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Theoretical and Experimental Exploration of 3D Transition Metal Clusters and Their Magnetic Properties

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Title:
Theoretical and Experimental Exploration of 3D Transition Metal Clusters and Their Magnetic Properties
Creator:
Poole, Katye M
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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Language:
english
Physical Description:
1 online resource (330 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Chemistry
Committee Chair:
CHRISTOU,GEORGE
Committee Co-Chair:
MURRAY,LESLIE JUSTIN
Committee Members:
TALHAM,DANIEL R
SMITH,BEN W
HAGELIN,HELENA AE
Graduation Date:
8/9/2014

Subjects

Subjects / Keywords:
Atoms ( jstor )
Ground state ( jstor )
Ions ( jstor )
Ligands ( jstor )
Magnetic fields ( jstor )
Magnetic permeability ( jstor )
Magnetism ( jstor )
Magnetization ( jstor )
Magnets ( jstor )
Molecules ( jstor )
Chemistry -- Dissertations, Academic -- UF
halide -- magnetism -- metal -- smm -- transition
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Chemistry thesis, Ph.D.

Notes

Abstract:
One of the main research interests in our group for a number of years has been the synthesis and characterization of transition metal compounds such as iron and manganese clusters, which usually contain chelating ligands to prevent polymerization. These complexes are of general interest for a number of reasons, including bioinorganic chemistry, magnetic materials, and oxidation of organic compounds. Manganese (Mn) is found at the active sites of many metallobiomolecules, with one of the most important being the water oxidation center (WOC) of plants and cyanobacteria, which contains a tetranuclear Mn cluster. Manganese clusters are also of interest due to interesting magnetic properties, and some Mn clusters have been found to be single molecule magnets (SMM). SMMs are molecules that can function as nanoscale magnets at low temperatures. This behavior results from a large ground state spin (S) due to unpaired electrons and a large and negative (easy axis type) magnetic anisotropy, D, which together give a significant barrier for magnetization reversal, which is characteristic of magnets. The use of halides (bromide, chloride, and iodide) and pseudohalides with 2 hydroxymethyl pyridine in a previously known reaction resulted in a family of Mn7 wheel compounds. The Mn7 wheel topology can be described as a hexagon with a another Mn ion in the center, and is with precedent in the literature, but this work has uncovered examples with a new intermediate spin ground state, S, for this topology. The magnetochemical characterization of these clusters emphasize how ground state spin values of significant magnitude can result from spin frustration effects even though all the pair wise exchange interactions are antiferromagnetic. A hexanuclear Mn clusters has been synthesized using Schiff base ligand, naphthsalproH3 (1,3 bis(salicylideneamino) 2 propanol). The structure is a twisted version of the classic oxime bridged [Mn6O2]much more closed than the previously reported butterfly like complexes as a result of the alkoxide oxygen of salpro bridging the two wingtip Mn atoms. Fitting of the dc magnetic susceptibility data revealed that the various exchange parameters are all antiferromagnetic, and the core thus experiences spin frustration effects. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: CHRISTOU,GEORGE.
Local:
Co-adviser: MURRAY,LESLIE JUSTIN.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2016-08-31
Statement of Responsibility:
by Katye M Poole.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Embargo Date:
8/31/2016
Resource Identifier:
968786267 ( OCLC )
Classification:
LD1780 2014 ( lcc )

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THEORETICAL AND EXPERIMENTAL EXPLORATION OF 3D TRANSITION METAL CLUSTERS AND THEIR MAGNETIC PROPERTIES By KATHERINE MARIA POOLE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014

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Katherine Maria Poole

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Dedicated to the Memory of my grandmother, Agnes Piscitello ( 1923200 5), my grandpa, Donald F. Harvey (1920 1996) and two of my friends and mentors Dr. Ted A. O’Brien (19722008), and Cynthia Kelley (1951201 1). Death l eaves a heartache no one can heal, Love leaves a memory no one can steal. anonymous Sorrow, who to this house scarce knew the way: Is, oh, heir of it, our all is his prey. This strange chance claims strange wonder, and to us Nothing can be so strange, as to weep thus. ‘Tis well his life’s loud speaking works deserve, And give praise too, our cold tongues could not serve: ‘Ti s well, he kept tears from our eyes before, That to fit this deep ill, we might have store. Oh, if a sweet briar climb up by a tree, If to a paradise that transplanted be, Or felled, and burnt for holy sacrifice, Yet, that must wither, which by it did r ise, As we for him dead: though no family E’er rigged a soul for heaven’s discovery With whom more ventrurers more boldly dare Venture their states, with him in joy to share. We lose what all friends loved, him; he gains now But by death, which worst foes would allow, If he could have foes, in whose practice grew All virtues, whose names subtle schoolmen knew; What ease, can hope that we shall see him, beget, When we must die first, and cannot die yet? His children are his pictures, oh they be Pictures of him dead, senseless, cold as he, Here needs no marble tomb, since he is gone, He, and about him, his, are turned to stone. John Donne, Elegy on the L.C.

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4 ACKNOWLEDGMENTS There are many people who have played an integral role my journey to this place in my life; therefore, it will be impossible to thank them all. First, I want to thank my mentor and advisor, George Christou for his very helpful and thought ful insights to my research and my career and the ever resounding question, “why?’ resonating in the back of my mind when analyzing pretty much everything. I thank my committee members, past and present, Professors Daniel Talham, Nigel Richards, Mark Meisel, Benjamin Smith, Leslie Murray and Helena Hagelin Weaver for challenging me to think above and beyond the obvious questions. I am also very grateful for the encouragement and mentoring I received from Professor Gail Fanucci along the way. Her mentoring was invaluable to my career as a female scientist and her constant reminders to use the correct scientific language and remove lab jargon from my discussions of my research will stay with me as I move forward in my career. I would like to acknowledge Adam, Otonye, Jackie, Rochelle, Tom, Mandy, Matt, Natasha, Lingna and the rest of the Fanucci group for friendship and stimulating discussions. Mandy who says your house was not big enough for two dogs! I would like to express my gratitude for friends, Coralie Richards and Pam Cohn, in the organic division for helpful discussions regarding ligand synthesis. I also want to acknowledge Joe and Lori for going above and beyond behind the scenes to make graduate students lives a little easier. I want to thank Antoni o Masello for his friendship and hours of entertainment whether it was translating words from English to Italian or making fun of the only words I spoke in Italian for being “old fashion” or just making up silly acronyms for things (i.e. TIMBBO). I am beyond grateful to Mike for his perception and wisdom at FAME and in NOLA, you are the only man for me! I want to thank Kylie Mitchell and Linh Pham for keeping me sane, listening to the countless hours of talking, and making me laugh on the bright and shiny days and the gray and gloomy days. Also, I would like to thank Kylie, Andrew and Linh for proofreading

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5 this document. Some of my greatest moments of my graduate school experiences have come in lab with Kylie and Linh discussing our science and trying to pre dict the questions George will ask before a meeting in his office or group meeting. For my grasshopper, I have very much enjoyed getting to know you and helping you develop in the beginning of your career. I value your friendship and encouragement and reme mber, I am only a phone call or text away. I will miss the days I have shared in lab and the many conversations with all of my lab mates past and present: Charis, Konstantina, Christos, Jennifer, XunGao, Emir, Garrett, Jenn, Antonio, Galia, Nemo, TianFu, Rakhika, Nick, Taketo, Ninetta, Dinos, Shreya, Arpita, Nemo, Mike, Matt, Tanmay, Jordi, Dimetris, Andy, Yan, Sofia, Maria, Margaret, Tu, Linh, Tuhin, Biju, Bayo, Andrew, Annaliese, Adeline, Daisuke, Jingwei, Kylie, Maria, and Amandine as well as anyone el se I may have forgotten to list here (there have been many visitors, high school students, undergrads, grad students and post doc along the way). I would also like to acknowledge Vivian, Alice, and Lori for all of their hard work and dedication to the students, without them we would be lost! I would also like to acknowledge Wolfgang Wernsdorfer for providing single crystal measurements on my Mn18 complex below 1.8 K using his microSQUID apparatus and for a very interesting conversation at a magnetism conf erence, the Alps sound amazing! I would like to express my gratitude to Khalil A. Abboud for all of his help and advice throughout my graduate studies as well as the teaching assistants, Patrick, Dan, Matt, Annaliese, and Ashley, for all of their hard work . I would like to acknowledge Stephen Hill and his group at the National High Magnetic Field Laboratory for highfield electron paramagnetic resonance (HFEPR) measurements and training. Also, I would like to acknowledge partial support from the National S cience Foundation Graduate Research Fellowship (DGE 0802270) and the National High Magnetic Field Laboratory which is supported by NSF/DMR grant DMR 1157490 and the State

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6 of Florida. I am grateful for the opportunity to collaborate with Drs. Anastasios Tas iopoulos, Constantina Papatriantafyllopoulou, Theocharis C. Stamatatos, and Malgorzata Holynska . My chemistry career is a reality because of four people: Mr. Linam, Susan Foster, Cynthia Kelley, and Ted O’Brien. Mr. Linam was my honors chemistry teacher fi rst per iod my junior year. I still to this day I do not know how I passed his class, I missed more classes then I attended and was late to pretty much every other one. Honestly, I think I may have been the cause of the attendance policy change the followi ng year. However, he found a way to leave a lasting impression in more than one way; the first was a life lesson and the other was that chemistry is fun. I remember one of our conversations vividly; he told me he was disappointed in me because he knew I co uld have had an A in his class if I had made it to half of the classes I missed. It took me awhile but I realized that it is important to “show up” and to be on time because it is the respectful thing to do. The second took a while to realize; however, whe n I went back to school to finish my psychology degree and obtain the new degree that would be my future. I thought back to his class and remembered how fun I thought it was and decided chemistry was going to be my second major. Thinking back now, it seems like a ridiculous reason to follow a path, but I still have the childlike enjoyment when I am trying to solve a problem or witness new results. Susan was the catalyst to my return to school because when we met I was filling vending machines for a living (a job I loved very much, but could not imagine do when I was 50 years old). She gave me the confidence to return to school, finish what I had started five years earlier, and to obtain my second major in chemistry. I will never forget the anxiety I felt wh en I sat down to take my Chemistry II laboratory final and saw my name listed on the board to talk with Cynthia Kelley when I was done. She was the “enforcer or goggle nazi” as most chemistry lab students referred to her behind her back. We

