can only be built from either ferromagnets or ferrimagnets, where net spin is present. Magnets retain their magnetization after the removal of an applied magnetic field. This property is evidenced in a form of hyster esis loops in a plot of magnetization ( M ) vs applied field ( H ) (Figure 1-2). Material s that exhibit net magnetic moments (ferromagnets and ferrimagnets) often exist as a series of magnetic domains with each magnetic domain having a net

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19 magnetization. On the absence of an applied magne tic field, despite the na ture of interactions, the most thermodynamically favored situation is achieved when magnetization of a particle is minimized, in other words, different domains are randomly oriented with respect to each other, resulting in overall spin of zero. At the origin of the hysteresis plot in Figure 1-2, the magnetization of the sample is zero due to th e random orientation of domains. When a magnetic field is applied, below a certain temperature, re ferred as a critical or blocking temperature ( TB), the spins of different domains orient themselves in the direction of the magnetic field, leading to an enhancement of the net magnetization. At some pa rticular value of the fi eld, the situation will be reached where all spins are aligned, ther efore, no domains are present and the net magnetization is at its saturation point (“spin-up” situation, Figur e 1-2). Upon the removal of the magnetic field, the spins remain aligned and th e material does not lose its magnetization: it maintains a remnant magnetization (point C in Figure 1-2). As alignment occurs, the interaction of spins becomes strong enough to overcome dipole interactions and entropy considerations that maintain the random alignment of the domains. Once magnetic domains are oriented, a significant energy barrier, which mainly arises fro m a formation of the domain walls, has to be overcome in order to randomize domains back ag ain. This is the factor that directly gives magnetic properties to the material. When ferroma gnetic or ferrimagnetic material is magnetized in one direction, its magnetization will relax (reorient) back to zero until a strong enough field is applied in the opposite directi on (coercive field) (point D in Figure 1-2). By further increasing the field, saturation of the net magnetization can be reached in the opposite direction (“spindown” situation, Figure 1-2). This property of a magnet to retain its magnetization after the removal of an applied magnetic field is curren tly employed in the cons truction of permanent magnets and magnetic memory storage devices. In fact, magnetic stor age has long been the

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20 highest density method for storing digital info rmation, resulting in its widespread use in computer hard drives, DVDs and other devices. Magnets also do not require power to retain information, which gives them great flexibility when incorporated into devi ces. There is a great interest by high-tech companies in increasing th e density of information storage, which means increasing the number of bits of information in a given area of a hard driv e or other device. To get more digital information in a given area, each magnetic particle must be smaller. As a result, the attention of scientific and industrial co mmunities has been directed toward magnetic materials of nanoscale dimensions. There are two major approaches of how to obtain nanoscale magnetic materials. The first one is known as the “top-down” approach, whic h involves the fragmenta tion of bulk ferroor ferrimagnets, such as iron, iron oxide to a si ze smaller than a single domain (20-200nm). Such magnetic particles are known as superparamagnets. Below TB, the spins within a single domain of a superparamagnetic particle can be ferromagnetically aligned via short-range magnetic ordering by the application of a magnetic field. Superparamagnets have no domain formation related remnants like in bulk ferromagnets, but instead they possess magnetic anisotropy associated with the shape of the particles, which determines the energy barrier to the reorientation (relaxation) of the magnetization direction. The main disadvantage of this approach is that it gives a distribution of particle shapes and sizes, wh ich obviously complicates detailed studies of these systems, making difficult an accu rate assessment of variation of properties as a function of particle size.3 In addition, these particles are poorly or not at all soluble in organic solvents, as the fragmentation gives oxide fragme nts in most of the cases. Several fragmentation techniques have been devised in order to obta in nanoscale magnetic particles of uniform size.

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21 These techniques are based on s canning tunneling microscopy,4 Fe Mssbauer spectroscopy5 and biomineralization.6 The idea of using molecules rather than the ionic or metallic lattices of traditional magnets represents the molecular or “ bottom-up” approach to nanoscale magnetic materials. The first molecular compounds exhibiting bu lk physical properties, such as long-range magnetic ordering and a spontaneous magnetization below a critical temperature, were reported during the late 1980s, with the molecular ferrimagnet containing organic building blocks like TCNE (TCNE = tetracyanoethylene) reported in 1987,7 followed by the report of the molecular ferrimagnet based on copper(II)-manganese(II) derivatives in 1988.8 Such molecular-based magnets consist of an arrangement of interacting disc rete units, or buildi ng blocks, that possess a large number of unpaired electrons and are called spin carriers. The family of Prussi an blue derivatives represents one of the most studied examples of this cla ss of magnetic materials, where the Verdaguer group et al. in 1995 reported a ferrimagnet comprising chromium (III), vanadium (II) and vanadium (III), which orders above room temperature.9 In a few cases, spin carrier s can be organic radicals, and the magnetism entirely arises from 2 p electrons. The important development in this class of materials was the discovery by Nakazawa et al. that purely organic ma tter can indeed order ferromagnetically,10 inspired by the work of Fujita et al. 11 who showed how extremely strong interactions can be observed in polycarbenes. The subsequent discoveri es of organic magnets with higher critical temperatur es have also been reported,12 among which Palacio and colleagues reported organic weak ferromagnets orderi ng at temperatures as high as 35 K.13 The magnetic properties may also be provided by both transi tion metal ions and or ganic radical ligands.14-18 One of the most successful syntheses of such molecular magnets has been developed by the Miller group, who showed that V(TCNE)xy(CH2Cl2)(x ~ 2; y ~ ) is a disordered ferrimagnet

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22 above room temperature.19-22 At the same time a particularly attractive area of research has emerged, which involves the development of molecular materials with multiple properties, such as superconductivity and magne tism, which are difficult or impossible to combine in a conventional inorganic solid with a continuous lattice. Kurmoo et al. reported an organic superconductor coexisting in the same lattice of a molecular paramagnet,23 while Coronado et al. reported a molecular ferromagnet hosting in the lattice of an organic conductor.24 In recent years, many scientific efforts have been directed toward the investigation of ch iral magnets and the use of light to influence the magne tic properties of the materials.25 The molecular-based magnets described above derive their magnetic properties from a long-range magnetic ordering and/or intermol ecular interactions. And it was not until 1993, when the first example of a molecule, [Mn12O12(O2CMe)16(H2O)4]MeCO2H4H2O ([Mn12Ac]), that was able to behave as a magnet by itself was discovered.26-28 Magnetic studies of [Mn12Ac], originally synthesized in 1980,29 showed that this molecule functions as a single-domain magnetic particle, which below its blocking temperature ( TB~ 4K) exhibits the classical macroscale property of a magnet – magnetization hysteresis. Thus, at low temperatures it behaves as a superparamagnet. It has been conclu sively established that the magnetic behavior of [Mn12Ac] is intrinsic to the molecule and not due to the long-range magnetic ordering as observed in nanoscale magnetic domains of bulk magnets. Support for this conclusion comes from several experiments such as magnetiz ation relaxation data for frozen solutions30 or polymer-doped samples, the absence of any anomaly in heat capacity measurements31 (no longrange ordering) and high-fre quency, high-field electron para magnetic resonance (HFEPR) data.28,32

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23 Not unique to [Mn12Ac], such superparamagnet-like ma gnetic behavior has been observed for a variety of polynuclear metal complexes, al l of which have been termed single-molecule magnets (SMMs).28,33 Manganese carboxylate clusters represen t the vast majority of SMMs. The most extensively studied and ch aracterized type of SMM is the family of dodecanuclear manganese complexes ([Mn12]), [Mn12O12(O2CR)16(H2O)x] (R = -Me, -Ph, -CH2Ph, -CH2But, C6F5, CHCl2, -C6H4-2-Cl, -C6H4-2-Br, x = 4; R = -Et, -CH2Cl, x = 3),34-44 which also possesses the highest blocki ng temperatures ( TB ~ 4K) of all known SMMs.28,45-47 Over the years, a number of other Mn12 derivatives have been reported, incl uding oneand two-electron reduced salts, [Mn12O12(O2CR)16(H2O)x] 32,48,49 and [Mn12O12(O2CR)16(H2O)x] 2-,50-52 mixed carboxylate,53 and mixed carboxylate/non-carboxylate versions.54-62 Other known SMMs are: [Mn2],63 [Mn3],64,65 [Mn4],66-90 [Mn5],91 [Mn6],92-95 [Mn7],96 [Mn9],97,98 [Mn11],99 [Mn12],88,100-105 [Mn16],93,106,107 [Mn18],108,109 [Mn19],110 [Mn21],109 [Mn22],111 [Mn25],112 [Mn26],113 [Mn30]114,115 and [Mn84]116, as well as mixed manganes e – lanthanide SMM: [Mn11Ln4]45+.117 In addition, Fe-, V-, Co-, Ni-containing SMMs have also been reported: [Fe4],118-122 [Fe8],123-125 [Fe9],126,127 [Fe10],128 [Fe11],129 [Fe19],130 [V4],131 [Co4],132 [Co6],133 [Ni4],134 [Ni8],135 [Ni12],136,137 [Ni21].138 The SMM phenomenon originates fro m a large spin ground state ( S ) combined with a large and negative Ising (easy-axis) type magnetoan isotropy, gauged by the axia l zero-field splitting (ZFS) parameter, D . This combination results in an energy barrier ( U ) for the reversal of the magnetization direction, defined as S2| D | for integer spins and ( S2-)| D | for half-integer spin systems. In the presence of a strong uniaxi al anisotropy, the ground state is split into 2 S + 1 sublevels, each characterized by a quantum number, ms ( ms is a spin projection onto the easy-axis ( z -axis), –S ms S ). The energy of each sublevel is given as E( ms) = ms 2 D . When the sign of D is negative, the highest ms value is the lowest in energy. Thus, the ms = + S state can be viewed

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24 as the “spin-up” situa tion, correspondingly the ms = S state as the “spin-down”. Schematic representations of the poten tial energy barrier of an S = 10 spin ground state, split by the negative zero-field splitting ( D ), are shown in Figure 1-3. Both diag rams are for zero external magnetic field and depict the change in potential energy as the magnetic moment of a given molecule reorients between the “spin-up” ( ms = -10) and “spin-down” ( ms = +10) orientations through the intermediate quantized ms levels. Thus, for a molecule to reorient its spin al ong the magnetic anisotropy axis from the “spinup” state to the “spin-down” position, it must overcome an energy barrier. At high enough temperatures there is enough thermal energy ( kT ) available to flip the sp ins from “up” to “down” ( i.e ., kT > U ), as a result the magnetization reorient s (relaxes) quickly. However, below the TB, the thermal energy is smaller than the height of the barrier and the spin of a SMM can be magnetized in one direction. What makes SMMs unique magnetic systems is the coexistence of cl assical and quantum mechanisms for spin reversal. In fact, besides the above-described thermal activation over the energy barrier (classical mechan ism), the spin reversal can also occur through the barrier via quantum tunneling of the magnetization (QTM).139 Initially discovered for [Mn12Ac] in 1996,140142 the quantum tunneling pathway for the magnetiz ation relaxation in SMMs is experimentally observed as steps in the hysteresis loops (Figure 1-4). Each step corr esponds to an increase in the relaxation rate of magnetization that occurs at a particular value of an external magnetic field ( H = n D / g B) when a ms sublevel on one side of the potenti al energy barrier coincides in energy with a ms sublevel on the other side (Figure 1-5). When the tunne ling takes place between the lowest energy ms sublevels, it is called pure quant um tunneling or ground state quantum tunneling of magnetization (Figure 1-5, (a)). A pplication of an external magnetic field

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25 energetically stabilizes ms < 0 states, while destabilizing ms >0 (Figure 1-5, (b)). When the tunneling involves higher energy ms sublevels, it is refer to as thermally assisted quantum tunneling (TAQTM). At non-zero external magnetic field, when the tunneling process takes place between the resonant ms levels on the opposite sites of a barrier, it is called resonance quantum tunneling. Thermally assisted quant um tunneling was first observed for [Mn12Ac], whereas [Mn4]72 and [Fe8]125,143 SMMs were the first to show the ground state tunneling. It is imperative to add, however, that an appreciable transverse anisotropy component, measured by the rhombic anisotropy parameter E and the fourth order transverse term B4 4, must be present in order for quantum tunneling to occur. Transverse terms characterize the magnetic anisotropy in the plane perpendicu lar to the magnetic easy-axis ( i.e ., the xy plane). Transverse interactions cause quantum admixing of ms states and facilitate the tunneling. Sources of transverse anisotropy include: (i ) dipolar and exchange fields from neighboring molecules and hyperfine fields from 55Mn ( I = 5/2) nuclei ; (ii) low-symmetry components of the crystal field. In recent years, developments in nano-technolo gy have directed the at tention of researchers to materials, properties of which are intermedia te between classical and quantum in nature, or with the coexistence of the two, emerging in to a new field of study known as mesophysics (Greek from “mesos”, meaning “something in be tween”). The observation of quantum effects in SMMs has intensified the interest in these molecules, especially in terms of using them as study models in the development of a fundamental understanding of new physics behind the quantum phenomena, occurring at the frontier between mo lecular and bulk magnetism. Under this respect, SMMs are particularly attractive sy stems to study, since each molecu le in a crystal has the same spin, orientation, magnetic anisotropy and struct ure. As a result, macroscopic measurements performed on SMMs can give direct access to si ngle molecule properties. In addition, the

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26 chemistry of SMMs provides several other bene ficial characteristics. These include room temperature synthesis, purity, so lubility in a wide range of so lvents, and well defined periphery of organic groups, amenable to different modifications (small vs bulky, hydrophilic vs hydrophobic, etc .). The future holds several feasible applicati ons of SMMs, the most obvious of these being their potential use as molecular devices for highdensity storage of digital information. Here, the main idea is that an individual molecule woul d store one bit of binary information as the direction of its magnetization, i. e ., with the “spin-up” state, for example, representing 0 and the “spin-down” state representing 1. Da ta storage density is of part icular importance in computer hard drives, where the distance between bits of information defines limitations upon the speed and the capacity of the computer. The use of SMMs, which are just several nanometers in diameter, could increase the surface storag e densities as high as 30 terrabits/cm2, approximately 10,000 times greater than can be achie ved with current technologies.144 Clearly, a significant challenge that must be met in order for this idea to come to fruition is the synthesis of an SMM, functioning at technologically accessible temperatures (77 K and above). This will require molecules possessing a very large barrier to magnetization reversal. Since the barrier ( U ) is defines as the product of S and D , one would like to have an SMM with a very large spin S and a large negative axial ZFS parameter D . Furthermore, since QTM leads to a rapid reversal of the magnetization direction, i.e ., to a loss of information, the id eal SMM for this application would exhibit no transverse anisotropy. At the same time, the quantum property of SMMs has a potential to be employed in quantum computing. It has been shown theoreti cally that SMMs could be used as qubits in quantum computers.145-148 In a 2-level quantum mechanical system the two basic states are 0 and

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27 1. A qubit can exist not only in a state corresponding to the state 0 or 1 as in a traditional bit, but also in states corresponding to a quantum superpos ition of 0 and 1 states. In other words, a qubit can exist as a zero, a one, or simultaneously as both 0 and 1. Qubits hold an exponentially larger amount if information than tradit ional bits, which can only take th e value 0 or 1. A single crystal of an SMM could potentially serve as the storage unit of a dynamic random access memory device in which fast electron spin resonance pul ses are used to read and write information.145,146 This application would take advantage of th e quantized transitions between the numerous ms sublevels of the ground state of an SMM. Such a device would have an estimated clock speed of 10GHz and could store any number between 0 and 22 S -2.149 Consequently, to maximize the amount of available memory, it is desirable to have as large S as possible, as well as the large D , to maintain the separation of different s ublevels within the gr ound state manifold. It is obvious that the practical use of SMMs requires the development of innovative synthetic procedures to new examples of SMMs, i .e ., those with larger spin ground states that experience significant negative magnetoanisotropy. Se veral strategic directions towards this goal have been investigated and are presented in this dissertation. One approach involves the synthesis of high-nuclearity cluste rs, with the aim of obtaining molecules composed of a very large number of magnetic centers and sizes in the mesoscopic regi me. The synthesis, structural and magnetic characterization of the two highest nuclearity SMMs, [Mn84] and [Mn70], are presented in Chapters 2 and 3. At the same time, it is not only necessary to synthesize large molecules, but it is also important to promote suitable magnetic interac tions between the paramagnetic centers within them. The role of bridging ligands is, thus, of vital importance. Among these the preudohalides, such as azide (N3 -) and isocyanate ions (NCO-), have been known for a long time to efficiently

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28 mediate magnetic coupling between transition-meta l ions. While the synt hetic routes involving azide ligand has been intensively studied, the us e of isocyanate ion, especially in manganese cluster chemistry is significantly less explore d. In this work, the carboxylate abstraction approach has been employed to incorporate brid ging isocyanato groups, l eading to the formation of new manganese clusters of different nuclearitie s. The synthesis, struct ural characterization and magnetic studies of new [Mn11], [Mn4] and [Mn3] complexes are presented in Chapter 5. In addition, as part of the ongoing study of the fundamental aspects that could provide important insights of the quantum tunneling process, the accurate determin ation of the electronic properties of [Mn4O3Cl(O2CMe)3(dbm)3] complex was performed using high-field highfrequency single crystal electr on paramagnetic resonance (HFEPR) technique. Obtained results are discussed in Chapter 4 along with the magnetic characterization of [Mn4O3(N3)(O2CMe)3(dbm)3] and [Mn4O3Cl(O2CMe)3(dbm)3 complexes.

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29 Figure 1-1. Types of magnetic materials dependi ng on the nature of the interaction between spins. Figure 1-2. Hysteresis curve of a magnet, where M is magnetization, H is the applied magnetic field and Ms is the saturation value of the magnetization. Ferromagnets Antiferromagnets Ferrim agnets Paramagnets

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30 Figure 1-3. Equivalent schematic representations of the pot ential energy barrier of an S = 10 spin ground state, split by the negative zero-field splitting, D , in the absence of an applied magnetic field. Arrows represent the relativ e orientation of the spin vector with respect to the easy-axis of the molecule.

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31 Figure 1-4. Magnetization vs magnetic field hysteresis loops for the [Mn12Ac] complex, measured at a constant field sweep rate of 0.004 T/s in the 1.3K to 3.6K temperature range. Figure 1-5. Schematic representation of th e potential energy diagra m of an SMM with S = 10: (a) at zero-external magnetic field ( H = 0), showing thermally assisted and pure quantum tunneling, and (b) at non-zero external field ( H = n D / g B), showing thermally activated relaxation and resonant quantum tunneling. -1 -0.5 0 0.5 1 -1-0.500.51 M/Ms 0H (T) 0.004 T/s 1.3 K 1.8 K 2 K 2.2 K 2.4 K 2.6 K 2.8 K 3 K 3.6 K

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32 CHAPTER 2 GIANT [Mn84] SINGLE-MOLECULE MAGNETS AS THE FIRST MEETING OF THE “BOTTOM-UP” AND “TOP-DOWN” A PPROACHES TO NANOSCALE MAGNETIC MATERIALS 2.1 Introduction For more than a decade, manganese carboxylate complexes have captured the attention of the magnetochemistry community, largely due to th e fact that many of these have been found to function as single-molecule magnets (SMMs).26-28,71 SMMs are molecules that function as single-domain magnetic particles which, below their blocking temperature ( TB), exhibit the classical macroscale property of a magnet — magnetization hysteresis. Thus, in many ways, SMMs display the superparamagnetic-like behaviour analogous to that of traditional magnetic materials such as Co metal, iron oxides, etc . However, in contrast to the traditional magnets, magnetic properties of SMMs are of a purely molecu lar origin, arising from the combination of a large ground-state spin ( S ) and an Ising (easy axis) magne toanisotropy (negative zero-field splitting parameter, D ), which results in an energy barrier ( U ) to magnetization relaxation. With sizes residing at the smaller e nd of nanostructural ma terials, SMMs represent the molecular or ‘bottom-up’ approach to nanoscale magnetic materials,45 and are also referred to as molecular nanomagnets. In addition to the classical prope rty of magnetization hy steresis, SMMs also display the quantum properties of a microsca le entity, such as quantum tunnelling of magnetization (QTM)140-142 and quantum phase interference.150 Both classical and quantum properties of SMMs could be potentially employed in such practical applications as high density in formation storage and quantum computing. 145-148The feasibility of using SMMs in practice, however, is direc tly related to the size of U . Since U is defined as S2 | D | for integer and ( S2 1/4) | D | for half-integer spin sy stems, several synthetic strategies have been identified as potentially successful routes to new examples of SMMs, likely

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33 to possess both large S and D values. One such strategy invol ves the synthesis of molecular clusters of a very large nuclearity. In the most recent approaches to high nuclearity clusters, the addition of an alcohol into the reaction system, either by itself or as a part of a solvent combination, has been shown to yield a variety of new Mn complexes of different nuclearities. One such synthetic approach has been developed in our group, termed the “reductive aggregation” procedure,104,105,107 in which a high oxidation state Mn source (MnO4) is gradually reduced by an al cohol in the presence of excess carboxylic acid; as this reaction proceeds, the aggr egation of the cluster occurs. In these reaction systems, MnO4 is used as both the source of Mn atoms and as an oxidizing agent to ensure a Mn3+ and/or Mn4+ oxidation level of a resulting Mn cluster. In turn, the alcohol is used not only as a reaction solvent a nd a reducing agent for Mn7+, but also as a potential source of RO bridging ligands. The presence of carboxylic acid provides a necessary acidic environment to prevent the formation of insolubl e Mn oxides and/or hydroxides. The reductive aggregation reaction of n -Bu4NMnO4 with benzoic acid in MeOH produced a new type of [Mn12] cluster, ( n -Bu4N)2[Mn12O12(OMe)2(O2CPh)16(H2O)2],104,105 whereas the same reaction, but using different carboxylic acids ( i.e. , phenylacetic acid, chloroacetic acid and bromoacetic acid) resulted in a formation of a different product: [Mn16O16(OMe)6(O2CR)16(MeOH)6] ([Mn16], R = -PhCH2, -ClCH2, -BrCH2).107 The acetate version of [Mn16], [Mn16O16(OMe)6(O2CMe)6(MeOH)3(H2O)3]6H2O, reported by Murray and et al .,106 was obtained from the comproportionation reaction of [Mn(NO3)2]4H2O with n Bu4NMnO4 in MeOH/MeCO2H. A similar comproportionation reaction of [Mn(O2CMe)2]4H2O with KMnO4 in a 60% solution of acetic acid in metha nol resulted in the formation of the chain polymer {[Mn(OH)(O2CMe)2]MeCO2HH2O}n. 151 Clearly, the reductiv e aggregation reactions

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34 are very complex, with the reaction solutions containing several speci es in equilibrium. A complicated combination of factors such as relati ve solubility, lattice en ergies, crystallization kinetics and/or other criteria determines the identity of the isolated product. Since the reactions of either MnO4 or various Mn salts with MnO4 in MeOH / RCO2H were successful in yielding different Mn com pounds, it is obviously worthwhile to further explore the reaction system using preformed high-nuc learity clusters as star ting materials. In the past, members of the [Mn12O12(O2CR)16(H2O)4] ([Mn12]) family of compounds have been shown to be excellent precursor complexes to ne w high-nuclearity products. For example, the alcoholysis of [Mn12O12(O2CCH2 tBu)16(H2O)4] in MeOH / CH2Cl2 resulted in the formation of [Mn21O24(OMe)8(O2CCH2 tBu)16(H2O)10],152 whereas the recrystallization of the same [Mn12] complex in a solvent mixture comprising CH2Cl2 and MeNO2 led to the isolation of such high nuclearity cluster as [Mn30O24(OH)8(O2CCH2 tBu)32(H2O)2(MeNO2)4].114,115 In addition, [Mn12] clusters represent a soluble source of Mn3+ ions. High-spin Mn3+ ions in near-octahedral geometry undergo the Jahn-Teller (JT) distortion and thus posse ss axially elongated axes whose parallel alignment provides a molecule w ith an axial easy-type magnetoanisotropy. Thus, in a continuing effort to prepare new high nuclearity Mn complexes with potentially interesting structural and/or magnetic propertie s, we have been investigating whether the alcoholysis reactions of [Mn12] complexes could lead to even larger SMMs, i.e. , with sizes approaching those of classical nanoscale magnetic particles; a nd, if so, whether such large SMMs could still demonstrate the coexistence of classical and quantum effects. Can the molecular (or ‘bottom-up’) approach reach the size regime of the classical (or ‘top-down’) approach to nanoscale magnetic ma terials? Indeed, herein we re port a new family of giant [Mn84]

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35 SMMs, which are both the largest SMMs and the largest manganese compounds to date. Structural and magnetic properties of [Mn84] complexes will be described in detail. 2.2 Results and Discussion 2.2.1 Syntheses As part of a detailed study of the alcoholysis reactions of [Mn12O12(O2CR)16(H2O)n] (R = various, n = 3, 4) complexes, the reaction of [Mn12O12(O2CMe)16(H2O)4]2MeCO2H4H2O ( 1 ) with 4 equivalents of n -Bu4NMnO4 was carried out in MeOH in the presence of 63 equivalents of acetic acid. The resultant red-brown solution was filtered, layered with a variety of solvents and left undisturbed over a period of several we eks. Initially, red-brown hexagonally shaped crystals were obtained from the layering of the reaction mixture with Et2O. The IR analysis indicated the formation of a new Mn co mplex with a very large and broad Mn-O2 region. However, the crystallographic identification of this compound turned out to be extremely challenging. The obtained crystals, once removed fr om the mother liquor, lost solvent extremely fast, resulting in their very quick disintegra tion and thus making it very difficult to collect crystallographic data due to the poor diffr action pattern. The synt hetic procedure was subsequently modified using other solvents of crys tallization. Over a period of several weeks, the layering of the reaction mixture with CHCl3 resulted in the formation of well shaped red-brown hexagonal crystals in ~20% yield (based on to tal Mn). However, even though the obtained crystals were significantly larger in size, the quality of the crystals was variable. Crystals suitable for X-ray diffraction studies were obtained approx imately 18 months after th e initial isolation of the compound, and were identified as [Mn84O72(O2CMe)78(MeO)24(MeOH)12(H2O)42(OH)6] ( 3 )H2OCHCl3. The formation of complex 3 is summarized in eq. 2-1.

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36 6 [Mn12O12(O2CMe)16(H2O)4] + 12 ( n -Bu4N)MnO4 + 24 MeCO2H + 36 MeOH + 54 H+ + 84e [Mn84O72(O2CMe)78(MeO)24(MeOH)12(H2O)42(OH)6] + 12 ( n -Bu4N)O2CMe + 30 MeCO2 + 24 H2O (2-1) The reaction system was further investigated by replacing complex 1 with an equivalent amount of Mn(O2CMe)2H2O. The red-brown hexagonally-shaped crystals were obtained from the layering of the reaction solution with either CHCl3 or CH2Cl2 and were identified by IR and X-ray unit cell analyses as being identical to 3 . In the case where Mn(O2CMe)2H2O was used as a starting material, however, it became appare nt that the amount of acetic acid is another important factor in the formation of 3 , since the use of a significan t excess of acetic acid led to the formation of complex 1 instead. The solubility tests performed on complex 3 showed that it is only moderately soluble in MeCN, which obvious ly limited further reac tivity studies of the giant [Mn84O72]108+ unit. Therefore, by using other members of the [Mn12] family of complexes, with more bulky carboxyl ate ligation (R = -C2H5, -C6H5, etc .) as starting ma terials instead of 1 , and corresponding RCOOH instead of MeCO2H, one would expect to obtain either a similar Mn84 analogue with a significantly improved solub ility or, possibly, a different giant cluster. Thus, the reaction of [Mn12O12(O2CEt)16(H2O)3]4H2Otoluene ( 2 ) with 4 equivalents of n Bu4NMnO4 in MeOH, immediately followed by an addi tion of 63 equivalents of propionic acid afforded a red-brown solution. The reaction solution was then layered with a variety of solvents and left undisturbed over a period of several weeks. However, in contrast to the formation of complex 3 , which required a long time to obtain a cr ystalline product, sl ow diffusion of MeNO2 into the reaction solution afforded red-brown needle s in an excellent yield of 56% (based on total Mn) within a week from the in itial crystallization setup. The obtained compound was found to be soluble in many organic solvents, such as CH2Cl2, MeCN, CHCl3, Et2O, etc. , in agreement with

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37 the initial assumptions. The IR spectrum and elem ental analysis indicated the formation of a large Mn cluster, which was identified by X-ra y crystallography as the propionate analogue of 3 , [Mn84O72(O2CEt)81(MeO)24(MeOH)18(H2O)30(OH)3]( 4 )x solvents. Attempts to repeat the same reaction with [Mn12O12(O2CR)16(H2O)4] and RCO2H (R = -Ph, -CH2Ph, -C6H4-2-Cl Ph), as well as [Mn12O12(O2CCH2 tBu4)16(H2O)4] and tBu4CH2CO2H instead of [Mn12O12(O2CMe)16(H2O)4] and MeCO2H, were also carried out . In the former case, bleaching of the reaction solutions and/or forma tion of white crystalline products was observed, indicating a complete reducti on of all Mn ions to Mn2+. In the later case, very thin red-brown needles were obtained by layeri ng the reaction solution with MeNO2. The IR and elemental analyses suggested a formation of a t -butylacetate analogue of 3 . However, numerous attempts to characterize the obtained crystals by X-ray cr ystallography were unsuc cessful due to a poor quality of the crystals. In addition, attempts to obtai n a benzoate analogue of 3 via the carboxylate substitution procedure,48 developed previously in our group and su ccessfully employed to synthesize various derivatives of the [Mn12] family of complexes, were also unsuccessful. The layering of the reaction solution with either Et2O or Et2O/hexanes produced a mixtur e of dark brown plates (~95%) and orange-brown needles (~5%), which we re identified by IR and elemental analysis as [Mn9O7(PhCO2)13(PhCO2H)2] and [Mn6O2(O2CPh)10(HO2CPh)4], respectively. Analogues of these complexes have been reported previously by our group153,154, all possessing a diamagnetic spin ground state. In all of the above cases no further inve stigations were pursued. 2.2.2. X-ray crystal structures of [Mn84O72(O2CMe)78(MeO)24(MeOH)12(H2O)42(OH)6](3)H2OCHCl3 and [Mn84O72(O2CEt)81(MeO)24(MeOH)18(H2O)30(OH)3](4)x solvents Data collection and structure re finement details for complexes 3 H2OCHCl3 and 4 x solvents are listed in Table 2-1. PovRay representation of the entire [Mn84] molecule of 3 ,

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38 highlighting a labeled core of the [Mn14] asymmetric unit is pr ovided in Figure 2-1a. A stereoview of 3 is shown in Figure 2-1b. PovRay repres entation of the molecular structure of 4 is provided in Figure 2-5. Selected interato mic distances and angles for complexes 3 are listed in Table A-1. Selected interatomic distances for complex 4 are listed in Table A-2. Complex 3 H2O12CHCl3 crystallizes in hexagonal space group P 6 with the asymmetric unit containing 1/6 of the [Mn84] molecule, [Mn14O12(O2CMe)13(MeO)4(MeOH)2(H2O)7(OH)1] (Figure 2-2), and approximately 25 H2O and 2 CHCl3 solvent molecules of crystallization, which ar e severely disordered. The structure can be described as a Mn84 torus composed of alternating near-linear [Mn3( 3-O)4] and cubic [Mn4( 3O)2( 3-OMe)2] subunits, linked together via 2-MeCO2 and 3-O2 groups. The structure has a C6 crystallographic symmetry and consists of six Mn14 repeating units, i.e ., [Mn14]6. All the metal centers are six-coordinate. Close insp ection of Mn-O bond lengths (Table A-1), bond valence sum (BVS) calculations155,156 for the Mn atoms (Table 22), and the detection of JahnTeller (JT) elongations as expected for a d4 metal ion in near-octahedral geometry, identified the metal ions of 3 as all being in the Mn3+ oxidation state. BVS calculati ons were also performed on the inorganic oxygen atoms of 3 to identify their degree of protonation (Table 2-3). These revealed that the asymmetric unit contain 12 3-O2 ligands, 4 3-OMe groups (bridging Mn ions of cubic subunits), 2 terminal MeOH mol ecules (O10, O35) (coordinated to Mn3 and Mn10 ions of [Mn3( 3-O)4] subunits), 6 terminal H2O molecules (O3, O9, O14, O23, O30, O31) and 1 terminal HO group (O12). The assignment of O12 as HO was made according to the following considerations: with all Mn ions being in the Mn3+ oxidation state, the overall charge balance of the neutral molecule would requ ire the assignment of either one of the methanolic groups (O10, O35) as MeO, or one of the terminal water molecules as being an HOgroup instead. Even

PAGE 39

39 though examples of a terminal MeO group bound to the Mn3+ ion on the Jahn-Teller (JT) elongated and non JT elo ngated axis are known,157,158 this coordination for the MeO group is extremely rare and in a majority of cases the terminal group is preferably MeOH. In contrast, many examples of a terminal OH group are known.159-163 In the present case, however, the fact that all terminal oxygen atoms in question are located on JT elongation axes makes the assignment of a particular oxygen atom as an HO group very difficult. Nevertheless, close examination of Mn-O bond lengths revealed that the Mn3–O12 distance (2.109 ) is the shortest one in comparison to those of other termin al Mn-O bonds (2.147 – 2.309) (Table 2-4), thus, making O12 the most feasible candidate for being a terminal HO. The BVS value of 0.339 obtained for the O12 atom is a little lower than that for a typical HO ion (BVS ~1), which may be due to the hydrogen-bonding contacts with solv ent molecules, abundantly present in the cavity of the [Mn84] torus. Crystallographic data refineme nt revealed that the MeCO2 group, bridging Mn10 and Mn11 (and their symmetry-related partners) has a 50% occupancy disorder with terminal H2O (O23), coordinated to Mn7. The arra ngement of Mn atoms in the [Mn3( 3-O)4] units is not completely linear but slightly V-shaped ( e.g ., Mn3-Mn2-Mn1 = 163.78 , Mn8-Mn9-Mn10 = 167.75 ). In addition, the planes, defined by Mn and 3-O2 ions of each [Mn3( 3-O)4] unit, are nearly perpendicular to one another, w ith a dihedral angle being equal to 81.2 .164 Such arrangement of Mn atoms could be an important c ontribution to not all of JT axes being parallel to one another (Figure 2-2). The non-parallel alig nment of JT axes redu ces the axial anisotropy of the molecule, and as a result influences its ma gnetic properties. A bett er appreciation of the structure and the size of the molecule is provid ed by the space-filling plots of Figure 2-3, which show that the torus has a diameter of about 4.2 nm and a thickness of about 1.2 nm, with a

PAGE 40

40 central cavity of diameter 1.9 nm. [Mn84] molecules order within a crystal in hexagonal packing manner, forming nanotubular stacks pa rallel to the crystallographic c axis and to their neighbors (Figure 2-4). The packing architecture closel y resembles densely packed straws in a box. Alternatively, since the molecules in the neighboring chains are ex actly adjacent, the crystalline structure of the [Mn84] torus can be also described as consisting of gr aphite-like [Mn84] sheets lying on top of each other with perfect registry. Complex 4 x solvents crystallizes in monoclinic space group P 21/c with the asymmetric unit consisting of the entire [Mn84] molecule. The final refinement of the crystal structure of 4 has proven to be extremely challenging due to a large degree of disorder in carbon atoms of the peripheral propionate ligands, which prevented the structure been accurately finalized. Nevertheless, the structure is of suffici ent accuracy to determine that complex 4 contains an identical core to that of 3 , composed of 12 altern ating near-linear [Mn3( 3-O)4] and 12 cubic [Mn4( 3-O)2( 3-OMe)2] subunits, linked together via 2-EtCO2 and 3-O2 groups. Examination of metric parameters, BVS calculations for the Mn atoms (Table B-1) and the presence of JT elongations on 84 Mn atoms, id entified all Mn atoms of 4 as being Mn3+. In comparison to the crystal structure of 3 , several structural differences have been identified: i) there are 81 bridgingRCO2 groups in the crystal structure of 4 instead of 78, with 3 additional carboxylate groups bridging Mn atoms of [Mn3( 3-O)4] subunits; ii) there are several differences in the number and positions of terminal H2O and MeOH ligands; and iii) 3 terminal HO groups have been assigned to complete the peripheral ligation of the molecu le. The assignment was based on charge balance considerations and the fact th at the crystal structure of 4 nearly analogous to that of 3 . Space-filling representations of complex 4 are shown in Figure 2-6 and Figure 2-7. The outer diameter of the molecule is about 4.4 nm with a thickness of about 1.4 nm, and a central

PAGE 41

41 cavity of approximately 1.8 nm (Figure 2-6). Similarly to 3 , [Mn84] molecules of 4 order within a crystal in a hexagonal close packing manner (Fi gure 2-7, a), forming supramolecular nano-size tubes in the direction of the crystallographic a -axis (Figure 2-7, c). In the case of complex 4 , however, molecules in neighboring tubular chai ns are not exactly adjacent as those in 3 , but alternate one another in a zigzag-t ype packing fashion (Figure 2-7, b). 2.2.3 Magnetochemistry of Complexes 3 and 4 2.2.3.1 Direct Current Magnetic Susceptibility Studies Direct current (DC) magnetic susceptibilit y studies involve the variable-temperature measurement of magnetization induced in a samp le by a constant applied magnetic field. The obtained data can be interpreted in te rms of molar magnetic susceptibility ( m) or effective magnetic moment ( eff) and contain information about the nu mber of unpaired electrons and the nature of their interactions. Va riable-temperature magnetic susc eptibility measurements were performed on a vacuum-dried microcrystalline sample of complex 3 H2O, restrained in eicosane to prevent torquing. The DC magnetic susceptibility data were collected in the 5.0 300 K range in a 1 kG (0.1 T) magnetic field. For 3 H2O, the mT value decreases steadily with decreasing temperature (F igure 2-8) from 166.49 cm3 mol-1 K at 300 K to ~ 95 cm3 mol-1 K at 50 K, below which mT decreases more rapidly to 23.32 cm3 mol-1 K at 5 K. The value of mT at 300 K is significantly lower than the value of 252 cm3 mol-1 (for g = 2), expected for a cluster of 84 non-interacting Mn3+ (S = 2) ions. Thus, the data strongly suggest the presence of predominantly antiferromagnetic exchange interactions within the molecule. Variable-temperature magnetic susceptibility measurements were also performed on vacuum-dried microcrystalline sample of complex 4 H2O, restrained in eicosane to prevent torquing. The magnetic behavior of complex 4 is very similar to that of 3 (Figure 2-9). The mT

PAGE 42

42 value decreases with decreas ing temperature from ~ 167.63 cm3 mol-1 K at 300 K to ~ 101.16 cm3 mol-1 K at 50 K, below which mT decreases more rapidly to 29.90 cm3 mol-1 K at 5 K, indicative of predominately antiferro magnetic exchange interactions. To determine the exact values of the many Mn2 pairwise exchange interactions ( Jij) within the [Mn84] molecule and to find all of the possible spin states and their energies, the spin Hamiltonian for this complex would have to be diagonalized.165 However, for a system of 84 S = 2 Mn3+ ions, the total degeneracy of the spin system is equal to (2 S +1)n, or 584. A matrixdiagonalization approach would invol ve a matrix of dimensions 584 584, which is clearly unfeasible with current computing capabilities. In addition, due to the very large size and the complexity of the system, it was not possible to apply the equivalent ope rator approach based on the Kambe vector coupling method,166 which is usually successf ully employed for smaller nuclearity systems to obtain a theoretical mT vs T expression for fitting the experimental data. However, it was important to id entify the ground state spin ( S ) of complexes 3 and 4 . The ground state spin value of a particular complex can be determined by performi ng variable-temperature, variable field magnetization ( M ) measurements, typically in the 1.8 – 10 K temperature range and in an applied DC field ( H ) ranging from 0.1-7.0 T. The experi mental data are then fit using the program MAGNET,167 by diagonalization of the spin Hamiltonian matrix using full powderaverage method that assumes that only the ground state is populated and incorporates axial zerofield splitting ( DSz 2) and Zeeman effects.86 However, attempts to f it the experimental data collected for complex 3 were not successful. This was not surprising and actually expected for such a high nuclearity complex in which the ex change interactions among many constituent Mn ions result in a very high density of spin states. As a result, there are many excited states that are low-lying in energy (relative to kT ) and thus are populated even at the lowest temperatures

PAGE 43

43 employed. With such an almost continuum spectrum of spin states present, there is always a danger that excited states will be populated and that ms levels of excited states with S values greater than those of the ground st ate will cross in energy with the ground state in the applied DC field, making the correct determination of S from the DC experiment ve ry difficult, if possible at all. The problem of low-lying excited states and the difficulty in re liably obtaining the ground state S from DC magnetization measurements have been previously discussed for other high nuclearity Mn clusters, such as [Mn16],107 [Mn18],108,168 [Mn21],152,169 [Mn30].114,115 In such situations, a much more reliable method of obtaining the ground state S is the alternating current (AC) magnetic susceptibility measurements, which do not employ a DC field. For this reason, AC susceptibility studies were performed on complexes 3 and 4 . 2.2.3.2 Alternating Current Magnetic Susceptibility Studies In an AC experiment, a weak field (typically 1-5 G), oscillating at a particular frequency (), is applied to a sample and the magnetization is measured with decreasing temperature. When there is enough thermal energy ( kT ) for the magnetization of the mo lecule to keep up with an applied oscillating ac field, only the real (in-phase) (m' ) component of AC susceptibility is observed (plotted as m'T vs T ), and it is equal to the DC susceptibility. At low enough temperature, the available thermal energy beco mes insufficient to overcome the barrier to magnetization relaxation. As a result, the magnetiza tion of the molecule cannot reorient (relax) fast enough to keep in-phase with the oscillating field. This effect is experimentally monitored as an appearance of a non-zero out-of-pha se AC susceptibility signal (m ") in a plot of m " vs T . The appearance of a frequency-dependent m" signal, accompanied by a concomitant frequencydependent decrease in the in-phase signal (m'T ), is indicative of slow magnetization relaxation, a diagnostic property of a SMM.

PAGE 44

44 The AC susceptibility data are also an excellent source of ki netic data. A maximum in the out-of-phase signal (m ") is observed when the rate at wh ich the magnetization of a molecule relaxes is equal to th e angular frequency ( = 2) of the oscillating AC field. Thus, the relaxation rates (1/, where is the relaxation time) at a give n temperature can be obtained from the = 1/ relationship at the maxima of the m " peaks. The 1/ vs T data are then used to obtain the effective energy barrier ( Ueff) to magnetization relaxation. AC susceptibility data were collected on vacuum-dried microcrystalline samples of complexes 3 H2O and 4 H2O in the 1.8-10 K temperature range in a zero DC field and a 3.5 G AC field, oscillating at ei ght frequencies ranging from 5 to 1500 Hz. The in-phase (m'T ) and out-of-phase ( m" ) signals for complexes 3 and 4 are shown in Figure 2-10 and Figure 2-11, respectively. Clearly, the m" peak maxima for both 3 and 4 lie at temperatures below the operating limit of our SQUID (1.8 K). Nevertheless, these AC da ta do suggest that complexes 3 and 4 might be SMMs. The confirmation of this fact and a detailed study of magnetization relaxation rates require studies at temperatures below 1.8 K, which will be discussed in the next section. For both complexes, the value of m'T decreases linearly as the temperature is lowered from 10 K until ~2.5 K and then drops dramaticall y. The abrupt frequency-dependent decrease in the m'T signal and the concomitant appear ance of the frequency-dependent m" signal below 2.5 K are indicative of slow magneti zation relaxation. It should be poi nted out, however, that the presence of a frequency-dependent m" signal is necessary but not sufficient proof that a molecule functions as a SMM, as such signals can also be due to intermolecular interactions and phonon-bottleneck effects.170

PAGE 45

45 At temperatures higher than those associat ed with slow magne tization relaxation, the m'T vs T plot does not displa y a plateau, but instead m'T value decreases significantly with decreasing T . For a well isolated ground state ( vs kT ), the m'T value at the employed temperatures would be expected to be esse ntially temperature-i ndependent. A downward slopping m'T vs T plot is a strong indication of low-lying excited states with S values greater that the ground state S . As a result of the depopulation of excited states with decreasing temperature, the m'T value decreases. The extrapolation of the in-phase m T signal down to 0 K, avoiding the drops due to the onset of slow magnetiz ation relaxation, gives values of ~16 and ~18 cm3 mol-1 K respectively for 3 and 4 . The obtained values of m'T are indicative of S = 6 spin ground state (for g < 2) for both compounds, since mT = ( g2/8)( S ( S +1)). Single-crystal magnetization hysteresis measurements were perf ormed in order to confirm the SMM behavior of 3 and 4 . 2.2.3.3 Hysteresis Studies below 1.8 K Magnetization hysteresis is a classical property of a magnet and is also a diagnostic feature of SMMs and superparamagnets below their blocking temperature ( TB). To establish whether complexes 3 and 4 are SMMs, magnetization vs applied DC field data down to 0.04 K were collected on singl e crystals of 3 H2O12CHCl3 and 4 x solvents using an array of microSQUIDs.171 The results obtained from the hysteresis studies of 3 and 4 are essentially the same and, thus, only those obtained for complex 3 will be discussed. The ma gnetization response at a 0.035 Ts-1 DC field sweep rate for complex 3 is shown in Figure 2-12 (top). Hysteresis loops for both 3 and 4 were observed below 1.5 K, establishing [Mn84] compounds as the largest nuclearity SMMs yet discovered. Coercivities (w idths) of hysteresis loops increase with decreasing temperature and increasing sweep rate (not shown), as expected for the

PAGE 46

46 superparamagnet-like properties of a SMM. The ma gnetization in Figure 2-12 (top) is plotted as spin ( S ) per molecule (determined using quantitativ e molar magnetization data). The saturation value indicates a molecu lar ground state spin of S = 6, thus establishing S = 6 as a ground state spin for complex 3 .Similarly, the ground state spin of 4 has been also assigned as S = 6. These results confirm the spin value that was prel iminary determined by the AC susceptibility measurements. The hysteresis loops do not display the step-like features indicative of QTM that are visible in the hysteresis loops of certain smaller nuclearity SMMs.72,73,82,125,141 It is possible, however, that steps are present but smeared out by broade ning effects arising from the presence of lowlying excited states and a distribution of magnetization relaxation barriers ( i.e ., a distribution of D values), consistent with a distribution of molecular environments. The separation between steps is directly proportional to D , thus a distribution in D values will cause a distribution in step positions and a resulting broadening of these steps. Distribution of molecular environments could result from disordered ligands and the large num ber of severely disordered solvent molecules present in the crystal structure. It is a well known fact that the magnetic properties of SMMs are very sensitive to even relatively small variations of local molecular environments, such as caused by disordered lattice solvent mol ecules and/or ligand disorder. For 3 and 4 , the large numbers of disordered solvent molecules in the central cavit y readily rationalize a di stribution of molecular environments. Hysteresis loops showing no QT M steps are not uncommon when studying larger SMMs and have been previously observed for [Mn18],108,168 [Mn21], 152,169 and [Mn30].114,115 However, even with no visible steps present, close examination of hysteresis loops of 3 revealed an important indication of QTM o ccurring in this large cluster. Be low 0.3 K, the coercivity of the loops becomes temperature-independent. This fa ct is indicative of th e ground state tunneling,

PAGE 47

47 occurring between the lowest energy ms 6 levels of the S = 6 spin manifold. To confirm this observation and to determine the effectiv e barrier to magnetization relaxation ( Ueff), AC magnetic susceptibility below 1.8K and magneti zation decay studies were performed down to 0.04 K on a single crystal of 3 H2O12CHCl3. In magnetization decay experiments, the magnetization was first saturated in one direction by application of a large DC field at 5 K, the temperature was then lowered to a chosen valu e in the 0.04 1 K range, the field was switched off, and the magnetization of the sample was m easured as a function of time. Both AC and magnetization decay methods provide a direct means of gauging the relaxation rate (1/). Obtained 1/ vs T data were then used to construct an Arrhenius plot (Fi gure 2-12 (bottom)), based on the Arrhenius relationship of eq 2-2, where Ueff is the effective barrier to magnetization relaxation, 0 is the pre-exponential factor, and k is the Boltzmann constant. = 0 exp( Ueff/ kT ) (2-2) The fit of the thermally activat ed region above ~ 0.5 K, shown as the dashed line in Figure 2-12, gave Ueff = 18 K and 0 = 5.7 10-9 s. The relaxation rate levels off below 0.5 K, and below ~0.2 K it is temperature-independent, cons istent with relaxation only by ground state tunneling. Such temperature-independent relaxa tion of magnetization due to QTM has been previously observed for seve ral other SMMs, including [Mn16],107 [Mn18],108,168 [Mn21],169 and [Mn22].111 2.2.4 Electronic Absorption Spectra of complex 3 The electronic spectra of complex 3 in the UV-Vis region were collected to investigate if the cluster retains its structure in solution. When a single species give rise to the absorption, a linear relationship between absorbance and conc entration of absorbing species is observed, i.e ., the Beer-Lambert law (or Beer's law) is strictly obeyed. The general Beer -Lambert law is written

PAGE 48

48 as: A = c l , where A is the absorbance, is the molar absorbtivity, c is the concentration of the compound in solution and l is the path length of the sample. The electronic spectra of complex 3 in MeCN is shown in Figure 2-13. A broad shoulder of a very high intensity peak is visible below 600 nm, with a maximum at 474 nm. Based on comparisons to the spectra reported for various mononuclear and dinuclear manganese complexes172 as well as for several manganese minerals,173 it is possible to suggest reasonable assignments of the observed bans. Generally, very intense high energy bands are assigned as the charge transfer (CT) bands, while the weaker absorptions above ~ 550nm are usually attributed to spin-allowed and symmetry forbidden d d transitions of a distorted octahedral geometry Mn3+. Four spin-allowed d d bands due to electronic transitions in Mn3+ at the distorted octahedral site are predicted to occur in spect ra. One of these transitions, re presenting an electron transfer between the two eg orbitals is expected to occur at comparativel y low energy, while three transitions involving electron tran sfer from each of the three t2g orbitals to the energetically highest eg orbital are expected to be closely spaced at higher ener gies. In Figure 2-13, no clearly visible bands are observed above 550 nm. The bands might be present, but significantly broadened by the close proximity of higher in tensity bands. The assignment of a shoulder band can be made based on the valu e of the molar absorbtivity ( ). For spin-allowed and symmetry forbidden d d bands, the expected value is in the 10-100 cm-1 M-1 range, whereas for CT bands the is generally in the 1000-10000’s cm-1 M-1 range.174 Figure 2-14 shows the plot of absorbance vs concentration for the transition at 474 nm. The linear leastsquare fit of the experimental data gave the value of = 30735 cm-1M-1, on which basis the 474 nm band can be reasonably assigned as a ligand-to-metal char ge transfer (LMCT) band, typical of Mn-oxo complexes.172 In addition, the linear relationship between the absorbance and concentration

PAGE 49

49 observed for complex 3 confirms the fact that this giant [Mn84] cluster retains its structure in MeCN solution. 2.3 Conclusions Alcoholysis of [Mn12] complexes has proven to be a successful synthetic route to exceptionally high nuclearity manganese clusters, i.e. , [Mn84] complexes 3 and 4 . These molecules are not only the highest nuclearity Mn clusters known to date, but are also soluble, monodesperese and crystalline, a nd retain their structure in so lution. They respectively possess 4.2 and 4.4 nm porous structures, and crystallize as highly ordered nanotubular stacks. Such large wheel-like structural types have been pr eviously seen only in molybdenum chemistry,175 with the largest curren tly known being the [Mo154]176 and [Mo176]177 compounds reported by Mller et al . Although they contain more metal atoms than [Mn84], the [Mo154] and [Mo176] wheels have diameters of ~3.4 and ~ 4.1 nm respectively. Thes e and other giant polyoxometallates,178,179 are diamagnetic, or nearly so, and n one of them has thus been found to exhibit SMM properties. Magnetic characterization of 3 and 4 revealed a relatively small spin ground state of S = 6, but low-temperature micro-SQUI D measurements confirmed the presence of hysteresis loops below 1.5K for both complexes, thus, firmly establishing 3 and 4 as new giant SMMs. Furthermore, what makes these molecules even more interesting is that apart from the classical property of magnetization hysteresis, they also display ground-state QTM, the occurrence of which was confirmed by the presence temperatur e-independent relaxation of magnetization at low temperatures. But although complexes 3 and 4 are very large by molecular standards, it is imperative to ask how they compare to classical nanoparticles. In Figure 2-15 are compared the sizes of [Mn4], [Mn12], [Mn30] and 3 and 4 SMMs with that of a 3 nm Co nanoparticle,180 all drawn to the same

PAGE 50

50 scale. With diameters of slightly larger than 4nm, Mn84 complexes are thus of comparable size to the smallest nanoparticles. For exampl e, the total number of atoms in 3 is 1032, the same as the 3 nm Co nanoparticle, which contains ~1000 Co atom s. Of course, the former has a very different shape, given its central cavity and essentially wheel-like rather than sp herical structure. An additional way, particularly in th e physics literature, of compari ng the ‘size’ of magnetic systems is by their Nel vector ( N , the sum of the individual spins), which are 7.5, 22, 61 and 168 for [Mn4], [Mn12], [Mn30] and [Mn84], respectively. This is the scal e used in Figure 2-15. With a value of 168, [Mn84] is a far larger spin system than a ny other molecular cluster and is at the lower limit of values found for classical nanopar ticles, which can range from a few hundred to many thousands depending on the precise size and constituent metal; for the 3 nm Co nanoparticle shown, the Nel vector is approximately 1000. Thus, molecular [Mn84] clusters, with dimensions compatible to those of cl assical magnetic nanopartic les and exhibiting both classical and quantum properties, can be essentia lly regarded as the firs t meeting point of the bottom-up and top-down approaches to nanoscale magnetic materials. 2.4 Experimental Section 2.4.1 Syntheses All preparations and manipulations were pe rformed under aerobic conditions at ambient temperature, using reagents and solvents as received, unless otherwise stated. [Mn12O12(O2CMe)16(H2O)4]( 1 )MeCO2H4H2O, [Mn12O12(O2CEt)16(H2O)3]( 2 )4H2Otoluene and n -Bu4NMnO4 were prepared as described elsewhere.29,48,181,182 [Mn84O72(O2CMe)78(MeO)24(MeOH)12(H2O)42(OH)6](3)H2OCHCl3: To a slurry of 1 (0.425 g, 0.206 mmol) in 15 ml of MeOH was adde d over a period of two minutes a freshlyprepared solution of n -Bu4NMnO4 (0.3 g, 0.831 mmol) in MeOH (10 ml) and glacial acetic acid (0.75ml, 13.05 mmol). The reaction mixture was left under magnetic stirring for a few more

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51 minutes, and then filtered to give a red-brown f iltrate. Equal amounts of th e filtrate were placed in five different vials and layered with chlo roform. After a few weeks reddi-brown hexagonal crystals appeared, and were left to grow for several more weeks to give well shaped X-rays quality crystals. The crystals of 3 H2O12CHCl3 were found to lose solvent when isolated, and therefore were kept in contact with their mother liquor for X-ray crystallography and other single-crystal studies, otherwise, the crystals were collected by f iltration, washed with chloroform and dried in vacuum. The yield wa s 0.10 g (20% based on total Mn). Vacuum-dried material analyzed as 3 0H2O. Anal. Calcd (Found) for 3 : C, 18.39 (18.35); H, 3.73 (3.45). Selected IR data (KBr, cm-1): 3405 (s,br), 1533(s), 1422(s), 1346(w), 1027(s), 666(w), 620(w), 580(w). [Mn84O72(O2CEt)81(MeO)24(MeOH)18(H2O)30(OH)3](4)x solvents : To a dark brown solution of 2 (0.427 g, 0.206 mmol) in 15 ml of MeOH was added a freshly prepared solution of n -Bu4NMnO4 (0.3 g, 0.831 mmol) in MeOH (10 ml), follo wed by the addition of propionic acid (1 ml, 13.33 mmol). The resulting reaction mixture was stirred for five minutes, filtered and the filtrate then layered with MeNO2. After several days, dark red-brown needles of 4 x solvents were obtained. These were maintained in moth er liquor for X-ray crystallography and other single-crystal studies, or the crystals were collected by filtration, washed with MeNO2 and dried in vacuum. The yield was 0.26 g (56% based on to tal Mn). Vacuum-dried crystals analyzed as 4 H2O. Anal. Calcd (Found) for 4 : C, 25.04 (24.95); H, 4.57 (4.29); N, 0.00 (0.02). Selected IR data (KBr, cm-1): 3429 (s, br), 1576 (w), 1521 (s), 1467 (s), 1427 (s), 1373 (w), 1301 (s), 1080 (s), 1030 (s), 888 (w), 821 (w), 691 (w), 626 (w), 549 (w), 503 (w). 2.4.2 X-ray Crystallography Data for complexes 3 H2O12CHCl3 and 4 x solvents were collected at 173 K on a Siemens SMART PLATFORM equipped with a CCD area detector and a graphite

PAGE 52

52 monochromator utilizing MoK radiation ( = 0.71073 ). Cell parameters were refined using up to 8192 reflections. A full sphere of da ta (1850 frames) was collected using the -scan method (0.3 frame width). The first 50 fr ames were remeasured at the e nd of data collection to monitor instrument and crystal stab ility (maximum correction on I was < 1%). Absorption corrections by integration were applied based on measured indexe d crystal faces. The structures were solved by the Direct Methods in SHELXTL6183 and refined using full-matr ix least squares. The non-H atoms were treated anisotropically, whereas the hydrogen atoms were calculated in ideal positions and were riding on th eir respective carbon atoms. For complex 3 the asymmetric unit consists of 1/6 of the [Mn84] cluster and an estimated 25 H2O and 2 CHCl3 molecules of crystallization. Most of the solvents are disordered and could not be modeled properly, thus program SQUEEZE,184 a part of the PLATON package185 of crystallographic software, was used to calcula te the solvent disorder area and remove its contribution to the overall intensity data. A total of 902 parameters were refined in the final cycle of refinement using 85636 reflections with I > 2 ( I ) to yield R 1 and wR 2 of 8.49 and 21.17%, respectively. Refinement was done using F2. A 2 cutoff of 45 was used to truncate the data because the CCD detector was moved to a dist ance 7.13 cm from the crystal in order to better resolve the condensed reciprocal lattice. At this distance, th e highest 2-theta reflection was 44.42. It should be noted that a cuto ff of 44 gives a 97% coverage. For complex 4 x solvents the asymmetric unit of consists of the [Mn84] cluster and an amount of crystallization solvent molecules. Most of the solvent molecules are severely disordered and could not be mode led properly, thus, program SQUEEZE,184 was used to calculate the solvent disorder area and remove its contribution to the overall intensity data. A total of 2505 parameters were refined in the fi nal cycle of refinement using 295799 reflections

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53 with I > 2 ( I ) to yield R 1 and w R 2 of 18.36 and 43.22%, respectively. Refinement was done using F2. A 2 cutoff of 40 was used to truncate the data because the CCD detector was moved to a distance 11 cm from the crys tal in order to better resolve the condensed reciprocal lattice. At this distance, the highest 2-thet a reflection was 44.42. It should be noted that a cutoff of 40 gives a 99.9% coverage. In this case the as ymmetric unit contained a complete [Mn84] molecule resulting in a unit cell volume of ~ 76000 3, i.e ., the size of a small protein. However, the most important reason for this low quality crystal analysis was the fact that most of the -carbon atoms of the propionate ligands were severely di sordered and some of them were not located. Although the very poor quality of the crystal an alysis prevents satisfactory convergence, the structure is of sufficient accura cy to determine the molecular c onnectivity and also the packing architecture of the [Mn84] molecules.

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54 Table 2-1. Crystallographic data and stru cture refinement details for complexes 3 and 4 . 3 4 formulaa C192H444O312Mn84 C285H612O309Mn84 fw, g mol-1 12360.24 13598.66 space group P 6 P 21/ c a , 41.345(2) 26.897(3) b , 41.345(2) 66.529(9) c , 14.180(14) 42.634(5) , deg 90 90 , deg 90 97.885(2) , deg 120 90 V , 3 20992.1(3) 75569.3(2) Z 1 4 T , K 123(2) 173(2) radiation, b 0.17073 0.17073 calc, Mg m-3 1.305 1.366 , mm-1 1.410 0.584 R 1 ( wR 2), %c , d 8.49 (21.17) 18.36(43.22) a Excluding solvent molecules. b Graphite monochromator. c R 1 = ||F0| – |Fc|| / |F0|. d wR 2 = [ [ w ( F0 2 Fc2)2] / [ w F0 2)2]]1/2 where S = [ [ w ( F0 2 – Fc2)2] / ( n p )]1/2, w = 1/[ 2( F0 2) + ( m * p )2 + n * p ], p = [max( F0 2, 0) + 2* Fc2]/3, and m and n are constants. Table 2-2. Bond valence sum (BVS) calculationsa for the Mn Atoms in 3 . Atom Mn(II) Mn(III) Mn(IV) Mn(1) 3.367 3.079 3.233 Mn(2) 3.377 3.089 3.243 Mn(3) 3.364 3.077 3.230 Mn(4) 3.111 2.846 2.988 Mn(5) 3.366 3.079 3.232 Mn(6) 3.362 3.260 3.355 Mn(7) 3.288 3.030 3.144 Mn(8) 3.355 3.064 3.217 Mn(9) 3.266 2.987 3.136 Mn(10) 3.418 3.127 3.283 Mn(11) 3.122 2.855 2.998 Mn(12) 3.489 3.191 3.351 Mn(13) 3.083 2.820 2.960 Mn(14) 3.190 2.918 3.064 a The underlined value is the one closest to the charge for whic h it was calculated. The oxidation state of a particular atom can be taken as th e nearest whole number to the underlined value

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55 Table 2-3. Bond valence sum (BVS) calculationsa for selected oxygen atoms in 3 . Atom zj Assignment Atom zj Assignment O(4) 1.952 O2O(9) 0.218 H2O O(5) 1.994 O2O(14) 0.282 H2O O(7) 1.909 O2O(23) 0.293 H2O O(8) 1.903 O2O(27) 0.206 H2O O(16) 1.791 O2O(30) 0.229 H2O O(22) 1.737 O2O(50) 0.307 H2O O(25) 1.934 O2O(12) 0.339 HOO(26) 1.956 O2O(15) 1.769 MeOO(33) 1.947 O2O(21) 1.804 MeOO(34) 1.916 O2O(41) 1.712 MeOO(42) 1.781 O2O(48) 1.706 MeOO(47) 1.840 O2O(10) 0.916 MeOH O(3) 0.250 H2O O(35) 0.998 MeOH a Bond valence sums for the oxygen atoms ar e calculated according to the equation sij = zj, where sij = (r/r0)-N, N and r0 are constants that are depe ndent upon the nature of the ij pair. The oxygen atom is an O2 if zj 2; the oxygen atom is an HO if zj 1; the oxygen atom is an H2O if zj 0. Table 2-4. Selected interatomic distances () for 3 . Parameter Distance, Terminal ligand Mn1-O3 2.228 H2O Mn2-O9 2.284 H2O Mn3-O12 2.109 HOMn4-O14 2.264 H2O Mn7-O23 2.165 H2O Mn8-O30 2.264 H2O Mn9-O27 2.309 H2O Mn-O50 2.147 H2O

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56 Mn1 Mn2 Mn3 O5 O7 O8 O4 Mn4 Mn5 Mn6 Mn7 O16 O22 O15 O21 O25 O26 O23 O34 O42 O41 O47 O48 Mn10 Mn9 Mn8 Mn11 Mn12 Mn13 Mn14 Mn1 Mn2 Mn3 O5 O7 O8 O4 Mn4 Mn5 Mn6 Mn7 O16 O22 O15 O21 O25 O26 O23 O34 O42 O41 O47 O48 Mn10 Mn9 Mn8 Mn11 Mn12 Mn13 Mn14 Mn1 Mn2 Mn3 O5 O7 O8 O4 Mn4 Mn5 Mn6 Mn7 O16 O22 O15 O21 O25 O26 O23 O34 O42 O41 O47 O48 Mn10 Mn9 Mn8 Mn11 Mn12 Mn13 Mn14 (a) (b) Mn1 Mn2 Mn3 O5 O7 O8 O4 Mn4 Mn5 Mn6 Mn7 O16 O22 O15 O21 O25 O26 O23 O34 O42 O41 O47 O48 Mn10 Mn9 Mn8 Mn11 Mn12 Mn13 Mn14 Mn1 Mn2 Mn3 O5 O7 O8 O4 Mn4 Mn5 Mn6 Mn7 O16 O22 O15 O21 O25 O26 O23 O34 O42 O41 O47 O48 Mn10 Mn9 Mn8 Mn11 Mn12 Mn13 Mn14 Mn1 Mn2 Mn3 O5 O7 O8 O4 Mn4 Mn5 Mn6 Mn7 O16 O22 O15 O21 O25 O26 O23 O34 O42 O41 O47 O48 Mn10 Mn9 Mn8 Mn11 Mn12 Mn13 Mn14 (a) (b) Figure 2-1. PovRay repres entations of complex 3 . (a) View along the crystallographic c -axis. The rectangle highlights the [Mn14] asymmetric unit; for clarity, its magnified and labeled core is shown above the structure. (b) Stereoview of 3 along the crystallographic c -axis. Hydrogen atoms are omitted for clarity. Color code: Mn blue; O red; C gray.

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57 Mn3 Mn1 Mn2 O12 O10 O6 O11 O9 O2 O8 O13 Mn4 O14 O4 O1 O16 O15 Mn5 O22 O17 Mn6 O21 O23 O18 O3 O5 O7 O20 O19 O29 O26 O25 O24 O38 Mn8 Mn9 Mn10 O30 O27 O31 O33 O28 O37 O35 O34 O39 Mn11 O42 Mn12 O32 O43 O45 O44 Mn13 O51 Mn14 O47 O50 O46 O41 O48 O49 O52 O40 O36 Mn7 Mn3 Mn1 Mn2 O12 O10 O6 O11 O9 O2 O8 O13 Mn4 O14 O4 O1 O16 O15 Mn5 O22 O17 Mn6 O21 O23 O18 O3 O5 O7 O20 O19 O29 O26 O25 O24 O38 Mn8 Mn9 Mn10 O30 O27 O31 O33 O28 O37 O35 O34 O39 Mn11 O42 Mn12 O32 O43 O45 O44 Mn13 O51 Mn14 O47 O50 O46 O41 O48 O49 O52 O40 O36 Mn7 Figure 2-2. PovRay representation of the asymmetric unit, [Mn14O12(O2CMe)13(MeO)4(MeOH)2(H2O)7(OH)1], of 3 . Hydrogen atoms are omitted for clarity. Jahn-Teller axes are highlighted in black. Color code: Mn blue; O red; C gray. .

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58 ~ 4.2 nm ~1.9 nm ~1.2 nm ~ 4.2 nm ~1.9 nm ~1.2 nm Figure 2-3. Space-filling representations of 3 (including hydrogen atoms), showing the dimensions of the molecule and its cent ral cavity. Color code: Mn blue; O red; C gray; H white.

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59 (a) (b) (c) (a) (b) (c) Figure 2-4. Space-filling representations of 3 , and its supramolecular aggregation into ordered nano-size tubes and sheets. (a) A view along the crystallographic c -axis, showing the hexagonal packing of neighboring molecu les. (b) An arrangement of [Mn84] molecules viewed from a direction perpe ndicular to the crystallographic c-axis, showing the exact registry of molecules in adjacent tubes. H atoms are omitted for clarity. (c) Ordered arrangement of [Mn84] molecules as nano-size supramolecular tubes. Color code: blue Mn; red O; grey C; H white.

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60 Figure 2-5. PovRay representation of 4 , shown along the crystallographic a -axis. Hydrogen atoms are omitted for clarity. Color code: Mn blue; O red; C gray.

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61 ~ 4.4 nm ~1.8 nm ~1.4 nm ~ 4.4 nm ~1.8 nm ~ 4.4 nm ~1.8 nm ~1.8 nm ~1.4 nm ~1.4 nm Figure 2-6. Space-filling representations of 4 (including hydrogen atoms), showing the dimensions of the molecule and its cent ral cavity. Color code: Mn blue; O red; C gray; H white.

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62 (a) (b) (c) (a) (b) (c) Figure 2-7. Space-filling representations of 4 , and its supramolecular aggregation into ordered nano-size tubes. (a) A view along the crystallographic a -axis, showing the hexagonal packing of neighbouring molecules. (b) An arrangement of [Mn84] molecules viewed from a direction perpendicular to the crystallographic a -axis (excluding hydrogen atoms), showing zigzag packing mode of molecules in neighbouring tubular chains. (c) Ordered arrangement of [Mn84] molecules (excluding hyd rogen atoms) as nanosize supramolecular tubes. Colour code: blue Mn; red O; gr ey C; white H.

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63 050100150200250300 0 30 60 90 120 150 180 mT (cm3mol-1K)T (K) 050100150200250300 0 30 60 90 120 150 180 mT (cm3mol-1K)T (K) mT (cm3mol-1K) T (K) 050100150200250300 0 30 60 90 120 150 180 mT (cm3mol-1K)T (K) 050100150200250300 0 30 60 90 120 150 180 mT (cm3mol-1K)T (K) mT (cm3mol-1K) T (K) Figure 2-8. Plot of mT vs T for a dried, microcrystalline sample of complex 3 in eicosane. m is the DC molar magnetic susceptibil ity measured in a 0.1 T field. 050100150200250300 0 30 60 90 120 150 180 mT (cm3mol-1K)T (K) 050100150200250300 0 30 60 90 120 150 180 mT (cm3mol-1K)T (K) Figure 2-9. Plot of mT vs T for a dried, microcrystalline sample of complex 4 in eicosane. m is the DC molar magnetic susceptibil ity measured in a 0.1 T field.

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64m'T(cm3mol-1K)T (K) 012345678910 10 15 20 25 30 35 40 45 50 55 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz m'T(cm3mol-1K)T (K) 012345678910 10 15 20 25 30 35 40 45 50 55 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K)m"(cm3mol-1) 1.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K)m"(cm3mol-1) 1.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz Figure 2-10. AC magnetic susceptibility data fo r a dried, microcrystalli ne sample of complex 3 in a 3.5 G field oscillating at the indicated frequencies. Top: plots of the in-phase (m' , plotted as m'T vs T ) AC magnetic susceptibility si gnals. Bottom: plots of the out-of-phase (m" , plotted as m" vs T ) AC magnetic suscep tibility signals.

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65 012345678910 10 15 20 25 30 35 40 45 50 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz m'T(cm3mol-1K)T (K) 012345678910 10 15 20 25 30 35 40 45 50 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz m'T(cm3mol-1K)T (K) 1.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K)m"(cm3mol-1) 1.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K)m"(cm3mol-1) Figure 2-11. AC magnetic susceptibility data fo r a dried, microcrystalli ne sample of complex 4 in a 3.5 G field oscillating at the indicated frequencies. Top: plots of the in-phase (m' , plotted as m'T vs T ) AC magnetic susceptibility si gnals. Bottom: plots of the out-of-phase (m" , plotted as m" vs T ) AC magnetic suscep tibility signals.

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66 Figure 2-12. The results of low temperature (< 1.8 K) magnetism studies performed on a singlecrystal of complex 3 . Top: magnetization ( M ) vs applied DC field ( 0H ) hysteresis loops, measured with the field applied along the c -axis (perpendicular to the [Mn84] torus plane) at the indicated temperatur es and a 0.035 T/s field sweep rate. The magnetization has been plotted as spin ( S ) per molecule. A background slope due to low-lying excited states has been subtracted from the data. Bottom: Arrhenius plot constructed using a combination of out-of-phase ac susceptibility ( m ) data and DC magnetization decay data. The dashed line is a fit of the thermally activated region to the Arrhenius relationship; see th e text for the fit parameters. -6 -4 -2 0 2 4 6 -3-2-10123 0.1 K 0.3 K 0.5 K 0.7 K 1.0 K 1.5 K S/molecule 0H (T) 0.035 T/s 10-510-310-110110310510710905101520 DC AC (s) 1/T (1/K) = 5.7e-9 * e^(18 K/ T) = 5.7 10-9ex p( 18 K/T )

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67 400450500550600650700750800 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.05 mM 0.04 mM 0.03 mM 0.02 mM 0.01mM 0.009 mM 0.005 mM 0.001 mM AbsorbanceWavelength (nm) 400450500550600650700750800 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.05 mM 0.04 mM 0.03 mM 0.02 mM 0.01mM 0.009 mM 0.005 mM 0.001 mM AbsorbanceWavelength (nm) Figure 2-13. Electronic spectra of complex 3 in MeCN. 0.000.010.020.030.040.050.06 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Experimental data Fit Absorbance[Mn84] (mM) 0.000.010.020.030.040.050.06 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Experimental data Fit Absorbance[Mn84] (mM) Figure 2-14. Plot of absorbance vs concentration (Beer’s law plot) for complex 3 at 474 nm. The solid line represents the least-square fit of the experimental data to Beer’s law. See text for fitting parameters.

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68 110100 1000N Quantum World Molecular (bottom-up) approach Classical World Classical (top-down) approachMn4Mn12Mn30Mn84Ac Co metal nanoparticle ~ 3 nm 4.4 nm 4.2 nm Mn84Pr 110100 1000N Quantum World Molecular (bottom-up) approach Classical World Classical (top-down) approachMn4Mn12Mn30Mn84Ac Co metal nanoparticle ~ 3 nm 4.4 nm 4.2 nm Mn84Pr Figure 2-15. The position of [Mn84] complexes on a size scale spanning atomic to na noscale dimensions. On the far right is shown a high-resolution transmission electron micr oscopy view along a [110] direction of a typical 3 nm diameter Co metal nanoparticle exhibiting a face-centered structur e and containing ~1000 Co atoms. Complexes 3 and 4 possess 4.2 nm and 4.4 nm diameter structures. For compar ison are shown smaller Mn SMMs, which are drawn to scale. The red arrows indicate the magnitude of the Nel vectors ( N ) for the indicated SMMs, which are 7.5, 22, 61 and 168 for [Mn4], [Mn12], [Mn30] and [Mn84], respectively. The red arrows from the Co nanopa rticle are merely meant to indicate that the N of nanoparticles can take many values, depending on the exac t size and the identity of the constituent metal.