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7 later joked about these nicknames. After my final, I went to speak with her and she invited me to work for her preparing all of the general chemistry labs. It was there that I gained the confidence in applying the skills I learned in the classroom in the laboratory. I always loved making 25 L of dilute acids because how often does one get to pour 250 mL of strong acid into a huge graduated cylinder. Note: it is also when I learned the gaseous vapors really burn your nose if you do not pour them in a vented hood. Anyway, s he was always willing to engage in scientific conversations about “off the wall” topics and supportive when there were more things to get done in a week than there seemed to be time for. Her encouragement and caring personality was vital to my development and gave me confidence in my scientific ability. It was my experiences in the laboratory that prepared me for the opportunity to work with Ted O’Brien. I am forever grateful for the friendship, mentoring and teaching I received from one of the greatest people I have ever met. My time with him was short but made a huge impression on me and will forever be carried in my heart. He taught me how to get up when I do not feel like getting up, how to stay quiet and prove through actions and not words, and that you have to have confidence in yourself. Ted believed in me when others did not and challenged me to believe in myself regardless of what others thought. I am still astonished that I did research with a theoretical/computational chemist as an undergraduate. I was intimidated and fearful that I would not be good enough but he saw the determination I had to not let him down. I loved the work I did with him and feel sad that I was not able to continue his work but he built a passion within me to want to know mor e and to try and explain the unexplainable experimental results through theoretical and computational means. Because of him, I know the value of looking at things from different points of view.

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8 I heard that the Ph.D. process was a challenge and tests people in different ways. I never realized how true that statement is/was until I was in the middle of this process. I am thankful for the opportunity to have embarked on this journey. I have quest ioned many things along the way and I have succeeded even when I was sure I would fail. For me, failure was not an option so when I fell I forced myself to stand again. I am stronger and know myself better for having been here the last six years. Words can not express how forever grateful I am for the unconditional love and support of my family throughout the years who have stood by me through all the great times and the tough times. I am grateful for my father, Joe Wayne Poole, for his relentless reminders that he has had worse scratches than that on his eyeball or what doesn’t kill you makes you stronger. These are the reminders that kept me moving through the tough times and if that was not enough, the pride with which he speaks about his ‘baby’ who is ge tting her doctorate was the added boost I needed to keep moving. I am grateful to Jeanne for her love and support and putting up with my dad for what seems to be forever. I am grateful to my mother , Mary A. Piscitello, who showed me how strong women real ly are throughout my life by somehow balancing a full time career, all the chores, and raising me with the endless list of activities that I pursued growing up. I know I would not be the person I am now without the family that helped my mom along the way, the truth is family are the people who are really there when it counts and not really about blood. I am forever grateful for Annmarie, the “mother” who knew how to throw a ball and fix things. I know without your love and support I would be a different per son and I am thankful for your advice regarding my PhD and life . I am grateful for Samee and Sa rah who were the brother and sister I never had growing up and I would not trade you for the world. Although, the miles keep us apart when we are together it is like we still live down the street from each other. My

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9 appreciation is endless for the support of my other family members including Patty, George, Joanne, Cara, and Richard who have supported me throughout my life during the good, bad and the ugly. Furthermore, I would like to thank my sisters , Darla, Debbie, and Sarah as well as their families for their belief in my abilities to achieve this goal eventhoug h we have not been active in eachother’s lives. There are many others that are not specifically named here but I am also grateful for their contributions to who I am today. I am appreciative of Jim and Sharon Shirazi for their support and encouragement to pursue a degree in the physical sciences. Finally, I am forever grateful to my penguin and the love of my life that somehow always makes my day brighter by simply giving me a hug or giving me a smile only meant for me. Thank you for all of your love and support throughout this process. We made itand I look forward to all the future has in store for us.

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10 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES .........................................................................................................................13 LIST OF FIGURE S .......................................................................................................................15 LIST OF ABBREVIATIONS ........................................................................................................21 ABSTRACT ...................................................................................................................................23 CHAPTER 1 INTRODUCTION TO MOLECULE BASED MAGNETS ..................................................25 2 EXPERIMENTAL TECHNIQUES ........................................................................................43 2.1 SQUID Magnetometry ......................................................................................................43 2.1.1 Instrument and sample preparation ........................................................................43 2.1.2 Interpretation of magnetization data .......................................................................45 2.2 Electron Paramagnetic Resonance ....................................................................................53 2.3 X Ray Crystallography .....................................................................................................56 2.4 Elemental (or CHN) Analysis ...........................................................................................57 2.5 Fourier Transform Infrared Spectroscopy (FT IR) ...........................................................58 2.6 Ultraviolet and Visible (UV VIS) Spectroscopy ..............................................................59 3 SPIN FRUSTRATION EFFECTS AND AN INTERMEDIATE S = 3 GROUND STATE IN AN FE6 CLUSTER: A QUANTITATIVE SPIN FRUSTRATION SCALE ......75 3.1 Introduction .......................................................................................................................75 3.2 Experimental Section ........................................................................................................77 3.2.1 Complexes studied ..................................................................................................77 3.2.2. Computational Studies ...........................................................................................79 3.2.3 Method for Calculating Percent Spin Compensation .............................................79 3.3 Results and Discussion .....................................................................................................81 3.3.1 Summary of Experimental Studies .........................................................................81 3.3.2 Computational Studies ............................................................................................83 3.3.3 A Spin Frustration Quantification Method .............................................................89 3.5 Conclusions .......................................................................................................................90 4 DINUCLEAR MANGANESE(III) COMPLEXES WITH UNUSUALLY STRONG FERROMAGNETIC COUPLING .......................................................................................111 4.1 Introduction .....................................................................................................................111 4.2 Experimental Section ......................................................................................................114

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11 4.2.1 Syntheses ..............................................................................................................114 4.2.2 Physical Measurements ........................................................................................115 4.2.3 Computational Studies ..........................................................................................116 4.3 Results and Discussion ...................................................................................................118 4.3.1 Structure Descriptions ..........................................................................................118 4.3.1.1 Complex 41 ...............................................................................................118 4.3.1.2 Complex 42 ...............................................................................................119 4.3.1.3 Complex 43 ...............................................................................................121 4.3.2 Magnetochemistry ................................................................................................121 4.3.2.1 Magnetochemical studies for complex 41 ................................................121 4.3.2.2 Magnetochemical studies for complex 42 ................................................125 4.3.2.3 Magnetochemical studies for complex 43 ................................................127 4.3.3 Computational Studie s ..........................................................................................129 4.4 Conclusions and Future Work ........................................................................................131 5 A FAMILY OF MN7 DISKLIKE COMPLEXES WITH AN UNUSUAL GROUND STATE SPIN OF S = 9 .........................................................................................................152 5.1 Introduction .....................................................................................................................152 5.2 Experimental Section ......................................................................................................153 5.2.1 Syntheses ..............................................................................................................153 5.2.2 X ra y Crystallography ..........................................................................................156 5.2.3 Physical Measurements ........................................................................................158 5.3 Results and Discussion ...................................................................................................158 5.3.1 Syntheses ..............................................................................................................158 5.3.2 Description of Structures ......................................................................................159 5.3.3 Magnetochemistry ................................................................................................160 5.3.3.1 Direct current magnetic susceptibility studies ...........................................160 5.3.3.2 Alternating current magnetic susceptibility studies. ..................................163 5.4 Conclusions and Future Work ........................................................................................166 6 NEW Mn5 AND Mn 18 MANGANESE CLUSTERS FROM THE USE OF CYANIDE IN PLACE OF AZIDE IN KNOWN REACTIONS ............................................................187 6.1 Introduction .....................................................................................................................187 6.2 Experimental Section ......................................................................................................188 6.2.1 Syntheses ..............................................................................................................188 6.2.2 X Ray Crystallography .........................................................................................189 6.3 Results and Discussion ...................................................................................................192 6.3.1 Syntheses ..............................................................................................................192 6.3.2 Descri ption of Structures ......................................................................................194 6.3.3 Magnetochemistry ................................................................................................196 6.3.3.1 Direct current magnetic susceptibility. ......................................................196 6.4 Conclusions and Future Work ........................................................................................202

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12 APPENDIX A SELECTED INTERATOMIC DISTANCES AND ANGLES ............................................226 B LIST OF COMPLEXES .......................................................................................................237 C MN 6CA4 COMPLEX ..........................................................................................................238 Description of Structure ........................................................................................................238 Magnetochemistry ................................................................................................................238 D [Mn6O2(naphthsao)6(MeCO2)2(EtOH)(H2O)]•xEtOH•yH2O ............................................248 E VAN VLECK EQUATIONS ...............................................................................................272 F HIGHFREQUENCY ELECTRON PARAMAGNETIC RESONANCE ...........................293 G PERMISSION TO REPRODUCE COPYRIGHTED MATERIAL .....................................305 LIST OF REFERENCES .............................................................................................................312 BIOGRAPHICAL SKETCH .......................................................................................................330