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69 CHAPTER 3 A NEW FAMILY OF GIANT [Mn70] SINGLE-MOLECULE MAGNETS EXHIBITING QUANTUM TUNNELING OF MAGNETIZATION 3.1 Introduction Since the initial discovery of the si ngle-molecule magnet (SMM) property in [Mn12O12(O2CMe)16(H2O)4]MeCO2H4H2O ( 1 ),26,27 the synthesis and subsequent characterization of polynuclear manganese comple xes has been an area of intense research, largely stimulated by the fact th at many of such clusters have been found to exhibit magnetic bistability.28 Below a certain blocking temperature, SMMs display magnetization hysteresis, a characteristic signature of any magnet, as well as quantum tunneling of magnetization (QTM)140,142 and quantum phase interference,150 the properties of a microscale entity. Two strictly molecular properties, namely ground state spin ( S ) and magnetoanisotropy (gauged by the negative zero-field sp litting (ZFS) parameter D ), define a barrier ( U ) to magnetization reversal equal to S2 | D | for integer and ( S2 1/4) | D | for half-integer spin systems. Therefore, SMMs of very large dimensions, i.e. , with sizes approaching th e size regime of classical magnetic nanoparticle, has long been the target of synthesis. From one point of view, such molecules, composed of a very large number of paramagnetic centers, in th e presence of suitable exchange interactions are expected to have large S values and consequently could lead to an increase of U . On the other hand, it has been also of interest to explore whether very large molecular clusters could still s how the coexistence of both cla ssical and quantum properties. In a pursuit to synthesize highnuclearity manganese clusters, several synthetic approaches have been developed. The three general categor ies of these include: i) aggregation of Mn2+/3+ salts,92,106,112,113,129,186-191 ii) alcoholysis of vari ous preformed Mn clusters111,116,152 and iii) the reductive aggregation procedure, in wh ich a high oxidation state Mn source (MnO4 ) is gradually

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70 reduced by an alcohol in the presence of exce ss carboxylic acid, followed by an aggregation step leading to the formation of the resultant cluster.104,105,107 The alcoholysis reaction, using 1 as a starting material, has b een successful in synthesizing a giant [Mn84]116 cluster, the largest know n SMM. Inspired by this in itial success, the reaction system was further investigated in EtOH and resu lted in the isolation of a new family of giant clusters. Herein we report the synthesis, st ructural and magnetic characterization of [Mn70] complexes. These giant molecules have b een identified as the second largest SMMs, unambiguously exhibiting QTM. 3.2 Results and Discussion 3.2.1 Syntheses The reaction of [Mn12O12(O2CMe)16(H2O)4]MeCO2H4H2O ( 1 ) with 4 equivalents of nBu4NMnO4 in MeOH in the presence of excess of acetic acid afforded [Mn84O72(O2CMe)78(MeO)24(MeOH)12(H2O)42(OH)6] ( 3 )H2O12CHCl3 complex, which is the highest nuclearity Mn cl uster synthesized to date.116 In this reaction MeOH serves as both, the reaction solvent and a ligand, providing methanol/methoxy groups to the cluster. The addition of acetic acid into the reaction mixtur e was also crucial to the formation of [Mn84] complex, since it provided the acidic environm ent necessary to prevent the formation of manganese oxides and/or hydroxides. With the initi al success of synthesi zing a cluster of such high nuclearity we decided to further investigat e this newly developed reaction system under a variety of conditions . One of the simplest modifications soug ht was to use a di fferent alcohol as a reaction solvent. T hus, the reaction of 1 with 4 equivalents of n -Bu4NMnO4, followed by an addition of 63 equivalents of acetic acid was performed in EtOH. The resulting reddish-brown solution was layered with a variety of solvents and left undisturbed over a period of several weeks at room temperature. Slow diffusion of MeNO2 into the reaction solution resulted in the

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71 formation of high quality red-brown needles, wh ich were crystallographically characterized as [Mn70O60(O2CMe)70(OEt)20(EtOH)16(H2O)22] ( 5 )MeCO2HEtOHH2O. Together with very good quality crystals of 5 , a small amount of a white crystalline impurity was also cocrystallized. Although numerous attempts were made to isolate compound 5 in a pure form, but this was proven impossible, at least without affecting the st ructure of the compound. Finally, pure red-brown needles of compound 5 were isolated manually under the microscope from the white byproduct. The formation of complex 5 is summarized in eq. 3-1. 5[Mn12O12(O2CMe)16(H2O)4] + 10( n -Bu4NMnO4) + 25MeCO2H + 46EtOH + 25H+ + 60e [Mn70O60(O2CMe)70(EtO)20(EtOH)16(H2O)20] + 10( n -Bu4N)OEt + 35MeCO2 + 40H2O (3-1) The same reaction was repeated in more basic alcohols than MeOH (pKa = 15.4) and EtOH (pKa = 15.6), such as PrOH, iPrOH, tBuOH (pKa ~ 16), and led either to yellow color or to the complete bleaching of the reaction solutio ns, often accompanied by the formation of paleyellow/white crystalline products, indicating that all Mn ions were reduced all the way to Mn2+. Therefore, the reaction system was further inve stigated by employing a mo re acidic alcohol than MeOH, such as 2-ClC2H4OH (pKa = 14.2). Thus, the reaction of 1 with 4 equivalents of n Bu4NMnO4 was performed in 2-ClC2H4OH, followed by an addition of 63 equivalents of acetic acid. Slow diffusion of MeNO2 into the reaction mixture resulte d in the formation of red-brown needles in 37% yield after 1 week. The crystals were maintained in mother liquor to avoid solvent loss and were crystall ographically characterized as [Mn70O60(O2CMe)70(OC2H4Cl)20(ClC2H4OH)18(H2O)22] ( 6 ) 60ClC2H4OHH2O. The compound was isolated in a pure form since the white crystalline byproduct was formed only

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72 when the solution was left undisturbed for a long period of time, i.e. , more than 2 weeks after the complete formation of 6 . 3.2.2. X-ray Crystal Structures of [Mn70O60(O2CMe)70(OEt)20(EtOH)16(H2O)22](5)MeCO2HC2H5OHH2O, and [Mn70O60(O2CMe)70(OC2H4Cl)20(ClC2H4OH)18(H2O)22](6)ClC2H4OHH2O Crystallographic data collection and stru cture refinement details for complexes 5 20MeCO2HC2H5OH32H2O and 6 60ClC2H4OH40H2O are summarized in Table 3-1. PovRay representation of complex 5 together with a labeled plot of the asymmetric unit are shown in Figure 3-1. PovRay representation of complex 6 together with a labeled core of the asymmetric unit are shown in Figure 3-4. Sele cted interatomic distances and angles for complexes 5 and 6 are listed in Tables A3 and A-4, respectively. Complex 5 20MeCO2HC2H5OH32H2O crystallizes in monoclinic space group C 2 /m with the asymmetric unit containing 1/4 of the [Mn70] molecule and approximately 5 MeCO2H, 8 EtOH and 8 H2O solvent molecules of crystalliz ation. The crystal structure of 5 can be described as a [Mn70] torus, composed of alternating near-linear [Mn3( 3-O)4] and cubic [Mn4( 3-O)2( 3OEt)2] subunits, linked together via 2-MeCO2 and 3-O2 groups. Complex 5 possesses crystallographic mirror plane, passi ng through the Mn atoms of the [Mn3( 3-O)4] unit (Mn1, Mn2, Mn3 and their symmetry equivalents) and crystallographic C2 axis, bisecting the [Mn4( 3O)2( 3-OMe)2] subunit (Mn18, Mn19, Mn18', Mn19' and their symmetry-related partners) via the 2-MeCO2 group, bridging Mn18 and Mn18' (and their sy mmetry-related partners) (Figure 3-1). Taking into account these symmetry considerations, the asymmetric unit can be described by the formula [Mn17.5O15(OCMe)17.5(OEt)5(EtOH)4(H2O)5.5]. All of the Mn atoms are six-coordinate with near-octahedral geometry, except for Mn2 (and its symmetry equivalent), which has been identified as five-coordinate. Close inspection of Mn-O bond lengt hs (Table A-3), bond valence

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73 sum calculations for the Mn atoms (Table B-2),155,156 and the detection of Jahn-Teller (JT) elongation axes revealed that all Mn ions in 5 are present as Mn3+. Bond valence sum calculations were also performed on the oxygen atom s of the cluster to id entify their degree of protonation, which revealed that compound 5 contains 60 3-O2 , 20 3-OEt, 16 terminal EtOH and 22 terminal H2O ligands (Table B-3). All terminal EtOH and H2O molecules are located on the JT elongation axes. The peri pheral ligation is completed by 70 2-MeCO2 bridging groups. Crystallographic data refineme nt revealed that the MeCO2 group, bridging Mn1 and Mn5 (and their symmetry equivalents) is disordered with H2O molecule over the mirro r plane. In addition, Mn16 (and its symmetry equivalents) has a 50% occupancy disorder between terminal H2O and EtOH ligands. The arrangement of Mn atoms in the [Mn3( 3-O)4] units is not completely linear but slightly V-shaped ( e.g , Mn3-Mn2-Mn1 = 167.30, Mn 8-Mn9-Mn10 = 171.87, and Mn15Mn16-Mn17 = 169.66). A better description of th e size and the packing architecture of the molecule is provided by space-filling plots in Figu re 3-2, which show that the molecule has an overall diameter of about 3.7 nm and a thickne ss of about 1.2 nm, with the diameter of the central cavity being ~ 1.4 nm. The [Mn70] molecules order within the crystal in a hexagonal close packing manner, forming supramolecular nano-size tu bes in a direction para llel to that of the crystallographic c -axis (Figure 3-3). Molecules in neighbor ing tubular chains are not adjacent, but alternate one another in the ABAB packing fashion (Figure 3-3, a). The crystal structure of 6 is nearly isostructural to that of 5 , except that i) in 5 there are 3ClC2H4O and terminal ClC2H4OH instead of 3-EtO and terminal EtOH, ii) there are several differences in number and positions of terminal ClC2H4OH and H2O molecules and iii) all Mn ions in 6 are six-coordinated in contrast to complex 5 , in which Mn2 (and its symmetry equivalent) is 5-coordi nated. All Mn atoms of 6 are in Mn3+ oxidation state. The assignment of

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74 oxidation states was based on the examination of metric parameters, char ge considerations, the existence of JT axial elongations in a ll Mn ions and bond valence sum calculations.155,192 Bond valence sums of O atoms c onfirmed the existence of 15 3-O2 , 5 3-ClC2H4O, 4.5 ClC2H4OH and 5.5 H2O ligands in the asymmetric unit.193 The [Mn70] molecule has an overall diameter of about 3.9 nm and a thickness of about 1.2 nm, with a diameter of central cavity being ~1.4 nm. The packing architecture of 6 (Figure 3-5) is analogous to that of 5 , and the closer examination of the former revealed that there are in termolecular hydrogen-bonding interactions between terminal ClC2H4OH and terminal H2O ligands of the neighboring [Mn70] molecules, with ClO separations of 3.135 . A comparis on between the structures of 5 and 6 and the giant [Mn84] wheel, described in Chapter 2, revealed a number of similarities and also differences. Both [Mn84] and [Mn70] compounds have a wheel-shaped stru cture with the repeating units constructing their structures having essent ially the same structural cores; [Mn84] compound and 5 and 6 are composed of alte rnating near-linear [Mn3( 3-O)4] and cubic [Mn4( 3-O)2( 3-OR)2] (R = Me, [Mn84]; R = Et, 5 ; R = C2H4Cl, 6 ) subunits, linked together via 2-MeCO2 and 3-O2 groups. Of course [Mn84] contains 12 such repeating subunits whereas 5 and 6 contain only 10. [Mn84] and [Mn70] molecules do not have only similarities but also important differences. Apart from the different alkoxy ligands, nuclearities and dimensions, they also differ in the way they pack in the crystal. [Mn84] packs in a very symmetric manner with each molecule being on the top of the other, forming cylindrical channels along one dimension; molecules in neighboring chains are exactly adjacent to one anothe r. In contrast, even though molecules of 5 and 6 also pack into nanotubular chains, the molecules in the neighboring chains a lternate one another in ABAB fashion. This results in larg er distances between the [Mn70] molecules of the same

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75 nanotubular chain (5.76 ) in comparison to the corresponding dist ance between the [Mn84] molecules (2.39 ). 3.2.3 Magnetochemistry of Complexes 5 and 6 3.2.3.1 Direct Current Magnetic Susceptibility Studies Solid-state, variable-temperature magnetic su sceptibility measurements were performed on vacuum-dried microcrystalline samples of complexes 5 0H2OMeNO2 and 6 MeNO2, suspended in eicosane to prevent tor quing. The DC magnetic susceptibility (m) data were collected in the 5.0 300 K range in a 1 kG (0.1 T) magnetic fi eld. The experimental data for 5 and 6 are plotted as mT vs T in Figure 3-6 The magnetic behavior of the two complexes is very similar, as expe cted on the basis of their similar structural cores. For 5 , the mT value decreases gradually from 149.24 cm3 mol-1 K at 300 K to 82.02 cm3 mol-1 K at 50 K, below which mT decreases more rapidly to 22.22 cm3 mol-1 K at 5 K (Figure 3-6 (top)). Likewise for 6 the mT value decreases steadily from 165.04 cm3 mol-1 K at 300 K to 103.76 cm3 mol-1 K at 50 K (Figure 3-6 (bottom)). Below 50 K the mT value again decreases more rapidly to 29.36 cm3 mol-1 K at 5 K. For both 5 and 6 , the value of mT at 300 K is significantly lower than the value of 210 cm3mol-1(for g = 2), expected for a cluster of 70 Mn3+ ( S = 2) non-interacting ions. Thus, the data strongly suggest the presence of predominantly antiferromagnetic exchange interactions within these complexes. To determine the exact values of the many Mn2 pairwise exchange interactions ( Jij) and to find all of the possible spin states and their energies, the spin Hamiltonian for this complex would have to be diagonalized.165 However, for a system of 70 S = 2 Mn3+ ions, the total degeneracy of the spin system is equal to (2 S +1)n, or 570. A matrix-diagonalization approach would involve a matrix of dimensions 570 570, which is clearly unfeasible with curr ent computing capabilities. In addition,

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76 due to the very large size and the complexity of the system, it is not possible to apply the equivalent operator approach base d on the Kambe vector coupling method,166 which is successfully used for smaller systems to derive a theoretical equation a nd fit the experimental mT vs T data. In order to characterize the ground states of complexes 5 and 6 , magnetization ( M ) data were collected in the 0.1.0 T field ra nge and the 1.80 K temperature range. For a system occupying only the ground state and experi encing no zero-field split ting (ZFS), various isofield lines would be superimpos ed and the reduced magnetization ( M/N B) would saturate at a value of gS . The non-superimposition of the isofield lines clearly indicates the presence of ZFS. Attempts were made to fit the experimental data collected for complexes 6 and 7 using the program MAGNET,167 which assumes that only the ground state is populated at these temperatures, includes axial ZFS and the Zeeman interaction with the applied field, and carries out a full powder average.86 Those attempts were not successful. This is indicative of the presence of excited states that ar e low-lying in energy (relative to kT ) and which are populated even at the lowest temperatures employed. Similarly to the [Mn84] case, the presence of lowlying excited states is actually expected for such high nuclearity clusters, in which the exchange interactions among many constituen t Mn ions result in a very high density of spin states. With such an almost continuum spectrum of spin st ates present, there is always a danger that mS components of excited states with S values greater than those of the ground state will cross in energy with the ground state in th e applied dc filed. This will cons equently lead to the incorrect determination of the ground state S . The problem of low-lying excite d states and the difficulty in reliably obtaini ng the ground state S from DC magnetization measurem ents have been previously discussed for the [Mn84]116 molecule as well as other high nuclearity Mn clusters, including [Mn16],107 [Mn18],108,109,168 [Mn21],152 [Mn30].50,51,194 A much more reliable value of the ground

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77 state can be obtained from AC magnetic susceptibility measur ements, which do not employ a DC field. 3.2.3.2 Alternating Current Magnetic Susceptibility Studies Alternating current (AC) susceptibility stud ies were performed on both vacuum-dried and wet (with mother liquor) microcrystalline samples of 5 H2OMeNO2 and 6 MeNO2 in the temperature range 1.8-10 K in a zero DC field and a 3.5 G AC fiel d oscillating at frequencies ranging from 5 to 1500 Hz. The in-phase (m'T ) and out-of-phase ( m" ) signals for complexes 5 and 6 are shown in Figures 3-7 and 3-8, respectively. For complex 5 , the maxima of two peak s are observable at the highest employed frequencies (1000 and 1500 Hz) at approximately 2 K (Figure 3-7). Clearly, the m" peak maxima at frequencies lowe r than 1000 Hz in the case of 5 and all of the m" peak maxima for 6 (Figure 3-8), lie at temperatures belo w the operating limit of our SQUID (1.8 K). Nevertheless, these AC data do suggest that complexes 5 and 6 might be SMMs. The confirmation of this fact and a detailed study of magnetization rela xation rates require studies at temperatures below 1.8K which will be discussed in the next section. The in-phase (m'T ) and out-of-phase ( m" ) signals for the wet samples of 5 and 6 are essentially the same with those of the vacuum-dried material and, thus, will not be discussed further. For both complexes, the value of m'T decreases linearly as the temperature is lowered from 10 K until ~2.4 K and then drops dramaticall y. The abrupt frequency-dependent decrease in m'T signal and the concomitant appear ance of the frequency-dependent m" signal below 2.4 K is indicative of slow ma gnetization relaxation, a ch aracteristic property of a SMM. It should be pointed out, however, that the pr esence of a frequency-dependent m" signal is necessary but not sufficient proof that a molecule functions as a S MM, as such signals can also be present due to

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78 intermolecular inte ractions and phonon-bottleneck effects.170 At temperatures higher than those associated with slow ma gnetization relaxation, the m'T vs T plot does not display a plateau, but instead m'T value decreases signif icantly with decreasing T . For a well isolat ed ground state ( vs kT ), the m'T value at the employed temperatures w ould be expected to be essentially temperature-independent. A slopping m'T vs T plot is a strong indica tion of low-lying excited states whose changing population with temperature affects the observed m'T . We have noted elsewhere on multiple occasions that th e in-phase AC susceptibility signal (m' ) is a useful way to determine the ground state spin S of a molecule, particularly when there are complications from low-lying excited states that interfere with determination of S from DC magnetization fits.104,105,107,114,152 Extrapolation of the in-phase m'T signal down to 0 K, where only the ground state will be populated and a voiding the region associated with the slow magnetization relaxation, gives values of ~12 cm3 mol-1 K for both 5 and 6 . The obtained values of m'T are indicative of an S = 5 ground state spin (for g < 2) for both complexes. 3.2.3.3 Magnetism Studies below 1.8 K The observation of out-of-phase AC signals is indicative of the fact that complexes 5 and 6 might be new SMMs, although such signals by themse lves are not sufficient to proof a SMM. To confirm whether 5 and 6 are indeed SMMs, magnetization vs DC field sweeps were performed on single crystals of 5 and 6 using an array of micro-SQUIDs.171 The obtained results are shown in Figures 3-9 to 3-12. The variable temperature data for complexes 5 and 6 at a 0.14 T/s sweep rate are shown in Figure 3-9 (top and bottom re spectively). In both cases, the coercivities (widths) of hysteresis loops increase with decreasing T , as expected for the superparamagnet-like properties of a SMM. The variable field sweep-rate data for complexes 5 and 6 are shown in Figure 3-10 (top and bottom respectively) at a cons tant temperature of 0.6 K and the coercivities

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79 increase with increasing sweep rate, again as expected for a SMM. Hysteresis loops for both complexes were observed below 1.5 K, thus establishing 5 and 6 as SMMs. The hysteresis loops do not display the step-like featur es indicative of QTM that are vi sible in the hysteresis loops of certain smaller nuclearity SMMs.72,73,82,125,140,142,150 It is possible, however , that steps are present but smeared out by broadening effects arising from the presence of low-lying excited states and a distribution of magnetizati on relaxation barriers ( i.e ., a distribution of D values), consistent with a distribution of mo lecular environments. The separation be tween steps is directly proportional to D , thus a distribution in D values will cause a distribution in step positions and a resulting broadening of these steps. Distri bution of molecular environments could result from the large number of severely disordered solvent molecules present in the crystal structure. Hysteresis loops showing no QTM steps are not uncommon when studying large nuclearity SMMs and have been previously observed for [Mn84],116 [Mn18],108,16858 [Mn21]169 and [Mn30].114 However, even with no visible steps present, close examination of hysteresis loops of 5 and 6 revealed an important indication of QTM occurr ing in these large clusters. Belo w 0.2 K, the coercivity of the loops become temperature-independent, but a scan rate measurements shows that the loops are still time-dependent (Figure 3-10). This fact is characteristic of the ground state tunneling between the lowest energy ms 5 levels of the S = 5 spin manifold. To confirm this observation and to determine the effective barrier to magnetization relaxation ( Ueff) AC magnetic susceptibility (below 1.8K) and magnetization d ecay studies were performed on single crystals of 5 and 6 . In magnetization decay experiments, the magnetization was first saturated in one direction by application of a large dc field at ~5 K, the temperature was then lowered to a chosen value and then the field was removed, and the magnetization decay was monitored with time. The results are shown in Figure 3-11. Both AC and magnetization de cay methods provide

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80 magnetization relaxation rate 1/ vs T data, which were used to construct an Arrhenius plot (Figure 3-12), based on th e Arrhenius relationship = 0 exp(Ueff/kT ), where Ueff is the effective barrier to magnetization relaxation, 0 is the pre-exponential factor, and k is the Boltzmann constant. The fit of the thermally activat ed region above ~ 0.5 K, shown as the dashed line in Figure 3-12, gave Ueff = 23 K and 0 = 1.7 10-10 s (for complex 5 ), and Ueff = 18 K and 0 = 1.6 10-10 (for complex 6 ). For both complexes, the relaxation rate levels off below 0.5 K, and below ~ 0.2 K becomes temperature-independent. The temper ature-independent rela xation of magnetization further confirms the presence of QTM in 5 and 6 , since in this temperature regime, the relaxation can occur only by the ground-state tu nneling (between the lowest energy ms = 5 levels of S = 5 manifold) as the thermally activated process becomes insignificant. Such temperatureindependent relaxation of magnetization due to QTM has been previously observed for [Mn84]116 and several other SMMs72,73,108,109,114,168,195 It is thus clear that [Mn70] compounds still exhibit the quantum behavior that has become a co mmon feature of the much smaller SMMs. 3.3 Conclusions In continuation of our studies of alcoholysis reactions of [Mn12] complexes, the reductive aggregation approach has been further inves tigated in different alcohols than MeOH, i.e. , in more basic EtOH and more acidic ClC2H4OH. The approach has been successful in isolating the second largest nuclearity manganese clusters, [Mn70] complexes 5 and 6 . Both complexes have been established as new SMMs, possessing S = 5 spin ground states and unambiguously exhibiting ground state QTM. In comparison to [Mn84] clusters, described in detail in Chapter 2, the [Mn70] giant wheel molecules can be described as composed of essen tially the same [Mn14] repeating units, five [Mn14] in case of [Mn70] complex and six in case of [Mn84], and having S =

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81 5 and S = 6 ground states, respectively. However, no simplified rationalization of obtained ground states is possible, based on the crystal st ructures alone or taking into the account the acidity of alcohols. For complex 5 , the obtained value of the effective energy barrier ( Ueff) is 23 K, which is larger than that obtai ned for structurally analogous complex 6 ( Ueff = 18 K). At the same time the larger nuclearity [Mn84] cluster posses the same value of Ueff as complex 6 . Clearly, there is a complex combination of factors that gov ern the value of Ueff for these clusters. The large value of Ueff for complex 5 might be rationalized either based on the differences in D values (larger D for complex 5 ) or due to the fact that complex 5 has slower tunneling rates in comparison to other complexes. However, the acc urate rationalization of obtained values of Ueff requires the precise knowledge of D values, which can be obtained from the HFEPR study. The preliminary attempts to study these complexes by HFEPR, however, turned out to be also very complex, which is not unexpected, due to the presence of only Mn3+ ions in these giant molecules. Nevertheless, complexes 5 and 6 are the second example of gi ant clusters, exhibiting both classical property of magnetization hysteres is and QTM. Such large nuclearity wheel-like molecules have been seen only in molybdenum chemistry,175 with the larges t currently known [Mo154]176 and [Mo176]177 compounds, prepared by Mller a nd co-workers. Although they are significantly larger in nuclearity from [Mn70], they have diameters of ~3.4 and ~ 4.1 nm, respectively, which are comparable to the ~3.7 nm diameter of complexes 5 and 6 . In addition, these and other giant polyoxometallates,178,179 are diamagnetic or nearly so, and none of them exhibit SMM properties. A useful way of comparing the ‘size’ of magnetic systems is by their Nel vector ( N is the sum of the individual spins). Th e comparison of the sizes of 5 and 6 to other classical

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82 nanoparticles and also to other known SMMs, base d on their Nel vectors is shown in Figure 313. With a 3.7 nm diameter and N = 140, [Mn70] molecules are the second largest molecular spin system after the [Mn84] complexes ( N ([Mn84]) = 168), by far larger than any other molecular cluster ( N ([Mn4]) = 7.5, N ([Mn12]) = 22, N ([Mn30]) = 61), and are also located close to the size regime of the smallest magnetic nanopartic les, such as a 3 nm Co nanoparticle ( N ~ 1000).180 The [Mn70] clusters, exhibiting both classical and quantum effects, represent a new category of giant SMMs that are placed at the interface between the bottom-up and top-down approaches to nanoscale magnetic materials. 3.4 Experimental Section 3.4.1 Syntheses All preparations and manipulations were pe rformed under aerobic conditions at ambient temperature, using reagents and solvents as received [Mn12O12(O2CMe)16(H2O)4]MeCO2H4H2O( 1 ) and n -Bu4NMnO4 were prepared as described elsewhere.181,182 [Mn70O60(O2CMe)70(OEt)20(EtOH)16(H2O)22](5)MeCO2HC2H5OHH2O . To a slurry of 1 (0.425 g, 0.206 mmol) in EtOH (10 ml) was added over a period of two minutes a freshly-prepared solution of n -Bu4NMnO4 (0.3 g, 0.831 mmol) in EtOH (8 ml), and glacial acetic acid (0.75ml, 13.05 mmol). The system was then le ft under magnetic stirri ng for a few minutes, and then filtered to give a red-brown f iltrate. The filtrate was layered with MeNO2. Over a period of several weeks well shaped X-ray quality redbrown elongated plates were obtained together with a small amount of a white crystalline byproduc t. The crystals were maintained in mother liquor for X-ray crystallography a nd other single-crystal studies, or manually separated from the white byproduct, washed with MeNO2 and dried in vacuum. The yield was 0.13g (24% based on total Mn). Vacuum-dried crystals ar e highly hygroscopic and analyzed as 5 H2OMeNO2.

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83 Anal. Calcd (Found) for 5 H2OMeNO2: C, 21.62 (21.54); H, 4.33 (3.83), N, 0.12 (0.10). Selected IR data of 2 (KBr, cm-1): 3423 (s,br), 1558(s), 1421(s), 1345(w), 1028(s), 665(w), 618(w), 580(w). [Mn70O60(O2CMe)70(OC2H4Cl)20(ClC2H4OH)18(H2O)22](6)ClC2H4OHH2O . The synthetic procedure was the same as that employed for complex 5 , except that instead of EtOH, 2-ClC2H4OH was used as the reaction solvent. After one week, red-brown needles of 4 were obtained. Formation of white crystalline byproduc t was not observed until two weeks after the formation of 6 . The crystals were maintained in moth er liquor for X-ray crystallography and other single-crystal studies, or coll ected by filtration, washed with MeNO2 and dried in vacuum. The yield was 0.22g (37% based on total Mn). Vacuum-dried crystals analyzed as 6 MeCO2HMeNO2. Anal. Calcd (Found) for 6 MeNO2: C, 20.96 (21.20); H, 3.46 (3.24), N, 0.11 (0.14). Selected IR data of 6 (KBr, cm-1): 3419 (s, br), 1576 (w), 1522 (s), 1436 (s), 1056 (w), 1024 (s), 693 (s), 664 (s), 626 (s), 578 (s), 548 (s), 501(w). 3.4.2 X-ray Crystallography Data for complexes 5 20MeCO2H32C2H5OH32H2O and 6 60ClC2H4OHH2O were collected at 173 K on a Siemens SMART PLATFORM equipped with a CCD area detector and a graphite monochromator utilizing MoK radiation ( = 0.71073 ). Cell parame ters were refined using up to 8192 reflections. A full sphere of data (1850 frames) was collected using the -scan method (0.3 frame width). The first 50 frames were remeasured at the end of data collection to monitor instrument and crystal stability (maximum correction on I was < 1%). Absorption corrections by integration were applied based on measured indexed crystal faces. The structures were solved by the Dir ect Methods in SHELXTL6,183 and refined using full-matrix least squares. The non-H atoms were treated anisotropically, whereas the hydrogen atoms were placed in calculated, ideal positions and refined as riding on their respective carbon atoms.

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84 For complex 5 the asymmetric unit consists of 1/4 of the [Mn70] cluster, 5 MeCO2H, 8 EtOH and 8 H2O molecules of crystalliza tion. All of the solvent molecules were disordered and could not be modeled prope rly, thus program SQUEEZE,184 a part of the PLATON package185 of crystallographic software, was used to calcula te the solvent disorder area and remove its contribution to the overall intensity data. One MeCO2 group, bridging Mn1 and Mn5 (and their symmetry-related partners) is disordered with H2O molecule over the mirror plane passing through the ring. Mn16 has a disorder between a H2O and EtOH ligands (50% occupancy). A total of 1199 parameters were refined in the fi nal cycle of refinement using 64265 reflections with I > 2 ( I) to yield R 1 and wR 2 of 6.94 and 16.23%, respectively. Refinement was done using F2. For complex 6 the asymmetric unit consists of a 1/4 [Mn70] ring (the rings are located on 2/m centers) and 15 ClC2H4OH and 10 H2O molecules of crystalliza tion. The solvent molecules were disordered and could not be modeled prop erly, thus program SQUEEZE, a part of the PLATON package of crystallographic software, wa s used to calculate the solvent disorder area and remove its contribution to the overall intensity data. There are several disorders of ligands on the ring. Some ClC2H4O groups have only the Cl atom disordered and others have CH2-CH2 moieties disordered and those were refined with 50% occupancy for each part. One MeCO2 group, bridging Mn17 and Mn18 (and their symmetry-re lated partners), is disordered with a H2O molecule along the mirror plane passing through the ring. The CCH3 moiety was thus refined with 50% occupancy and H atoms of H2O molecules were not located nor were they included in the final refinement model. A total of 1264 para meters were refined in the final cycle of refinement using 15761 reflections with I > 2 ( I ) to yield R 1 and wR 2 of 6.18 and 17.22%, respectively. Refinement was done using F2.

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85 Table 3-1. Crystallographic data and stru cture refinement details for complexes 5 and 6 . parameter 2 3 formulaa C212 H450 Mn70 O258 C216 H424 Mn70 O260 Cl38 fw, g mol-1 10973.46 12374.51 space group C 2/ m C 2/ m a, 40.264(4) 40.554(4) b, 52.631(5) 52.190(6) c, 15.3486(16) 17.1744(19) , deg 108.878(2) 108.378(1) V, 3 30776(5) 34496(6) Z 2 2 T, K 173(2) 173(2) radiation, b 0.71073 0.71073 calc, g/cm3 1.473 1.733 , cm-1 1.474 1.704 R1c , d 6.94 6.18 wR2c , e 16.23 17.22 a Excluding solvent molecules. b Graphite monochromator. c I > 2 ( I ). d R 1 = ||F0| – |Fc|| / |F0|. e wR 2 = [ [ w ( F0 2 Fc2)2] / [ w F0 2)2]]1/2, w = 1/[ 2( F0 2) + ( m * p )2 + n * p ], p = [max( F0 2, 0) + 2* Fc2]/3, and m and n are constants.

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86 m C2 m m C2 C2 Mn1 Mn2 Mn3 Mn5 Mn4 Mn7 Mn6 Mn10 Mn9 Mn8 Mn11 Mn12 Mn14 Mn13 Mn15 Mn16 Mn17 Mn19 Mn18 O1 O3 O2 O4 O11 O5 O49 O10 O48 O50 O7 O6 O51 O53 O8 O52 O15 O9 O14 O17 O18 O54 O12 O13 O24 O22 O20 O21 O55 O16 O19 O56 O57 O23 O27 O25 O26 O58 O59 O60 O28 O29 O31 O61 O30 O42 O32 O62 O41 O33 O35 O63 O39 O38 O37 O40 O65 O34 O64 O36 O45 O67 O46 O66 O44 O43 O47 O47’ Mn1 Mn2 Mn3 Mn5 Mn4 Mn7 Mn6 Mn10 Mn9 Mn8 Mn11 Mn12 Mn14 Mn13 Mn15 Mn16 Mn17 Mn19 Mn18 O1 O3 O2 O4 O11 O5 O49 O10 O48 O50 O7 O6 O51 O53 O8 O52 O15 O9 O14 O17 O18 O54 O12 O13 O24 O22 O20 O21 O55 O16 O19 O56 O57 O23 O27 O25 O26 O58 O59 O60 O28 O29 O31 O61 O30 O42 O32 O62 O41 O33 O35 O63 O39 O38 O37 O40 O65 O34 O64 O36 O45 O67 O46 O66 O44 O43 O47 O47’ Figure 3-1. PovRay representati ons of the asymmetric unit (t op) and the overall structure (bottom) of 5 . Crystallographic mirror plane ( m ) is shown in green; crystallographic C2 axis is shown in red. Hydr ogen atoms are omitted for clarity. Color code: Mn blue, O red, C gray. .

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87 ~3.7 nm ~1.4 nm ~1.2 nm ~3.7 nm ~1.4 nm ~3.7 nm ~3.7 nm ~1.4 nm ~1.4 nm ~1.2 nm ~1.2 nm Figure 3-2. Space-filling representations of 5 (including hydrogen atoms) from viewpoints perpendicular (top) and parallel (bottom) to the plane of the torus, showing the dimensions of the molecule and its central cavity.

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88 (a) (b) (c) (a) (b) (c) Figure 3-3. Space-filling representations, of the supramolecular aggregation of 5 into ordered nano-size tubes. (a) An arrangement of [Mn70] molecules (excluding hydrogen atoms) viewed perpendicular to the crystallographic c -axis, showing ABAB packing mode of molecules in adjacent tubular chains. (b) A view along the crystallographic c -axis, showing the hexagonal packing of neighbouri ng molecules. (c) Ordered arrangement of [Mn70] molecules as nano-size supramol ecular tubes. Hydrogen atoms are excluded. Color code: Mn blue, O red, C gray. .

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89 Mn2 Mn11 Mn17 Mn18 Mn19 O65 O64 Mn16 Mn13 Mn14 Mn15 O65 Mn10 Mn12 Mn8 Mn9 Mn7 Mn6 Mn5 Mn4 Mn3 Mn1 O53 O57 O54 O52 O46 O42 O35 O33 O26 O27 O25 O24 O19 O17 O6 O11 O1 O7 Mn11 O64 Mn2 Mn2 Mn11 Mn17 Mn18 Mn19 O65 O64 Mn16 Mn13 Mn14 Mn15 O65 Mn10 Mn12 Mn8 Mn9 Mn7 Mn6 Mn5 Mn4 Mn3 Mn1 O53 O57 O54 O52 O46 O42 O35 O33 O26 O27 O25 O24 O19 O17 O6 O11 O1 O7 Mn11 O64 Mn2 Mn2 Mn11 Mn17 Mn18 Mn19 O65 O64 Mn16 Mn13 Mn14 Mn15 O65 Mn10 Mn12 Mn8 Mn9 Mn7 Mn6 Mn5 Mn4 Mn3 Mn1 O53 O57 O54 O52 O46 O42 O35 O33 O26 O27 O25 O24 O19 O17 O6 O11 O1 O7 Mn11 O64 Mn2 Figure 3-4. PovRay representation of 6 excluding hydrogen atoms. Th e rectangle is highlighting the asymmetric unit, the co re of which is shown above the structure with carbon atoms omitted for clarity (except for those of the chloroethanol groups to clarify their positions in the asymmetric unit). Color code: Mn blue, O red, Cl green, C gray. .

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90 a b c a b c a b c Figure 3-5. PovRay representation of the supramolecular aggregation of 6 emphasizing the ABAB packing mode of molecules in adjacent tubular chains. 050100150200250300 0 25 50 75 100 125 150 175 2 3 mT(cm3mol-1K)T (K) 050100150200250300 0 25 50 75 100 125 150 175 2 3 mT(cm3mol-1K)T (K) 5 6 050100150200250300 0 25 50 75 100 125 150 175 2 3 mT(cm3mol-1K)T (K) 050100150200250300 0 25 50 75 100 125 150 175 2 3 mT(cm3mol-1K)T (K) 5 6 Figure 3-6. Plots of mT vs T for complexes 5 and 6 in a 0.1T DC field.

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91 m'T(cm3mol-1K)T (K) 012345678910 5 10 15 20 25 30 35 40 1500 Hz 1000 hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz m'T(cm3mol-1K)T (K) 012345678910 5 10 15 20 25 30 35 40 1500 Hz 1000 hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz 1.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 2.5 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K)m"(cm3mol-1) 1.52.02.53.03.5 0.0 0.5 1.0 1.5 2.0 2.5 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K)m"(cm3mol-1) Figure 3-7. AC magnetic susceptibility data for a dried, microcrystalline sample of complex 5 in a 3.5 G field oscillating at th e indicated frequencies. Top: plots of the in-phase (m' , plotted as m'T vs T ) AC magnetic susceptibility signa ls. Bottom: plots of the out-ofphase (m" , plotted as m" vs T ) AC magnetic susceptibility signals.

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92 012345678910 5 10 15 20 25 30 35 40 45 50 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz m'T(cm3mol-1K)T (K) 012345678910 5 10 15 20 25 30 35 40 45 50 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz m'T(cm3mol-1K)T (K) 1.52.02.53.03.5 0.0 0.3 0.6 0.9 1.2 1.5 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K)m"(cm3mol-1) 1.52.02.53.03.5 0.0 0.3 0.6 0.9 1.2 1.5 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K)m"(cm3mol-1) Figure 3-8. AC magnetic susceptibility data for a dried, microcrystalline sample of complex 6 in a 3.5 G field oscillating at th e indicated frequencies. Top: plots of the in-phase (m' , plotted as m'T vs T ) AC magnetic susceptibility signa ls. Bottom: plots of the out-ofphase (m" , plotted as m" vs T ) AC magnetic susceptibility signals.

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93 -1 -0.5 0 0.5 1 -1-0.500.51 0.04 K 0.2 K 0.3 K 0.4 K 0.5 K 0.6 K 0.7 K 0.8 K 0.9 K 1.0 K 1.2 K 1.4 K M/Ms 0H (T) 0.14 T/s -1 -0.5 0 0.5 1 -1-0.500.51 0.04 K 0.2 K 0.3 K 0.4 K 0.5 K 0.6 K 0.7 K 0.8 K 0.9 K 1.0 K 1.2 K 1.4 K M/Ms 0H (T) 0.14 T/s Figure 3-9. Magnetization ( M ) vs applied DC magnetic field ( 0H ) hysteresis loops, measured at a constant sweep rate of 0.14 T/s for a si ngle crystal (wet with mother liquor) of complexes 5 (top) and 6 (bottom) at the indicated temperatures. M is normalized to its saturation value, Ms.

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94 -1 -0.5 0 0.5 1 -1-0.500.51 0.140 T/s 0.070 T/s 0.035 T/s 0.017 T/s 0.008 T/s 0.004 T/s 0.002 T/s M/Ms 0H (T) 0.6 K -1 -0.5 0 0.5 1 -1-0.500.51 0.140 T/s 0.070 T/s 0.035 T/s 0.017 T/s 0.008 T/s 0.004 T/s 0.002 T/s M/Ms 0H (T) 0.6 K Figure 3-10. Magnetization ( M ) vs applied DC magnetic field ( 0H ) hysteresis loops, measured at a constant temperature of 0.6 K for a si ngle crystal (wet with mother liquor) of complexes 5 (top) and 6 (bottom) at the indica ted field sweep rates. M is normalized to its saturation value, Ms.

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95 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.11101001000 M/Ms t (s)1.4 K 1.3 K 1.2 K 1.05 K 0.6 K 0.04 K 0.2 K 0.3 K 0.4 K 0.5 K 0.8 K 0.7 K 0.92 K 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.11101001000 M/Ms t (s) 1 K 0.6 K 0.04 K 0.2 K 0.3 K 0.4 K 0.5 K 0.8 K 0.7 K 0.9 K 0.95 K 0.85 K 0.75 K 0.65 K 0.55 K 0.45 K Figure 3-11. Magnetization ( M ) vs time decay plots for a single crystal of complexes 5 (top) and 6 (bottom). M is normalized to its saturation value Ms.

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96 10-510-310-110110310510710905101520 DC (s) 1/T (1/K) = 1.7x10-10 * e23 K/T = 1.7 10-10exp(23 K/T) 10-510-310-110110310510710905101520 DC (s) 1/T (1/K) = 1.7x10-10 * e23 K/T = 1.7 10-10exp(23 K/T) 10-510-310-110110310510710905101520 DC (s) 1/T (1/K) = 1.6x10-10 * e18 K/T = 1.6 10-10exp(18 K/T) 10-510-310-110110310510710905101520 DC (s) 1/T (1/K) = 1.6x10-10 * e18 K/T = 1.6 10-10exp(18 K/T) Figure 3-12. Arrhenius plot of the relaxation time ( ) vs 1/ T for complexes 5 (top) and 6 (bottom) using data obtained from a single crysta l DC magnetization decay measurements. The dashed line is the fit of the data in the thermally activated region to the Arrhenius relationship; see the text for the fit parameters.

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97 110100 1000N Quantum World Molecular (bottom-up) approach Classical World Classical (top-down) approachMn4Mn12Mn30Mn84Co metal nanoparticle ~ 3 nm 4.3 nm Mn703.7 nm 110100 1000N Quantum World Molecular (bottom-up) approach Classical World Classical (top-down) approachMn4Mn12Mn30Mn84Co metal nanoparticle ~ 3 nm 4.3 nm Mn703.7 nm Figure 3-13. The position of [Mn70] molecules on a size scale spanning atomic to na noscale dimensions. On the far right is shown a high-resolution transmission electron mi croscopy view along a [110] direction of a typical 3nm cobalt nanoparticle exhibiting a face-centered st ructure and containing ~1000 Co atoms. The [Mn84] molecule has a ~ 4.2 nm diameter , whereas [Mn70] compounds have a ~3.7 diameter. Also shown for comparison are the indicated smaller Mn SMMs, which are drawn to scale. The red arrows i ndicate the magnitude of the Nel vectors ( N = the sum of individual spins) for the indicated SMMs, which are 7.5, 22, 61, 140 and 168 B for [Mn4], [Mn12], [Mn30], [Mn70] and [Mn84], respectively. The red arrows from the Co nanoparticle ar e merely meant to indicate that the N of nanoparticles can take many values, depending on the exact size and the id entity of the constituent metal.

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98 CHAPTER 4 SINGLE-MOLECULE MAGNETS: STUDY OF DISTORTED CUBANE [MnIVMnIII 3O3X(O2CMe)3(dbm)3] (X = Cl, N3, NCO) COMPLEXES 4.1 Introduction Considerable amount of research has been directed towards studying single-molecule magnets (SMMs) due to, at leas t two major reasons. Firstly, S MMs are viewed as attractive candidates to function as nanoscale magnetic memory units,28,45 since such molecules, below their blocking temperature ( TB) exhibit the macroscale propert y of a magnet magnetization hysteresis. Secondly, since SMMs also exhibit quan tum properties, such as quantum tunneling of magnetization (QTM)140,142 and quantum phase interference,150 they are also considered as excellent molecular systems to study the chemistr y and physics of nanomagnets at the interface of the classical and quantum regimes. Since the first discovery of the SMM behavior in [Mn12O12(O2CMe)16(H2O)4]MeCO2H4H2O,26,27 various manganese compounds of different nuclearities have been synthe sized and magnetically characte rized, many of these complexes have been shown to function as SMMs.28,45 Among other known SMMs, tetranuclear manganese complexes possessing a distorted-cubane [MnIVMn3 IIIO3X]6+ (X = halide, MeCO2, NCO, etc .) core represent the second largest and second most studied family of SMMs after the [Mn12] family of complexes. An important subgroup of this class of complexes is the family of tetranuclear manganese clusters of formula [Mn4O3X(O2CR)3(dbm)3] (R = Me, Et, Ph, O2CPhR'; R' = H, p -Me, p -OMe, o -Cl), where X ligand is va riously Cl, Br, F, MeCO2, PhCO2, NO3, Me3SiO, MeO, PhO, OH, N3, NCO and dbm is the anion of dibenzoylmethane.33,70,72-80,196 All members of this family of Mn clusters contain the [MnIVMnIII 3( 3-O)3( 3-X)]6+ distorted cubane core, composed of a MnIII 3MnIV trigonal pyramid with the MnIV ion at the apex, a 3-X ion bridging the basal Mn3 face, and three 3-O2ions

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99 bridging each of the vertical Mn3 faces (Figure 4-1). The periphe ral ligation is provided by three chelating dbmand three 2-MeCO2 groups (Figure 4-2). The MnIIIMnIV and MnIIIMnIII distances of ~2.81 and ~3.3 , respectively, obser ved for these clusters , emphasize the severe distortion from true cubane ( Td) symmetry. Except for complex with X = Me3SiO, possessing crystallographic C3 symmetry, the crystallographic sy mmetry of other clusters is C1. The virtual symmetry is CS for the X = PhCO2 complex, whereas the remaini ng clusters possess a virtual C3 v symmetry, with a pseudoC3 axis passing through MnIV and X ions The initial interest in studying tetranucle ar, mixed-valence, oxide-bridged manganese carboxylate clusters was based on th eir potential relevance to the water oxidation center (WOC) in Photosystem II (PSII) of green plants and cyanobacteria.197 The [Mn4O3] trigonal-pyramidal unit, which is compatible with the [Mn4( 3-O3)3( 3-X)]6+ core, was one of the topologies proposed by De Rose et al .198 in their consideration of units consistent with WOC Extended Xray Absorption Fine Structure (E XAFS) data. It was found later, however, that the structure of this class of distorted cubane compounds does no t fit well with the most recent data obtained from EXAFS199-201 and X-ray crysta llography studies.202,203 It is important to point out that even though the distorted-cubane complexes of C3 v symmetry could be excluded as a topological model for the Mn cluster in the WOC, the c ubane compounds do point to future synthetic approaches for modeling the WOC active site. The si te specific variation of X ligands of these compounds has allowed the investiga tion of small species known to be present at, or to interact with, the native WOC, such as the substrate (H2O), cofactors (Cl, Br), i nhibitors (F), and other molecules similarly relevant to PSII, and to st udy their influence on the properties of the [Mn4] cluster .

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100 Distorted-cubane manganese clusters continue to attract the attenti on of researchers not only due to their biological relevanc e, but also due to their ability to function as SMMs. Over the past several years, magnetic properties of the [Mn4O3X(O2CR)3(dbm)3] family of compounds have been characterized in great detail by ou r group, and are summarized herein based on the corresponding [Mn4O3Cl(O2CMe)3(dbm)3]( 8 ) complex. In fact, complex 8 was the first tetranuclear cluster for which SMM properties were discovered.73 Magnetic susceptibility studies performed on complex 8 have established S = 9/2 spin ground state, where the MnIIIMnIV interactions are antiferromagnetic ( J34 = -28.4 cm-1) and MnIIIMnIII are ferromagnetic ( J33 = + 8.3 cm-1).196 Clearly, the predominant antiferromagnetic MnIIIMnIV exchange interactions force the spins of the MnIII atoms to align antiparallel to the spin of the MnIV atom, leading to an overall S = 9/2 value of the spin ground state. The S = 9/2 ground state is well isolated with th e lowest energy excited state ( S = 7/2) being 185 cm-1 higher in energy. Large magnetic anisotropy was evident from fitting of the variable-field magnetic susceptibility data. The origin of this anisotropy is zero-field splitting in the S = 9/2 ground state. Axial zero-field splitting (ZFS) is defined by the D z 2 term of the spin Hamiltonian, where D is the parameter that gauges the magnitude of the splitting. Each MnIII atom in a tetragonally elongated coordination geometry po ssesses an appreciable single-ion ZFS. Since the Mn ions are exchange coupled in 8 , the vectorial addition of the single-io n zero-field interactions present at each MnIII atom of the cluster give rise to the ZFS for the S = 9/2 ground state of the molecule. Variable-field magnetization data could be equally well fit with either a positive D parameter ( D = 0.45 cm-1) or a negative one ( D = -0.35 cm-1). Thus, to characterize th e electronic structure of complex 8 and determine the sign and magnitude of D , high-field high-frequency electron

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101 paramagnetic resonance (HFEPR) spectroscopy studi es were performed on a microcrystalline sample of 8 .72 HFEPR is a powerful technique for the magnetic characterization of molecular complexes with large anisotropy.204-206 EPR signal is observed when the energy difference between the two spin states matches the energy of the radiation. Fine stru cture, that is, a series of relatively constantly spaced transitions, is seen due to the ZFS of the ground state. Large ZFS makes the allowed ( ms = 1) transitions between the spin sublevels inaccessible to the microwave energy quantum used in conventional EPR (X-band: ~ 9 GHz (0.3 cm -1); Q-band: ~35 GHz (1.2 cm -1)) or makes them appear at fields much above t hose available in conventional EPR spectrometers. In such cases, the obvious advantage of HFEPR is offered by the possibility of resolving the complete fine structure of the cluster, even in the presence of large ZFS.207-209 An important feature of the HFEPR spectra is that changes in relative intensities of EPR peaks reflect changes in Boltzmann populations and can be used to directly determine the sign of ZFS parameter D . The sign of D can be determined by observing the temperature dependence of the peaks of the fine stru cture. For a complex with S = 9/2 ground state, when the field is oriented either parallel or perpendicu lar to the easy axis of the complex, 2 S resonances, i.e. , 9 allowed transitions are expected in the EPR spectrum when all of the ms states are populated. When the magnetic field is oriented parallel to th e principal axis of magnetic anisotropy and D < 0 (Figure 4-3 (top)) at very low temperatures only the lowest energy ms zero-field component is thermally populated, that is, all molecules are in the lowest ms = 9/2 state and only the 9/2 7/2 transition is observed. As the temper ature is increased, higher energy states are populated and therefore additional transition can be observed. Thus, for a parallel field orientation when D < 0, the -9/2 -7/2 transition is seen at the lowest field position and all the

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102 other transitions are seen at higher values of the field. If D > 0, the -9/2 -7/2 transition occurs at the highest field position in the fine structure series. The HFEPR spectra collected on a microcrystalline sample of complex 8 at several different frequencies and temperatures in th e 0-13 T magnetic field range, showed a well resolved fine structure, composed of five peaks, with the highest intensit y resonance (assigned as the -9/2 -7/2 transition) visible at the lowest fields employed and, whereas lower intensity peaks, corresponding to the -7/2 -5/2, -5/2 -3/2, -3/2 -1/2 and -1/2 1/2 transitions, were observed at higher fields. Thus, it was concluded that the sign of D is negative. The analysis of HFEPR spectra provided a very prec ise determination of the following parameters: S = 9/2, g = 2.00, D = -0.53 cm-1 and B4 0 = -7.4-5 cm-1 ( B4 0 is the quartic longitudinal (axial) zero-field interaction parameter). It is impera tive to add, however, that no transverse spin Hamiltonian parameters ( e.g. , the rhombic E term), characterizing the anisotropy in the xy plane, was taken into the consideration. It is a well known fact that transv erse terms are essential for the full characterization of SMMs si nce they represent the major source of mixing of states on opposite sides of the energy barrier to magnetiz ation reversal, thereby making possible the QTM.210 Transverse interactions cause quantum admixing of ms = 2 states and facilitate the tunneling. AC magnetic susceptibility studies perf ormed on a microcrystalline sample of 8 revealed the presence of frequency-dependent out-of-phase si gnals, characteristic of slow relaxation of the magnetization.73 The observation of hyste resis loops below 0.9K in the plots of magnetization vs external magnetic field confirmed that complex 8 is a SMM.72 The kinetic data, obtained from magnetization relaxation and AC susceptibility st udies, were fit to an Arrhenius relationship ( = 0 exp( Ueff/ kT ), where Ueff is the effective barrier to magnetization relaxation, 0 is the pre-

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103 exponential factor, and k is the Boltzmann constant) to give Ueff = 11.8 K and 0 = 3.6-7 s.72 The obtained value of Ueff was smaller than the calculated U = ( S2 – 1/4) |D| = 15.7K for S = 9/2 and the D value obtained from HFEPR studies for this complex, indicative of the fact that the magnetization reversal in this SMM occurs not only via the thermal activation over the potential energy barrier, but also via the QTM. The QTM was also evidenced by the presence of steps in the hysteresis loops, where each step corresponds to an increase in the magnetization relaxation rate at a particular value of an applied ma gnetic field (when the ms state on one side of the potential energy barrier to magnetiza tion reversal matches in energy the ms state on the opposite side). Hysteresis loops also showed a large step in zero applied field, in dicative of a ground-state quantum tunneling occurring between the lowest energy ms = -9/2 and ms = 9/2 levels of the S = 9/2 ground state manifold. The occurrence of the ground state QTM was further confirmed by the observation of a temperature-independent relaxation below 0.6 K, evidenced from the Arrhenius plot, with 1/ = 3.2-2 s-1. A molecule with a half-int eger ground state such as S = 9/2 should not exhibit resonant tunnelin g in the absence of a magnetic field. For a half-integer spin system, each pair of ms levels in zero-field exhibits Kramer’s degeneracy. The Kramer’s theorem211,212 states that no matter how unsymmetric the crystal field is, an ion possessing an odd number of electrons must have a ground state th at is at least doubly de generate, even in the presence of crystal field and spin-orbit interactions. Thus, S = 9/2 molecule should not be able to tunnel coherently between ms = -9/2 and ms = 9/2 levels or between any ms and ms pair in the absence of a magnetic field. Despite this, th e occurrence of ground state QTM is clearly evidenced in complex 8 . Undoubtedly, transverse inte ractions that admix the ms states must be present in such Kramer’s degenerate system to allow the QTM to occur in zero external fields.210

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104 Such transverse interaction can be provided by the transverse com ponents of dipolar and exchange fields from neighboring mo lecules and hyperfine fields from 55Mn ( I = 5/2) nuclei. Inelastic Neutron Scattering (INS ) studies performed on complex 8 further confirmed that inclusion of the rhombic term in the zero-field sp litting (ZFS) Hamiltonian is essential to explain the INS intensities and observed transitions.81 Since the symmetry of the cluster is only approximately C3 v, the actual Cs crystallographic symmetry leads to non-zero E term. A precise determination of the spin Hamiltoni an parameters, including transverse terms, could be obtained from the single-crystal HFEPR m easurements. In this ch apter, single-crystal HFEPR studies of complex 8 are presented. Additionally, as a part of th e detailed study of complexes, incorporating pseudohalides (N3 , NCO), magnetic characterization of [Mn4O3(N3)(O2CMe)3(dbm)3] ( 9 ) and [Mn4O3Cl(O2CMe)3(dbm)3]( 10 ) will be described in detail. 4.2 Results and Discussion 4.2.1 Syntheses Several synthetic routes were available from previous work for the formation of distorted cubane family of complexes with the general formula [Mn4O3X(O2CMe)3(dbm)3] (X = Cl, Br, etc .). [Mn4O3Cl(O2CMe)3(dbm)3]( 8 ) complex was initially synt hesized in our group by the disproportionation reaction (eq. 4-1) of the butterfly complex, [Mn4 IIIO2(O2CMe)6(dbm)2(py)2], triggered by the carboxylate abstracti on with trimethyls ilyl chloride (Me3SiCl) (eq.4-1): 3[Mn4O2]8+ + 2Cl 2[Mn4O3Cl]6+ + 2Mn2+ + 2Mn3+ (4-1) An important synthetic breakthrough wa s the preparation of the X = MeCO2 analogue of complex 8 , [Mn4O3(O2CMe)4(dbm)3] ( 7 ), by controlled potential electrolysis of the above mentioned butterfly-like [Mn4 III] complex. The optimized high-yield synthesis of complex 7 , involving the direct reaction between Mn(O2CMe)2H2O and KMnO4 in a presence of

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105 dibenzoylmethane (dbmH) and acetic aci d, was subsequently reported. Complex 7 was the first derivative of this class of complexes not to cont ain halides in the core and has served as an excellent precursor compound for the prepar ation of various de rivatives of the [Mn4O3X(O2CMe)3(dbm)3] (X = Cl, Br, F, OMe, OH, Me3SiO, N3, NCO) family of complexes. Complex 7 contains three 2, 2-MeCO2 groups and one 1, 3MeCO2 group bridging the three MnIII ions. The general mechanism of the reaction leading to the formation of [Mn4O3X(O2CMe)3(dbm)3] complexes involves the abstraction of 1, 3MeCO2 group by Me3SiX reagent, driven by the strength of the Si-O bond, immediately followed by the coordination of the corres ponding anion (X) to the [Mn4O3]6+ core. The 1, 3-MeCO2 group is more amenable to the electr ophilic attack than the other carboxyl ates bound at the 2 sites since it lies at the intersection of the th ree Jahn-Teller axes. Ligands locat ed along this axis have longer bond distances and are therefore weakly bound. An a lternative synthetic pro cedure has also been reported in which the 3-carboxylate group is removed via the protonation imposed by the mineral acid, HX (X = F, Cl, Br, NO3), followed by subsequent incorporation of the X group. The syntheses of complexes [Mn4O3(N3)(O2CMe)3(dbm)3]( 9 ) and [Mn4O3(NCO)(O2CMe)3(dbm)3]( 10 ) were initially reported in 1995,77 and involved the addition of 1.5 equivalents of Me3SiX (X = N3, NCO) to a slurry of [Mn4O2(O2CMe)6(dbm)2(py)2] complex in hot MeCN (~ 75 C), from wh ich brown microcrystal line precipitate of corresponding complexes 9 and 10 began to deposit. In each case, the mixture was allowed to cool to room temperature and after ~ 18 hours products were is olated by filtration and washed with MeCN. Yields were 12% (complex 9 ) and 27% (complex 10 ) based on total Mn. X-ray

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106 quality crystals of 9 and 10 were obtained when CH2Cl2 solutions of isolated solids were layered with MeCN and MeCN: Et2O (2:1), respectively, and stored at 5 C over a period of 2-5 days. In the present work, complexes 8 10 were synthesized taking a dvantage of the previously described site-specific carboxylat e abstraction pr ocedure, using 7 as a precursor complex. A CH2Cl2 solution of complex 7 was treated with 1.5 equivalents of Me3SiX (X = N3, NCO) under an inert atmosphere. Crystalline products were obtained by diffusing respectively Et2O, MeCN and MeCN:Et2O (2:1) into the reaction mixture of complexes 8 , 9 and 10 at 5C over a period of 5-7 days. Yields of about 30-40% have been obtained for all of the complexes. The transformations are summarized in eq. 4-2: [Mn4O3(O2CMe)4(dbm)3] + Me3SiX [Mn4O3X(O2CMe)3(dbm)3] + Me3SiO2CMe (4-2) The formation of complexes 8 10 was confirmed by the IR and elemental analyses. The IR spectrum of complex 8 was identical to that of complex 7 , except for the absence of the 1682 cm-1 absorption, characteristic of a monodentate acetate gr oup. Similarly, IR spectra of 9 and 10 , displayed no absorption at 1682 cm-1. The IR spectrum of complex 9 additionally displayed a strong absorption at 2071 cm-1 consistent with the presence of bound azide.213 The observation of a very strong absorption at 2168 cm-1 in the IR spectrum of complex 10 similarly confirmed the presence of a bridging cyanate group. 4.2.2 Single-Crystal High-Frequency Electro n Paramagnetic Resonance Studies of Complex 8 In order to obtain detailed information on the spin Hamiltonian and to verify the S = 9/2 ground state spin of complex 8 , a high-frequency electron pa ramagnetic resonance (HFEPR) spectroscopy study was performed on a single crystal. The analysis of HFEPR spectra can provide very precise informati on such as the exact value of S ,214 the sign and magnitude of D ,215 the location in energy of exited spin states relative to the ground state,216 and, most importantly,

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107 information concerning transverse spin Hamiltoni an parameters that are responsible for the magnetic quantum tunneling, e.g . the rhombic E term.217 The spin Hamiltonian ( H ) describing the S = 9/2 ground state spin of 8 is given by eq. 4-3: H = g B H + D z 2 + E( x 2 y 2) + B4 0‘4 0 (4-3) The first term is the Zeeman term, which desc ribes the interaction between the electron spin, S , and the applied external magnetic field, H ; i is the spin projection opera tor along the i (= x, y, z) axis, B is the Bohr magneton and g is the Land factor. The sec ond term gauges the axial zerofield splitting in the ground state, where D is the uniaxial anisotropy (ZFS) parameter. The third term is the rhombic (transverse) zero-field interaction term, where E is the rhombic zero-field parameter, characterizing the magnetic anisotro py in the plane perpendicular to the magnetic easy ( z ) axis, i.e. , the xy plane. The fourth term is the qua rtic longitudinal (axial) zero-field interaction term; the operator ‘4 characterizes fourth order crystal-field interactions. For the strictly axial case, i. e. , no transverse terms present, the energy spectrum of the S = 9/2 system and D < 0 consists of ten (= 2S +1 ) energy levels (Figure 4-4 (top)). Each energy level can be labeled by a quantum number ms ( -S ms S ), which represents the projection of S on the easy axis of the molecule. Acco rding to the EPR selection rule ( ms = 1), nine (= 2 S ) transitions are expected to be seen in the spec trum. However, this is the case when all ten ms states are populated. With decr easing temperatures, the Boltzm ann population of higher energy ms states is significantly reduced, leading to the smaller number of observed transitions. At very low temperature only the lowest energy ms state is populated and only one EPR transition is seen in the spectrum. Figure 4-4 (top) shows the en ergy level diagram for the S = 9/2 ground state ( D < 0) when magnetic field is applied along the easy axis of the molecule. In this field orientation, the

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108 transverse anisotropy terms operate at very high orders of pert urbation theory, and, essentially, vanish. Thus, the energy of each sp in state is solely determined by the uniaxial anisotropy terms and the Zeeman term. The energy difference diagram between adjacent levels can then be constructed accordingly as function of magne tic field. EPR spectra, shown in Figure 4-4 (bottom), were collected on a single crystal of complex 8 at two different frequencies (113 and 146 GHz) and the field was app lied along the easy/hard plane( i.e. , xz plane) of the molecule at = 10 angle away from the magnetic easy axis. The temperature was kept constant at 10 K in each case. The fine structure pattern is clearly seen in the 146 GHz spectrum. Within the 0-7 T field range, five out of nine e xpected EPR transitions can be s een in the spectrum. Based on the fact that relative intensitie s of the peaks directly reflect Boltzmann populations of ms states, each resonance was assigned to the corresponding transition. In the 146 GHz spectrum, the resonance at the lowest field corresponds to the -9/2 -7/2 transition. The resonances that follow correspond to the -7/2 -5/2, -5/2 -3/2, -3/2 -1/2, -1/2 1/2 transitions. The diminishing intensity of transitions with the increasing field is observed due to the reduced thermal populations of the higher energy ms levels at this temperature. An ms dependence of the transition probability accounts for the fact that the -7/2 -5/2 transition is stronger than -9/2 -7/2 transition. Since the -9/2 -7/2 transition in each fine structure group (for a parallel orientation of the field) was obs erved at the lowest field positi on, it was concluded that the sign of ZFS parameter D is negative. The measurements were repeated with the fiel d applied perpendicular to the easy axis of the molecule. Figure 4-5 (top) shows the energy level diagram for an S = 9/2 ground state ( D < 0) for the perpendicular orientati on of the field. EPR spectra for th is field orientation, obtained at three different frequencies (83, 113, 146 GHz) ar e shown at the bottom of Figure 4-5. The

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109 temperature was kept constant at 10 K in each case. In the transverse applied field when the sign of parameter D is negative the transition from the ground st ate to the first exited state is expected to be seen at the highest field as the most intense peak in the fine structure. Such fine structure pattern is observed in the 146 GHz spectrum, wh ere the most intense transition, seen at the highest field, was assigned to the -9/2 -7/2 transition and other tr ansitions were observed at lower fields. The spectra, obtained at lower fr equencies were more complex. Weak low-field resonances, visible in the 113 GHz and 146 GHz spect ra, increase in intensity in an irregular way in the 83 GHz spectrum, additionally the -9/2 -7/2 transition decreases in its intensity. Such spectra pattern at lower fi eld values is observed due to the strong mixing of ms levels, caused by the transverse components of an applied field. Wh en the magnetic field is applied along the hard axis, the transverse anisotropy, wh ich essentially vanishes in the axial case, becomes a zero order perturbation to the Hamiltonian, and the energies of spin levels are determined by both axial and transverse ZFS parameters. As a result, at the lower field values many more allowed transitions ( ms = 2) are possible and addition al different intensity peaks appear in the spectra. The measurements for both orientations of the applied magnetic field were repeated at many closely spaced frequencies. Figure 4-6 sh ows the frequency dependence of the EPR transitions with the magnetic field applied para llel to the magnetic easy axis of the molecule. 218.6 GHz data were taken from HFEPR studies pe rformed on the microcrystalline sample of complex 8 .72 Each solid circle in the graph corresponds to a certain transition occurring at a particular frequency and at a particular value of an applied magnetic field. For the transitions involving negative ms states, the values of a frequency at which a certain transition occurs increase with the increasing field. For exampl e, with an increasing frequency the -9/2 -7/2 transition shifts to higher fi elds. The opposite is seen for th e transitions involving positive ms

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110 states. This is consistent with the negative sign of parameter D . Also, the linear frequency vs applied magnetic field dependence of the EPR tran sitions is indicative of the fact that the Zeeman term in eq. 4-3 is the l eading term. The experimental data were fit to eq. 4-1 and the best fit is shown as the solid lines. The fit of the easy ax is data is insensitive to the transverse terms in eq. 4-3. Instead, it provides a very precise determin ation of the diagonal (a xial) spin Hamiltonian parameters ( D , B4 0, gz). By extrapolating the positions of re sonances to zero magnetic field, the fitting parameters were found to be D = -0.529(3) cm-1 and B4 0 = -7.3(3)-5 cm-1. The easy axis g value, gz = 2.00 was obtained from the slopes of the li near fits to the data. The obtained axial parameters were used as a basis for determining th e transverse parameters from the fitting of the transverse field data. Figure 4-7 shows the frequency dependence of EPR transitions obtained with the magnetic field applied perpendicular to the easy axis. The solid lines represent si mulations of the data using eq. 4-3. The fit of hard axis data is sens itive to both the diagonal and transverse terms in eq. 4-3. As mentioned earlier, the transverse externally applied ma gnetic field represents another source of transverse anisotropy, along with the rhombic term E (eq. 4-3) . In eq. 4-3 the Zeeman term is defined as g BH , where H could be written as: H Hx x+ Hy y+ Hz z, where Hz is the z -component of the magnetic field strength (the field component pa rallel to the easy axis), Hx and Hy are field components perpendicular (transvers e) to the easy axis. In a case of a parallel orientation of the field, the leading Zeeman te rm gives rise to a lin ear dependence of each transition frequency on the z -component of the ma gnetic field strength ( Hz). However, in a case of the perpendicular field orientation, the transverse components ( Hx, Hy) of an applied magnetic field as well as other transverse terms in eq. 4-3 become import ant. Two distinctive regions are seen in Figure 4-7. The curvature re gion is seen at lower field values , and this curvature is due to

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111 the competing Zeeman and transverse anisotropy terms. In this region, the strong mixing of ms states leads to increased numb er of allowed transitions ( ms = 2). At high fields the Zeeman term predominates and EPR transitions with ms = 1 are seen in the spectra. The fitting of the hard axis data gave a very precise determination of the value of the rhombic term E as well as the values of gx and gy: E = 0.022(2) cm-1, gx = gy = 2.00. As shown in Table 4-1, experimentally determined spin Hamiltonian parameters for complex 8 are in an excellent agreem ent with those obtained from inelastic neuron scattering (INS) measurements as well as with those determ ined by HFEPR studies of the microcrystalline sample of this complex. The obtained non-zero E value is consistent with the fact that the symmetry of complex 8 is only virtually C3 v and the actual crystallographic symmetry is Cs. The obtained values of D and E are comparable to those determined for other distorted-cubane complexes with virtual C3 v symmetry ( D = – 0.38 to – 0.53 cm-1; E = 0.017 – 0.025 cm-1). 4.2.3 Description of Structu res of Complexes 8 10 Data collection and structure re finement details for complexes 8 10 were reported previously.77,196 Labeled ORTEP represen tations of complexes 8 , 9 and 10 are presented in Figures 4-2, 4-8 and 4-9, respectivel y. Comparisons of selected in teratomic distances and angles for 8 10 are shown in Tables 4-2 and 4-3. The structures of 8 10 consist of a [MnIVMnIII 3( 3-O)3( 3-X)]6+ (X = Cl( 8 ), N3( 9 ), NCO ( 10 )) distorted cubane core with periphera l ligation provided by three bridging MeCO2 and three chelating dbmligands. On the basis of charge consid erations, close examination of metric parameters and detection of Jahn-Teller (JT) di stortions (elongations), Mn2, Mn3 and Mn4 were assigned as the MnIII atoms and Mn1 as the MnIV atom in all of the structures. The JT axes are the ones that include the MnIII X bonds, thus, are significantly elongated (Table 4-2). Close

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112 inspection of metric parameters in all three comp lexes (Tables 4-2 and 4-3) revealed that (i) in comparison to the Mn Cl distances in complex 8 (2.642(7) – 2.656(14) ), the MnIII N distances in 9 and 10 are significantly shorter, with the MnIII N distances in 9 (2.302(15) – 2.329(14) ) being appreciably shorter th an the corresponding ones in complex 10 (2.320(9) – 2.403(9) ); (ii) the MnIII N MnIII angles in 9 (86.47(33) – 86.86(34)) and 10 (84.86(28) – 85.54(29)) are larger than MnIII Cl MnIII angles (75.36(20) – 75.80(19) ), consistent with the shorter MnIII N bonds; and (iii) MnIIIMnIII separations, nearly identical in 9 and 10 ( 3.19 ), are larger in 8 (3.237(3) – 3.262(9) ). In contrast, the MnIIIMnIV distances are very similar in all three structures. 4.2.4 Magnetochemistry of Complexes 9 and 10 4.2.4.1 Direct Current Magnetic Susceptibili ty Studies of Complexes 9 and 10 Variable-temperature magnetic susceptibility measurements were performed on powdered polycrystalline samples of complexes 9 and 10 , restrained in eicosane to prevent torquing, in a 1 kG (0.1 T) field and in the 5.0-300 K range. The data are shown as mT vs T plots in Figure 4-10. The value of mT for complex 9 increases from 9.83 cm3 mol-1 K at 300 K to a plateau value of ~ 12 cm-3 mol-1 K at 70 K and below 15 K mT decreases more rapidly to 11.65 cm3mol-1K at 5 K (Figure 4-10 (top)). Complex 10 exhibits similar behavior, with mT increasing from 9.70 cm-3 mol-1 K at 300 K to a to a plateau value of ~ 11.9 cm-3 mol-1 K at 70 K, and then decreasing to 11.82 cm3 mol-1 K at 5.0 K (Figure 4-10 (bottom)). The maximum mT for each of the two complexes is slightly below the spin-only 12.38 cm3 mol-1 ( g = 2) value expected for a complex with a S = 9/2 ground state, and this is consistent with g < 2.0, as expected for Mn. If there were no exchange interactions between the metal ions in a Mn3 IIIMnIV complex, the mT value would be temperature in dependent. Thus, an increase of mT value with

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113 decreasing temperature, observed for both 9 and 10 , is indicative of the presence of predominantly ferromagnetic exchange interactions within these molecule s. The decrease in the mT value at the lowest temperatures is likely du e to zero-field splitti ng (ZFS), Zeeman effects from the applied field, and any weak antiferro magnetic exchange interactions. At higher temperatures, the decrease in mT is due to the thermal popula tion of excited states with S < 9/2. In order to determine the Mn2 pairwise exchange interacti ons within the molecule, the mT vs T data for complexes 9 and 10 were fit to the theoretical mT vs T expression, derived for a Mn3 IIIMnIV trigonal pyramid of C3v symmetry. The isotropic Heis enberg spin Hamiltonian for this C3v symmetry is given in eq. 4-4, where J33 = J (MnIIIMnIII), J34 = J (MnIIIMnIV): = 2 J33( 23 + 24 + 34) 2 J34( 12 + 13 + 14) (4-4) In order to solve this Hamiltonian for the appr opriate eigenvalue expr ession, the Kambe vector coupling method166 was used. By an operator replacement technique, using the substitutions A = 2 + 3, B = A + 4 and T = B + 1, where ST is the spin of the complete Mn4 molecule, the spin Hamiltonian of eq. 4-4 can be convert ed to the equivalent form of eq. 4-5: = J33( A 2 – 2 2 – 3 2+ B 2 – A 2 – 4 2) J34( T 2 – B 2 – 1 2) (4-5) The eigenvalues of this Hamiltoni an are then given by eq. 4-6, wh ere constant terms contributing to all states have been omitted. E ( ST, SB) = J33[ SB( SB+1)] J34[ ST( ST+1) – SB( SB+1)] (4-6) For complexes 9 and 10 , S2 = S3 = S4 = 2 (MnIII), S1 = 3/2 (MnIV), and the overall multiplicity of the spin system is 500, ma de up of 70 individual sp in states ranging from ST = 1/2 to 15/2. A theoretical mT vs T expression was derived using the ST values, their energies E ( ST, SB), and the Van-Vleck equation218 (derived in Appendix C), and this expression was used to fit the experimental data. Data below 15 K were om itted because the low-temperature decrease is

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114 caused by factors not included into the fitting model. A temperature-independent paramagnetism (TIP) term was included, held fixed at 600 10-6 cm3 mol-1. Good fits were obtained for both complexes, and these are shown as the solid lines in Figure 4-10. The fit parameters for 9 are J33 = 8.7 cm-1, J34 = -47.9 cm-1, and g = 1.97; those for 10 are J33 = 9.2 cm-1, J34 = -31.0 cm-1, and g = 1.96. Comparison of the obtained results with the previously reported one s for the structurally related [Mn4O3X(O2CR)3(dbm)3] (X = Cl, Br, MeCO2) complexes with the C3 v symmetry 78 (Table 4-4) shows that N3 and NCO groups have not drastica lly altered the various exchange interactions in the cuba ne cluster, although the N3 seem to strengthen the antiferromagnetic J34, which could be a result of slightly shorter MnIII N distances (larger MnIII N MnIII angles) in complex 9 . The obtained J values establish that complexes 9 and 10 have an ST = 9/2 ground state, the | ST, SB> = |9/2, 6> state, well isolated from the nearest excited state, ST = 7/2 (Table 4-4). This ground state corre sponds to the three S = 2 MnIII spins being aligned parallel to give a resultant SB = 6, which is aligned antiparallel to the S = 3/2 MnIV spin to give an ST = 9/2 total spin. 4.2.4.2 Magnetization versus Direct Current Magn etic Field Studies for Complexes 9 and 10 To confirm the ST = 9/2 ground states for 9 and 10 and to determine the magnitude of the zero-field splitting parameter D , magnetization ( M ) vs DC field data were collected in the 1.8 10 K and 1-70 kG temperature and field range s, respectively. The data for complexes 9 and 10 are shown in Figure 4-11 as reduced magnetization ( M / N B) vs H / T plots, where M is the magnetization, N is Avogadro’s number, B is the Bohr magneton, and H is the magnetic field. For complexes populating only the ground state a nd possessing no axial ze ro-field splitting (ZFS), i.e ., D = 0, the magnetization versus field plot follows the Brillouin function and the