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13 LIST OF TABLES Table page 31 Structural Parameters and Magnetic Properties for the Two Chair like Complexes with the [FeIII 6( 3O)2( OR)8]6+ Core .............................................................................93 32 Results of ZILSH calculations on complex 31. See text for discussion. .........................94 33 Spin couplings BASS UHF computed from ZILSH UHF wavefu nctions for spin components of compound 31. ...........................................................................................95 34 Structural Classes and Ground State S Values of Known FeIII 6 Clusters ..........................96 35 Nonzero exchange constants ( 2J convention) obtained for compounds 31, 33, and 34 with ZILSH calculations and empirical fits of magnetic susceptibility data. ............99 36 Calculated spin ground states holding all J constant except J23. .....................................100 37 Exchange couplings (J, cm1), spin couplings (
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14 65 Bond valence sum calculations for 63. ...........................................................................207 A 1 Selected Interatomic Distances () and Angles (o) for Complex 41. .............................226 A 2 Selected Interatomic Distances () and Angles (o) for the Cation of Complex 42. .......227 A 3 Selected interatomic distances () and angles () for 43. ..............................................228 A 4 Selected interatomic distances () and angles () for 51. ..............................................228 A 5 Selected interatomic distances () and angles () for 52. ..............................................229 A 6 Selected interatomic distances () and angles () for 54. ..............................................230 A 7 Selected interatomic distances () and angles () for 61. ..............................................231 A 8 Selected interatomic distances () and angles () for 62. ..............................................232 A 9 Selected interatomic distances () and angles () for 63. .............................................233 A 10 Selected interatomic distances and angles for D 1. .........................................................235 D 1 Selected X ray data for D 1. ............................................................................................260 D 2 Results of the BVS calculations for D 1. .........................................................................260 D 3 MnMn distances in D 1 and in the reported example of “classical” [Mn6O2] core compounds in ascending order. ........................................................................................261

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15 LIST OF FIGURES Figure page 11 A diamagnet (left) and a paramagnet (right) in a magnetic field. ......................................38 12 Representations of magnetic dipole arrangements in (a) paramagnetic (b) ferromagnetic, (c) antiferromagnetic, and (d) ferrimagnetic materials ..............................38 13 Typical hysteresis loop of a magnet, where M is magnetization, B is the applied magnetic field and Ms is the saturation value of the magnetization. .................................39 14 Structure of [Mn12O12(O2CCH3)16(H2O)4] viewed along the crystal c axis. ...................40 15 Structure of [Mn12O12(O2CCH3)16(H2O)4] viewed along the crystal baxis. The thick black bonds indicate t he J T axes of the Mn(III) ions ..............................................40 16 Structure of [Fe4O2(O2CCH3)7(bpy)2]+ complex (top). Stereopair of [Fe4O2(O2CCH3)7(bpy)2]+ (bottom). ...............................................................................41 17 Some examples of 2,2’ bipyridine and 2,2’ bipyridine derivatives, pyridyl alcohols, pyridyl oximes, nonpyridyl alcohols, and nonpyridyl oximes. .......................................42 21 Schematic of a SQUID magnetometer. ..............................................................................61 22 Photographs of sample preparation stepwise (a d) and a completely prepared sample in a straw (e). ......................................................................................................................62 23 Schematic of centering a sample in the coils (top) and photograph of software after performing automated centering of a sample (bottom). .....................................................63 24 Examples of MT vs T plots, (left) demonstrates predominate antiferromagnetic interactions and (right) demonstrates predominate ferromagnetic interactions. ................64 25 Example of an E(ST3+ 3 complex. ..................................64 26 Plots of reduced magnetization ( M / NB) vs H / T ...............................................................65 27 Energy diagram of two states with increasing field. ..........................................................65 28 Schematic of the oscillating field with the lagging magnetic moment from the material (i.e. single molecule magnet). ..............................................................................66 29 Examples of inphase M isolated ground state and (right) not a well isolated ground state. ........................................................................................66 210 Examples of out of phase M of phase just beginning resulting in a “tails” and (right) full out of phase peaks. ..................................67

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16 211 Example of an Arrhenius plot. ...........................................................................................67 212 Argand (or Cole Cole) plots of [Mn12O12(O2CC6F5)16(H2O)4]z+. .....................................................................................68 213 Example of a ln ( " / ) 1 / plot. ...............................................................................69 214 Plot showing the allowed, quantized spin states, Ms, of the spin vector of a molecule with S = 10 like Mn12O12(O2CR)16(H2O)4 (top left). .......................................................70 215 Energy level diagram for the Zeeman and hyperfine splittings of an S = spin on a nucleus with I = 1. ..............................................................................................................71 216 Schematic of a singlecrystal X ray diffractometer. ..........................................................72 217 Bragg’s Law as it relates to x ray diffraction. ...................................................................72 218 CHN combustion analysis instrument illustration. ............................................................73 219 Schematic of the functional parts of an FT IR spectrometer. ............................................73 220 Schematic for a double beam UV VIS spectrometer. .......................................................74 31 Schematic of [Fe6O2(hmp)10(H2O)2](NO3)4 , complex 31. ..........................................102 32 Schematic of [Fe6O2(OH)2(O2CBut )10(hep)2], complex 33. .........................................102 33 Schematic of [Fe6O2(OH)(O2CBut)9(hep)4], complex 34. ............................................103 34 The alignments of the z component of two FeIII ions ranging from completely satisfied to completely frustrated. ....................................................................................103 35 The core of complex 31, defining the structural and magnetic parameters listed in Table 3 1. .........................................................................................................................104 36 Multiple ways that ms states can combine to give ST = 0; however, all combinations give unique B AS S values. ..........................................................................................104 37 Schematic of complex 31 with J values, values, and spin alignments. ...........105 38 Plot of J23 versus J13 showing how their relative magnetudes affect the spin ground state. .................................................................................................................................106 39 Schematic of complex 33 (top) and 34 (bottom) showing J values, values, and spin alignments. The frustrated pathways are indicated with dashed l ines. ..............107 310 Percent Frustration ( ) calculated for all values of for two FeIII (S = 5/2) ions . ..................................................................................................................................108

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17 311 All possible spin alignments for two high spin d4 metals (i.e. MnIII). .............................109 41 Structure of ligands: 2,2' bipyridine (bpy) and 1,2 bis(2,2' bipyrididyl 6 yl)ethane (bbe). ................................................................................................................................135 42 The structure of complex 41 (top), a stereopair (middle), and the labeled core. ............136 43 The structure of complex 42 (top), a stereopair (middle), and the la beled core .............137 44 The structure of complex 43 (top), a stereopair (middle), and the labeled core .............138 45 Plots of MT vs T for complexes 41 4 2 ..........................139 46 J vs g root mean square error surface for 41. .................................................................140 47 Plot of reduced magnetization for 4 1. ............................................................................141 48 D vs. g root mean square error surface for 41. ...............................................................142 49 Plots of in phase M M of phase M susceptibility for complex 41. ........................................................................................143 410 J vs g root mean square error surface for 42. .................................................................144 411 Magpack simulations for complex 42 with varying values of J. ....................................145 412 Plot of the reduced magnetization for 42; see text for fit parameters. ............................146 413 D vs g root mean square error surface for 42. ................................................................146 414 Plots of in phase M M of phase M tom) ac susceptibility for complex 42. ........................................................................................147 415 Plot of M T vs T for complex 43. ..................................................................................148 416 Plot of M vs T for complex 43 ......................................................................................148 417 Energy ladder for Complex 43. ......................................................................................149 418 Plot of Energy/Jbb vs Jbb/Jwb for complex 43. ................................................................149 419 Plot of the reduced magnetization for complex 43. ........................................................150 420 Plots of in phase M M of phase M susceptibility for complex 43. ........................................................................................151 51 Structure of 51, side on view (top); topdown view (middle ); labelled stereoview (bottom) ............................................................................................................................170

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18 52 Structure of 52, side on view (top); topdown view (middle); and labelled stereoview ........................................................................................................................171 53 Structure of 53, side on view (top); topdown view (m iddle); and labelled stereoview ........................................................................................................................172 54 Structure of 54, side on view (top); topdown view (m iddle); and labelled stereoview ........................................................................................................................173 55 The stereopair of 51, side on view (top); topdown view with J T axes shown in bright green (bottom) .......................................................................................................174 56 The stereopair of 52, side on view (top); topdown view (bottom). Hydrogen atoms have been omitted for clarity ...........................................................................................175 57 The stereopair of 51 (top) and 52 (bottom) with J T axes shown in bright green. .......176 58 The core of 52 hydrogenbonding with perchlorate (top); stereoview of 52 hydrogen bonding to the perchlorate counter ion ............................................................177 59 Weighted root mean square deviation of 51 and 52; stick diagram (top) and stereoview ........................................................................................................................178 510 Plots of MT vs T for complexes 51 , 52, 53, 54, and 55. ..........................................179 511 Reduced magnetization plot for complex 51 ..................................................................180 512 Root mean square error surface for D vs g plot for complex 51. ...................................181 513 Reduced magnetization plot for complex 52 ..................................................................182 514 Root mean square error surface for D vs g for complex 52. ..........................................183 515 Alternating current susceptibility studies for 51, 52, 53, 54 , and 55 plotted as M’T vs T. ........................................................................................................................184 516 Plot of M” vs T for complex 51. ...................................................................................185 517 Labelled structures of complexes 56 and 57 .................................................................186 518 Labelled structures of complexes 56 and 57 with the ground state rationalization based on theoretical calculations of the exchange couplings. ..........................................186 61 Structure of ligands: (left) 2 hydroxymethyl pyridine (hmpH), (center) 2,6pyridine dimethanol (pdmH2) and (right) 1,1,1 tris(hydroxymethyl)ethane (thmeH3). ................207 62 Structure of 61 (top), stereoview (middle), and partially labeled core (bottom). ...........208 63 Structure of 62 (top), stereoview (middle), and partially labeled core (bottom). ...........209