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115 isofield lines all superimpose and saturate at a value of gS . The experimental data of complexes 9 and 10 in Figure 4-12 clearly do not superimpose, indicating significant magnetic anisotropy (zero-field splitting) in the ground state. The da ta were fit by diagonalization of the spin Hamiltonian matrix using program MAGNET,167 which assumes that only the ground state is populated, includes axial ZFS ( D z 2) and Zeeman interactions, and incorporates a full powder average.79 In both cases, good fits were obtained (shown as solid lines in Figure 4-11) with the fit parameters, in the format 9 / 10 , of S = 9/2 (for both), g = 1.96/1.95, and D = -0.46/-0.47 cm-1. To ensure that the global fitting minimum had been obtained, root-mean square error surfaces for the D vs g fit were generated us ing the program GRID.219 Twoand threedimensional representations of error surfaces for 9 and 10 are shown in Figures 4-12 and 4-13, respectively, for the D = 1 to -1 cm-1 and g = 1.8 to 2.1 ranges. In both cases, the fit has a hard ( i.e. , well defined) mi nimum with negative D , in contrast to much shallower minimum with positive D . Clearly, for both complexes, the value corresponding to the negative anisotropy parameter D is the global minima. The obtained D values are in the range observed for the analogous distorted cubane complexes with virtual C3v symmetry (– 0.38 to – 0.53 cm-1).71,72,78 The negative value of the anisotropy parameter ( D ) along with a relatively high spin ground state ( S ) results in a substantia l potential ener gy barrier ( U ) for the reversal of the direction of the magnetization. For half-integer spin systems the upper limit to this barrier is given by U = ( S2-1/4)| D |, and is equal to 20| D | for complexes 9 and 10 , although the actual or effective barrier ( Ueff) is usually much smaller than U due to QTM. 4.2.4.3 Alternating Current Magnetic Susceptibi lity Studies of Complexes 9 and 10 To investigate the magnetization dynamics of complexes 9 and 10 alternating current (AC) magnetic susceptibility studies were performed in the 1.8 15 K temperature range with zero DC field and with 3.5 G AC field oscillating at 50, 250 and 1000 Hz range. The obtained data for

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116 dried, microcrystalline samples of 9 and 10 are presented in Fi gure 4-14 and Figure 4-15, respectively. In each figure, the upper panel s hows the in-phase component of AC magnetic susceptibility (m' ), plotted as m'T vs T , whereas in the lower panel is given a plot of the out-ofphase ( m" ) AC magnetic susceptibility vs T . Both complexes display a plateau at > 5 K in the m'T vs T plot, at a value in the 12.3 12.4 cm3 mol-1 K range consistent with a well-isolated S = 9/2 ground state and g slightly less than 2. At lower temper atures, the in-phase signal decreases and a frequency-dependent m" signal appears, indicative of the slow relaxation of the magnetization, characteristic property of a S MM. However, the peak maxima for both 9 and 10 lie at temperatures below 1.8 K, suggestive of a smaller relaxation barrier in comparison to other members of distorted-cuba ne family with virtual C3V symmetry, whose M peaks are visible at temperatures slightly above 1.8 K when the highest oscillation frequencies are employed.71 Regardless of the exact position of the M signals in Figures 4-14 and 4-15, their presence as well as the overall similarity of magnetic properties of complexes 9 and 10 to other members of [Mn4] family of SMMs, do suggest that 9 and 10 are also SMMs. 4.3 Conclusions HFEPR studies, performed on a single crystal of complex 8 provided a very accurate determination of spin Hamiltonian parameters: D = -0.529 cm-1, E = 0.022 cm-1, B4 0 = -7.33-5 cm-1. In the previous HFEPR studies performed on a microcrystalline sample of this compound, no transverse anisotropy terms ( e.g ., E term) were taken into c onsideration. However, as indicated previously by INS studi es and further confirmed in th is work, transverse terms are essential for the full magnetic characterization of this cluster, since the presence of non-zero transverse interactions play a crucial role in dr iving QTM in such half-integer spin systems. The obtained values of the spin Hamiltonian paramete rs are in a good agreement with those obtained

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117 by INS and HFEPR studies performed on a microc rystalline sample of this compound. This study further confirmed the negative sign of the axial ZFS parameter D for complex 8 . Detailed magnetic susceptibility stud ies of distortedcubane complexes 9 and 10 have shown that N3 and NCO ligands have not altered significantly the pairwise exchange interactions within these molecu les. The exchange parameters, J33/ J34 = 8.7/-47.9 cm-1 and J33/ J34 = 9.2 /-31.0 cm-1, obtained for complexes 9 and 10 , respectively, are similar (or nearly so) to those obtained previously for the structurally related [Mn4O3X(O2CR)3(dbm)3] complexes, for which J33 and J34 values fall within the ranges of 5.3 to 10.8 cm 1 and -21 to -34 cm 1, respectively. As a result, complexes 9 and 10 maintain the same well isolated S = 9/2 ground state as previous [Mn4O3X]6+ structures. The obtained results are also conclusive of the fact that the primary superexchange pathway for the ma gnetic exchange interactions between MnIIIMnIII and MnIIIMnIV pairs is controlled by the oxide bridge s rather than by the ligand framework. The obtained D values (-0.46 and -0.47 cm-1 for 9 and 10 , respectively) lie at the higher end of the values observed for the analogous cubane complexes with virtual C3v symmetry (– 0.38 to – 0.53 cm-1). However, in the AC magnetic suscep tibility measurements only tails of frequency-dependent out-of-phase signals have been observed, s uggestive of a smaller relaxation barrier in comparison to other me mbers of the distorted-cubane family. At the same time, the presence of frequency dependent out-of-phase signals strongly suggests that complexes 9 and 10 belong to the [Mn4] family of SMMs. 4.4 Experimental Section Syntheses All preparations were performed under an iner t atmosphere at ambient temperature, using reagents and solvents as received, unless otherwise stated. Me3SiNCO was stored under inert

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118 atmosphere. CH2Cl2 and Et2O were distilled over molecu lar sieves, MeCN over CaH2. [Mn4O3(O2CMe)4(dbm)3] ( 7 ) was prepared as described elsewhere. [Mn4O3(N3)(O2CMe)3(dbm)3] ( 9 ) A dark brown solution of complex 7 (0.5 g, 0.43 mmol) in distilled CH2Cl2 (40 ml) was treated with 1.5 equivalents of Me3Si N3 (84 l, 0.64 mmol) to give a deep red-brown solution. The resulti ng reaction mixture was stirred for 15 minutes, filtered and the filtrate then layered with Me CN. Slow diffusion of MeCN into the reaction solution at 5C over a period of 5-7 days produc ed black-brown plates in 36% yield (0.18 g) (based on total Mn). Crystals were isolated by filtration, wash ed with MeCN, and dried under vacuum. Dried crystals analyzed as solvent free. Anal. Calcd (Found) for 9 : C, 52.96 (52.99); H, 3.66 (3.58), N, 3.63 (3.34). Se lected IR data of 9 (KBr, cm-1): 2071 (s), 1520 (s), 1480 (w), 1393 (s), 1343 (s), 1227 (w), 1071 (w), 1024 (w), 940 (w), 767 (s), 725 (s), 686 (s), 646 (s), 590 (s), 574 (s), 525 (w). [Mn4O3(NCO)(O2CMe)3(dbm)3] ( 10 ). A dark brown solution of complex 7 (0.5 g, 0.43 mmol) in distilled CH2Cl2 (40 ml) was treated with 1.5 equivalents of Me3Si NCO (85 l, 0.64 mmol) to give a deep red-brown solution. The resulting reaction mixture was stirred for 15 minutes and filtered. The filtrate was layered with MeCN:Et2O (2:1) and left undisturbed at 5C. After 3 days, well shaped brown-black plates were formed in 42% yield (0.21 g) (based on total Mn). Crystals were isolated by f iltration, washed with MeCN and Et2O, and dried under vacuum. Dried crystals analyzed as solv ent free. Anal. Calcd (Found) for 10 : C, 54.00 (53.74); H, 1.21 (1.13), N, 3.66 (3.63). Selected IR data of 10 (KBr, cm-1): 2169 (s), 1576 (s), 1520 (s), 1479 (w), 1392 (s), 1344 (s), 1227 (w), 1071 (w), 1024 (w), 941 (w), 767 (s), 724 (s), 687 (s), 647 (s), 591 (s), 574 (s), 526 (w).

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119 Table 4-1. Comparison of the spin Hamiltonian parameters obtained from a single-crystal HFEPR study, and those determined from INS measurements and HFEPR studies of the microcrystalline sample of complex 8 . Parameter D (cm-1) E (cm-1) B4 0 (cm-1) This study -0.529 0.022 -7.33-5 HFEPR (microcrystalline sample) -0.530 N/A -7.30 10-5 INS studies -0.529 0.022 -6.50 10-5 Table 4-2. Comparison of selected interatomic distances () for [Mn4O3X(O2CMe)3(dbm)3] complexes (X = Cl ( 8 ), N3 ( 9 ) or NCO ( 10 )). Range 8 9 10 MnIIIX 2.642(7) – 2.656(14) 2.302(15) – 2.329(14) 2.320(9) – 2.403(9) MnIIIMnIII 3.237(3) – 3.262(9) 3.164(15) – 3.208(20) 3.162(8) – 3.208(9) MnIIIMnIV 2.792(12) – 2.797(6) 2.785(10) – 2.801(10) 2.781(4) – 2.805(6) Table 4-3. Comparison of selected bond angles () for [Mn4O3X(O2CMe)3(dbm)3] complexes (X = Cl ( 8 ), N3 ( 9 ) or NCO ( 10 )). Range 8 9 10 MnIIIXMnIII 75.36(20) – 75.80(19) 86.47(33) – 86.86(34) 84.86(28) – 85.54(29) MnIIIOMnIII 112.92(66) – 115.40(73) 110.43(30) – 112.22(32) 110.62(34) – 112.61(30) MnIIIOMnIV 94.34(64) – 95.22(68) 94.54(33) – 94.99(33) 94.87(29) – 96.43(27) Table 4-4. Comparison of exchange parameters, g -values and low-lying el ectronic states of [Mn4O3X(O2CR)3(dbm)3] complexes. X Parametera N3 ( 9 )c NCO ( 10 )c Cl ( 8)d Brd MeCO2d J33, cm-1 8.7 9.2 8.3 7.4 5.4 J34, cm-1 -47.9 -31.0 -28.4 -30.1 -33.9 g 1.97 1.96 2.00 2.01 1.96 ground ST 9/2 9/2 9/2 9/2 9/2 E( ST = 7/2)b 248 203 185 179 167 a J33 = J (MnIIIMnIII), J34 = J (MnIIIMnIV). b Energy of the ST = 7/2 first excited state above the ground state. c This work. d Reference 78.

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120 MnIIIMnIIIMnIIIMnIVX MnIIIMnIIIMnIIIMnIVX Figure 4-1. Pov-Ray represen tation of the labeled centr al distorted-cubane [MnIVMnIII 3O3X]6+ core. Jahn-Teller axes related to the [Mn4] core are highlighted in bold. Color code: MnIII blue; MnIV violet blue; O red; X green. Mn1 Mn3 Mn2 Mn4 O1 O2 O3 Cl1 Mn1 Mn3 Mn2 Mn4 O1 O2 O3 Cl1 Figure 4-2. Pov-Ray repr esentation of the [Mn4O3Cl(O2CMe)3(dbm)3]( 8 ) complex with the labeled core. Hydrogen atoms are omitted for clarity. Jahn-Teller axes are highlighted in bold. Color code: MnIII blue; MnIV violet blue; O red; Cl green; C gray.

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121 Energy (cm ) Energy (cm ) H (T) Energy (cm ) Energy (cm ) Energy (cm ) Energy (cm ) H (T) Figure 4-3. Plot of the energy vs the external magnetic field ( H ) for the 10 zero-field split components of the S = 9/2 ground state and D 0. Top: the magnetic field is oriented parallel to the principal axis of magnetic anisotropy. Bottom: the magnetic field is oriented perpendicular to the magnetic easy axis of the molecule. Vertical lines indicate allowed transitions.

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122 Energy (cm-1)20 012 3 45 6 7 -30 -20 -10 0 10 ms= -9/2 ms= -7/2 Magnetic field (T) 01 2 3 45 T = 10 K 146 GHz 113 GHzCavity transmission (offset)Magnetic field (T)20 012 3 45 6 -30 -20 -10 0 10 = -9/2 = -7/2 01 2 3 45 T = 10 K 146 GHz 113 GHz-9/2 -7/2 -7/2 -5/2 -5/2 -3/2 -3/2 -1/2 -1/2 -1/2 -7/2 -5/2 -5/2 -3/2 -3/2 -1/2 Energy (cm-1)20 012 3 45 6 7 -30 -20 -10 0 10 ms= -9/2 ms= -7/2 Magnetic field (T) 01 2 3 45 T = 10 K 146 GHz 113 GHzCavity transmission (offset)Magnetic field (T)20 012 3 45 6 -30 -20 -10 0 10 = -9/2 = -7/2 01 2 3 45 T = 10 K 146 GHz 113 GHz-9/2 -7/2 -7/2 -5/2 -5/2 -3/2 -3/2 -1/2 -1/2 -1/2 -7/2 -5/2 -5/2 -3/2 -3/2 -1/2 Figure 4-4. Top: energy level diagram for the S = 9/2 ground state and D < 0 when the external magnetic field is applied parallel to the easy ( z ) axis of the molecule. Bottom: HFEPR spectra recorded on a si ngle-crystal of complex 8 at 113 and 146 GHz with the external magnetic field a pplied at an angle of = 10 away from the easy axis in the easy/hard plane of the sample; the temperature is 10 K in each case.

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123 Energy (cm-1)Magnetic field (T) Cavity transmission (offset)ms= -9/2 0 1 23 45 6 -30 -20 -10 0 10 20 30 0 1 23 45 6 -30 -20 -10 0 10 20 30 0 1 23 45 6 7 -20 -10 0 10 20 30 0 1 2 3 4 5 6 T = 10 K 113 GHz 146 GHz 83 GHz1 2 3 4 5 6 T = 10 K 113 GHz 146 GHz 83 GHz = -9/2 7Magnetic field (T) Energy (cm-1)Magnetic field (T) Cavity transmission (offset)ms= -9/2 0 1 23 45 6 -30 -20 -10 0 10 20 30 0 1 23 45 6 -30 -20 -10 0 10 20 30 0 1 23 45 6 7 -20 -10 0 10 20 30 0 1 2 3 4 5 6 T = 10 K 113 GHz 146 GHz 83 GHz1 2 3 4 5 6 T = 10 K 113 GHz 146 GHz 83 GHz = -9/2 7Magnetic field (T) Figure 4-5. Top: energy level diagram for the S = 9/2 ground state and D < 0 when the external magnetic field is applied perpendicular to the easy ( z ) axis of the molecule. Bottom: HFEPR spectra recorded on a single-crystal of complex 8 at 83, 113 and 146 GHz with the external magnetic field applie d perpendicular to the easy axis; the temperature is 10 K in each case.

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124 12345678 0 50 100 150 200 Frequency (GHz)Magnetic field (T)0 9 /2 7 /2 7 / 2 5 /25 / 2 3 / 2-3 /2 1 / 2+ 1 /212345678 0 50 100 150 200 0 ---1 /2 D = -0.529(3) cm-1B4 0= -7.3(3)10-5 cm-1gz= 2.0012345678 0 50 100 150 200 Frequency (GHz)Magnetic field (T)0 9 /2 7 /2 7 / 2 5 /25 / 2 3 / 2-3 /2 1 / 2+ 1 /212345678 0 50 100 150 200 0 ---1 /2 D = -0.529(3) cm-1B4 0= -7.3(3)10-5 cm-1D = -0.529(3) cm-1B4 0= -7.3(3)10-5 cm-1gz= 2.00 Figure 4-6. The frequency dependence of EPR tr ansitions obtained with the magnetic field applied at = 10 angle away from the easy axis in the easy/hard plane of the sample. The solid data points correspond to the re sonant field positio ns obtained from measurements at several diffe rent frequencies. Solid lines are fits for the data; the obtained diagonal spin Hamiltonian parameters are shown. 01234567 0 25 50 75 100 125 150 Frequency (GHz)Magnetic field (T) 01234567 0 25 50 75 100 125 150 E = 0.022(2) cm-1gx= gy= 2.00 ms= 1 ms= 2 01234567 0 25 50 75 100 125 150 Frequency (GHz)Magnetic field (T) 01234567 0 25 50 75 100 125 150 E = 0.022(2) cm-1gx= gy= 2.00 ms= 1 ms= 2 Figure 4-7. The frequency dependence of EPR tr ansitions obtained with the magnetic field applied along the hard axis of the molecu le. The solid data points correspond to the resonant field positions obtained from measurements at several different frequencies. Solid lines are fits for the data; the obtained transverse spin Hamiltonian parameters are shown.

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125 N1 N2 N3 Mn3 Mn2 Mn4 Mn1 O2 O3 O1 N1 N2 N3 Mn3 Mn2 Mn4 Mn1 O2 O3 O1 Figure 4-8. PovRay representation of complex 9 with the labeled core. Hydrogen atoms are omitted for clarity. Jahn-Teller axes ar e highlighted in bold. Color code: MnIII blue; MnIV violet blue; O red; N green; C gray.

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126 Mn1 Mn4 Mn2 N8 C72 O73 O5 O6 O7 Mn3 Mn1 Mn4 Mn2 N8 C72 O73 O5 O6 O7 Mn3 Figure 4-9. PovRay representation of complex 10 with the labeled co re. Hydrogen atoms are omitted for clarity. Jahn-Teller axes ar e highlighted in bold. Color code: MnIII blue; MnIV violet blue; O red; N green; C gray.

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127 050100150200250300 9 10 11 12 13 mT(cm3mol-1K)T (K) 050100150200250300 9 10 11 12 13 mT(cm3mol-1K)T (K) mT(cm3mol-1K)T (K) 050100150200250300 9 10 11 12 13 mT(cm3mol-1K)T (K) 050100150200250300 9 10 11 12 13 Figure 4-10. Plot of mT vs T for dried, microcrystalline samples of complex 9 (top) and complex 10 (bottom) in eicosane. m is the DC molar magnetic su sceptibility measured in a 0.1 T field. The solid lines are the fit of th e experimental data to the theoretical expression; see text for the fit parameters.

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128 010203040 0 2 4 6 8 10 0.1 T 0.5 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit H/T (kG/K)M/NB 010203040 0 2 4 6 8 10 0.1 T 0.5 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit H/T (kG/K)M/NB 010203040 0 2 4 6 8 10 0.1 T 0.5 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit H/T (kG/K)M/NB 010203040 0 2 4 6 8 10 0.1 T 0.5 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit H/T (kG/K)M/NB Figure 4-11. Plots of reduced magnetization ( M / N B) vs H / T for dried, microcrystalline samples of complex 9 (top) and complex 10 (bottom) at the indicated applied fields. The solid lines are the fit of the data by the method described in the te xt; see the text for the fit parameters.

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129 1.801.851.901.952.002.052.10 -1.0 -0.5 0.0 0.5 1.0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 0.040.08 0.12 0.16 0.20 0.24 0.28 0.32 0.20 0.24 0.28 0.32D, cm-1g 1.801.851.901.952.002.052.10 -1.0 -0.5 0.0 0.5 1.0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 0.040.08 0.12 0.16 0.20 0.24 0.28 0.32 0.20 0.24 0.28 0.32D, cm-1g 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 1.9 2.0 2.1 -1.0 -0.5 0.0 0.5 1.0ErrorgD , c m1 Figure 4-12. Representations of the error surface for the D vs g fit of reduced magnetization ( M / N B) vs H / T for complex 9 . Top: twodimensional co ntour plot. Bottom: threedimensional mesh plot.

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130 1.801.851.901.952.002.052.102.15 -1.0 -0.5 0.0 0.5 1.0 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 0.08D, cm-1g0.12 0.16 0.20 0.24 0.20 0.24 0.28 1.801.851.901.952.002.052.102.15 -1.0 -0.5 0.0 0.5 1.0 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 0.08D, cm-1g0.12 0.16 0.20 0.24 0.20 0.24 0.28 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.8 1.9 2.0 2.1 -1.0 -0.5 0.0 0.5 1.0ErrorgD , c m1 Figure 4-13. Representations of the error surface for the D vs g fit of reduced magnetization ( M / N B) vs H / T for complex 10 . Top: twodimensional c ontour plot. Bottom: threedimensional mesh plot.

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131 m'T(cm3mol-1K)T (K)m"(cm3mol-1) 8 9 10 11 12 13 14 1000 Hz 250 Hz 50 Hz 0246810121416 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1000 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) 8 9 10 11 12 13 14 1000 Hz 250 Hz 50 Hz 0246810121416 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1000 Hz 250 Hz 50 Hz Figure 4-14. Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried mi crocrystalline sample of complex 9 at the indicated oscillation frequencies.

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132 7 8 9 10 11 12 13 1000 Hz 250 Hz 50 Hz 0246810121416 0.0 0.5 1.0 1.5 2.0 2.5 1000 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) 7 8 9 10 11 12 13 1000 Hz 250 Hz 50 Hz 0246810121416 0.0 0.5 1.0 1.5 2.0 2.5 1000 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) Figure 4-15. Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried mi crocrystalline sample of complex 10 at the indicated oscillation frequencies.

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133 CHAPTER 5 INCORPORATION OF A FERROMAGNE TIC COUPLER VIA CARBOXYLATE ABSTRACTION: NEW [Mn 11], [Mn4] AND [Mn3] COMPLEXES WITH END-ON ISOCYANATES 5.1 Introduction Single-molecule magnets (SMMs) posse ss an intrinsic energy barrier ( U ) to magnetization relaxation (reorientation) and f unction as nanoscale magnetic part icles below a certain blocking temperature.26,28 The barrier U arises from a combined eff ect of a high ground state spin ( S ) and large negative axial zero-field split ting (ZFS, measured by parameter D ), and is defined as S2| D | for integer and ( S2-1/4)| D | for half-integer spin systems. In pr actice, the true or effective barrier Ueff is less than U due to the quantum tunneling of magnetization (QTM),140-142,150 which provides an alternative pathway for the relaxati on of the magnetizati on through the barrier. A significant value of Ueff is a key factor to the practical use of SMMs in such applications as magnetic storage media and/or molecular electronics.145,146 For more than a decade, since the initial discovery of the SMM property in [Mn12O12(O2CMe)16(H2O)4],26 the highest values of Ueff are possessed by the Mn12 family of complexes (the current record of 74.4 K reported for [Mn12O12(O2CH2Br)16(H2O)4]).39 The highest blocking temperatures, however, are all limited to about 4K. Clearly, practical applications of S MMs would require molecules with much larger barriers, which would permit these molecular clus ters to function at te chnologically accessible blocking temperatures ( i.e ., at least 77 K and ideally the ro om temperature). Consequently, a significant challenge in this field lies in th e preparation of new SMMs possessing both large S and appreciable negative D values. High S values can be achieved when the superexchange interactions between paramagnetic metal centers of a molecule are predominantly ferroor ferrimagnetic in nature, as well as in the presence of spin-frustration effects, indu ced by competing antiferromagnetic exchange

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134 interactions.220 On the other hand, there are several po ssible competing cont ributions to the D value. These include a single-ion ZFS, anisot ropic and dipolar exchange, and the relative orientations of the single-ions and the cluster magnetic axis.28,45,221 Over the years, one of the most fruitful synt hetic strategies to ne w examples of SMMs has been the serendipitous assembly approach. The general methodology involves a self-assembly to polynuclear molecular species from either simple metal salts or preformed clusters in the presence of flexible organic groups such as carb oxylates or alcoxides, which play simultaneously the roles of bridging and periphera l ligands and enable the stabili zation of discrete molecules. The self-assembly approach has been successful in preparing such high nuclearity manganese carboxylate clusters as [Mn16],93,106,107 [Mn21],89,109 [Mn30]114 and record -high [Mn70] and [Mn84].116 However, in most of the complexes with predominantly carboxylate and/or alcoxide ligation (or the combination of these), even in th e presence of a large assembly of paramagnetic metal ions, the resultant spin ground state remain s relatively low. The nature of the synthetic approach itself as well as the fact that magne tic exchange interactions transmitted through O2, RCO2, HO, RO ligands are generally antiferromagnetic in character, makes it difficult to envision the outcome topology that woul d result in a high-spin cluster. An alternative synthetic strategy to high S values involves the use of bridging groups that are known to propagate ferromagnetic coupli ng. Under this respect, the pseudohalides (N3, NCO, CN, NCS, etc ) are particularly attract ive candidates. The pseudohalide ions, especially the azide ion, have been demonstrated as extrem ely versatile bridging liga nds and also excellent magnetic couplers.222 Among the various bridging modes of the azide ligand, the most commonly observed are -1,1 (end-on, EO),223-228 -1,3 (end-to-end, EE),229-232. The magnetic exchange mediated via such bridges can be either ferro or antiferromagnetic, depending on the

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135 bridging mode and structural para meters of the bridging moiety.233-236 It has been found that the exchange is generally ferromagnetic for the EO coupling mode222,229,231,237 and antiferromagnetic for the EE mode,222,224,238-240 although an increasing number of exceptions have also been reported.241-246 The property of pseudohalides to mediate th e ferromagnetic coupling has only recently been employed in the preparation of SMMs. Among other pseudohalides, the N3 ion has been the most intensively exploited. In the majo rity of cases the incorporation of the N3 group has been achieved via the direct reaction of an azide salt ( e.g. , NaN3) with either a simple metal salt or a preformed cluster, in the pr esence of other ligands and/or chelates. For example, the reaction of MnCl2H2O with pdmH2 (pdmH2 = pyridine-2,6-dimethanol), NaN3 and Me4NOH in a mixture of MeOH and MeCN resulted in the formation of the [Mn25O18(OH)2(N3)12(pdm)6(pdmH)6](Cl)2 cluster with an excep tionally high ground state spin S = 51/2.112 Similar reaction of MnCl2H2O with 2,6-dihydroxymethyl-4-methylphenol (HL), NaN3 and NaO2CMe in MeOH/MeCN afforded the [Mn19O8(N3)8(HL)12(MeCN)6]Cl2 complex with the record high ground state spin of S = 83/2.110 The reaction of Mn(NO3)2H2O, hmpH (hmpH = 2-hydroxymethyl pyridine), Et3N and NaN3 in MeCN/MeOH had led to the isolation of [Mn10O4(N3)4(hmp)12](N3)2, possessing S = 22 ground state.247 In all of the above cases, even though the S values are very large, obtained clus ters possess a very small or no magnetic anisotropy. A different synthetic approach for the prep aration of azido complexes has been employed by Perlepes et al . , in which the 4-OHgroups of a preformed [M9(OH)2(O2CMe)8((2-py)2CO2)4] (M = Co2+, Ni2+, Fe2+; ((2-py)2CO2)4)2 = the doubly deprotonated di -2-pyridyl ketone) cluster were substituted by 4-N3 groups to yield a structur ally analogous azido complex,

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136 [Co9(N3)2(O2CMe)8((2-py)2CO2)4].248-250 The substitution resulted in a drastic change of the magnetic behavior (from antiferroto ferroma gnetic), induced by the end-on azido ligands. While the synthetic routes involving N3 ions have been intensively studied, the use of NCO ion, especially in manganese cluster chemistr y is significantly less e xplored. In this work, as part of our continued effort to synthesize new Mn complexes with interesting structural and/or magnetic properties, the carboxylate abstraction synthetic procedure has been employed to incorporate NCO groups, using te tramethylsilyl isocyanate (Me3SiNCO) as a carboxylate abstractor. The synthesis, st ructural characterization and magnetic studies of new [Mn11], [Mn4] and [Mn3] complexes will be described in detail. 5.2 Results and Discussion 5.2.1 Syntheses Over the years, the use of preformed manga nese carboxylate clusters has proven to be a successful synthetic strategy for th e formation of new manganese complexes, often leading to an increase in the nuclearity of the resultant produc t. For example, trinuclear complexes of the general formula [Mn3O(O2CR)6(L)3]+,0 (R = various, L = pyridin e, imidazole) have been extensively used as starting materials in a variet y of reactions with different chelating ligands, carboxylate-abstracting reagents (Me3SiX, X = Cl, Br, etc .), affording complexes of nuclearity ranging from 2 to 22.47 In addition to the [Mn3] family of complexes, another class of useful starting material is represented by the family of tetranuclear clus ters, possessing the [Mn4O2]8+ core with a bent or “butterf ly” arrangement of the four MnIII ions. These clusters have proven on several occasions to be excelle nt stepping-stones to other sp ecies with the same or higher nuclearities. In particular th e reactions of these tetranucl ear complexes with carboxylateabstracting reagents, Me3SiX (X = Cl, Br), have been a rich source of new products. For example, the disproportionation reaction of [Mn4O2(O2CMe)6(dbm)2(py)2] (dbm = the anion of

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137 dibenzoylmethane; py = pyridine) in MeCN with 1.5 equivalents of Me3SiCl resulted in the formation of distorted cubane complex [Mn4O3Cl(O2CMe)3(dbm)3],196 whereas the analogous reaction in CH2Cl2 led to the isolation of [Mn7O4(O2CMe)10(dbm)4] salts.251 An interesting example includes the reaction of [Mn4O2(O2CMe)7(bpy)2](ClO4) (bpy = 2,2’-bipyridine) with 4 equivalents of Me3SiCl that led to both disproportionation and a nuclearity change to give [Mn11O10Cl2(O2CMe)11(bpy)2(MeCN)2(H2O)2](ClO4) complex.252 Among the other members of the butterfly family of complexes the ( n -Bu4N)[Mn4O2(O2CPh)9(H2O)]( 11 ) cluster has been found as a pa rticularly attractive precursor compound. What makes complex 11 a unique and efficient starting ma terial is that its peripheral ligation consists of only carboxylate and water ligation, i.e ., it has no Oand/or N-based chelates, such as 2,2’-bipyridine, 4-imidazolate, 2-pico linate, 8-hydroxyquinolinat e, or deprotonated dibenzoylmethane, present in othe r members of th e butterfly [Mn4O2]8+ family of clusters.253-258 As a result, its increased reactivity towards a va riety of reagents has been successfully employed in the past to afford such high nuclearity clusters as ( n -Bu4N)[Mn8O6Cl6(O2CPh)7(H2O)2]259, [Mn9Na2O7(O2CPh)15(MeCN)2],259 (NBun 4)[Mn8O4(O2CPh)12(Et2mal)2(H2O)2] (Et2malH2 = 2,2'diethylmalonic acid)260 and [K4Mn18O16(O2CPh)22(phth)2(H2O)4] (phthH2 = phthalic acid)261. Additionally, complex 11 is readily soluble in a variet y of organic solvents and, thus, represents a convenient soluble source of MnIII ions. In the present work, with a goal of obtaining new clusters with NCO bridging ligands, the carboxylate abstraction synthetic me thodology has been further inves tigated in different organic solvents, using complex 11 as starting material. Thus, to a dark-red solution of complex 11 , under an inert atmosphere in Me2CO were added 4-5 equivalents of Me3SiNCO to give a clear solution with no noticeable color change. The re sultant solution was stirred for approximately

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138 10-15 min, filtered, and then layered with a variet y of solvents. After tw o weeks, no crystalline products were observed when solutions were left undisturbed at room temperature. Thus, the crystallization attempts were re peated at 5 C. Over a period of 5-7 days, the layering of the reaction mixture with Et2O resulted in the formation of red-br own needles in ~ 22% yield (based on total Mn). The IR analysis indicated the forma tion of a new cluster and the IR spectrum also displayed a strong absorption at 2174 cm-1, characteristic of the pr esence of bound isocyanate. However, the crystallographic characterization of obtained crystals was not successful due to their poor quality. The synthetic procedure was s ubsequently modified using other solvents of crystallization. Slow diffusion of hexanes into the reaction mixture at 5C over a period of 5-7 days resulted in the formation of well shaped red-brown plates in 19% yield (based on total Mn). The IR spectrum indicated the formation of an iden tical product to that is olated from the layering with Et2O, and was further confirmed by the elemental analysis. The crystals were maintained in mother liquor to avoid solvent loss and were crystallographica lly characterized as ( n -Bu 4N)2[Mn 11O10(NCO)6(O2CPh)11(H2O)4] ( 12 )Me2CO. An investigation of the dependence of the yield of complex 12 on the 11 :Me2SiNCO ratio indicated an optimal yield at a 1:5 ratio. The overall transformati on is summarized in eq. 5-1: 3[Mn4O2(O2CPh)9(H2O)] + 6Me3SiNCO + 5H2O [Mn 11O10(NCO)6(O2CPh)11(H2O)4]2 + 6Me3SiO2CPh + 10PhCO2 + 8H+ + Mn2+ + e (5-1) Since the reaction in Me2CO resulted in a high-nuclear ity product, it was further investigated in CH2Cl2. Thus, to a solution of complex 11 in CH2Cl2 under an inert atmosphere were added 5 equivalents of Me3SiNCO to give a clear red-br own solution. Then, the obtained solution was filtered and layered with a variety of solvents. Over a period of 5-7 days, slow diffusion of Et2O into the reaction mixture at room temper ature resulted in the formation of red-

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139 orange plates in 19% yield (based on total Mn ). The observation of a very strong absorption at 2168 cm-1 in the IR spectrum confirmed the pr esence of bound isocyanate groups. Obtained crystals were recrystallized twice from CH2Cl2/Et2O to give X-ray quality crystals, which were subsequently identified as ( n -Bu 4N)3[Mn 4O3(NCO)7(O2CPh)3]( 13 ). The overall formation of complex 13 is summarized in eq. 5-2: 2[Mn4O2(O2CPh)9(H2O)] + 7Me3SiNCO + 2H+ [Mn 4O3(NCO)7(O2CPh)3]3 + 7Me3SiO2CPh + 8PhCO2 + Mn2+ + 3Mn3+ + H2O (5-2) During the scaled up preparation of complex 13 , the reaction was repeated, using the double amount of the starting material and redu cing the amount of reacti on solvent by 1/3. After 3 days, large and essentially black crystals were observed at the bottom of each vial. The yield was ~30% (based on total Mn)The IR spectrum of obtained crystals was clearly different from that of complex 13 , indicating that a new product has been obtained. The spectrum also displayed a very large and broad absorption at 2198 cm-1, confirming the presence of the isocyanate groups in the cluster. The obtained crystals were of excellent X-ray quality and have been identified as ( n -Bu4N)2[Mn3O(NCO)6(O2CPh)3]( 14 )CH2Cl2. The formation of complex 14 is described by eq. 5-3: [Mn4O2(O2CPh)9(H2O)] + 6Me3SiNCO + 2H+ [Mn3O(NCO)6(O2CPh)3]2 + 6Me3SiO2CPh + 2H2O + Mn3+ (5-3) Clearly, the formation of complexes 13 and 14 must involve complicated fragmentation and rearrangement steps. The reaction solutions likely contain several Mnx species in equilibrium, where the identity of species that are preferably crys tallized is determined by their relative solubilities, lattice energies, crysta llization kinetics and/ or other criteria

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140 5.2.2. Description of Structures 5.2.2.1 X-ray Crystal Structure of ( n -Bu 4N)2[Mn 11O10(NCO)6(O2CPh)11(H2O)4](12) 13Me2CO Crystallographic data collection and stru cture refinement details for complex 12 Me2CO, are summarized in Table 5-1. PovRay representations of th e anion of complex 12 and its labeled core (including terminal NCO groups) are s hown in Figure 5-1. Packing diagrams of 12 are shown in Figure 5-2. Selected interatomic dist ances and angles are listed in Table A-5. Complex 12 Me2CO crystallizes in a triclinic space group 1 P with the asymmetric unit containing the complete [Mn11]2anion , two tetrabutylammonium cations and approxymately 13 Me2CO molecules of crystallization. Complex 12 does not possess any crystallographic symmetry element although the virtual symmetry is Cs with the virtual mirror plane passing through Mn5, Mn6 and Mn7. The structure of the [Mn11]2 anion consists of a [Mn2 IVMn9 III( 3O)10( 3-NCO)2]13+ core, composed of two cubic [MnIVMn4 III( 3-O)2( 3-O)10( 3-NCO)2] subunits and a central near-linear [Mn3 III( 3-O)4] subunit, linked together via 2-PhCO2 and 3-O2 groups. All the metal centers are six-coordinate, with near-octahedral geometry. The oxidation levels of the Mn ions were assigned on th e basis of bond valence sum (BVS) calculations155,156 (Table 5-2), close examination of the metric para meters (Table A-5) and detection of Jahn-Teller (JT) distortions, revealin g the trapped-valence [MnIV 2MnIII 9] oxidation state description for the complex. Two MnIV atoms (Mn2 and Mn10) are located in the cubic [MnIVMn4 III( 3-O)2( 3O)10( 3-NCO)2] subunits (one MnIV per [Mn4] unit). All MnIII centers (Mn1, Mn3, Mn4, Mn5, Mn6, Mn7, Mn8, Mn9, and Mn11) display JT di stortions as expected for high spin d4 ions in near-octahedral geometry. These take the form of axial elongations, and the JT axes are indicated as solid black bonds in Figure 5-1. Each of the two cubic [MnIVMn4 III( 3-O)2( 3-O)10( 3-NCO)2] subunits possess a distorted-cubane core, where the MnIIIMnIII separations are in the range

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141 3.087(2)-3.219(2) and the MnIIIMnIV distances are in the range 2.792(4)-2.825(3) . All six NCO groups are located in the cubic subunits. Two of these are 3NCO, bridging Mn1, Mn3, Mn4 and Mn8, Mn9, Mn11 atoms of correspondi ng cubic subunits. Four remaining NCO groups are all terminal NCO, two of these are linked to Mn1 and the other two to Mn11. The arrangement of Mn atoms in the [Mn3 III( 3-O)4] units is not completely linear but slightly Vshaped ( e.g ., Mn5-Mn6-Mn7 = 166.70(5) ). BVS calculations were also performed on the oxygen atoms of 12 to identify their degree of protonation (Table 5-3). These confirmed that ten triply bridging O atoms (O1, O2, O3, O4, O5, O9, O10, O11, O12, O13) are all deprotonated and O6, O7, O8 and O42 atoms are terminal H2O molecules. Close inspection of the crystal packing reve aled the presence of weak intermolecular stacking interactions between th e phenyl rings of some PhCO2 groups of neighboring [Mn11] molecules (an average di stance is ~ 3.39 ). Complex 12 joins a relatively small family of undecanuclear manganese clusters. The overall geometry of the complex clos ely resembles the previously reported [Mn11O10Cl2(O2CMe)11(bpy)2(MeCN)2(H2O)2](ClO4) cluster, possessing a [Mn2 IVMn9 III( 3O)10( 3-Cl)2]13+ core.252 Another known [Mn11] complex is [Mn11O2(OH)2(nmpd)(pdmH)5(pdm)5(Cl)6] (nmpd is the anion of 2-nitro-2-methyl-1,3propanediol; pdmH is the pyridine-2,6-dimetha nol), however, it is structurally completely different from 12 .99 Therefore, complex 12 represent the first example of a [Mn11] cluster with no chelating ligands present in the crystal structure. 5.2.2.2 X-ray Crystal Structure of ( n -Bu4N)3[Mn4O3(NCO)7(O2CPh)3](13) Crystallographic data collection and stru cture refinement details for complex 13 are collected in Table 5-1. PovRay representations of the anion of complex 13 and its labeled core

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142 are shown in Figure 5-3. Packing diagrams of 13 are shown in Figur e 5-4, and selected interatomic distances and angles are listed in Table A-6. Complex 13 crystallizes in monoclinic space group P 21/ n with the asymmetric unit containing the complete [Mn4]3 anion and three tetrabutylammonium cations. Complex 13 has no crystallographically imposed symmetr y, althought the virtual symmetry is C3 v with the pseudoC3 axis passing through Mn2 and N5. The structure of the anion of 13 consists of a [MnIVMnIII 3( 3-O)3( 3-NCO)]6+ distorted cubane core, simila r to other distorted cubane complexes,78 and can be described as a Mn4 trigonal pyramid with the MnIV ion (Mn2) at the apex. The three vertical faces are capped by a 3-O2 and a 3NCO ion bridging the basal plane. The peripheral ligation is prov ided by six terminal NCO and three 2-PhCO2 groups. The molecule is the first example in the series of distorted cubane complexes, possessing no Oor N-based chelates, such as pyr idine, 4-imidazolate, or deprot onated dibenzoylmethane, in its peripheral ligation. Examination of the bond distan ces (Table A-6), charge considerations, and BVS calculations (Table 5-4) rev eal that Mn1, Mn3 and Mn4 are MnIII ions and Mn2 is the MnIV. As expected, each of the MnIII ions exhibit Jahn-Teller (JT) elongation, and the JT axes are the ones that include the MnIII-N5 bonds. BVS calculations perf ormed on the inorganic O atoms confirm that O5, O6 and O11 are O2 (Table 5-5). The MnIIIMnIII (3.198(1)-3.203(1) ) and MnIIIMnIV (2.811(1)-2.817(1) ) distances emphasi ze the distortion from true cubane ( Td ) symmetry. Inspection of the crysta l packing reveals the absence of any significant intermolecular interactions. 5.2.2.3 X-ray Crystal Structure of ( n -Bu4N)2[Mn3O(NCO)6(O2CPh)3](14)CH2Cl2 Crystallographic data collection and stru cture refinement details for complex 14 CH2Cl2 are collected in Table 5-1. PovRay representations of the anion of complex 14 and its labeled

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143 core are shown in Figure 5-5. Packing diagrams of 14 are shown in Figure 5-6 and selected interatomic distances and angles are listed in Table A-7. Complex 14 CH2Cl2 crystallizes in monoclinic space group P 21/ n with the asymmetric unit containing the entire [Mn3]3, three tetrabutylammonium cations and one CH2Cl2 molecule. Complex 14 does not possess any crystallographic symmetry element although the virtual symmetry is C3. The structure of the anion of 14 consists of a [Mn3 III( 3-O)( 3-NCO)3]4+ core, which can be described as a near-equilateral [MnIII 3] triangle capped by a 3-O2 ion O13, positioned 0.664 above the Mn3 plane. Each edge is bridged by 2-PhCO2 and 3-NCO groups. Three terminal NCO groups provide the peripheral ligation and make each Mn ion sixcoordinate. The MnIII oxidation states and O2 protonation level were assigned based on BVS calculations (Table 5-6), charge considerations , and the presence of JT elongations along the Mn1-N6, Mn2-N2 and Mn3-N4 bonds (2.390(5)-2.400( 9) ). As expected, the JT axes are oriented as to avoid the Mn-O2 bonds, which are the shortest and strongest bonds in the molecule (1.875(3)-1.879(3) ). The Mn-N-M n angles lie in the range 86.81(15)-86.97(16) and the Mn-O-Mn angles are in the range 108.12(14)-108.30(14) . Examination of the crystal packing reveals the presence of weak intermolecular -stacking inter actions involving the phenyl rings of neighboring [Mn3] molecules (an average distance is ~ 3.32 ). 5.2.3 Magnetochemistry of Complexes 12-14 5.2.3.1 Direct Current Magnetic Susceptibility Studies Variable-temperature DC magnetic suscep tibility measurements were performed on vacuum-dried microcrystalline samples of complexes 12, 13 and 14 , restrained in eicosane to prevent torquing. The DC magnetic susceptibility data were collect ed in the 5.0 300 K range in a 1 kG (0.1 T) magnetic field. The data are shown as mT vs T plots in Figures 5-7, 5-8 and 5-9.