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19 64 The Mn5 topology of complex 61, emphasizing the trigonal bipyramidal description and top down view of the core of 61 ..............................................................................210 65 Weighted root mean square deviation between complexes 61 and 62. ........................211 66 Structure of 63 (top), stereoview (middle), and partially labeled core (bottom). ...........212 67 Stereoview of 63 from the top down view .....................................................................213 68 Spacefilling stereoview structures of complex 63 .........................................................214 69 Core of 63 with JahnTeller axes highlighted in cyan ....................................................215 610 A single [3X3] layer of the core of complex 63 .............................................................216 611 Plot of MT vs T for complexes 61 ................................................................................217 612 Direct current magnetic susceptibility studies plotted as MT vs T for complex 62. ....217 613 Direct current susceptibility studies plotted at MT vs T for complex 63 ......................218 614 Plot of reduced magnetization ( M/NB) vs. H/ T for complex 61 at applied fields of 0.1 7.0 T in the 1.8 10 K temperature range ................................................................218 615 Root mean square error surface of D vs. g for complex 61 ...........................................219 616 Plot of reduced magnetization ( M/NB) vs. H/ T for complex 63 at applied fields of 0.1 7.0 T in t he 1.8 10 K temperature range ................................................................219 617 Root mean square error surface of D vs. g for complex 63. ..........................................220 618 Plots of in phase M' (as M T ) vs. T (top) and out of phase M vs. T (bottom) alternating current signals or complex 61 at the indicated frequencies. .........................221 619 Plots of in phase M' (as M T ) vs. T (top) and out of phase M vs. T (bottom) alternating current signals or complex 62 at the indicated frequencies. .........................222 620 Plots of in phase M' (as M T ) vs. T (top) and out of phase M vs. T (bottom) alternating current signals or complex 63 at the indicated frequencies. .........................223 621 Magnetization ( M ) vs. direct current field hysteresis loops for a single crystal of 63 at the indicated field sweep rate .......................................................................................224 622 Magnetization ( M ) vs. dc field hysteresis loops for a single crystal of 63 at the indicated temperature .......................................................................................................225 C 1 Stereoview of complex C 1 (top), stereoview of the core of C 1 (middle) and partially labeled core of C 1 (bottom) .............................................................................243

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20 C 2 Plot of MT vs T for complex C 1 ..................................................................................244 C 3 Labeling scheme employed in Equation C 1. ..................................................................245 C 4 Plot of reduced magnetization ( M/NB vs H/T ) for complex C 1 ...................................245 C 5 Two dimensional contour plot of the root mean square error surface for the D vs g fit for complex C 1. .........................................................................................................246 C 6 In phase susceptibility ( M’ data plotted as M’T) of complex C 1 in a 3.5 G ac field oscillating at the indicated frequencies. ...........................................................................247 D 1 Coordination modes of the ligand in complex D 1. .........................................................262 D 2 Structure of D 1 (top); Stereoview of complex D 1 (middle); the complex core (bottom). ...........................................................................................................................262 D 3 Complex D 1 core with cagemotif highlighted with black bonds (left) and an overlap diagram (right) of D 1 and a “classical core” (dashed lines) example. ..............263 D 4 Plot of MT vs T for complex D 1 ..................................................................................263 D 5 Alternating current magnetic susceptibility studies for D 1 in phase plotted as M (top) and out of phase plotted as M (bottom). ..............................................................264 D 6 Arrhenius plot for the vacuum dried sample of D 1 ........................................................265 D 7 Alternating current magnetic susceptibility studies for D 1 (pristine sample) in phase plotted as M of phase plotted as M ....................................266 D 8 Arrhenius plot for the high temperature pristine sample of D 1 .....................................267 D 9 Alternating current magnetic susceptibility studies for D 1 (dry) in phase plotted as M of phase plotted as M ....................................................268 D 10 Thermogravimetric diagram obtained for a sample of D 1. ............................................269 D 11 Simulated and experimental powder diagram recorded for a powdered sample of D 1........................................................................................................................................269 D 12 Temperature dependent of HFEPR spectra of complex [Mn6O2] ...................................270 D 13 (a) Easy axis ( z axis) and (b) hard plane (xyplane) frequency dependent EPR data for complex [Mn6O2] .......................................................................................................271

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21 LIST OF ABBREVIATIONS AC Alternating current b be 1,2 bis(2,2' bipyridyl 6 yl)ethane Bu t tertiary butyl b py 2,2’ bipyridine BVS Bond valence sum CV Cyclic voltammogram. D Axial zero field splitting parameter dc Direct current DPV Differential pulse voltammogram g Land factor EPR Electron paramagnetic resonance HFEPR High frequency electron paramagnetic resonance hmpH 2 hydroxymethyl pyridine JT Jahn Teller MeCN acetonitrile MeOH methanol pdmH 2 2,6 pyridine dimethanol PS II Photosystem II p y Pyridine salproH 3 1,3 bis(salicylideneamino) 2 propanol RM Reduced magnetization SMM Single molecule magnet SQUID Super quantum interference device

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22 t acn triazacyclononane TIP Temperature independent paramagnetism thmeH 3 1,1,1 tris hydroxymethyl ethane WOC Water oxidizing complex ZFS Zero field splitting ZILSH Semiempirical methods based on ZINDO

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23 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THEOR ETICAL AND EXPERIMENTAL EXPLORATION OF 3D TRANSITION METAL CLUSTERS AND THEIR MAGNETIC PROPERTIES By Katherine Maria Poole August 2014 Chair: George Christou Major: Chemistry Transition metal complexes are of general interest for a number of reasons, including bioinorganic chemistry, magnetic materials, and oxidation of organic compounds. Manganese (Mn) is found at the active sites of many metallobiomolecules, with one of the most important being the water oxidation center (WOC) of plants and cyanobacteria, which contains a tetranuclear Mn cluster. Manganese clusters are also of interest due to interesti ng magnetic properties, and some Mn clusters have been found to be single molecule magnets (SMM). SMM behavior results from a large ground state spin (S) due to unpaired electrons and a large and negative (easy axis type) magnetic anisotropy (D), which together give a significant barrier for magnetization reversal, which is characteristic of magnets. Thus, the goal in synthesis of large manganese clusters is obtain all manganese(III) ions with ferromagnetic exchange interactions (parallel alignment of the individual spins) and parallel JahnTeller elongation axes to maximize the ground state spin (S) and the large, negative magnetic anisotropy (D). However, antiferromagnetic coupling is much more common and typically is also significantly stronger than ferro magnetic coupling. The investigation of bis bpy in Mn2 chemistry resulted in a similar but different structure from bpy, which has led to record strength ferromagnetic coupling between Mn(III) ions. The synthesis, structures, magnetic properties and theore tical calculations

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24 are discussed. Theoretical studies involve calculating the many exchange interactions (J) values within Mx clusters (x up to 10), and using the obtained values to figure out the individual alignments of the metal spin vectors, and theref ore explaining the origin of the observed ground state, S. However, the exchange couplings alone do not always tell the full story because J’s give the preferred alignment not the actual alignment, thus making it important to calculate of spin couplings, , to determine how the spins align. Due to the high frequency of spin frustration in iron(III) complexes, a quantitative scale of spin frustration based on the spin coupling between each pair of adjacent spins was developed. The scale measures as a percen tage the degree of spin frustration, from ‘fully frustrated’ (100%) through ‘fully satisfied’ (0%), and the intermediate situations. This scale will provide a way of comparing different complexes in the area of magnetism and inorganic chemistry. Currently, only vague qualitative terms are used when discussing spin frustration and why a molecule has a particular S value. The use of halides (Br-, Cl-, and I-) and pseudohalides (N3 -, NCO-, etc.) with 2hydroxymethyl pyridine in a previously known reaction re sulted in a family of Mn7 wheel compounds. The Mn7 wheel topology can be described as a hexagon with another Mn ion in the center, and is with precedent in the literature, but this work has uncovered examples with a new intermediate spin ground state S = 9 for this topology. The substitution of potassium cyanide for sodium azide in two known reactions resulted in the isolation of two Mn5 trigonal bipyramidal complexes and one Mn18 double decker [3 x3] grid complex. The magnetochemical characterization of the se clusters emphasizes how unusual ground state spin values can result from spin frustration effects.