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144 For complex 12 , two different sets of mT vs T data were collected on dry microcrystalline samples, obtained from crystallizations with Et2O ( 12a H2O) and hexane ( 12b H2O). For 12a , the value of mT increases steadily with decreasing temperature (Figure 5-7) from 23.93 cm3 mol1 K at 300 K to a maximum value of 42.18 cm3 mol-1 K at 8 K, below which mT decreases more rapidly to 41.58 cm3 mol-1 K at 5 K. This behavior indica tes the presence of predominantly ferromagnetic exchange interactions between the spin centers of the complex, and the maximum value of mT is close to the theoretical spin-only ( g = 2) value expected for a complex with S = 9 spin ground state (45 cm3 mol-1 K). Complex 12b exhibits similar behavior, with mT increasing from 22.69 cm3 mol-1 K at 300 K to a maximum at 36.91 cm3 mol-1 K at 8 K, followed by a decrease to 36.01 cm3 mol-1 K at 5 K (Figure 5-8). In this case, however, the maximum mT is slightly smaller than that obtained for 12a , but still suggestive of an S = 9 spin ground state ( g < 2). The decrease in the mT value at the lowest temperatures is likely due to zero-field splitting (ZFS), Zeeman effects from the applied field, an d any weak antiferromagne tic interactions. To determine the exact values of the many pairwise Mn2 exchange parameters and to find all the possible spin states and their energies, the sp in Hamiltonian for this complex needs to be diagonalized.165 However, for a system consisting of 11 Mn3+ ( S = 2) ions, the total degeneracy of the spin system is equal to (2 S +1)n, or 511.A matrix-diagonalization approach would involve a matrix of dimensions 511 511, which is essentially unfeasible with current computing capabilities. In addition, due to th e complexity of the system, it is also not possible to apply the equivalent operator approach, base d on the Kambe vector coupling method,166 which is usually successfully employed for smaller nuclea rity systems to obtain a theoretical mT vs T expression for fitting the experimental data. In addition, ma gnetization data collected in the 0.1-70 kG and 1.8-10.0 K field and temperat ure ranges could not be satisfactor ily fit to a model that assumes

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145 only the ground state is populated.167 Such behavior is indicative of the presence of low-lying excited states and is not uncomm on for a high nuclearity cluster, in which exchange interactions between the constituent atoms will le ad to high density of spin states. In addition, spin frustration effects arising from the presence of Mn3 triangular units in the structure of 12 can also lead to small energy differences between many of the re sulting spin states. Thus, further assessment of the ground state spin value for complex 12 was carried out using AC magnetic susceptibility studies, described in more de tail in the next section. For complex 13 , the value of mT increases very slightly with decreasing temperature (Figure 5-9) from 12.00 cm3 mol-1 K at 300 K to a value of ~12.20 cm3 mol-1 K at 90 K, below which mT decreases more rapidly to 11.50 cm3 mol-1 K at 10 K and then drops sharply to 11.24 cm3 mol-1 K at 5 K. The value of mT at 300 K is significantly larger than the value calculated for non-interacting 3MnIII and MnIV ions (10.85 cm3 mol-1). The latter in combination with the plateau-like mT vs T behavior in the 300-90 K range ar e indicative of the presence of appreciable ferromagnetic exchange interactions w ithin the molecule even at room temperature. The maximum mT value is comparable with the spin-only ( g = 2) value of 12.38 cm3 mol-1 K expected for a S = 9/2 spin grounds state. To determine the Mn2 pairwise exchange interactions within the molecule, the mT vs T data for complexes 13 were fit to the theoretical mT vs T expression, derived for a Mn3 IIIMnIV trigonal pyramid of C3 v symmetry (discussed in more detail in Chapter 4). The full expression of the Van Vleck equation for a distor ted cubane cluster is availabl e in the Appendix C. The data below 35 K were omitted because of the low temperature decrease caused by factors not included in the fitting model. A good fit was obtai ned (solid line in Figure 5-9) having fitting parameters J33 = 8.5 cm-1, J34 = -43.7 cm-1, and g = 1.93, with temperature-independent

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146 paramagnetism (TIP) held constant at 600 10-6 cm3 mol-1. The obtained J values indicate a well isolated ST = 9/2 spin ground state wi th the first excited state S = 7/2 located 232 cm-1 higher in energy. The ST and J values obtained for complex 13 are compared in Table 5-7 with those obtained previously for [Mn4O3X(O2CR)3(dbm)3] (X = Cl, Br, N3, NCO) complexes with the C3 v symmetry. As can be seen, th e overall magnetic behavior of 13 is unchanged in comparison to other distorted cubane complexes: in all cases, the J33 is ferromagnetic and J34 is antiferromagnetic leading to S = 9/2 ground state. This is expected, since the core of 13 , [MnIVMnIII 3( 3-O)3( 3-NCO)]6+, has not been altered dramatica lly. As discussed previously in Chapter 4, the primary pathways for the superexcha nge interactions between Mn ions involve the bridging O2 groups and not X ligands. The vari ation in absolute magnitude of J33 and J34 values can be rationalized due to the pr esence of different structural di stortions in the cores of these complexes as a result of different solid-state packing forces. The calculated energy gap to the ST = 7/2 first state for 13 is the largest among these clusters , consistent with a plateau-like mT vs T behavior in the 300-90 K region, as the ground state is very well isolated even at the room temperature. To confirm the ST = 9/2 ground state spin and to determine the magnitude of ZFS parameter D , magnetization ( M ) vs DC field measurements were performed on a microcrystalline sample of 13 in the 1.8 10 K and 1-70 kG temperature and field ranges, respectively. The data are shown in Figure 5-10 as reduced magnetization ( M / N B) vs H / T plots, where M is the magnetization, N is Avogadro’s number, B is the Bohr magneton, and H is the applied magnetic field. As can be seen, the isofield lines do not superimpose for complex 13 , indicating that the ground state is zero-field split. The data were fit using the program MAGNET,167 by diagonalization of the spin Hamiltonian matrix using a full powder average method that assumes

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147 that only the ground state is populated and incorporates axial zero field splitting ( D z 2) and Zeeman effects. Fitting of the data gave S = 9/2, g = 1.99, and D = -0.48 cm-1. To ensure that the global fitting minimum had been obtained, a root-mean square error surface for the D vs g fit were generated using the program GRID.219 Twoand three-dimensional representations of the error surface for 13 are shown in Figure 5-11. Clearly, the value corresponding to the negative anisotropy parameter D is the global minima. The obtained D value falls within the range of values previously observed for other di storted cubane complexes with virtual C3 v symmetry (– 0.38 to – 0.53 cm-1).71,72,78 For complex 14 , the value of mT increases with decreasing temperature (Figure 5-12) from 10.21 cm3 mol-1 K at 300 K to a maximum value of 18.40 cm3 mol-1 K at 10 K, below which mT drops sharply to 17.96 cm3 mol-1 K at 5 K. The data indicate the presence of predominantly ferromagnetic exchange interactions within the cluster. The maximum mT value of 18.40 cm3 mol-1 K is slightly below the spin-only ( g = 2) value expected for a complex with S = 6 spin ground state (21 cm3 mol-1 K), and this is consistent with g < 2, as expected for Mn. The low temperature decrease is likely due to Zeem an effects, ZFS, and/or weak intermolecular interactions. In order to determine the Mn2 pairwise exchange interacti ons within the molecule, the mT vs T data for complex 14 were fit to the theoretical mT vs T expression. It has been noticed previously that the mT vs T data of [Mn3O(O2CR)6(L)3]+,0 (R = various, L = pyridine, Imidazole) and related metal comple xes of triangular geometry ca nnot be satisfactory fit to a 1 J model ( i.e. , an equilateral triangle model). Equilate ral triangles undergo Ja hn-Teller distortions, resulting in an isosceles (2 J ) situation. Thus, th e data for complex 14 were fit to the theoretical mT vs T expression, derived for a Mn3 III isosceles triangle. The is otropic (Heisenberg) spin

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148 Hamiltonian describing an exchange-coupled MnIII 3 ( S1 = S2 = S3 = 2) trinuclear complex of an isosceles geometry is given by eq. 5-1, usi ng the numbering scheme of Figure 5-13, where J = J (Mn1Mn2) = J (Mn2Mn3) and J = J (Mn1Mn3): = 2 J ( 12 + 23) 2 J ( 13) (5-1) This equation can be ex pressed in an equivalent form (eq. 5-2) by using Kambe’s vector coupling method166 and the coupling scheme: A = 1 + 3, and T = A + 2, where ST is the spin of the complete Mn3 molecule. = – J ( T 2 A 2 – 2 2) – J ( A 2 – 1 2 – 3 2) (5-2) The eigenvalues of this Hamiltonian are th en given by eq. 5-3, where constant terms contributing to all states have been omitted E ( ST , SA)= – J [ ST( ST+1) – SA( SA+1)] – J [ SA ( SA+1)] (5-3) A theoretical mT vs T expression was derived using the ST values, their energies E ( ST, SA), and the Van-Vleck equation218 (derived in Appendix C), and this expression was used to fit the experimental data. Data below 10 K were omitte d because the low-temperature decrease is caused by factors not included in the fitting model. A temperature-independent paramagnetism (TIP) term was fixed at 600 10-6 cm3 mol-1. A good fit was obtained (so lid line in Figure 5-13) and fitting parameters were J = 0.48 cm-1, J = 5.93 cm-1, and g = 1.88. Complex 14 represent the first example of the ferromagnetically coupled [Mn3] cluster, incorporating end-on bridging NCO ligands. The only other reported exam ple of the ferromagnetically coupled [Mn3] complex is the [Mn3O(O2CMe)3(mpko)3](ClO4) complex (mpko = is the anion of the methyl-2-pyridyl ketone oxime).64 All the previous complexes of the general formula [Mn3O(O2CR)6(L)3]+ are antiferromagnetically coupled.182 In the latter, the antiferromagnetic exchange interactions are mediated through the central O2 ions, positioned in the Mn3 plane. Any distortion away from

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149 planarity is expected to weaken the antiferroma gnetic coupling between Mn centers. In the case of 14 , the O2 ion is positioned 0.664 above the Mn3 plane and MnIII-O-MnIII angles are in the range 108.12(14)-108.30(14) , thus, the antiferromagnetic contribution to the observed J value ( Jobs, where the Jobs is the sum of ferro-and antiferroma gnetic contributions) is significantly weakened. Thus, the incorporati on of the NCO groups (the MnIII-N-MnIII angels are in the range 86.81(15)-86.97(16) ) leads to the overall ferromagnetic behavior. To confirm the ST = 6 ground state of 14 and to determine the magnitude of ZFS parameter D , magnetization ( M ) vs DC field measurements were performed on a microcrystalline sample of 14 in the 1.8 10 K and 1-70 kG temperature and field ranges, respectively. The data are shown in Figure 5-14 as reduced magnetization ( M / N B) vs H / T plots, where N is Avogadro’s number, B is the Bohr magneton, and H is the applied magnetic field. The data were fit using the program MAGNET,167 and the fit (solid line s in Figure 5-14) gave S = 6, g = 1.87, and D = -27 cm-1. In order to confirm that the obtained paramete rs were the true global rather than a local minimum, a root-mean square D vs g error surface for the fit wa s generated using the program GRID.219 Twoand three-dimensional repres entations of the error surface for 14 are shown in Figure 5-15. As can be seen, the value corr esponding to the negativ e anisotropy parameter D is the global minima. 5.2.3.2 Alternating Current Magnetic Susceptibility Studies of Complex 12 Alternating current (AC) magnetic susceptibility studies were performed to investigate the magnetization dynamics of complex 12 and to confirm the spin ground state of this cluster. Measurements were performed in the 1.8 15 K te mperature range in a zero DC field and a 3.5 G AC field oscillating at four frequencies (50, 250, 750 and 1000 Hz). If the magnetization vector of the molecule can relax fast enough to keep up with the oscillating field, then there is no imagin ary (out-of phase) susceptibility signal ( m" ), and the real

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150 (in-phase) susceptibility (m' ) is equal to the DC magnetic suscep tibility. However, if the barrier to magnetization relaxation is signifi cant compared to thermal energy ( kT ), then there is an increase in the m" signal and concomitant decrease in the in-phase signal. In addition, the m" signal and the decrease in the in -phase signal will be both fre quency-dependent. Such frequencydependent AC signals are indicative of the s uperparamagnet-like slow relaxation of a SMM. Although such signals are not suffi cient proof of the SMM propert y, they are a strong indicator that a complex behaves as a SMM. For complex 12 , AC susceptibility measurement we re performed on both vacuum-dried ( 12a H2O and 12b H2O) and fully solvated 12a xMe2CO and 12b Me2CO (wet with mother liquor) microcrystalline samples. For a dry sample of 12a , two sets of frequency-dependent outof-phase ( m" ) signals are visible in the plot of m"vs T in the Figure 5-16, ch aracteristic of two distinct relaxation processes. Higher-temperature (HT) signa ls are observed at ~ 5.5 K and lower-temperature (LT) signals at ~3 K. Th ese are accompanied by two frequency-dependent step-like decreases in the in-phase m'T vs T plot. Appearance of fre quency-dependent signals indicates that the magnetization of 12a cannot relax fast enough to stay in-phase with the oscillating field and that complex 12a is most likely a SMM. Above ~ 8 K, the m'T vs T plot is essentially temperature-independent. Extr apolation of the plot to 0 K gives a m'T value of ~44.7 cm3 K mol-1. In the absence of a m" signal, the m'T value reflects the ground state spin value without the possible complications of the Zeeman effect from an applied DC magnetic field. The value expected for an S = 9 state with g = 2 is 45 cm3 K mol-1. Thus, the observed value of ~ 44.7 cm3 K mol-1 confirms an S = 9 ground state for 12a with a g value slightly less than 2. The expected values of m'T ( g = 2) for S = 8 and S = 10 states are 36 and 55 cm3 K mol-1, respectively.

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151 For a dry sample of 12b , two frequency-dependent out-of-phase ( m" ) signals are also observed (Figure 5-17), but in this case both HT and LT signals are shifted to lower temperatures in comparison to those of 12a . The HT m" signals are visible at ~5.5 K, but the maxima of the LT signals clearly lie at temperatures below th e 1.8 K operating limit of our SQUID instrument. The m'T value at temperatures above 8 K is also noticeably smaller. Extrapolation of the m'T vs T plot to 0 K gives 38.8 cm3 K mol-1, which is still consistent with an S = 9 ground state ( g < 2), since mT = ( g2/8)( S ( S +1)). Since 12a and 12b exhibit different m" vs T behavior, AC measurements were also performed on fully solvated 12a xMe2CO and 12b Me2CO (wet with mother liquor) samples of these complexes. The m" vs T data, obtained for wet samples of 12a and 12b , are presented in Figure 5-18 and Figure 5-19, resp ectively. Both complexes, once fully solvated, display drastically different AC beha vior to that of dry samples. For a wet sample of 12a , only tails of frequency-dependent m" signals are visible at temperatures above 1.8 K (Figure 5-18). In the case of a wet 12b sample, the temperatures at which HT and LT m" signals appear is identical to that of a dry sample, however, the intensity of the peaks is significantly reduced (Figure 5-19), suggestive of much smaller barr ier to magnetization relaxation in comparison to that of a dry 12b . Clearly, the magnetic behavior of 12 displays a significant depende nce on the solvation of the complex, as well as the choice of a crystallization solvent. Solvent dependence in SMM behavior has been also observed in other compounds. [Mn12O12(O2CR)16(H2O)x] complexes display solvation dependence in the fo rm of Jahn-Teller (JT) isomerism,36,55,262 in which solvent molecules stabilize different or ientation of some of the MnIII JT axes, leading to m" signals in different temperature regimes depending on the particular JT isomer. In the

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152 [Mn4(O2CMe3)2(pdmH)6](ClO4)2 complex (pdmH = 2,6-pyridinedimethanol), the anhydrous form possess an S = 8 ground-state spin while the hydrated form possesses an S = 9 ground state.84,85 In [Mn12O8Cl4(O2CPh)8(hmp)6] (hmp is the anion of 2-hydrohymethyl pyridine), the unsolvated form is a SMM with an S = 6 or 7 ground state, while the ground state of a fully solvated form is S = 0.263 The solvation dependence in 12 can be interpreted in term s of the presence of weak intermolecular antiferromagnetic exchange interactions mediated by the -stacking of aromatic rings, leading to a predominately antife rromagnetic behavior and/or long-range antiferromagnetic ordering in the fully solvated form. As the solvent is lost, the loss of crystallinity diminishes the -stacking interactions and, thus, th e behavior approaches that of isolated molecules, exhibiting SM M properties. The loss of crysta llization molecules likely cause the structural rearrangement of th e packing architecture of complex 12 , resulting in different molecular environments ( i.e. , different magnetization relaxation barriers) of some molecules in comparison to others. Such structural rearrangement most probably is the origin of two sets (LT and HT) of frequency-dependent out-of-phase si gnals in the AC plots of dry forms of 12 . 5.2.3.3 Alternating Current Magnetic Susceptibi lity Studies of Complexes 13 and 14 AC magnetic susceptibility studies were performed on vacuum-dried microcrystalline samples of 13 and 14 in the 1.8 15 K temperature range in a zero DC field and a 3.5 G AC field oscillating at 50, 250, and 1000 Hz frequencies. Th e obtained data are presented in Figures 5-20 and 5-21. The upper panel of each figure shows the in-phase component of AC magnetic susceptibility (m' ), plotted as m'T vs T , whereas the lower panel shows a plot of the out-ofphase ( m" ) AC magnetic susceptibility vs T .

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153 For complex 13 , at temperatures above 4 K the m'T vs T plot display a plateau, at a value ~ 12.3 cm3 mol-1 K, consistent with a well isolated S = 9/2 ground state and g 2 (Figure 5-20); no m" signals are observed. At temperatures belo w ~ 3 K the in-phase signal decreases and a frequency-dependent m" signal appears, indicati ve of the slow relaxation of a SMM. However, the peak maxima clearly lie at temperatures below 1.8 K, the operating limit of our instrument. Regardless of the exact position of the M signals, their presence as well as the overall similarity of magnetic properties of complex 13 to other distorted cubane SMMs, suggest that 13 is also a SMMs. For complex 14 , a frequently-dependent decrease in the in-phase signal and a concomitant appearance of the out-of-phase si gnal are visible at temperatur es below ~ 3.5 K (Figure 5-21), suggesting that complex 14 is most likely a SMM. The maxima in the M signals clearly occur at temperatures below 1.8 K. At temperatures above ~ 4 K, the m'T value is essentially constant at ~ 17.8 cm3 mol-1 K and corresponds to an S = 6 system with g < 2, consistent with the DC magnetization results. 5.3 Conclusions The carboxylate abstraction procedure has proven to be a successful synthetic route for the incorporation of NCO ligands into the crystal structures of Mn clusters and has led to the formation of three new complexes: ( n -Bu 4N)2[Mn 11O10(NCO)6(O2CPh)11(H2O)4]( 12 ), ( n -Bu 4N)3[Mn 4O3(NCO)7(O2CPh)3]( 13 ) and ( n -Bu4N)2[Mn3O(NCO)6(O2CPh)3]( 14 ). Magnetic susceptibility studies revealed the presence of predominant ferromagnetic exchange interactions in all clusters, thus, justifying the use of NCO ligands as eff ective ferromagnetic couplers. In addition, all complexes exhibit frequency-depe ndent out-of-phase signa ls, suggestive of SMM behavior.

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154 5.4 Experimental Section 5.4.1 Syntheses All preparations were performed under an iner t atmosphere at ambient temperature, using reagents and solvents as received, unless otherwise stated. Me3SiNCO was stored under inert atmosphere. CH2Cl2 and Et2O were distilled over molecular sieves. ( n -Bu4N)[Mn4O2(O2CPh)9(H2O)]( 11 ) was prepared as described elsewhere.260 ( n -Bu 4N)2[Mn 11O10(NCO)6(O2CPh)11(H2O)4](12)Me2CO . A solution of 11 (0.4 g, 0.25 mmol) in Me2CO (40 ml) was treated w ith 5 equivalents of Me3SiNCO (166 l, 1.25 mmol) to give a clear red-brown solution. The reaction mixture was left under magnetic stirring for ~ 15 minutes and then filtered. The filtrate was layered with Et2O and left undisturbed at 5C. After 10-14 days red-brown needles were obtained in 0. 12 g yield (22% based on total Mn). Obtained crystals were redissolved in Me2CO, layered with hexanes and le ft undisturbed at 5C. After approximately one week, red-brown plates were formed in 19% yield (based on total Mn). Crystals were maintained in mother liquor fo r X-ray crystallography st udies, or isolated by filtration, washed with Et2O and dried under vacuum. Vacuum-dried crystals analyzed as 12 H2O. Anal. Calcd (Found) for 12 H2O: C, 46.11 (46.10); H, 4.88 (4.79), N, 3.74 (3.51). Selected IR data of 12 H2O (KBr, cm-1): 2963 (s), 2875(w), 2174 (s), 1596 (w), 1557 (7), 1514 (s), 1401 (s), 1176 (w) 1025 (w), 722 (s), 680 (w), 625 (s, br), 568 (w), 517 (w). ( n -Bu 4N)3[Mn 4O3(NCO)7(O2CPh)3](13) . A solution of 11 (0.4 g, 0.25 mmol) in CH2Cl2 (42 ml) was treated with 5 equivalents of Me3SiNCO (166 l, 1.25 mmol) to give a clear redbrown solution. The reaction mixture was left unde r magnetic stirring for ~ 15 minutes, and then filtered. The filtrate was layered with Et2O and left undisturbed at r oom temperature. After one week red-orange elongated plates were obtained in 0.1 g yield (19% based on total Mn). Crystals were maintained in mother liquor for X-ray cr ystallography studies, or isolated by filtration,

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155 washed with Et2O and dried in vacuum. Vacuum-dried crystals analyzed as solvent free. Anal. Calcd (Found) for 13 : C, 55.24 (55.17); H, 7.50 (7.72), N, 8.48 (8.25). Selected IR data of 12 H2O (KBr, cm-1): 2963 (s), 2875 (w), 2214 (s), 1598 (w ), 1558 (s), 1485 (w), 1396 (s), 1374 (s), 722 (s), 606 (w), 568 (w), 516 (w). ( n -Bu 4N)2[Mn3O(NCO)6(O2CPh)3](14)CH2Cl2. To a solution of 11 (0.8 g, 0.25 mmol) in CH2Cl2 (30 ml) were added 5 equivalents of Me3SiNCO (332 l, 2.5 mmol). The reaction mixture was left under magnetic stirring for severa l minutes and then filtered. The filtrate was layered with Et2O and left undisturbed at room temperat ure. After 2-3 days essentially black plates were obtained in 0.26 g yi eld (30% based on total Mn). Cr ystals were maintained in mother liquor for X-ray crystallography studies, or isolated by filtration, washed with Et2O and dried in vacuum. Vacuum-dried crystals analy zed as solvent free. Anal. Calcd (Found) for 14 : C, 55.31 (55.36); H, 6.84 (6.94), N, 8.75 ( 8.40). Selected IR data of 14 (KBr, cm-1): 2965 (s), 2876 (w), 2198 (s, br), 1595 (w), 1557 (s), 1483 (w), 1378 (s), 1174 (w), 1026 (w), 882 (w), 723 (s), 622 (s, br), 515 (w), 474 (s). 5.4.2 X-ray Crystallography Data for complexes 12 Me2CO, 13 and 1 4 CH2Cl2 were collected at 173 K on a Siemens SMART PLATFORM equipped with a CCD area detector and a gra phite monochromator utilizing MoK radiation ( = 0.71073 ). Cell parameters were refined using up to 8192 reflections. A full sphere of data (1 850 frames) was collected using the -scan method (0.3 frame width). The first 50 frames were remeasur ed at the end of data collection to monitor instrument and crystal stab ility (maximum correction on I was < 1%). Absorption corrections by integration were applied based on measured indexe d crystal faces. The structures were solved by the Direct Methods in SHELXTL6183 and refined using full-matr ix least squares. The non-H

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156 atoms were treated anisotropically, whereas the hydrogen atoms were calculated in ideal positions and were riding on th eir respective carbon atoms. For complex 12 , the asymmetric unit consists of the [Mn11] cluster anion, two tetrabutylammonium cations and 13 acetone molecu les of crystallization. Three of those are too close to the cluster and were kept but the ot her 10 were very disordered and could not be modeled properly, t hus program SQUEEZE,184 a part of the PLATON185 package of crystallographic software, was used to calcula te the solvent disorder area and remove its contribution to the overall intensity data. The clus ter also has two disordered benzoate ligands and a disordered NCO ligand. A total of 128 para meters were refined in the final cycle of refinement using 34763 reflections with I > 2 ( I ) to yield R 1 and wR 2 of 8.83% and 20.86%, respectively. Refinement was done using F2. For complex 13 , the asymmetric unit consists of the [Mn4] cluster anion and three tetrabutylammonium cations. Each of the latter cations has a sm all disorder. The methyl atoms on C35 and C47 as well as the propyl group on C61 are disordered and each was refined in two parts with their site occupation factors dependently refine d. A total of 953 parameters were refined in the final cycle of refi nement using 12113 reflections with I > 2 ( I ) to yield R 1 and wR 2 of 3.89% and 9.50%, respectivel y. Refinement was done using F2. For complex 14 , the asymmetric unit consists of the [Mn3] cluster anion, two tetrabutylammonium cations and a dichloromethane molecule. The latter has one of its chlorine atoms, Cl2, disordered and it was refined in tw o parts. One cation has an ethyl group at C45 disordered and the other has a methyl group disord ered. Each disorder wa s refined in two parts with their site occupation fact ors dependently refined. The [Mn3] cluster has two disorders; O9 and O9’, C1O1 and C1’O1’, where each disorder was refined in two parts. A total of 772

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157 parameters were refined in the final cycl e of refinement using 8562 reflections with I > 2 ( I ) to yield R 1 and wR 2 of 6.78 and 17.55%, respectivel y. Refinement was done using F2.

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158 Table 5-1. Crystallographic data and stru cture refinement details for complexes 12 , 13 and 14 Parameter 12 13 14 formulaa C154H213N8O55Mn11 C76H123N10O16Mn4 C69H89N8O14Cl2Mn3 fw, g mol-1 3660.66 1652.60 149.20 space group 1 P P 21/ n P 21/ c a , 15.793(14) 15.303(12) 20.495(2) b , 21.523(19) 23.201(18) 15.790(17) c , 24.500(2) 23.965(19) 22.476(3) , deg 103.2 90 90 , deg 95.25 94.27(0) 108.108(2) , deg 97.6 90 90 V , 3 7927.3(12) 8484.92(12) 6913.6(13) Z 2 4 4 T , K 173(2) 173(2) 173(2) radiation, b 0.17073 0.17073 0.17073 calc, Mg m-3 1.272 1.294 1.432 , mm-1 0.439 0.648 0.687 R 1 ( wR 2), %c , d 8.83 (20.86) 3.89 (9.50) 6.78 (17.55) aIncluding solvent molecules. bGraphite monochromator. cR 1 = ||F0| – |Fc|| / |F0|. dwR 2 = [ [ w ( F0 2 Fc2)2] / [ w F0 2)2]]1/2 where S = [ [ w ( F0 2 – Fc2)2] / ( n p )]1/2, w = 1/[ 2( F0 2) + ( m * p )2 + n * p ], p = [max( F0 2, 0) + 2* Fc2]/3, and m and n are constants. Table 5-2. Bond valence sum (BVS) calculationsa for the Mn atoms in 12 . Atom Mn(II) Mn(III) Mn(IV) Mn(1) 3.487 3.294 3.288 Mn(2) 4.18 3.823 4.014 Mn(3) 3.279 3.199 3.266 Mn(4) 3.287 3.219 3.282 Mn(5) 3.333 3.048 3.2 Mn(6) 3.175 2.904 3.048 Mn(7) 3.242 2.966 3.113 Mn(8) 3.305 3.229 3.293 Mn(9) 3.393 3.319 3.382 Mn(10) 4.166 3.81 4.000 Mn(11) 3.493 3.082 3.143 Mn(12) 3.487 3.294 3.288 a The underlined value is the one closest to the charge for whic h it was calculated. The oxidation state of a particular atom can be taken as th e nearest whole number to the underlined value

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159 Table 5-3. BVS calculationsa for selected oxygen atoms in 12 . Atom zj Assignment O1 1.935 O2O2 1.776 O2O3 1.917 O2O4 1.915 O2O5 1.941 O2O6 0.230 H2O O7 0.207 H2O O8 0.236 H2O O9 1.930 O2O10 1.921 O2O11 1.884 O2O12 1.761 O2a Bond valence sums for the oxygen atoms are calculated according to the equation sij = zj, where sij = (r/r0)-N, N and r0 are constants that are depe ndent upon the nature of the ij pair. The oxygen atom is an O2 if zj 2; the oxygen atom is an HO if zj 1; the oxygen atom is an H2O if zj 0. Table 5-4. BVS calculationsa for the Mn atoms in 13 . Atom Mn(II) Mn(III) Mn(IV) Mn(1) 3.443 3.27 3.237 Mn(2) 4.134 3.781 3.97 Mn(3) 3.519 3.355 3.301 Mn(4) 3.364 3.173 3.1765 a The underlined value is the one closest to the charge for whic h it was calculated. The oxidation state of a particular atom can be taken as th e nearest whole number to the underlined value Table 5-5. BVS calculationsa for selected oxygen atoms in 13 . Atom zj Assignment O14 1.747 O2O15 1.815 O2O16 1.705 O2a The oxygen atoms is O2 if zj 2, OH if zj 1, and H2O if zj 0. Table 5-6. BVS calculationsa , b for the Mn atoms and for selected oxygen atoms in 14 Atom Mn(II) Mn(III) Mn(IV) Mn(1) 3.437 3.236 3.248 Mn(2) 3.331 3.136 3.147 Mn(3) 3.069 3.006 3.068 Atom zj Assignment O13 2.084 O2a The underlined value is the one closest to the charge for whic h it was calculated. The oxidation state of a particular atom can be taken as th e nearest whole number to the underlined value b The oxygen atoms is O2 if zj 2, OH if zj 1, and H2O if zj 0.

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160 Table 5-7. Comparison of exchange parameters, g -values and low-lying el ectronic states of [Mn4O3X(O2CR)3(dbm)3] and ( n -Bu4N)3[Mn4O3(NCO)7(O2CPh)3]( 13 ) complexes with virtual C3v symmetry. X Parametera ( 13 )c N3 ( 9 )c NCO ( 10 )c Cl ( 8)d Brd MeCO2d J33, cm-1 8.5 8.7 9.2 8.3 7.4 5.4 J34, cm-1 -43.7 -47.9 -31.0 -28.4 -30.1 -33.9 g 1.93 1.97 1.96 2.00 2.01 1.96 ground ST 9/2 9/2 9/2 9/2 9/2 9/2 E( ST = 7/2)b 232 248 203 185 179 167 a J33 = J (MnIIIMnIII), J34 = J (MnIIIMnIV). b Energy of the ST = 7/2 first excited state above the ground state. c This work. d Reference 78.

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161 Mn1 Mn2 Mn3 Mn4 Mn5 Mn6 Mn7 Mn8 Mn9 Mn10 Mn11 O12 O13 O11 O9 O10 O4 O5 O3 O2 O1 N4 N3 N1 N2 N5 N6 O14 O15 O16 O17 O18 O19 Mn1 Mn2 Mn3 Mn4 Mn5 Mn6 Mn7 Mn8 Mn9 Mn10 Mn11 O12 O13 O11 O9 O10 O4 O5 O3 O2 O1 N4 N3 N1 N2 N5 N6 O14 O15 O16 O17 O18 O19 Mn1 Mn2 Mn3 Mn4 Mn5 Mn6 Mn7 Mn8 Mn9 Mn10 Mn11 O12 O13 O11 O9 O10 O4 O5 O3 O2 O1 N4 N3 N1 N2 N5 N6 O14 O15 O16 O17 O18 O19 Figure 5-1. PovRay representations of th e anion of complex 12 and its labeled core (including terminal NCO groups). Hydrogen atoms are om itted for clarity. Jahn-Teller axes are highlighted in bold. Color code: MnIII blue; MnIV violet blue; O red; N green; C gray.

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162 Figure 5-2. PovRay representa tions of the packing of 12 , excluding tetrabutylammonium groups and solvent molecules. Top: view along the crystallographic a -axis. Bottom: view along the crystallographic b -axis.

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163 Mn1 Mn2 Mn3 Mn4 O5 O6 O11 N5 N1 N2 N3 N4 N6 N7 O3 O4 O9 O10 O12 O13 O14 Mn1 Mn2 Mn3 Mn4 O5 O6 O11 N5 N1 N2 N3 N4 N6 N7 O3 O4 O9 O10 O12 O13 O14 Mn1 Mn2 Mn3 Mn4 O5 O6 O11 N5 N1 N2 N3 N4 N6 N7 O3 O4 O9 O10 O12 O13 O14 Figure 5-3. PovRay representations of th e anion of complex 13 and its labeled core (including terminal NCO groups). Hydrogen atoms are om itted for clarity. Jahn-Teller axes are highlighted in bold. Color code: MnIII blue; MnIV violet blue; O red; N green; C gray.

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164 Figure 5-4. PovRay representa tions of the packing of 13 , excluding tetrabutylammonium groups. Top: side view. Bottom: vi ew along the cr ystallographic b -axis.

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165 Mn1 Mn2 Mn3 N1 N2 N3 N4 N5 N6 O1 O4 O13 O5 O8 O9 O12 Mn1 Mn2 Mn3 N1 N2 N3 N4 N5 N6 O1 O4 O13 O5 O8 O9 O12 Mn1 Mn2 Mn3 N1 N2 N3 N4 N5 N6 O1 O4 O13 O5 O8 O9 O12 Figure 5-5. PovRay representations of th e anion of complex 14 and its labeled core (including terminal NCO groups). Hydrogen atoms are om itted for clarity. Jahn-Teller axes are highlighted in bold. Color code: MnIII blue; MnIV violet blue; O red; N green; C gray.

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166 Figure 5-6. PovRay rep6resenta tions of the packing of 14 , excluding tetrabutylammonium groups and solvent molecules. Top: view along the crystallographic b -axis. Bottom: view along the crystallographic c -axis.

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167 mT(cm3mol-1K)T (K) 050100150200250300 20 25 30 35 40 45 mT(cm3mol-1K)T (K) 050100150200250300 20 25 30 35 40 45 Figure 5-7. Plot of mT vs T for a dried, microcrystalline sample of complex 12a in eicosane. m is the DC molar magnetic susceptibility measured in a 0.1 T field. mT(cm3mol-1K)T (K) 050100150200250300 21 24 27 30 33 36 39 mT(cm3mol-1K)T (K) 050100150200250300 21 24 27 30 33 36 39 mT(cm3mol-1K)T (K) 050100150200250300 21 24 27 30 33 36 39 Figure 5-8. Plot of mT vs T for a dried, microcrystalline sample of complex 12b in eicosane. m is the DC molar magnetic susceptibility measured in a 0.1 T field.

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168 050100150200250300 10 11 12 13 14 mT(cm3mol-1K)T (K) 050100150200250300 10 11 12 13 14 mT(cm3mol-1K)T (K) Figure 5-9. Plot of mT vs T for a dried, microcrystalline sample of complex 13 in eicosane. m is the DC molar magnetic susceptibility measur ed in a 0.1 T field. The solid line is the fit of the experimental data to the theoretical expression; see text for the fit parameters. H/T (kG/K)M/NB 010203040 0 2 4 6 8 10 0.1 T 0.2 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit H/T (kG/K)M/NB 010203040 0 2 4 6 8 10 0.1 T 0.2 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit Figure 5-10. Plots of reduced magnetization ( M / N B) vs H / T for dried, microcrystalline samples of complex 13 at the indicated applied fields. The solid lines are the fit of the data by the method described in the text; see the text for the fit parameters.

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169 1.801.851.901.952.002.052.102.15 -1.0 -0.5 0.0 0.5 1.0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 0.04D, cm-1g0.08 0.12 0.16 0.20 0.24 0.24 0.28 0.32 1.801.851.901.952.002.052.102.15 -1.0 -0.5 0.0 0.5 1.0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 0.04D, cm-1g0.08 0.12 0.16 0.20 0.24 0.24 0.28 0.32 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 1.9 2.0 2.1 -1.0 -0.5 0.0 0.5 1.0Erro r gD , c m 1 Figure 5-11. Representations of the error surface for the D vs g fit of reduced magnetization ( M / N B) vs H / T for complex 13 . Top: twodimensional c ontour plot. Bottom: threedimensional mesh plot

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170 050100150200250300 10 12 14 16 18 20 mT(cm3mol-1K)T (K) 050100150200250300 10 12 14 16 18 20 mT(cm3mol-1K)T (K) Figure 5-12. Plot of mT vs T for a dried, microcrystalline sample of complex 14 in eicosane. m is the DC molar magnetic susceptibility meas ured in a 0.1 T field. The solid line is the fit of the experimental data to the theoretical expression; see text for the fit parameters. J J J Mn1Mn2Mn3J = J (Mn1 Mn2) = J (Mn2 Mn3) J = J (Mn1 Mn3) S1= S2= S3= 2 J J J Mn1Mn2Mn3J = J (Mn1 Mn2) = J (Mn2 Mn3) J = J (Mn1 Mn3) S1= S2= S3= 2 Figure 5-13. Schematic representation of the pairwise exchange interactions J and J between MnIII ions of complex 14 .

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171 H/T (kG/K)M/NB 010203040 0 2 4 6 8 10 0.1 T 0.2 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit H/T (kG/K)M/NB 010203040 0 2 4 6 8 10 0.1 T 0.2 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit Figure 5-14. Plots of reduced magnetization ( M / N B) vs H / T for dried, microcrystalline samples of complex 14 at the indicated applied fields. The solid lines are the fit of the data by the method described in the text; see the text for the fit parameters.

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172 1.701.751.801.851.901.95 -0.4 -0.2 0.0 0.2 0.4 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 0.08 0.12 0.16 0.20 0.24 0.32 0.36 0.40D, cm-1g 1.701.751.801.851.901.95 -0.4 -0.2 0.0 0.2 0.4 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 0.08 0.12 0.16 0.20 0.24 0.32 0.36 0.40 1.701.751.801.851.901.95 -0.4 -0.2 0.0 0.2 0.4 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.04 0.08 0.12 0.16 0.20 0.24 0.32 0.36 0.40D, cm-1g 0.0 0.3 0.6 0.9 1.2 1.5 1.8 1.70 1.75 1.80 1.85 1.90 1.95 -0. 4 -0.2 0.0 0.2 0.4E r r o rgD , c m1 Figure 5-15. Representations of the error surface for the D vs g fit of reduced magnetization ( M / N B) vs H / T for complex 14 . Top: twodimensional c ontour plot. Bottom: threedimensional mesh plot.

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173 5 10 15 20 25 30 35 40 45 50 1000 hz 750 Hz 250 Hz 50 Hz 0246810121416 0.0 0.3 0.6 0.9 1.2 1.5 1.8 1000 Hz 750 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) 5 10 15 20 25 30 35 40 45 50 1000 hz 750 Hz 250 Hz 50 Hz 0246810121416 0.0 0.3 0.6 0.9 1.2 1.5 1.8 1000 Hz 750 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) Figure 5-16. Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried microcrystalline sample of 12a at the indicated oscillation frequencies.

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174 m'T(cm3mol-1K)T (K)m"(cm3mol-1) 10 15 20 25 30 35 40 45 1000 Hz 750 Hz 250 Hz 50 Hz 0246810121416 0.0 0.3 0.6 0.9 1.2 1.5 1000 Hz 750 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) 10 15 20 25 30 35 40 45 1000 Hz 750 Hz 250 Hz 50 Hz 0246810121416 0.0 0.3 0.6 0.9 1.2 1.5 1000 Hz 750 Hz 250 Hz 50 Hz Figure 5-17. Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried microcrystalline sample of 12b at the indicated oscillation frequencies.

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175 T (K)M" (emu) 0246810121416 0.0 2.0e-6 4.0e-6 6.0e-6 8.0e-6 1.0e-5 1.2e-5 1000 Hz 250 Hz 50 Hz T (K)M" (emu) 0246810121416 0.0 2.0e-6 4.0e-6 6.0e-6 8.0e-6 1.0e-5 1.2e-5 1000 Hz 250 Hz 50 Hz Figure 5-18. Plot of the out-of-phase ( Mm") AC magnetic susceptibility signals vs temperature for a fully solvated sample of 12a at the indicated oscillation frequencies. 0246810121416 0 1e-6 2e-6 3e-6 4e-6 5e-6 1000 Hz 250 Hz 50 Hz T (K)M" (emu) 0246810121416 0 1e-6 2e-6 3e-6 4e-6 5e-6 1000 Hz 250 Hz 50 Hz T (K)M" (emu) Figure 5-19. Plot of the out-of-phase ( Mm") AC magnetic susceptibility signals vs temperature for a fully solvated sample of 12b at the indicated oscillation frequencies.

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176 7 8 9 10 11 12 13 14 1000 Hz 250 Hz 50 Hz 0246810121416 0.0 0.5 1.0 1.5 2.0 2.5 1000 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) 7 8 9 10 11 12 13 14 1000 Hz 250 Hz 50 Hz 0246810121416 0.0 0.5 1.0 1.5 2.0 2.5 1000 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) Figure 5-20. Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried mi crocrystalline sample of complex 13 at the indicated oscillation frequencies.

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177 13 14 15 16 17 18 19 1000 Hz 250 Hz 50 Hz 0246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 1000 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) 13 14 15 16 17 18 19 1000 Hz 250 Hz 50 Hz 0246810121416 0.0 0.1 0.2 0.3 0.4 0.5 0.6 1000 Hz 250 Hz 50 Hz m'T(cm3mol-1K)T (K)m"(cm3mol-1) Figure 5-21. Plot of the in-phase (as m' T ) and out-of-phase (m") AC magnetic susceptibility signals vs temperature for a vacuum-dried mi crocrystalline sample of complex 14 at the indicated oscillation frequencies.

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178 APPENDIX A BOND DISTANCES AND ANGLES Table A-1. Selected interatomic di stances () and angles () for 3 . Mn1-O4 1.826(9) Mn5-O18 2.204(7) Mn10-O38 1.939(9) Mn1-O5 1.840(9) Mn5-O15 2.245(8) Mn10-O36 1.968(11) Mn1-O51#1 1.944(11) Mn6-O22 1.871(10) Mn10-O37 2.111(14) Mn1-O1 2.003(10) Mn6-O26 1.878(8) Mn10-O35 2.283(12) Mn1-O3 2.229(10) Mn6-O20 1.898(11) Mn11-O34 1.895(8) Mn1-O2 2.243(11) Mn6-O16 1.946(7) Mn11-O48 1.916(8) Mn2-O5 1.867(8) Mn6-O19 2.217(8) Mn11-O42 1.950(8) Mn2-O8 1.870(9) Mn6-O21 2.251(8) Mn11-O40 1.962(10) Mn2-O7 1.888(8) Mn7-O25 1.862(8) Mn11-O39 2.156(13) Mn2-O4 1.904(8) Mn7-O15 1.924(8) Mn11-O41 2.339(10) Mn2-O9 2.284(13) Mn7-O24 1.940(8) Mn12-O42 1.840(9) Mn2-O6 2.334(11) Mn7-O22 1.943(8) Mn12-O33 1.869(8) Mn3-O7 1.850(8) Mn7-O23 2.165(12) Mn12-O44 1.905(13) Mn3-O8 1.894(8) Mn7-O21 2.359(11) Mn12-O47 1.917(7) Mn3-O52#1 1.945(10) Mn8-O26 1.855(9) Mn12-O43 2.216(9) Mn3-O11 1.949(9) Mn8-O33 1.875(9) Mn12-O41 2.244(8) Mn3-O12 2.109(14) Mn8-O32 1.896(11) Mn13-O7#2 1.906(8) Mn3-O10 2.284(12) Mn8-O29 1.975(11) Mn13-O41 1.910(8) Mn4-O8 1.881(8) Mn8-O31 2.217(11) Mn13-O47 1.965(8) Mn4-O21 1.936(8) Mn8-O30 2.264(10) Mn13-O49 1.970(8) Mn4-O16 1.940(8) Mn9-O33 1.878(8) Mn13-O50 2.147(13) Mn4-O13 1.944(9) Mn9-O26 1.884(8) Mn13-O48 2.341(10) Mn4-O14 2.180(13) Mn9-O34 1.889(8) Mn14-O47 1.817(9) Mn4-O15 2.389(10) Mn9-O25 1.919(8) Mn14-O5#2 1.892(8) Mn5-O16 1.836(10) Mn9-O27 2.309(13) Mn14-O42 1.936(7) Mn5-O4 1.895(8) Mn9-O28 2.362(11) Mn14-O46 1.964(12) Mn5-O22 1.930(8) Mn10-O25 1.851(8) Mn14-O45 2.226(8) Mn5-O17 1.943(11) Mn10-O34 1.855(8) Mn14-O48 2.258(9) Mn1-O4-Mn5 133.0(5) Mn8-O26-Mn6 132.0(5) Mn1-O4-Mn2 97.6(4) Mn8-O26-Mn9 97.4(4) Mn5-O4-Mn2 126.8(5) Mn6-O26-Mn9 128.9(5) Mn1-O5-Mn2 98.4(4) Mn12-O33-Mn8 131.8(4) Mn3-O7-Mn2 98.8(4) Mn12-O33-Mn9 129.0(5) Mn2-O8-Mn4 131.4(4) Mn8-O33-Mn9 96.9(4) Mn2-O8-Mn3 97.9(4) Mn10-O34-Mn9 98.6(4) Mn4-O8-Mn3 123.6(5) Mn10-O34-Mn11 125.3(5) Mn7-O15-Mn5 94.6(3) Mn9-O34-Mn11 129.8(4) Mn7-O15-Mn4 98.6(4) Mn13-O41-Mn12 95.1(3) Mn5-O15-Mn4 83.8(3) Mn13-O41-Mn11 100.2(4) Mn5-O16-Mn4 110.1(4) Mn12-O41-Mn11 84.8(3) Mn5-O16-Mn6 95.8(4) Mn12-O42-Mn14 96.0(4) Mn4-O16-Mn6 104.5(3) Mn12-O42-Mn11 109.3(4)

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179 Table A-1. Continued. Mn4-O21-Mn6 94.1(3) Mn14-O42-Mn11 104.4(3) Mn4-O21-Mn7 99.2(4) Mn14-O47-Mn12 97.4(4) Mn6-O21-Mn7 84.3(3) Mn14-O47-Mn13 110.1(4) Mn6-O22-Mn5 95.2(4) Mn12-O47-Mn13 104.7(4) Mn6-O22-Mn7 108.5(4) Mn11-O48-Mn14 94.3(3) Mn5-O22-Mn7 104.9(4) Mn11-O48-Mn13 100.0(4) Mn10-O25-Mn7 127.3(5) Mn14-O48-Mn13 84.8(3) Mn10-O25-Mn9 97.6(4) Mn8-O26-Mn6 132.0(5) Table A-2. Selected interatomic distances () for 4 . Mn1-O18 1.881(25) Mn29-O32" 1.856(35) Mn57-O6 1.934(29) Mn1-O7 1.889(26) Mn29-O95' 1.921(41) Mn57-O39 1.940(32) Mn1-O4 1.902(28) Mn29-O83" 1.925(34) Mn57-O125 1.983(34) Mn1-O11 1.919(28) Mn29-O71 1.938(28) Mn57-O163 1.985(42) Mn1-O10" 2.266(37) Mn29-O307 2.237(37) Mn57-O77 2.204(32) Mn1-O28' 2.275(36) Mn29-O126 2.244(33) Mn57-O62" 2.256(34) Mn2-O11 1.853(31) Mn30-O34 1.868(34) Mn58-O179 1.837(35) Mn2-O2 1.928(27) Mn30-O33" 1.892(34) Mn58-O59" 1.873(30) Mn2-O31' 1.942(34) Mn30-O2 1.937(27) Mn58-O65" 1.914(31) Mn2-O188 1.981(30) Mn30-O28 1.970(44) Mn58-O315 1.929(39) Mn2-O117 2.054(35) Mn30-O188 2.237(28) Mn58-O90' 2.219(30) Mn2-O9" 2.335(30) Mn30-O99" 2.240(34) Mn58-O57' 2.336(30) Mn3-O7 1.870(27) Mn31-O8 1.899(29) Mn59-O10 1.817(30) Mn3-O154 1.896(33) Mn31-O115 1.901(29) Mn59-O160 1.823(30) Mn3-O2 1.909(30) Mn31-O30 1.935(35) Mn59-O3 1.855(26) Mn3-O34 1.933(30) Mn31-O43 1.994(29) Mn59-O39 1.866(34) Mn3-O84' 2.190(34) Mn31-O49 2.104(36) Mn59-O51" 2.212(40) Mn3-O9" 2.234(28) Mn31-O93 2.318(33) Mn59-O141 2.272(36) Mn4-O11 1.869(29) Mn32-O69 1.841(32) Mn60-O102 1.856(34) Mn4-O18 1.933(28) Mn32-O21 1.86(3) Mn60-O65" 1.882(29) Mn4-O19 2.005(34) Mn32-O136 1.894(32) Mn60-O80" 1.945(29) Mn4-O87 2.043(28) Mn32-O24 1.899(36) Mn60-O69" 1.961(30) Mn4-O20 2.087(35) Mn32-O44' 2.339(31) Mn60-O124 2.262(30) Mn4-O33 2.244(37) Mn32-O325 2.471(38) Mn60-O57' 2.301(32) Mn5-O21 1.885(30) Mn33-O63 1.848(32) Mn61-O132 1.868(33) Mn5-O191 1.894(30) Mn33-O97 1.871(28) Mn61-O135 1.871(32) Mn5-O25 1.911(28) Mn33-O174 1.928(30) Mn61-O81" 1.905(40) Mn5-O194 1.949(34) Mn33-O71' 1.953(47) Mn61-O152 1.981(38) Mn5-O149 2.249(32) Mn33-O23" 2.218(38) Mn61-O98 2.209(31) Mn5-O174 2.285(34) Mn33-O191 2.294(36) Mn61-O48 2.241(27) Mn6-O42 1.910(27) Mn34-O39" 1.878(34) Mn62-O26" 1.896(30) Mn6-O56 1.922(31) Mn34-O170 1.907(31) Mn62-O119 1.906(28) Mn6-O79 1.940(38) Mn34-O103 1.945(38) Mn62-O72" 1.947(34) Mn6-O86 1.961(28) Mn34-O312 1.957(34) Mn62-O93' 1.967(34) Mn6-O28" 2.227(30) Mn34-O90" 2.110(37) Mn62-O63" 2.236(39)

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180 Table A-2. Continued. Mn6-O81 2.308(30) Mn34-O145 2.328(35) Mn62-O66 2.315(31) Mn7-O18 1.839(26) Mn35-O98" 1.874(33) Mn63-O61' 1.860(26) Mn7-O1 1.947(27) Mn35-O70 1.913(27) Mn63-O27 1.898(27) Mn7-O54 1.953(28) Mn35-O22' 1.921(42) Mn63-O54" 1.953(38) Mn7-O78 1.961(33) Mn35-O13 1.949(35) Mn63-O9' 1.971(31) Mn7-O85 2.232(29) Mn35-O11" 2.151(29) Mn63-O4' 2.061(36) Mn7-O97" 2.326(33) Mn35-O193 2.283(34) Mn63-O317 2.324(38) Mn8-O161 1.816(33) Mn36-O7 1.856(28) Mn64-O15 1.882(31) Mn8-O56' 1.890(39) Mn36-O4 1.868(26) Mn64-O95 1.902(30) Mn8-O45 1.895(31) Mn36-O66' 1.952(29) Mn64-O114 1.938(39) Mn8-O308 1.922(41) Mn36-O40 1.98(3) Mn64-O70" 2.046(34) Mn8-O78' 2.154(32) Mn36-O133 2.155(33) Mn64-O304 2.093(42) Mn8-O196 2.225(51) Mn36-O197 2.245(28) Mn64-O49" 2.344(50) Mn9-O43" 1.864(29) Mn37-O36 1.915(29) Mn65-O32" 1.889(33) Mn9-O25 1.890(26) Mn37-O116 1.919(28) Mn65-O63 1.907(35) Mn9-O97 1.894(32) Mn37-O24" 1.941(28) Mn65-O47 2.038(40) Mn9-O10' 1.930(38) Mn37-O187 1.959(33) Mn65-O76 2.084(40) Mn9-O91 2.163(28) Mn37-O57 2.190(34) Mn65-O310 2.254(40) Mn9-O191 2.266(34) Mn37-O162 2.289(30) Mn65-O303 2.469(39) Mn10-O10 1.881(31) Mn38-O170 1.858(32) Mn66-O42 1.865(28) Mn10-O16 1.888(28) Mn38-O85' 1.926(34) Mn66-O27 1.875(28) Mn10-O126 1.914(30) Mn38-O23 1.966(28) Mn66-O61' 1.903(27) Mn10-O73" 1.962(34) Mn38-O122 2.018(37) Mn66-O17" 1.928(27) Mn10-O83" 2.267(33) Mn38-O72 2.200(29) Mn66-O14 2.215(38) Mn10-O314 2.276(33) Mn38-O145 2.253(30) Mn66-O322 2.376(37) Mn11-O1 1.855(31) Mn39-O116 1.843(28) Mn67-O94 1.835(34) Mn11-O4 1.861(26) Mn39-O37 1.850(29) Mn67-O108 1.842(36) Mn11-O5 1.936(26) Mn39-O26" 1.869(29) Mn67-O102 1.889(32) Mn11-O155 1.960(36) Mn39-O119 1.871(29) Mn67-O179 1.907(34) Mn11-O63' 2.145(28) Mn39-O20' 2.217(34) Mn67-O302 2.203(41) Mn11-O97" 2.315(27) Mn39-O79" 2.323(41) Mn67-O321 2.381(42) Mn12-O56 1.867(30) Mn40-O45 1.878(30) Mn68-O21 1.869(31) Mn12-O61' 1.870(28) Mn40-O161 1.911(32) Mn68-O24 1.880(33) Mn12-O311 1.905(34) Mn40-O135 1.938(32) Mn68-O32' 1.992(35) Mn12-O7" 1.992(34) Mn40-O132 1.958(33) Mn68-O85" 2.056(34) Mn12-O118 2.213(32) Mn40-O20" 2.239(32) Mn68-O43' 2.143(36) Mn12-O81 2.325(31) Mn40-O306 2.468(37) Mn68-O5" 2.454(45) Mn13-O33" 1.821(30) Mn41-O24 1.843(35) Mn69-O30 1.799(34) Mn13-O15 1.833(28) Mn41-O49' 1.920(33) Mn69-O32 1.847(33) Mn13-O95 1.862(34) Mn41-O93 1.931(34) Mn69-O22 1.874(29) Mn13-O41" 1.945(32) Mn41-O112 1.932(29) Mn69-O67" 1.918(34) Mn13-O44" 2.234(41) Mn41-O65 2.121(36) Mn69-O324 2.21(4) Mn13-O53" 2.354(35) Mn41-O8 2.279(31) Mn69-O50" 2.297(39) Mn14-O67 1.860(35) Mn42-O92 1.842(35) Mn70-O15 1.882(29) Mn14-O173 1.883(41) Mn42-O128 1.907(35) Mn70-O70 1.897(28)

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181 Table A-2. Continued. Mn14-O71 1.901(31) Mn42-O36 1.945(31) Mn70-O193 2.006(34) Mn14-O16 1.903(27) Mn42-O64 2.005(34) Mn70-O96' 2.021(40) Mn14-O144 2.215(34) Mn42-O40" 2.207(32) Mn70-O67' 2.108(43) Mn14-O126 2.259(28) Mn42-O187 2.248(32) Mn70-O44 2.278(35) Mn15-O50 1.886(31) Mn43-O67 1.872(36) Mn71-O42 1.851(28) Mn15-O9 1.894(28) Mn43-O43" 1.890(29) Mn71-O17" 1.860(29) Mn15-O24' 2.021(35) Mn43-O3" 1.989(39) Mn71-O45" 1.998(35) Mn15-O52 2.039(34) Mn43-O30" 1.999(31) Mn71-O39' 2.030(33) Mn15-O143 2.112(36) Mn43-O190 2.202(39) Mn71-O17 2.238(32) Mn15-O76" 2.248(37) Mn43-O2" 2.279(30) Mn71-O31 2.256(27) Mn16-O45 1.881(28) Mn44-O37 1.863(28) Mn72-O160 1.87(3) Mn16-O5 1.893(27) Mn44-O145 1.912(34) Mn72-O71 1.891(31) Mn16-O97" 1.967(27) Mn44-O23 1.935(26) Mn72-O16 1.897(32) Mn16-O41 1.985(35) Mn44-O88' 1.985(33) Mn72-O151 1.898(44) Mn16-O198 2.079(40) Mn44-O31" 2.197(32) Mn72-O89" 2.232(34) Mn16-O54 2.320(31) Mn44-O312 2.313(32) Mn72-O83" 2.300(28) Mn17-O92 1.844(33) Mn45-O32 1.848(34) Mn73-O41" 1.821(30) Mn17-O36 1.862(33) Mn45-O84 1.896(46) Mn73-O33" 1.893(35) Mn17-O26" 1.863(30) Mn45-O112 1.925(29) Mn73-O89 1.987(44) Mn17-O82 1.892(43) Mn45-O115 1.932(33) Mn73-O19" 2.007(36) Mn17-O36" 2.200(31) Mn45-O59' 2.161(37) Mn73-O131 2.292(28) Mn17-O162 2.254(28) Mn45-O93 2.282(34) Mn73-O38 2.351(35) Mn18-O132 1.790(34) Mn46-O59 1.834(44) Mn74-O22 1.860(28) Mn18-O86 1.880(32) Mn46-O119 1.844(28) Mn74-O21' 1.904(41) Mn18-O60 1.893(39) Mn46-O23 1.848(31) Mn74-O66" 1.916(35) Mn18-O56 1.927(28) Mn46-O170 1.946(28) Mn74-O166 1.917(29) Mn18-O13" 2.191(30) Mn46-O312 2.199(30) Mn74-O309 2.225(43) Mn18-O311 2.293(30) Mn46-O45' 2.231(31) Mn74-O35" 2.322(33) Mn19-O27 1.905(29) Mn47-O186 1.879(47) Mn75-O136 1.824(31) Mn19-O57' 1.920(29) Mn47-O108 1.928(34) Mn75-O91' 1.918(34) Mn19-O59" 1.922(30) Mn47-O6 1.946(33) Mn75-O69 1.921(33) Mn19-O88 2.006(33) Mn47-O125 2.034(29) Mn75-O86" 2.03(4) Mn19-O46" 2.203(34) Mn47-O178 2.217(34) Mn75-O172 2.175(38) Mn19-O80" 2.359(30) Mn47-O56" 2.271(29) Mn75-O26 2.253(28) Mn20-O92" 1.805(40) Mn48-O30 1.842(32) Mn76-O128 1.809(37) Mn20-O166 1.861(29) Mn48-O22 1.922(28) Mn76-O129 1.853(38) Mn20-O22" 1.89(4) Mn48-O68" 1.970(34) Mn76-O98" 1.873(34) Mn20-O46 1.896(38) Mn48-O8" 2.026(36) Mn76-O13' 1.989(41) Mn20-O66" 2.198(34) Mn48-O74" 2.199(40) Mn76-O42' 2.186(43) Mn20-O181 2.221(34) Mn48-O88" 2.259(42) Mn76-O29" 2.288(30) Mn21-O135 1.830(29) Mn49-O86 1.889(31) Mn77-O67" 1.813(34) Mn21-O1 1.914(27) Mn49-O161 1.907(34) Mn77-O166 1.895(34) Mn21-O5 1.927(31) Mn49-O12" 1.925(35) Mn77-O46 1.912(34) Mn21-O164 1.964(36) Mn49-O81 1.961(28) Mn77-O35 1.956(49) Mn21-O37' 2.189(29) Mn49-O176 2.218(33) Mn77-O60" 2.108(35)

PAGE 182

182 Table A-2. Continued. Mn21-O54 2.211(29) Mn49-O311 2.339(34) Mn77-O309 2.357(38) Mn22-O3 1.845(26) Mn50-O17" 1.837(29) Mn78-O39" 1.875(36) Mn22-O125 1.862(28) Mn50-O59" 1.903(33) Mn78-O62' 1.885(33) Mn22-O56" 1.927(29) Mn50-O65" 1.906(29) Mn78-O52" 1.960(44) Mn22-O62 1.985(32) Mn50-O19' 1.918(37) Mn78-O94" 2.009(52) Mn22-O74 2.140(36) Mn50-O14" 2.258(33) Mn78-O36' 2.021(45) Mn22-O77 2.203(35) Mn50-O80" 2.296(29) Mn78-O313 2.439(35) Mn23-O136 1.896(29) Mn51-O95 1.864(35) Mn79-O309 1.904(41) Mn23-O25 1.910(31) Mn51-O34 1.889(28) Mn79-O46 1.920(35) Mn23-O97 1.937(29) Mn51-O9" 1.903(30) Mn79-O62' 1.927(34) Mn23-O1" 1.984(39) Mn51-O96 1.984(34) Mn79-O1D 2.000(47) Mn23-O168 2.192(34) Mn51-O6" 2.144(33) Mn79-O96" 2.283(39) Mn23-O174 2.269(28) Mn51-O188 2.343(30) Mn79-O66" 2.335(39) Mn24-O50 1.841(29) Mn52-O10 1.880(29) Mn80-O108 1.849(35) Mn24-O44 1.866(30) Mn52-O3 1.899(28) Mn80-O179 1.897(37) Mn24-O13 1.868(28) Mn52-O75" 1.943(41) Mn80-O61" 2.033(46) Mn24-O11' 1.943(35) Mn52-O177 1.977(36) Mn80-O55" 2.046(40) Mn24-O51 2.253(41) Mn52-O72' 2.143(37) Mn80-O87" 2.28(3) Mn24-O193 2.290(38) Mn52-O50' 2.203(40) Mn80-O79' 2.358(40) Mn25-O41" 1.84(3) Mn53-O94 1.852(33) Mn81-O85' 1.859(36) Mn25-O70 1.844(32) Mn53-O127 1.871(34) Mn81-O92" 1.896(39) Mn25-O13 1.932(30) Mn53-O6 1.909(29) Mn81-O42" 1.916(38) Mn25-O55 1.948(53) Mn53-O77 1.924(32) Mn81-O15' 1.995(39) Mn25-O316 2.218(34) Mn53-O109 2.240(32) Mn81-O73 2.262(35) Mn25-O44 2.268(28) Mn53-O56" 2.281(35) Mn81-O58" 2.268(33) Mn26-O9 1.834(30) Mn54-O9 1.877(31) Mn82-O39 1.850(31) Mn26-O90 1.897(32) Mn54-O98" 1.884(36) Mn82-O57" 1.903(41) Mn26-O92 1.934(33) Mn54-O128 1.896(34) Mn82-O160 1.950(33) Mn26-O162 1.99(3) Mn54-O50 1.919(28) Mn82-O8' 1.951(39) Mn26-O187 2.284(35) Mn54-O61 2.238(37) Mn82-O77" 2.232(35) Mn26-O75 2.289(33) Mn54-O86' 2.331(37) Mn82-O16" 2.268(37) Mn27-O116 1.856(26) Mn55-O112 1.831(34) Mn83-O62' 1.788(34) Mn27-O37 1.932(28) Mn55-O69 1.849(32) Mn83-O85' 1.816(36) Mn27-O87' 1.997(33) Mn55-O83 1.956(39) Mn83-O39" 1.860(35) Mn27-O68 2.000(33) Mn55-O115 1.976(30) Mn83-O92" 1.920(39) Mn27-O38" 2.142(32) Mn55-O8 2.242(29) Mn83-O91" 2.19(4) Mn27-O71" 2.235(40) Mn55-O15" 2.266(34) Mn84-O67" 1.895(34) Mn28-O67 1.864(33) Mn56-O102 1.880(34) Mn84-O305 1.897(43) Mn28-O43" 1.885(31) Mn56-O94 1.919(36) Mn84-O32 1.936(36) Mn28-O32" 1.889(35) Mn56-O37" 1.951(40) Mn84-O4" 1.986(47) Mn28-O63 1.901(33) Mn56-O21" 2.001(35) Mn84-O82" 2.199(53) Mn28-O323 2.301(38) Mn56-O27" 2.207(33) Mn84-O47" 2.230(37) Mn28-O301 2.371(42) Mn56-O195 2.332(35)

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183 Table A-3. Selected interatomic di stances () and angles () for 5 . Mn1-O49 1.868(7) Mn7-O15 1.948(9) Mn13-O60 2.267(7) Mn1-O49' 1.868(7) Mn7-O14 2.187(7) Mn14-O63 1.870(7) Mn1-O2' 1.985(9) Mn7-O53 2.306(8) Mn14-O59 1.921(7) Mn1-O2 1.985(9) Mn8-O56 1.868(7) Mn14-O61 1.926(6) Mn1-O1 2.169(13) Mn8-O54 1.884(7) Mn14-O33 1.960(7) Mn1-O3 2.354(13) Mn8-O17 1.981(8) Mn14-O32 2.147(8) Mn2-O49 1.845(7) Mn8-O19 1.981(7) Mn14-O60 2.427(7) Mn2-O49' 1.845(7) Mn8-O16 2.180(9) Mn15-O64 1.875(6) Mn2-O48 1.897(7) Mn8-O18 2.217(7) Mn15-O63 1.876(6) Mn2-O48' 1.897(7) Mn9-O54 1.880(6) Mn15-O35 1.976(7) Mn2-O4 2.225(11) Mn9-O56 1.895(6) Mn15-O36 1.986(7) Mn3-O48' 1.867(7) Mn9-O57 1.920(7) Mn15-O34 2.132(8) Mn3-O48 1.867(7) Mn9-O55 1.924(7) Mn15-O37 2.296(8) Mn3-O6 1.961(8) Mn9-O20 2.211(8) Mn16-O65 1.866(6) Mn3-O6' 1.961(8) Mn9-O21 2.429(15) Mn16-O64 1.893(6) Mn3-O5 2.197(14) Mn10-O57 1.884(6) Mn16-O63 1.905(6) Mn3-O7 2.235(10) Mn10-O55 1.904(6) Mn16-O62 1.915(6) Mn4-O48 1.883(6) Mn10-O25 1.967(7) Mn16-O38 2.188(8) Mn4-O52 1.897(6) Mn10-O24 1.993(7) Mn16-O47 2.300(6) Mn4-O50 1.917(7) Mn10-O23 2.137(8) Mn17-O62 1.840(6) Mn4-O8 1.977(8) Mn10-O22 2.250(8) Mn17-O65 1.884(6) Mn4-O9 2.235(8) Mn11-O57 1.855(6) Mn17-O40 1.966(8) Mn4-O51 2.257(7) Mn11-O60 1.938(7) Mn17-O42 2.005(7) Mn5-O50 1.879(7) Mn11-O58 1.947(6) Mn17-O39 2.199(8) Mn5-O49 1.910(7) Mn11-O26 1.977(7) Mn17-O41 2.240(6) Mn5-O11 1.927(9) Mn11-O27 2.158(8) Mn18-O65 1.875(6) Mn5-O53 1.950(7) Mn11-O59 2.369(7) Mn18-O66 1.882(7) Mn5-O10 2.188(9) Mn12-O56 1.869(6) Mn18-O66' 1.931(6) Mn5-O51 2.391(8) Mn12-O58 1.904(7) Mn18-O43 1.971(8) Mn6-O55 1.850(6) Mn12-O61 1.913(6) Mn18-O44 2.202(7) Mn6-O52 1.914(6) Mn12-O29 2.007(8) Mn18-O67 2.284(6) Mn6-O51 1.958(7) Mn12-O28 2.223(7) Mn19-O64 1.887(6) Mn6-O13 1.962(7) Mn12-O59 2.268(7) Mn19-O66 1.914(6) Mn6-O12 2.270(7) Mn13-O61 1.874(6) Mn19-O67' 1.944(6) Mn6-O53 2.377(8) Mn13-O62 1.876(6) Mn19-O45 1.961(7) Mn7-O54 1.867(6) Mn13-O58 1.894(6) Mn19-O46 2.269(7) Mn7-O52 1.923(7) Mn13-O30 1.962(8) Mn19-O67 2.340(8) Mn7-O50 1.937(7) Mn13-O31 2.215(7) Mn3-O48-Mn4 130.6(4) Mn13-O58-Mn12 96.6(3) Mn3-O48-Mn2 97.4(3) Mn13-O58-Mn11 105.3(3) Mn4-O48-Mn2 128.7(4) Mn12-O58-Mn11 108.1(3) Mn2-O49-Mn1 97.8(3) Mn14-O59-Mn12 93.5(3) Mn2-O49-Mn5 133.3(4) Mn14-O59-Mn11 101.3(3) Mn1-O49-Mn5 123.7(4) Mn12-O59-Mn11 84.5(2)