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25 CHAPTER 1 INTRODUCTION TO MOLECULE BASED MAGNETS 1.1 Introduction The history of magnetism began with a legend dating back 4000 years, when Magnes, an elderly Cretan shepherd in Northern Greece, stumbled upon a large black rock to which the nails in his shoes became firmly stuck. The rock, also known as lodestone, is more commonly known as magnetite which has a general formula of Fe3O4. While this is the most popular legend, the only certainty is that stories of these “magic” stones date back to about 600 B.C.E. in the writings of Thales of Miletus. While the story of magnetic materials began many years ago, the past two decades has seen the focus shift to molecular based magnets which has been driven by both a fundamental understanding and their potential applications in highdensity storage devices and quantum computing. In particular there has been a thriving interest in developing molecula r based magnets known as single molecule magnets where their magnetism is an intrinsic property of each molecule rather than an extrinsic property, as with magnetite. Single molecule magnets exhibit slow relaxation of their magnetization and magnetization hysteresis loops at low temperatures. The SMM’ s ability to preserve its spin polarization without applied external fields makes it a great candidate for high density data storage. Chemists have been highly motivated by the design and synthesis of new and better single molecule magnets. Physicists are equally excited by the development of new and better SMMs due to their properties straddling the classical and quantum regimes. 1.2 Magnetism Magnetism is the phenomenon associated with a moving charge and its effects on other materials. Thus, a magnetic field is created by the presence of a moving charged particle. Electrons, for example, have both spin and angular momenta that define their mot ion. Despite

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26 the ubiquity of electrons, there are very few materials that exhibit magnetism due to the fact that most electrons lie in closed shell configurations. Consequently, the individual magnetic moments cancel one another out resulting in a zero net magnetization vector; these materials are known as diamagnetic materials or diamagnets. Materials known as paramagnetic materials or paramagnets contain at least one unpaired electron. The quantitative measurement, susceptibility ( ), is the magnetic response of a given substance to an applied external field. The susceptibility is related to the external magnetic field (H0) and the magnetization (M) through Equation 1 1. = (1 1) Magnetism is divided into two broad classifications whic h are defined by their response to a magnetic field: diamagnetism and paramagnetism. Diamagnetism is a property of all matter and arises from the interaction of electron pairs with an external field, H0, generating a field opposing H0. Diamagnetic materia ls have small values ( 105 to 106 cm3 mol1 ) and tend to move to regions of lowest field strength (Figure 1 1). When magnetization (M) is negative (diamagnetic), is positive based on Equation 12. = (1 2) This means the energy (E) of the system increas es with increasing H0; therefore, movement to lower H0 decreases the energy and stabilizes the system. Paramagnetic materials also have a diamagnetic contribution that must be accounted for in order to determine the true ma gnetic susceptibility due to the unpaired electrons (Equation 13). = + (1 3) This can be accomplished in multiple ways; however, Pascal’s constants are the most common method to account for the diamagnetic contributions.

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27 Paramagnetic materials have a positive value (103 to 105 cm3 mol1) (i.e. positive M), so they are stabilized by moving to stronger fields. The strength of the attraction is based on the number of unpaired electrons and the nature of the interactions of its spins (or unpaired electrons). Paramagnetism results from the interaction of the external magnetic field, H0, with the field generated by the unpaired electrons due to the ir spin and orbital angular momentum. Diamagnetic susceptibilities are temperature and field independent; however, paramagnetic susceptibilities are inversely proportional to temperature (Equation 1 4), = (1 4) where C is the Curie constant . 1 A modified expression called the Curie Weiss defines the relationship when spins on different metal ions interact weakly with ea ch other (Equation 15) ,1 , 2 = ( ) (1 5) where is proportional to the strength of coupling between adjacent spins and is known as the Weiss constant. The various types of paramagnetism are distinguished by both the temperature dependence and the absolute magnitude of . Materials where the magnetic mom ents of unpaired electrons on different metal ions are independent of each other are known as simple paramagnets. In the absence of an external applied field, individual magnetic moments or spins are randomly oriented (Figure 1 2). When an external field i s applied, the randomly oriented spins begin to align with the field; however, this alignment is still opposed by the randomizing effect of thermal energy (kT). Other paramagnetic materials display temperature dependence due to the magnetic moments of the unpaired electrons not being independent of each other as in simple paramagnets. If the spins align parallel, this results in a ferromagnetic response, which is known as ferromagnetic coupling. If the spins align antiparallel, this is known as antiferroma gnetic or ferrimagnetic behavior. Antiferromagnetism describes the situation where

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28 all spins effectively cancel one another out resulting in no net spin of the system. Ferrimagnetism refers to the situation where all magnetic moments align antiparallel but result in a non zero magnetization.1 Iron, cobalt, nickel and several of the rare earth metals and their alloys are examples of fer romagnets; however, magnetite, Fe3O4, is a ferrimagnet. Ferro , antiferro and ferrimagnetic ordering occurs below a critical temperature, Tc or TN. Below the critical temperature , Tc, the magnetic moments for ferriand ferromagnets align in small domai ns. In the absence of an applied magnetic field, a net zero magnetization is entropically favored regardless of the nature of the interactions due to the randomization between the domains even though the magnetic moments within each domain have a nonzero magnetization. The thermally favored randomization of the domains can be overcome by the application of a strong magnetic field to align all domains with the field and ultimately with each other. The interaction of spins becomes sufficiently strong to over come dipole interactions and entropy considerations as the alignment occurs between spins, domains, and the field. 1 , 3 If the field application and field removal occur below the Tc then the net magnetization i n the material induced by the field remains partially or completely. Conversely, simple paramagnets randomize as soon as the applied magnetic field is removed. For suppression of remnant (or left over) magnetization, the application of a coercive field in the opposite direction, inducing realignment of the spins in the opposite direction, result s in a hysteresis loop (Figure 1 3). The hysteresis loop is a distinguishing characteristic of a magnet. The term hyst eresis came from the ability of a material to h ave a history of magnetization. Other magnetic ordering phenomena exist such as spin glass, metamagnetism, and canted ferro/antiferromagnetism behavior.4 1.3 Single Molecule M agnets There are three types of magnetic materials: traditional magnets, molecular arrays, and single molecule magnets. One appr oach to making smaller magnets or nanomagnets is the so-

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29 called “top down” approach, where larger magnetic material s are subject to fragmentation which produces powders with varying size distributions. With this approach fragments as small as a single domai n (20200 nm) have been isolated which define the limit of superparamagnets.5 The size distribution obtained from fragmentation causes many technological difficulties.6 , 7 An alternate approach for making nanomagnets is the so called “bottom up” approach which consists of using molecular building blocks to construct a larger magnet ic array . Depending on the building blocks used to construct these 3D molecul e based magnets, they can display unique magnetic properties that are different than the magnetic properties of molecular fragments. The first molecule based magnet, [Fe(dtc)2Cl] (dtc = diethyldithiocarbamate), was discovered in 1967 by Wickman et al .8 10 Then in 1987, a donor acceptor magnetic system comprised of [Fe(C5(CH3)5)2]+ (decamethylferrocenium cation) as the donor and [TCNE](tetracyanoethylene anion) as the acceptor was discovered as the first molecu le based magnet with its magnetic properties heavily dependent on intermolecular interactions.1 Kahn and coworkers focused their wo rk on creating molecular chains based on linking CuIIbridge MnII units and noticed that interchain interactions depended on the peripheral ligation.11 From this point in time, many groups became involved in the syntheses of these magnetic compounds with a variety of metals and ligands. The most interesting magnetic properties came from first row transition metal (i.e. Mn, Fe, V, and Co) complexes with a host of different ligands. The newest magnetic material discovered from this type of chemistry is single molecule magnets (SMMs). Singlemolecule magnet behavior in transition metal complexes arises from the coexistence of a large ground state spin, S , and a large negative Ising (or easy axis) type magnetic anisotropy as measured by the axial zero field splitting parameter, D.1215 In the case of lanthanide based SMMs, it is important to consider the total quantum number, J, instead of the spinonly quantum number, S.

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30 This combination gives rise to a significant energy barrier to the reversal of the magnetization, whose upper limit, U, is given by S2|D| for integer spins and (S21/4)|D| for half integer spins. Note: there must be virtually no intermolecular interactions otherwise the magnetism displayed will be that of a 1 , 2, or 3D molecul e based magnet. Single molecule magnets are unique for many reasons: they are zero dimensional, monodisperse, crystalline, and truly soluble. Furthermore, protection of the magnetic core from interactions with other molecules is feasible through use of or ganic ligands.16 SMMs display experimental properties consistent with superparamagents , such as frequency dependent out of phase ac susceptibility and hysteresis loops which are typical of any magnetic material. However, SMMs are anomalies to the magnetic community since their physical properties clearly display both classical and quantum physical properties which has intrigued chemists and physicists alike.17 The most famous and exhaustively studied (or the socalled “Drosophila of single mole cule magnetism”) is the SMM family of the [Mn12O12(O2CR)16(H2O)4] complexes. The structure is comprised of a central cubane containing four Mn(IV) ions surrounded by a crown of eight Mn(III) ions with twelve bridging oxides and sixteen carboxylate ligands with its coordination sphere completed by four water molecules (Figure 1 4, [Mn12O12(O2CMe)16(H2O)4]). The nearly parallel Jahn Teller (J T) axes provide a relatively large negative anisotropy for the molecule and its ST =10 ground state makes it one of t he best SMMs to date (Figure 1 5). [Mn12O12(O2CMe)16(H2O)4] remains the most popular SMM to study due to its ease of preparation, crystallinity, high S and D values, and high symmetry which allows for the si mplification of the Heisenberg s pin Hamiltonian by making the secondorder transverse terms (or rhombic terms) negligible. 1.4 Computati onal Studies for Transition metal C omplexes The importance of spin in both bioinorganic and magnetic materials chemistry has motivated the study of magnetic interactions in protein active sites, single molecule magnets, and

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31 many synthetic analogues and precursors. The interactions between metal spins in polynuclear complexes are often described with the Heisenberg spin Hamiltonian (HSH), BABAABSSJ2H (1 6) where A and B refer to metal centers. The exchange constants {JAB} specify the strengths and signs of magnetic couplings between pairs of high spin metals. The energy of a particular spin state with spin S is then given by SBABAAB0SSSJ2EE (1 7) where E0 is a sum of energy terms that are independent of spin, such as nuclear nuclear repulsion and electronnuclear attraction. The wavefunctions of the spin states are given by iMiMiNBACSSSMS (1 8) where S is the total spin, M is the total zcomponent of spin, and the {Si} are the spins of the metal ions. The MiC are expansion coefficients, and the basis functions M i are components of the form iNNi22i11MiMSMSMS (1 9) The Mi are differentiated by different values of the Mi, with the restriction that i N i 2 i 1M M M M . For small complexes, we often use the more compact notation i N i 2 i 1 M iM M M to represent a component.