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184 Table A-3. Continued Mn5-O50-Mn4 109.1(3) Mn11-O60-Mn13 92.8(3) Mn5-O50-Mn7 106.3(3) Mn11-O60-Mn14 98.8(3) Mn4-O50-Mn7 94.9(3) Mn13-O60-Mn14 83.2(2) Mn6-O51-Mn4 91.9(3) Mn13-O61-Mn12 97.0(3) Mn6-O51-Mn5 100.7(3) Mn13-O61-Mn14 110.3(3) Mn4-O51-Mn5 83.3(3) Mn12-O61-Mn14 105.7(3) Mn4-O52-Mn6 105.7(3) Mn17-O62-Mn13 133.0(3) Mn4-O52-Mn7 96.0(3) Mn17-O62-Mn16 96.5(3) Mn6-O52-Mn7 108.8(3) Mn13-O62-Mn16 128.1(3) Mn5-O53-Mn7 91.3(3) Mn14-O63-Mn15 123.3(4) Mn5-O53-Mn6 101.5(3) Mn14-O63-Mn16 132.4(3) Mn7-O53-Mn6 83.6(3) Mn15-O63-Mn16 96.7(3) Mn7-O54-Mn9 130.7(4) Mn15-O64-Mn19 128.1(4) Mn7-O54-Mn8 130.8(4) Mn15-O64-Mn16 97.1(3) Mn9-O54-Mn8 96.5(3) Mn19-O64-Mn16 131.6(3) Mn6-O55-Mn10 128.7(4) Mn16-O65-Mn18 131.5(4) Mn6-O55-Mn9 132.0(3) Mn16-O65-Mn17 96.7(3) Mn10-O55-Mn9 95.5(3) Mn18-O65-Mn17 130.3(3) Mn8-O56-Mn12 131.7(4) Mn18-O66-Mn19 109.1(3) Mn8-O56-Mn9 96.5(3) Mn18-O66-Mn18#2 95.6(3) Mn12-O56-Mn9 129.7(4) Mn19-O66-Mn18#2 105.2(3) Mn11-O57-Mn10 124.1(4) Mn19#2-O67-Mn18 92.1(3) Mn11-O57-Mn9 132.2(3) Mn19#2-O67-Mn19 102.8(3) Mn10-O57-Mn9 96.3(3) Mn18-O67-Mn19 83.9(2) Table A-4. Selected interatomic di stances () and angles () for 6 . Mn1-O6 1.897(7) Mn7-O26 1.921(6) Mn13-O39 2.139(11) Mn1-O1 1.933(6) Mn7-O16 1.990(9) Mn13-O54 2.475(9) Mn1-O7 1.941(7) Mn7-O28 2.235(9) Mn14-O46 1.857(7) Mn1-O2 1.968(8) Mn7-O25 2.316(7) Mn14-O57 1.916(7) Mn1-O4 2.086(10) Mn8-O33 1.859(7) Mn14-O52 1.965(8) Mn1-O1' 2.437(8) Mn8-O26 1.909(7) Mn14-O49 1.987(10) Mn2-O11 1.845(7) Mn8-O24 1.930(7) Mn14-O50 2.233(8) Mn2-O7 1.926(8) Mn8-O31 1.955(10) Mn14-O54 2.298(7) Mn2-O7' 1.935(7) Mn8-O29 2.204(8) Mn15-O64 1.848(8) Mn2-O9 1.942(10) Mn8-O27 2.236(8) Mn15-O57 1.908(8) Mn2-O8 2.219(10) Mn9-O35 1.857(7) Mn15-O52 1.931(7) Mn2-O1' 2.268(7) Mn9-O26 1.910(7) Mn15-O55 1.941(11) Mn3-O17 1.865(7) Mn9-O25 1.930(7) Mn15-O53 2.236(7) Mn3-O11 1.907(8) Mn9-O36 1.952(8) Mn15-O51 2.243(9) Mn3-O10 1.977(8) Mn9-O30 2.225(8) Mn16-O65 1.871(7) Mn3-O15 1.980(9) Mn9-O27 2.376(8) Mn16-O57 1.922(7) Mn3-O13 2.181(11) Mn10-O43 1.885(8) Mn16-O66 1.963(9) Mn3-O12 2.267(7) Mn10-O35 1.897(7) Mn16-O54 1.985(7) Mn4-O6 1.885(7) Mn10-O37 1.938(9) Mn16-O58 2.179(9)

PAGE 185

185 Table A-4. Continued Mn4-O11 1.889(7) Mn10-O41 1.970(8) Mn16-O53 2.447(9) Mn4-O17 1.902(7) Mn10-O38 2.085(11) Mn17-O65 1.873(7) Mn4-O19 1.916(6) Mn10-O40 2.290(9) Mn17-O65' 1.874(7) Mn4-O14 2.296(10) Mn11-O33 1.886(7) Mn17-O67 2.024(10) Mn4-O20 2.352(9) Mn11-O46 1.897(7) Mn17-O67' 2.024(10) Mn5-O19 1.861(7) Mn11-O35 1.918(7) Mn17-O59 2.187(13) Mn5-O6 1.877(7) Mn11-O43 1.923(7) Mn17-O68 2.277(13) Mn5-O21 1.981(8) Mn11-O44 2.223(11) Mn18-O65' 1.891(8) Mn5-O3 1.997(8) Mn11-O34 2.353(11) Mn18-O65 1.891(8) Mn5-O5 2.151(10) Mn12-O46 1.856(7) Mn18-O64 1.924(8) Mn5-O18 2.282(8) Mn12-O33 1.884(8) Mn18-O64' 1.924(8) Mn6-O19 1.892(6) Mn12-O48 2.004(9) Mn18-O62 2.260(2) Mn6-O24 1.906(7) Mn12-O32 2.017(9) Mn18-O60 2.313(15) Mn6-O27 1.922(7) Mn12-O45 2.198(10) Mn19-O64' 1.885(8) Mn6-O22 1.957(8) Mn12-O47 2.280(7) Mn19-O64 1.886(8) Mn6-O23 2.210(8) Mn13-O43 1.869(7) Mn19-O56 2.013(10) Mn6-O25 2.390(8) Mn13-O52 1.910(7) Mn19-O56' 2.013(10) Mn7-O17 1.857(7) Mn13-O53 1.936(8) Mn19-O63 2.160(17) Mn7-O24 1.886(8) Mn13-O42 1.965(9) Mn19-O61 2.330(12) Mn1/O1/Mn2#1 93.4(3) Mn8/O33/Mn12 131.1(4) Mn1/O1/Mn1#1 101.2(3) Mn8/O33/Mn11 130.3(4) Mn2#1/O1/Mn1#1 83.4(2) Mn12/O33/Mn11 95.6(3) Mn5/O6/Mn4 98.1(3) Mn9/O35/Mn10 128.3(4) Mn5/O6/Mn1 122.1(4) Mn9/O35/Mn11 129.9(4) Mn4/O6/Mn1 130.7(4) Mn10/O35/Mn11 96.4(3) Mn2/O7/Mn2#1 95.5(3) Mn13/O43/Mn10 122.8(4) Mn2/O7/Mn1 108.2(4) Mn13/O43/Mn11 130.0(4) Mn2#1/O7/Mn1 104.6(3) Mn10/O43/Mn11 96.7(3) Mn2/O11/Mn4 130.5(4) Mn12/O46/Mn14 132.3(4) Mn2/O11/Mn3 131.2(4) Mn12/O46/Mn11 96.2(3) Mn4/O11/Mn3 95.5(3) Mn14/O46/Mn11 129.0(4) Mn7/O17/Mn3 131.8(4) Mn13/O52/Mn15 105.9(3) Mn7/O17/Mn4 129.5(4) Mn13/O52/Mn14 108.0(3) Mn3/O17/Mn4 96.4(3) Mn15/O52/Mn14 94.2(3) Mn5/O19/Mn6 128.1(4) Mn13/O53/Mn15 94.3(3) Mn5/O19/Mn4 97.6(3) Mn13/O53/Mn16 102.2(4) Mn6/O19/Mn4 127.4(4) Mn15/O53/Mn16 83.7(3) Mn7/O24/Mn6 110.6(4) Mn16/O54/Mn14 90.7(3) Mn7/O24/Mn8 95.5(3) Mn16/O54/Mn13 99.8(4) Mn6/O24/Mn8 105.5(3) Mn14/O54/Mn13 82.0(3) Mn9/O25/Mn7 91.9(3) Mn15/O57/Mn14 96.5(3) Mn9/O25/Mn6 103.9(3) Mn15/O57/Mn16 109.6(4) Mn7/O25/Mn6 82.9(2) Mn14/O57/Mn16 105.5(3) Mn8/O26/Mn9 109.7(3) Mn15/O64/Mn19 132.0(4)

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186 Table A-4. Continued. Mn8/O26/Mn7 95.0(3) Mn15/O64/Mn18 128.6(4) Mn9/O26/Mn7 106.3(3) Mn19/O64/Mn18 95.3(3) Mn6/O27/Mn8 94.1(3) Mn16/O65/Mn17 125.7(5) Mn6/O27/Mn9 104.6(4) Mn16/O65/Mn18 130.5(4) Mn8/O27/Mn9 85.2(3) Mn17/O65/Mn18 96.7(3) Table A-5. Selected interatomic di stances () and angles () for 12 . Mn1-N1 1.901(8) Mn6-O9 1.924(4) Mn1-O2 1.940(5) Mn6-O41 2.221(6) Mn1-N2 1.946(8) Mn6-O7 2.306(6) Mn1-O1 1.960(5) Mn6-Mn7 2.8518(15) Mn1-O20 2.193(6) Mn7-O5 1.871(4) Mn1-N3 2.276(7) Mn7-O10 1.874(5) Mn1-Mn2 2.7967(19) Mn7-O36 1.951(5) Mn1-Mn4 3.1935(16) Mn7-O27 1.958(5) Mn1-Mn3 3.2191(17) Mn7-O42 2.236(6) Mn2-O3 1.845(5) Mn7-O8 2.252(5) Mn2-O1 1.860(5) Mn8-O9 1.848(4) Mn2-O2 1.862(5) Mn8-O11 1.917(5) Mn2-O21 1.941(6) Mn8-O31 1.936(5) Mn2-O22 1.949(5) Mn8-O12 1.970(5) Mn2-O28 1.951(6) Mn8-O32 2.194(6) Mn2-Mn3 2.7978(18) Mn8-N4 2.260(8) Mn2-Mn4 2.8252(17) Mn8-Mn10 2.8133(17) Mn3-O4 1.863(5) Mn8-Mn9 3.0866(15) Mn3-O3 1.903(5) Mn8-Mn11 3.1957(17) Mn3-O24 1.945(5) Mn9-O10 1.842(4) Mn3-O1 1.950(5) Mn9-O11 1.920(5) Mn3-O23 2.201(6) Mn9-O37 1.924(5) Mn3-N3 2.301(7) Mn9-O13 1.943(5) Mn3-Mn4 3.1193(16) Mn9-O34 2.217(6) Mn4-O5 1.852(5) Mn9-N4 2.229(8) Mn4-O26 1.923(5) Mn9-Mn10 2.8170(17) Mn4-O3 1.924(5) Mn9-Mn11 3.1929(17) Mn4-O2 1.953(5) Mn10-O12 1.850(6) Mn4-O29 2.230(5) Mn10-O11 1.852(5) Mn4-N3 2.286(8) Mn10-O13 1.855(5) Mn5-O4 1.859(5) Mn10-O38 1.919(6) Mn5-O9 1.863(4) Mn10-O33 1.965(6) Mn5-O30 1.941(5) Mn10-O35 1.982(6) Mn5-O25 1.951(5) Mn10-Mn11 2.806(2) Mn5-O40 2.215(7) Mn11-N6 1.906(8) Mn5-O6 2.263(6) Mn11-N5 1.924(9) Mn5-Mn6 2.8483(15) Mn11-O12 1.950(6) Mn6-O5 1.903(4) Mn11-O13 1.954(5)

PAGE 187

187 Table A-5. Continued. Mn6-O4 1.919(4) Mn11-O39 2.205(7) Mn6-O10 1.924(4) Mn11-N4 2.285(7) Mn2-O1-Mn3 94.5(2) Mn9-O10-Mn7 130.5(2) Mn2-O1-Mn1 94.1(2) Mn9-O10-Mn6 130.6(2) Mn3-O1-Mn1 110.8(3) Mn7-O10-Mn6 97.3(2) Mn2-O2-Mn1 94.7(2) Mn10-O11-Mn8 96.5(2) Mn2-O2-Mn4 95.5(2) Mn10-O11-Mn9 96.6(2) Mn1-O2-Mn4 110.2(2) Mn8-O11-Mn9 107.1(3) Mn2-O3-Mn3 96.5(2) Mn10-O12-Mn11 95.1(2) Mn2-O3-Mn4 97.1(2) Mn10-O12-Mn8 94.8(2) Mn3-O3-Mn4 109.2(3) Mn11-O12-Mn8 109.2(3) Mn5-O4-Mn3 130.1(2) Mn10-O13-Mn9 95.7(2) Mn5-O4-Mn6 97.8(2) Mn10-O13-Mn11 94.9(2) Mn3-O4-Mn6 130.6(3) Mn9-O13-Mn11 110.0(3) Mn4-O5-Mn7 130.3(2) Mn1-N3-Mn4 88.9(3) Mn4-O5-Mn6 130.1(2) Mn1-N3-Mn3 89.4(3) Mn7-O5-Mn6 98.2(2) Mn4-N3-Mn3 85.7(3) Mn8-O9-Mn5 130.4(2) Mn9-N4-Mn8 86.9(3) Mn8-O9-Mn6 130.2(2) Mn9-N4-Mn11 90.0(3) Mn5-O9-Mn6 97.5(2) Mn8-N4-Mn11 89.4(3) Table A-6. Selected interatomic di stances () and angles () for 13 . Mn1-O6 1.9298(15) Mn2-Mn4 2.8156(5) Mn1-N2 1.943(2) Mn2-Mn3 2.8166(5) Mn1-O5 1.9527(15) Mn3-O11 1.9277(15) Mn1-N1 1.963(2) Mn3-N4 1.945(2) Mn1-O1 2.1787(16) Mn3-N3 1.946(2) Mn1-N5 2.341(2) Mn3-O6 1.9568(15) Mn1-Mn2 2.8108(5) Mn3-O8 2.1806(16) Mn1-Mn3 3.1991(5) Mn3-N5 2.3426(19) Mn1-Mn4 3.2029(6) Mn3-Mn4 3.1980(5) Mn2-O6 1.8527(15) Mn4-O5 1.9343(16) Mn2-O5 1.8555(15) Mn4-N7 1.943(2) Mn2-O11 1.8569(15) Mn4-O11 1.9448(15) Mn2-O16 1.9561(15) Mn4-N6 1.958(2) Mn2-O2 1.9562(15) Mn4-O15 2.1734(16) Mn2-O7 1.9598(15) Mn4-N5 2.3417(19) O6-Mn1-N2 91.61(8) N3-Mn3-O8 93.05(7) O6-Mn1-O5 80.69(6) O6-Mn3-O8 87.03(6) N2-Mn1-O5 172.18(8) O11-Mn3-N5 81.36(6) O6-Mn1-N1 174.47(8) N4-Mn3-N5 96.30(8) N2-Mn1-N1 92.66(9) N3-Mn3-N5 96.81(8) O5-Mn1-N1 94.95(8) O6-Mn3-N5 81.15(6)

PAGE 188

188 Table A-6. Continued. O6-Mn1-O1 90.36(6) O8-Mn3-N5 164.91(7) N2-Mn1-O1 96.65(8) O11-Mn3-Mn2 40.95(4) O5-Mn1-O1 84.79(6) N4-Mn3-Mn2 133.82(7) N1-Mn1-O1 92.64(8) N3-Mn3-Mn2 132.47(6) O6-Mn1-N5 81.75(6) O6-Mn3-Mn2 40.92(4) N2-Mn1-N5 96.55(8) O8-Mn3-Mn2 78.11(4) O5-Mn1-N5 81.13(7) N5-Mn3-Mn2 86.81(5) N1-Mn1-N5 94.26(8) O11-Mn3-Mn4 34.50(4) O1-Mn1-N5 164.79(6) N4-Mn3-Mn4 94.56(7) O6-Mn1-Mn2 40.96(4) N3-Mn3-Mn4 143.56(6) N2-Mn1-Mn2 131.59(7) O6-Mn3-Mn4 79.73(5) O5-Mn1-Mn2 41.11(4) O8-Mn3-Mn4 121.71(4) N1-Mn1-Mn2 135.38(7) N5-Mn3-Mn4 46.93(5) O1-Mn1-Mn2 78.61(4) Mn2-Mn3-Mn4 55.388(11) N5-Mn1-Mn2 86.98(5) O11-Mn3-Mn1 79.74(4) O6-Mn1-Mn3 34.88(4) N4-Mn3-Mn1 143.09(7) N2-Mn1-Mn3 93.20(6) N3-Mn3-Mn1 94.10(6) O5-Mn1-Mn3 79.74(4) O6-Mn3-Mn1 34.33(4) N1-Mn1-Mn3 141.17(7) O8-Mn3-Mn1 121.13(5) O1-Mn1-Mn3 124.64(5) N5-Mn3-Mn1 46.89(5) N5-Mn1-Mn3 46.94(5) Mn2-Mn3-Mn1 55.270(11) Mn2-Mn1-Mn3 55.441(11) Mn4-Mn3-Mn1 60.089(12) O6-Mn1-Mn4 79.95(5) O5-Mn4-N7 93.19(8) N2-Mn1-Mn4 143.10(7) O5-Mn4-O11 80.56(6) O5-Mn1-Mn4 34.33(4) N7-Mn4-O11 173.74(8) N1-Mn1-Mn4 94.53(7) O5-Mn4-N6 173.26(8) O1-Mn1-Mn4 119.06(4) N7-Mn4-N6 92.78(9) N5-Mn1-Mn4 46.85(5) O11-Mn4-N6 93.44(8) Mn2-Mn1-Mn4 55.372(11) O5-Mn4-O15 87.87(6) Mn3-Mn1-Mn4 59.938(11) N7-Mn4-O15 92.93(8) O6-Mn2-O5 85.35(6) O11-Mn4-O15 87.20(6) O6-Mn2-O11 85.12(6) N6-Mn4-O15 94.94(8) O5-Mn2-O11 85.00(6) O5-Mn4-N5 81.48(6) O6-Mn2-O16 178.09(7) N7-Mn4-N5 97.80(8) O5-Mn2-O16 94.24(6) O11-Mn4-N5 81.04(6) O11-Mn2-O16 92.99(6) N6-Mn4-N5 94.62(8) O6-Mn2-O2 95.00(6) O15-Mn4-N5 165.25(7) O5-Mn2-O2 92.25(6) O5-Mn4-Mn2 40.96(4) O11-Mn2-O2 177.23(7) N7-Mn4-Mn2 132.93(7) O16-Mn2-O2 86.87(6) O11-Mn4-Mn2 41.03(4) O6-Mn2-O7 92.32(6) N6-Mn4-Mn2 133.72(6) O5-Mn2-O7 177.56(7) O15-Mn4-Mn2 78.43(5) O11-Mn2-O7 95.54(6) N5-Mn4-Mn2 86.85(5) O16-Mn2-O7 88.12(6) O5-Mn4-Mn3 80.01(5) O2-Mn2-O7 87.22(6) N7-Mn4-Mn3 144.61(7)

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189 Table A-6. Continued. O6-Mn2-Mn1 43.06(5) O11-Mn4-Mn3 34.15(4) O5-Mn2-Mn1 43.79(5) N6-Mn4-Mn3 93.31(7) O11-Mn2-Mn1 92.22(4) O15-Mn4-Mn3 121.17(5) O16-Mn2-Mn1 136.92(5) N5-Mn4-Mn3 46.96(5) O2-Mn2-Mn1 86.00(4) Mn2-Mn4-Mn3 55.418(11) O7-Mn2-Mn1 133.78(5) O5-Mn4-Mn1 34.70(4) O6-Mn2-Mn4 92.55(5) N7-Mn4-Mn1 95.27(7) O5-Mn2-Mn4 43.10(5) O11-Mn4-Mn1 79.42(4) O11-Mn2-Mn4 43.43(5) N6-Mn4-Mn1 141.34(6) O16-Mn2-Mn4 85.88(5) O15-Mn4-Mn1 122.24(5) O2-Mn2-Mn4 133.81(5) N5-Mn4-Mn1 46.83(5) O7-Mn2-Mn4 137.93(5) Mn2-Mn4-Mn1 55.231(12) Mn1-Mn2-Mn4 69.397(14) Mn3-Mn4-Mn1 59.973(12) O6-Mn2-Mn3 43.77(5) C19-N5-Mn1 121.37(18) O5-Mn2-Mn3 92.44(5) C19-N5-Mn4 123.28(18) O11-Mn2-Mn3 42.88(5) Mn1-N5-Mn4 86.32(6) O16-Mn2-Mn3 134.45(5) C19-N5-Mn3 138.13(18) O2-Mn2-Mn3 137.82(5) Mn1-N5-Mn3 86.17(7) O7-Mn2-Mn3 86.36(4) Mn4-N5-Mn3 86.11(6) Mn1-Mn2-Mn3 69.289(12) Mn2-O5-Mn4 95.94(7) Mn4-Mn2-Mn3 69.195(13) Mn2-O5-Mn1 95.10(7) O11-Mn3-N4 93.82(8) Mn4-O5-Mn1 110.97(7) O11-Mn3-N3 173.06(8) Mn2-O6-Mn1 95.97(7) N4-Mn3-N3 93.04(9) Mn2-O6-Mn3 95.31(7) O11-Mn3-O6 80.46(6) Mn1-O6-Mn3 110.79(7) N4-Mn3-O6 174.01(8) Mn2-O11-Mn3 96.17(7) N3-Mn3-O6 92.65(8) Mn2-O11-Mn4 95.54(7) O11-Mn3-O8 87.48(6) Mn3-O11-Mn4 111.35(7) N4-Mn3-O8 94.54(8) N3-Mn3-O8 93.05(7) Table A-7. Selected interatomic di stances () and angles () for 14 . Mn1-O13 1.877(3) Mn2-N4 2.011(4) Mn1-N1 1.910(4) Mn2-O6 2.187(3) Mn1-O11 1.933(3) Mn2-N2 2.390(4) Mn1-N2 2.010(4) Mn2-Mn3 3.0391(9) Mn1-O2 2.162(3) Mn3-O13 1.875(3) Mn1-N6 2.400(4) Mn3-O7 1.938(3) Mn1-Mn3 3.0408(10) Mn3-N5 1.941(4) Mn1-Mn2 3.0414(10) Mn3-N6 2.000(4) Mn2-O13 1.879(3) Mn3-O10 2.189(3) Mn2-N3 1.935(4) Mn3-N4 2.394(4) Mn2-O3 1.950(3) O13-Mn1-N1 177.07(17) N2-Mn2-Mn3 86.89(9) O13-Mn1-O11 89.67(13) O13-Mn2-Mn1 35.91(9)

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190 Table A-7. Continued. N1-Mn1-O11 91.11(16) N3-Mn2-Mn1 141.51(13) O13-Mn1-N2 86.26(14) O3-Mn2-Mn1 81.31(9) N1-Mn1-N2 92.85(18) N4-Mn2-Mn1 94.79(12) O11-Mn1-N2 175.34(15) O6-Mn2-Mn1 120.07(9) O13-Mn1-O2 84.61(11) N2-Mn2-Mn1 41.31(10) N1-Mn1-O2 98.17(16) Mn3-Mn2-Mn1 60.01(2) O11-Mn1-O2 92.96(12) O13-Mn3-O7 89.80(13) N2-Mn1-O2 88.91(13) O13-Mn3-N5 174.99(16) O13-Mn1-N6 75.77(13) O7-Mn3-N5 89.99(16) N1-Mn1-N6 101.44(17) O13-Mn3-N6 86.58(14) O11-Mn1-N6 87.51(14) O7-Mn3-N6 176.02(15) N2-Mn1-N6 89.30(15) N5-Mn3-N6 93.46(18) O2-Mn1-N6 160.38(13) O13-Mn3-O10 84.86(12) O13-Mn1-Mn3 35.82(8) O7-Mn3-O10 93.04(13) N1-Mn1-Mn3 141.61(14) N5-Mn3-O10 100.15(16) O11-Mn1-Mn3 81.27(9) N6-Mn3-O10 88.30(15) N2-Mn1-Mn3 94.10(12) O13-Mn3-N4 76.25(12) O2-Mn1-Mn3 119.65(8) O7-Mn3-N4 87.49(14) N6-Mn1-Mn3 41.05(10) N5-Mn3-N4 98.74(16) O13-Mn1-Mn2 35.95(9) N6-Mn3-N4 90.03(15) N1-Mn1-Mn2 143.79(13) O10-Mn3-N4 161.10(12) O11-Mn1-Mn2 124.67(10) O13-Mn3-Mn2 35.99(9) N2-Mn1-Mn2 51.71(11) O7-Mn3-Mn2 81.36(10) O2-Mn1-Mn2 76.64(8) N5-Mn3-Mn2 139.10(14) N6-Mn1-Mn2 86.97(10) N6-Mn3-Mn2 94.72(11) Mn3-Mn1-Mn2 59.96(2) O10-Mn3-Mn2 120.08(8) O13-Mn2-N3 177.08(16)

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191 APPENDIX B BOND VALENCE SUM CALCULATIONS Table B-1. Bond valence sum (BVS) calculationsa for the Mn atoms in 4 . Atom Mn(II) Mn(III) Mn(IV) Mn(1) 3.306 3.024 3.175 Mn(2) 3.282 3.002 3.151 Mn(3) 3.366 3.079 3.232 Mn(4) 3.077 2.815 2.955 Mn(5) 3.226 2.951 3.098 Mn(6) 3.059 2.867 2.985 Mn(7) 3.195 2.942 3.057 Mn(8) 3.580 3.275 3.438 Mn(9) 3.424 3.132 3.288 Mn(10) 3.213 2.938 3.085 Mn(11) 3.360 3.073 3.227 Mn(12) 3.257 2.979 3.127 Mn(13) 3.561 3.257 3.419 Mn(14) 3.441 3.147 3.304 Mn(15) 3.067 2.805 2.945 Mn(16) 3.221 2.946 3.093 Mn(17) 3.629 3.320 3.485 Mn(18) 3.577 3.272 3.435 Mn(19) 3.025 2.767 2.905 Mn(20) 3.686 3.586 3.687 Mn(21) 3.503 3.243 3.342 Mn(22) 3.441 3.148 3.305 Mn(23) 3.131 2.863 3.006 Mn(24) 3.460 3.165 3.323 Mn(25) 3.422 3.130 3.286 Mn(26) 3.196 2.923 3.069 Mn(27) 3.125 2.858 3.000 Mn(28) 3.325 3.041 3.193 Mn(29) 3.267 2.988 3.137 Mn(30) 3.226 2.950 3.097 Mn(31) 3.183 2.912 3.057 Mn(32) 3.350 3.064 3.217 Mn(33) 3.329 3.045 3.196 Mn(34) 3.240 3.185 3.263 Mn(35) 3.368 3.104 3.221 Mn(36) 3.323 3.040 3.191 Mn(37) 3.099 2.835 2.976 Mn(38) 3.087 2.823 2.964 Mn(39) 3.627 3.317 3.483 Mn(40) 3.058 2.797 2.937 Mn(41) 3.374 3.086 3.240 Mn(42) 3.205 2.931 3.077 Mn(43) 3.096 2.831 2.976 Mn(44) 3.161 2.892 3.036 Mn(45) 3.377 3.089 3.243 Mn(46) 3.643 3.332 3.498

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192 Table B-1. Continued. Mn(47) 3.025 2.766 2.904 Mn(48) 3.107 3.015 3.103 Mn(49) 3.306 3.067 3.149 Mn(50) 3.358 3.072 3.225 Mn(51) 3.291 3.010 3.160 Mn(52) 3.277 2.998 3.147 Mn(53) 3.395 3.105 3.260 Mn(54) 3.320 3.037 3.188 Mn(55) 3.329 3.045 3.197 Mn(56) 3.045 2.785 2.924 Mn(57) 2.934 2.683 2.817 Mn(58) 3.387 3.098 3.253 Mn(59) 3.822 3.496 3.670 Mn(60) 3.210 2.936 3.083 Mn(61) 3.328 3.044 3.196 Mn(62) 3.082 3.030 3.104 Mn(63) 3.470 3.214 3.309 Mn(64) 3.135 2.868 3.011 Mn(65) 2.713 2.481 2.605 Mn(66) 3.327 3.043 3.194 Mn(67) 3.532 3.230 3.391 Mn(68) 3.000 2.744 2.881 Mn(69) 3.657 3.345 3.512 Mn(70) 3.097 2.832 2.973 Mn(71) 3.131 2.864 3.007 Mn(72) 3.381 3.092 3.247 Mn(73) 3.081 2.819 2.959 Mn(74) 3.299 3.017 3.168 Mn(75) 3.256 2.978 3.127 Mn(76) 3.533 3.327 3.459 Mn(77) 3.672 3.418 3.493 Mn(78) 3.236 2.960 3.107 Mn(79) 2.981 2.726 2.862 Mn(80) 2.899 2.652 2.784 Mn(81) 3.197 2.924 3.070 Mn(82) 3.235 2.959 3.106 Mn(83) 3.559 3.256 3.418 Mn(84) 3.178 2.907 3.052 a The valence sum rule (Pauling's second rule) is defined as follows sij = zj, where zj is the valence of atom j connecting i-j bonds with all neighboring i atoms. The valences of individual bonds ( sij) are calculated according to the equation sij = exp[( r0rij)/ b ], where rij is the observed bond length , r0 is a constant that is depe ndent upon the nature of the ij pair, and b is usually taken to be 0.37. Values of r0 are available for Mnn+ (n= 2, 3, 4, and 7) in a Mn-O base ligation environment. The underlined value is the one clos est to the charge for which it was calculated. The oxidation state of a particular atom can be takes as the nearest whole number to the underlined valu

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193 Table B-2. BVScalculationsa for the Mn atoms in 5 . Mn(II) Mn(III) Mn(IV) Mn(1) 3.159 2.890 3.034 Mn(2) 3.299 3.017 3.168 Mn(3) 3.287 3.006 3.156 Mn(4) 3.199 2.926 3.072 Mn(5) 3.165 2.895 3.039 Mn(6) 3.091 3.003 3.089 Mn(7) 3.282 3.023 3.140 Mn(8) 3.218 2.943 3.090 Mn(9) 3.211 2.937 3.083 Mn(10) 3.167 2.896 3.041 Mn(11) 3.128 2.860 3.003 Mn(12) 3.179 2.907 3.052 Mn(13) 3.332 3.048 3.200 Mn(14) 3.170 2.899 3.044 Mn(15) 3.208 2.934 3.081 Mn(16) 3.139 2.871 3.014 Mn(17) 3.231 2.956 3.103 Mn(18) 3.062 2.801 2.940 Mn(19) 3.062 2.801 2.940 a The underlined value is the one closest to the charge for whic h it was calculated. The oxidation state of a particular atom can be taken as the nearest whole number to the underlined value. Table B-3. Bond valence sum (BVS) calculationsa for selected oxygen atoms in 5 . Atom zj Assignment O(48) 1.900 O2O(49) 1.950 O2O(50) 1.751 O2O(52) 1.746 O2O(54) 1.928 O2O(55) 1.850 O2O(56) 1.867 O2O(57) 1.882 O2O(58) 1.731 O2O(61) 1.785 O2 O(62) 1.937 O2 O(63) 1.893 O2 O(64) 1.886 O2 O(65) 1.940 O2 O(66) 1.760 O2 O(51) 1.756 EtOO(53) 1.775 EtO O(59) 1.575 EtO O(60) 1.837 EtO O(67) 1.646 EtO

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194 Table B-3. Continued. O(3) 1.236 1/2EtOH O(21) 1.156 EtOH O(22) 1.336 EtOH O(47') 1.043 1/2EtOH O7 0.246 1/2H2O O12 0.226 H2O O18 0.257 H2O O41 0.243 H2O O47 0.210 1/2H2O O46 0.226 H2O O10 0.276 1/2H2O a Bond valence sums for the oxygen atoms are calculated according to the equation sij = zj, where sij = (r/r0)-N, N and r0 are constants that are depe ndent upon the nature of the ij pair. The oxygen atom is an O2 if zj 2; the oxygen atom is an HO if zj 1; the oxygen atom is an H2O if zj 0.

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195 APPENDIX C VAN VLECK EQUATIONS Distorted-cubane complex with a virtual C3 v symmetry MnIIIMnIIIMnIIIMnIVX MnIIIMnIIIMnIIIMnIVXJ33= J (MnIII MnIII) J34= J (MnIII MnIV) MnIIIMnIIIMnIIIMnIVX MnIIIMnIIIMnIIIMnIVXJ33= J (MnIII MnIII) J34= J (MnIII MnIV) kT g NB A m32 2 [Num / Den]+ TIP Num = 7.5exp(-5.25 m +6 n ) + 75exp(-2.25 m +6 n ) + 262.5exp(2.75 m +6 n ) + 630exp(9.75 m +6 n ) + 4.5exp(-1.25 m +2 n ) + 45exp(1.75 m +2 n ) + 57.5exp(6.75 m +2 n ) + 60exp(-8.25 m +12 n ) +210exp(-3.25 m +12 n ) + 504exp(3.75 m +12 n ) +990exp(12.75 m +12 n ) + 15exp(3.75 m +0 n ) +157.5exp(-11.25 m +20 n ) +378exp(-4.25 m +20 n ) +742.5exp(4.75 m +20 n ) +1287exp(15.75 m +20 n ) +252exp(-14.25 m +30 n ) +495exp(-5.25 m +30 n ) +858exp(5.75 m +30 n ) +1365exp(18.75 m +30 n ) +247.5exp(-17.25 m +42 n ) +429exp(-6.25 m +42 n ) +682.50exp(6.75 m +42 n ) +1020exp(21.75 m +42 n ) Den = +10exp(-5.25 m +6 n ) +20exp(-2.25 m +6 n ) +30exp(2.75 m +6 n ) +40exp(9.75 m +6 n ) +6exp(-1.25 m +2 n ) +12exp(1.75 m +2 n ) +18exp(6.75 m +2 n ) +16exp(-8.25 m +12 n ) +24exp(3.25 m +12 n ) +32exp(3.75 m +12 n ) +40exp(12.75 m +12 n ) +4exp(3.75 m +0 n ) +18exp(-11.25 m +20 n ) +24exp(-4.2500 m +20 n ) +30exp(4.75 m +20 n ) +36exp(15.75 m +20 n ) +16exp(-14.25 m +30 n ) +20exp(-5.25 m +30 n ) +24exp(5.75 m +30 n ) +28exp(18.75 m +30 n ) +10exp(-17.25 m +42 n ) +12exp(-6.25 m +42 n ) +14exp(6.75 m +42 n ) +16exp(21.75m +42 n )

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196 m = J34/ kT n = J33/ kT NA = Avogadro'snumber g = Lande's factor k = Boltzmann's constant T = temperature TIP = temperature independent paramagnetism Trinuclear complex: 2J model J J J Mn1Mn2Mn3J= J(Mn1Mn2) = J(Mn2Mn3) J = J(Mn1Mn3)S1= S2= S3= 2 J J J Mn1Mn2Mn3J= J(Mn1Mn2) = J(Mn2Mn3) J = J(Mn1Mn3)S1= S2= S3= 2 kT g NB A m32 2 [Num / Den]+ TIP m = J /kT n = J/kT Num = 30exp(6 m + 0 n ) + 6exp(0 m + 2 n ) + 30exp(4 m + 2 n ) + 84exp(10 m + 2 n ) + 0exp(-6 m + 6 n ) + 6exp(-4 m + 6 n ) + 30exp(0 m + 6 n ) + 84exp(6 m + 6 n ) + 180exp(14 m + 6 n ) + 6exp(-10 m + 12 n ) +

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197 30exp(-6 m + 12 n ) + 84exp(0 m + 12 n ) + 180exp(8 m + 12 n ) + 330exp(18 m + 12 n ) + 30exp(-14 m + 20 n ) + 84exp(-8 m + 20 n ) + 180exp(0 m + 20 n ) + 330exp(10 m + 20 n ) + 546exp(22 m + 20 n )] Den = 5exp(6 m + 0 n ) + 3exp(0 m + 2 n ) + 5exp(4 m + 2 n ) + 7exp(10 m + 2 n ) + 1exp(-6 m + 6 n ) + 3exp(-4 m + 6 n ) + 5exp(0 m + 6 n ) + 7exp(6 m + 6 n ) + 9exp(14 m + 6 n ) + 3exp(-10 m + 12 n ) + 5exp(6 m + 12 n ) + 7exp(0 m + 12 n ) + 9exp(8 m + 12 n ) + 11exp(18 m + 12 n ) + 5exp(-14 m + 20n ) + 7exp(8 m + 20 n ) + 9exp(0 m + 20 n ) + 11exp(10 m + 20 n ) + 13exp(22 m + 20 n )] APPENDIX D PHYSICAL MEASUREMENTS Infrared spectra were recorded in the solid state (KBr pelle ts) from on a Nicolet Nexus 670 FT-IR spectrometer in the 400-4000 cm-1 range at the University of Florida. Elemental analyses (C, H, and N) were performed at the in-house faci lities of the University of Florida Chemistry Department. Electronic spectra were collected on a Jasco V 570 spectrophotometer at the University of Florida. Variable-temperature di rect current (DC) and al ternating current (AC) magnetic susceptibility data down to 1.8 K were collected on a MPMS-XL SQUID susceptometer equipped with a 7 T DC magnet at the University of Florida. Pascal's constants were used to estimate the diamagnetic corrections , which were subtracted from the experimental susceptibility to give the mola r paramagnetic susceptibility ( m). Samples were embedded in solid eicosane to prevent torquing. Low-temperature ( 1.8 K) hysteresis loop and DC relaxation measurements were performed at Gre noble using an array of micro-SQUIDs.171 The high sensitivity of this magnetometer allows the study of single crystals of SMMs of the order of 10500 m. The field can be applied in any direction by separately dr iving three orthogonal coils.

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198 Single-crystal high frequency electron para magnetic resonance (HFEPR) measurements were performed at the University of Florida P hysics Department. The high degree of sensitivity, required for the single crystal measurements, was achieved using a multiple high-frequency (20 – 200 GHz) cavity perturbation technique.264 Measurements were performed in the 40 to 146 GHz frequency range, using a millimeter-wave vector network analyzer (MVNA) . Data were obtained by sweeping magnetic field at a cons tant frequency and temperature. Single crystals were mixed with silicone grease immediately after removal from the mother liquor in or der to prevent solvent loss.

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216 BIOGRAPHICAL SKETCH Born in Vilnius, Lithuania on October 13,1976, Alina Vinslava received a Bachelor of Science degree from the Vilnius University in June 1998, followed by a Master of Science degree in Inorganic chemistry in October 2000. During her graduate studies at the Vilnius University, she performed research in the gr oup of Professor Vytautas Daujotis, primarily focusing on the areas of Physical Chemistry and Catalysis. The last year of her Master degree program, Alina spent at the University of Pittsbur gh as a visiting research associate, where she studied the kinetics of the in terconversion of satu rated hydrocarbons on sulfated zirconia catalyst. After the completion of her master degr ee studies, Alina joined the research group of Professor George Christou at the University of Florida in August, 2001. Her doctoral research primarily involves the preparation, physical and magnetic characteri zation of polynuclear manganese complexes that functi on as single-molecule magnets.