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32 In many applicati ons of the Heisenberg Spin Model (HSM) to polynuclear complexes, the exchange constants are assumed to be empirical parameters, and are adjusted to reproduce the solid state variable temperature magnetic susceptibility (VTMS) for a complex. This is done by diagonalizing the HSH in a basis of spin components for a given set of constants (in favorable cases, the spin state energies can be obtained analytically by coupling the local spins using symmetry approximations which is referred to as the Kamb method18 ). A Boltzmann distribution of populations of the various spin st ates is assumed, and the magnetic susceptibility is calculated using the Van Vleck Equation, = ( )( ) ( ) ( ) ( ) 19 where E(ST) is defined as in Equation 17. Then, the exchange constants are varied until a good fit to the experimental data is obtained. Fitting in this way is actually rather difficult for complexes with more than a few metals, for two reasons. First, the number of parameters often precludes finding a meaningful fit. In the case of even six metals there are potentially fifteen nonzero coupling constants. Secondly, and more importantly, the number of basis functions of the HSH quickly becomes prohibitively large as the number of metal atoms increases. In the case of six Fe3+ ions there are 4332 basis functions with M = 0. For complexes with more than six or so metals, fitting in the manner described above becomes very difficult. The total spin of the complex can often be determined from a variable field magnetization experiment, but if exchange constants cannot be obtained for a complex, the details of how the local spins couple to give the total spin cannot be understood. The often unclear relationship between magnetic interactions in a complex and measurable quantities such as variabletemperature magnetic susceptibility (VTMS) data suggests that a combi nation of experiment and theory could be useful. This combination has been successful in other areas of chemistry, such as the study of organic reaction

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33 mechanisms,20, 21 where theory is often used to complement experiment. Unfortunately, polynuclear transition metal complexes are known to be difficult to treat with quantum chemistry, because of their large size and the weak magnetic interactions between open shell metal ions. Though some less expensive calculations based on density functional theory (DFT) on large complexes have started to appear in the literature, rather severe simplifying assumptions are often necessary.2224 In the case of recent calculations on the complex [Fe10(OCH3)20(O2CCH2Cl)10], for example, all hydrogen and chlorine atoms were omitted, and only one spin component was treated.25 With the latter restriction, estimates of the exchange constants between metals could not be made. Calculations of this sort a re not yet a general tool for studying exchange interactions in polynuclear transition metal complexes. 1.5 Spin F rustration The concept of spin frustration is well established for discrete inorganic complexes.26, 27 Spin frustration refers to a situation where spins are forced to align in the way not preferred by the inherent nature of their coupling by other, stronger exchange intera ctions. A good example of this is provided by complexes with the [Fe4O2]+8 butterfly core. 2833 These complexes have four large, antiferromagnetic wingtip body interactions Jwb that are typically considered to be equivalent, and one weaker antiferromagnetic bodybody interaction Jbb. The interaction between wingtip ions, Jww, is negligible. In the S = 0 ground states of these complexes, the spins of the two body metal ions align in a parallel fashion despite the antiferromagnetic nature of the pathway. This is caused by the much larger antiferromagnetic interactions of the body ions with the two wingtip ions. In the most stable arrangement, the spins of the body ions align parallel, and the wingtip spins align parallel to each other but antiparallel to the body spins. This way, the spins in all four of the much more strongly antiferromagnetic wingtip body pathways are aligned antiparallel. In Chapter 3, the connection between the spin alignments and total energy of a

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34 complex is considered, and how pathways experiencing spin frustration can be identified on the basis of exch ange constants and spin couplings B AS S is demonstrated. The butterfly complex [Fe4O2(OAc)7(bpy)2]+ 28 is used to illustrate these concepts (Figure 1 6). The average value of the spin coupling between two metal centers, BASS , is straightforward to evaluate for a wavefunction of the form of Equation 18. Matrix elements between components, M j B A M iS S , are computed using the elementary algebra of angular momentum operators in forming the HSH matrix. Details can be found elsewhere.34 The expectation value of the operator for a particular spin state NBASSSMS reduces to sums over these matrix elements, weighted b y the expansion coefficients obtained from diagonalizing the HSH matrix. The new implementation of ZILSH computes BASS for each pair of metals in the lowest energy state of each spin. Any other state can be treated as well if needed. Th e quantity BAS S reflects the alignment of the spins SA and SB in the spin state being considered, with a positive val ue if they are aligned parallel (or nearly so) and a negative value if they are aligned antiparallel (or nearly so) . For example, in the case of two isolated Fe3+ ions, 21S S is +6.25 in the case of perfectly parallel alignment, and –8.75 in the case of perfectly antiparallel alignment. This reflection of the actual alignment of spins contrasts with what is indicated by the exchange constant, which is the preferred alignment of the spins. This preference can be parallel (for positive J) or antiparallel (negative J), or no preference if the exchange constant has a negligible value. In cases of spin frustra tion, the preferred spin alignment is not obeyed, as discussed above. Since BAS S is negative for antiparallel spins and positive for parallel spins, then if the spin coupling and exchange constant of a pathway differ in

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35 sign, that pathwa y is experiencing some degree of spin frustration. As will be seen in the next section, this is very convenient for interpreting spin distributions in the ground states of polynuclear complexes. The product of the spin coupling and exchange constant of a pathway provides a quantitative measure of the degree to which an exchange pathway is frustrated. In Equation 17 for the energy of a state according to the HSM, the product BAABSSJ2 represents the contribution made by the exchange pathway between A and B to the total energy of the complex. Thus if JAB and BAS S have the same sign, the total energy is lowered by the interaction of spins across the pathway. If they have different signs (i.e., if the interaction is frustrated ), then the total energy increases due to the interaction of spins. On this basis, spin frustration can be defined as an increase in the total energy of a complex caused by interaction of two spins across an exchange pathway. The magnitude of the product B A ABS S J 2 gives an indication of the size or extent of the spin frustration. When the preferred spin alignment is obeyed across a pathway, on the other hand, the total energy is reduced by the interaction. This energy lowering across a path way, which might be referred to as “spin satisfaction,” is also quantified by the product BAABS S J 2 . Spin frustration occurs in the ground state of a complex only if the resulting spin alignment allows a larger increase in spin gratification e lsewhere in the complex. 1.6 Synthetic Routes to Single Molecule Magnets The magnetic properties of these molecules originate from the magnetic core which typically consists of transition metal ions with unpaired electrons, for example, manganese or iron. The magnetic core is usually surrounded by organic or nonmagnetic ligands to protect the magnetic cores from interacting with other complexes in the crystal or external materials which

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36 could cause longer range ordering effects. To this end, one of the main research interests in the Christou group for a number of years has been the synthesis and characterization of homoand heterometalic transition metal compounds, which usually employ ligand precursors that have the potential to behave as bridging and chelating ligands to yield high nuclearity clusters and prevent polymerizati on. There are many synthetic routes to single molecule magnets, with the two most important decisions to be made being which magnetic ions will be used along with which ligand or ligands. There are many options regarding the magnetic ions; however, typical ly manganese, iron, lanthanides or some combination are used. The choice of ligand can be much more challenging because any compound with donor electrons can act as a ligand. Again, nitrogen and/or oxygen donor ligands such as 2,2 bipyridine and its deri vatives, pyridyl alcohols, pyridyl oximes, nonpyridyl alcohols, and nonpyridyl oximes are used; some examples are shown in Figure 17. Once those decisions are made, the reaction conditions can be varied significantly to isolate new products and optimize reaction mixtures and crystallization techniques to provide the best quality crystals. Some typical synthetic approaches start with simple metal salts or preformed metal clusters, with the ligand or ligands of choice added to the solution. Usually a basic solution is used to aid in the aerial oxidation of metals like manganese(II) and to deprotonate the ligand precursors. Another synthetic approach is to use ligand substitution on preformed clusters to modify physical properties35 or to link similar units together to isolate larger clusters.3638 When using acidic reaction conditions, the best way to isolate higher oxidation state clusters is through comproportionation reactions where the ratio of a low oxidation state metal salt and high oxidation state metal source can be tuned to obtain MnIII/MnIV clusters.39 Over the years, many groups have experimented with the addition of halides and pseudohalides to try and tune the

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37 exchange interactions in high nuclearity clusters, for example, azide is known to promote ferromagnetic coupling and chloride is known to promote relatively strong antiferromagnetic coupling. Both types of couplings can lead to large ground state spins , which are necessary for many applications. While it is difficult to predict the exact nuclearity or topology a reaction will produce, there are many ‘tools’ in the high nuclearity synthetic ‘toolbox’ to optimize and tune reactions to relatively specific products with desired properties based on the reaction mixture employed. Thus, many polynuclear clusters containing 3d transition metals that have been reported to be SMMs4043 an d Mn complexes6 , 14, 4446 with a variety of ligands make up the majority . 1.7 Scope of Dissertation The focus of this research is the continuation of understanding new and interesting magnetic phenomenon of transition metal complexes, specifically iron and manganese complexes. The development of new synthetic routes by slight reaction modifications has led to the discovery of novel complexes that exhibit unusual physical properties. The synthesis, structure and characterization of these compounds will be discussed in Chapters 4, 5, and 6. Chapter 2 gives a brief explanation of the physical techniques used to characterize the complexes. Chapter 3 reports an investigation of spin frustration effects in a common Fe6 topology and the development of a scale to quantify spin frustration in transition metal comple xes.

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38 Figure 11. A diamagnet (left) and a paramagnet (right) in a magnetic field. Figure 12. Representations of magnetic dipole arrangements in (a) paramagnetic (b) ferromagnetic, (c) antiferromagnetic, and (d) ferrimagnetic materials

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39 Figure 13. Typical hysteresis loop of a magnet, where M is magnetization, B is the applied magnetic field and Ms is the saturation value of the magnetization.

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40 Figure 14. Structure of [Mn12O12( O2CCH3)16(H2O)4] viewed along the crystal c axis . Color Sc heme: Mn(IV), purple; Mn(III), green; O , red ; C , grey. Figure 15. Structure of [Mn12O12( O2CCH3)16(H2O)4] viewed along the crystal baxis. The thick black bonds indicate the J T axes of the Mn(III) ions. Color Scheme: Mn(IV), purple; Mn(III) , green; O , red ; C , grey.

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41 Figure 16. Structure of [Fe4O2(O2CCH3)7(bpy)2]+ comple x (top). Stereo pair of [Fe4O2( O2CCH3)7(bpy)2]+ (bottom). Color scheme: Fe3+, orange; O, red; N, blue; C, grey; H, white.

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42 Figure 17. S ome examples of 2,2’ bipyridine and 2,2’ bipyridine derivatives , pyridyl alcohols, pyridyl oximes, nonpyridyl alcohols, and nonpyridyl oximes .

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43 CHAPTER 2 EXPERIMENTAL TECHNIQUES For a synthetic chemist in a physical inorganic group, it is important to not only be able to perform physical c haracterization techniques but also to understand some underlying theory and understand how the instruments/techniques work in order to trouble shoot any potential issues which may arise during research. For this reason, this chapter is dedicated to such understanding and potential insight for the reader of this document. This is not meant to be an exhaustive account of each technique. 2.1 SQUID Magnetometry 2.1.1 Instrument and sample preparation Super quantum interference device (SQUID) magnetometers are one of the most highly sensitive experimental instruments to detect magnetic moments. Depending upon the setup and capabilities of the instrument, they are used for a variety of applications ranging from detection of changes in magnetic moments within the brain of a mouse to characterization of magnetic materials. The goal of this section is to give a general understanding of how this instrument works, how the data will be plotted , and what information can be obtained from each data set or plot. The super quantum interference devices are amplifiers that are typically used in magnetometers due to their sensitivity to small magnetic fields (~1014 T). SQUIDs are based on Josephson junctions, which consist of two superconducting joints with a weak link that all ows quantum tunneling between the two regions without bulk transport.47 , 48 Typically, Josephson junctions take the form of microbridges made by patterned lithography using niobium or a niobium alloy.49 While Josephson junctions are very sensitive, they must be incorporated in to a larger SQUID circuit to act as a magnetometer. The main components of a SQUID circuit are

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44 the transformer coil which is coupled to the signal co il through a weak link that allows flux coupling. The transformer coil must be large enough to interact with the sample and the signal coil is fabricated symmetrically with a radio frequency (RF) detector coil. Data collection occurs through a multi step p rocess: first, the magnetic sample causes a change in the magnetic flux which induces current in the transformer; second, through mutual induction the changes in the transformer couple directly to the detector coil; and third, the RF voltage across the detector can be measured once it is passed through a conditioning circuit and fit to determine the associated field of the sample.47, 50, 51 The variabletemperature dc and ac magnetic susceptibility data presented herein were collec ted at the University of Florida using a Quantum Design MPMS XL SQUID magnetometer equipped with a 7 T magnet and operating in the 1.8 – 300 K range as well as an AC detection board. The majority of the information given will pertain to the MPMS XL SQUID i nstrument.52 54 A general schematic of a SQUID magnetometer is shown in Figure 21. Sample preparation consists of gently powdering the crystals, weighing a specific mass (1040 mg) of the sample, placing the powder in a gelatin capsule, adding a couple drops of eicosane (to prevent torqueing), placing the other portion of the gel capsule on top, taping (diamagnetic tape) the two parts of the capsule together and placing the gelatin capsule within a commercially available straw which serve as the diamagnetic sample rod. The use of a diamagnetic sample r od such as the commercially available straw allows translation of the sample through the detector coils within the SQUID magnetometer. The diamagnetic background (or contribution) from the straw, tape, gelatin capsule, and eicosane were subtracted based on measurements made on the sample preparation without adding a paramagnetic sample to the capsule (Figure 2 2). Quantum Design magnetometers utilize second derivative transformer coils

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45 to measure sample flux and couple it to the SQUID multi coil system, Fig ure 23. The multi coil system has the advantage of inherent background subtraction of signals with a wavelength longer than approximately 4 cm for dc experiments and 6 cm for AC experiments due to the length of the transformer and the instrumental setup f or the sequence used for the experiment. For example, the extraneous signal (noise) will appear as a positive voltage in the top coil, a negative voltage in the second and third coil, and a positive voltage in the fourth coil which sum to zero and cause no net effect in the signal. Thus, it is a necessity to ensure the sample is centered within the correct area before executing an experimental sequence. 2.1.2 Interpretation of magnetization data Direct current magnetic susceptibility studies tend to give i nformation regarding the nature of exchange interactions and ground state spin, S, Figure 24. Our group and other chemists within the single molecule magnetism community plot these data as MT vs T. Plotting these data as MT vs T is convenient due to the ease with which S can be estimated based on the mathematical relationship shown in Equation 21 = ( ) (2 1) where g is the Land factor, S is the spin ground state of the system. This expression can be s implified for systems with g ~ 2 to E quation 22. = ( ) (2 2) For manganese clusters and any transition metal with less than half filled d orbitals (i.e. d1 d4), g is slightly less than two and any transition metal with dorbitals gre ater than half filled (i.e. d6 d10) will have a g slightly larger than two. An advantage of MT vs T (and M vs T) plots beyond just obtaining the predominate nature of the exchange interactions is the ability to fit the data using the van Vleck19 equation

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46 (Equation 23) when complexes are relatively small or highly symmetric to reduce the number of interactions to a maximum of three. = ( )( ) ( ) ( ) ( ) () ( ) (2 3) ST is the total spin, N is Avogadro’s number, k is the Boltzmann constant, g is the Land factor, is the electron Bohr magneton, and E(ST) is the energy of each ST state. The data is fit to the van Vleck equation to obtain the exchange interactions, J and g. When attempting to fit the data for a large complex, for example, Mn5 with trigonal bipyramidal geometry (Chapter 6) it is necessary to use the Kambe18 coupling method to reduce the equivalent exchange pathways to fewer number of terms in the van Vleck equation. The van Vleck equation is unique to the geometry, number of metals and the spin of each metal. Once a reasonable fit has been obtained, it is possible to rationalize the ground state spin, determine the energy of each ST, and plot the energies of the spin states versus the ratio of J/J to determine how the ratio affects the spin state as shown in Figure 2 5. The sensitivity of the ground state to this ratio is discussed further in Chapter 3. Reduced magnetization studies can provide information about the ground state spin and the magnitude of the zero field spl itting parameter, D. These experiments are variable temperature measurements carried out at variable fields and typically plotted as M/N B vs H/T. The experimental data are fit by diagonalization of the spin Hamiltonian matrix, assuming only the ground sta te is populated, incorporating axial anisotropy ( D z 2) and a Zeeman term, and employing a full powder average: = D z 2 + g B0 (2 4)

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47 When isofield data are superimposable, this is indicative of a ZFS parameter, D, close to zero (Figure 2 6, right). Conversely, if isofield lines have gaps between them, it is indicative of a larger D value , low lying excited states, or intramolecular interactions (Figure 2 6, left). Poor RM fits become a problem in manganese chemistry, for example, when: Mnx complexes are of high nuclearity, one or more MnI I ions are present, and/or spin frustration effects are present. When Mnx clusters are of high enough nuclearity, there is a high density of spin states resulting from the exchange interactions among t he man y constituent Mn ions. MnII ions typically give very weak (and usually antiferromagnetic) exchange interaction’ s and thus small energy separations between the different spin states. Spin frustration effects by definition are competing antiferromagnetic exchange interactions within triangular subunits , which can lead to small energy separations between different spin states. As a result, there are many excited states that are low lying in energy (relative to kT), which can make it difficult to reliably obtai n the ground state S from dc magnetization measurements (i.e. RM fits). Another potential problem occurs when low lying excited states have a larger spin than that of the ground state. In the presence of a large enough dc field, ms components of the excited states can approach in energy the lowest lying ms of the ground state or even cross below it in energy which can result in the incorrect determination of the ground state, S, (Figure 2 7). This is due to the relationship between the energy, ms, and field which is described in Equation 25. E = msBH (2 5) For example, in Figure 24, if S = 6 is the true ground state and S = 10 is the first excited state, if the dc field is large enough then the first excited state will become lower in energy than the ground state (Figure 21). The fit would incorrectly determine the S =10 to be the ground state due to the ms = 10 component of the S = 10 state being at lower energy.

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48 Two methods are typically used to determine the spin gr ound state S in the presence of low lying excited states: ac susceptibility measurements and low field RM. In an alternating current (ac) magnetic susceptibility experiment, magnetization is measured in a zero dc field and in the presence of a weak ac fiel d (typically 3.5 G), oscillating at a particular frequency, Equation 25. H(t) = h*cos( t) (2 5) where H(t) is the oscillating field, H(t) induces a time variation of the magnetization which is described by Equation 26. M(t) = m*cos( t) (2 6) An assembly of electron spin magnetic moments may not always be capable of immediately following the changes of this external ac field and there can be a phase shift between M(t) and H(t) due to relaxation effects which can result in a sample response, Equation 27. M(t) = m*cos( t ) (2 7) is the phase angle by which the magnetization lags behind the oscillating component of the magnetic field (Figure 2 8). Rewriting equation 2 6 using the identity, cos (a b) = cos(a)cos(b) + sin(a)sin(b) results in Equation 2 8. M(t) = m*cos( )cos( t) + m*sin( )sin( t) (2 8) Then, if we divide through by h and remember that = m/ h, where m is the magnetization and h is the field, then Equation 28 becomes Equation 29. = cos( t) + sin( t) (2 9) where is the in phase response since it varies in phase with the driving field (cos( t)) and is the out of phase response since it varies out of phase with the driving field (sin( t)). These are usually referred to as real and imaginary components respectively, = – i .

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49 (the spin vectors are aligned with the oscillating field) , the inphase ac susceptibility is equal to the dc susceptibility ( M = M ). Thus, f rom a plot of the M T vs T data the following information can be obtained by extrapolation of the data to 0 K, from temperatures above 4 K avoid the effect of we ak intermolecular interactions ( dipolar and super exchange ) to corroborate the ground state estimated from the T plot . The slope of the data from 15 to 5 K (or the temperature where the slow reversal of magnetization appears in the data) gives information regarding the population of the ground state (Figure 2 9). If the data has zero slope, this is indicative of a wellisolated grou nd state which means that a good fit of the reduced magnetization data can most likely be obtained. Remember, the fits of RM data assume only the ground state is populated. If the M T vs T data displays a large slope (negative or positive) to the data, th is is typically an indication of thermally populated low lying excited states which makes fitting reduced magnetization data very difficult or impossible. At low temperatures, if a frequencydependent decrease in M T (in phase) and a concomitant rise in (out of phase) are present in the data, this is indicative of a significant barrier (i.e. the barrier is larger than kT) of the magnetization vector which is a property of an SMM (Figure 2 10). Similar phenomena are observed without frequencydependence in materials with long range ordering. An Arrhenius plot is necessary to quantify the effective barrier. Data collection at multiple frequencies is necessary to construct the Arrhenius plot to determine the effective energy barrier, Ueff, which is typically different than the theoretical energy barrier. To construct an Arrhenius plot to determine the relaxation rate (1/ where is the relaxation time) it is necessary to plot the M value at the peak maxima for all frequencies of the oscillating field versus the inverse of the temperature at the peak maxima (Figure 2 11). The peak maximum for

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50 each frequency is the point where the relaxation rate is equal to the angular frequency (2) of the oscillating ac field ; thus, the data can be fit to the Arrhenius Equation 210. 1/ = (1/ 0)exp( Ueff/kT) (2 10) The theoretical energy barrier (U) is equal to S2|D| for whole integer spin systems and (S21/4)|D| for half integer spin syst ems. The experimental energy barrier (Ueff) is typically lower due to the presence of quantum tunneling of the magnetization in SMMs. For a single relaxation process which is typical of molecular magnets due to their relatively similar environments, the and behavior is a function of angular frequency, which can be seen in Equations 2 11 and 212, respectively, ( ) = + ( ) (2 11) " ( ) = ( ) (2 12) where S ( ) is the adiabatic susceptibilit y, T ( is the magnetization relaxation time. The dc susceptibility corresponds to the isothermal susceptibility when paramagnets obey the Curie Law. A distribution of relaxation processes is typically caused by a distribution of molecular environments in the crystal which is associated with a range of Ueff barrier heights. The modified expressions for a distribution of relaxation processes are shown in Equations 213 and 214 ( ) = + ( ) ( ) ( ) ( ) ( / ) ( ) ( ) (2 13) " ( ) = ( )( ) ( ) ( ) ( ) ( ) (2 14)

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51 where has a value between 0 and 1 and gauges the width of the distribution. When equals zero (i.e. no distribution), Equations 213 and 214 are reduced to Equations 211 and 212, respectively. In order to determine if a sample has one or more relaxation process, data is collected at different frequencies at a several temperatures centered on the temperature where the maximum peak height was observed in the vs T plot. Then, the data is plotted as ( and ( ) and fit to the previous equations (Equations 211, 212, 213, and 214) determine if there is a single relaxation process or a distribution of single relaxation processes. Another method to determine if there is a single species (or environment) is to use ac data to make a versus plot which is known as a Cole Cole or an Argand plot by plotting the data as versus temperature (T) to see h ow the distribution ( ) changes with change in temperature (Figure 2 12).16, 55 A symmetric shape to the Cole Cole plot suggests a single environment or species present in the sample. The steeper the slope of the data in the ColeCole plot the greater the distribution of environments with change in temperature. An alternative method to quantify the energy barrier and relaxation time for complexes in the absence of peak maxima (i.e. tails in the out of phase) is to apply Equation 215 recently developed by Bartolom et al. This method is not as accurate as the previously discussed method; however, it provides an approximate value for the energy barrier and relaxation time (Figure 2 13). ln " = ln ( ) + (2 15) The most accurate method for determining re laxation time and energy barrier when only a ‘tail’ is observed in the M vs T plot is using a microSQUID. Micro SQUID measurements are carried out on a single crystal instead of a microcrystalline powder. Magnetization vs time decay

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52 studies are carried out on a sample by first saturating the magnetization in one direction at ~5 K with a large applied dc field, the temperature is then decreased to a chosen value, and the field is removed and the magnetization decay is monitored with time. From these measu rements an Arrhenius plot can be constructed (as discussed previously) and fit to complement the ac out of phase data to confirm the effective energy barrier. When a sample is believed to be a single molecule magnet, micro SQUID measurements can confirm the hypothesis through the observation of hysteresis loops in the magnetization vs. dc field scans. Typically, SMMS display a temperature dependence and scan rate dependence of their hysteresis loops with increasing coercivity with decreasing temperature and increasing scan rate (Figure 2 14, right). For SMMs, it is typical to see steps in the hysteresis loops at periodic values of applied field due to quantum tunneling of the magnetization (QTM), which is caused by an increase in the relaxation as the Ms l evels on the opposite sides of the energy barrier come in to resonance at those field positions (Figure 2 14, left). The field separation, H, between the steps is proportional to D and is given by equation 216 H =| D |g B (2 16) It is possible to corroborate the D value determined from magnetization data by using the H value to determine D and assuming g = 2. With whole integer spins, the first step tends to appear at zero applied field where half integer spin ground states tend not to show a ste p at zero applied field. This is due to the spinparity effect in half integer spin system which leads to Kramer’s degeneracy where QTM is allowed in integer spin systems.56 It is still unusual to see no indication of a step though because it is impossible to guarantee that there is absolutely zero external field. For example in manganese, the dipolar fields of neighboring molecules and

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53 hyperfine fields from the 55Mn nuclei ( I = 5/2, ~100 % natural abundance) provides means for quantum tunneling of the magnetization to occur at zero apparent applied field.57 2.2 Electron Paramagnetic Resonance Electron paramagnetic Resonance (EPR) is a spectroscopic technique for studying the interactions of magnetic moments and their environments including external applied magnetic fields. Materials without at least one unpaired electron are known as EPR silent. There are many parallels between the main concepts of the more popular technique nuclear magnetic resonance (NMR) and EPR except in EPR unpaired electrons are excited instead of the nuclei. EPR uses microwave radiation (10 GHz – 1 THz) as a magnetic dipole transition source.58 EPR experiments require that the external magnetic field breaks the degeneracy of the spin states which is not required in other optical spectroscopy methods. A typical EPR experiment sweeps the magnetic field and holds the microwave at a fixed frequency using a narrow band resonant c avity. The application of the resonant cavity increases sensitivity of the signal during measurements. Frequency sweep experiments are possible; however, there are problems with sensitivity due to small quality factor, Q, poor signal to noise ratio and var iation of the detected power. The origin of an EPR signal is most easily understood in the case of a single electron with a spin quantum number, S = with components of ms = + . A pictorial form of the following description is found in Figure 215. In the absence of a field the two m s states are degenerate (of the same energy); however, when an external field is applied with strength B0 the electron’s magnetic moment aligns with the field (either parallel or antiparallel). Each possible alignment has a specific energy given by Equation 217. E = msgBB0 (2 17)

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54 where g is the Land factor and B is the Bohr magneton. Thus, the separation between the two states is E = g BB0 (2 18) Equation 2 18 implies that the energy gap is proportional to the strength of the applied field. Electrons can move between the two energy levels by either absorbing or emitting a photon of energy h (h = Planks constant) where the resonance condition, E = h . Combining Equations 2 17 and 21 8 gives the fundamental equation for electron paramagnetic resonance spectroscopy. gBB0 (2 19) When the applied external field is increased until the gap between the energy states matches the energy of the microwaves, the electrons can move freely between the two states. Since there tends to be a higher population of electrons in the lower energy st ate due to the Boltzmann distribution there is a net absorption of energy. The net absorption it detected and converted into a spectrum. The focus of EPR spectroscopy is on the unpaired electrons and the change of states of those electrons; however, the interaction between an unpaired electron with nearby nuclear spins results in additional energy states and a multiline spectrum for a single electron system. The spacing between the spectral lines gives an indication of the degree of interaction between t he unpaired electron and the nuclei. This is known as the hyperfine interaction and has two common mechanisms, Fermi contact and dipolar interactions. The former is independent of sample orientation and typically applies to isotropic interactions. The latter is dependent on sample orientation and typically applies to anisotropic interaction. Different letters are employed for the

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55 two types of hyperfine coupling constants, a or A is used for isotropic (symmetric) interactions and b or B is used for anisotropic interactions.59 In many cases, it is possible to predict the number of lines with Equation 2 20, 2MI + 1 (2 20) where M is the number of equivalent nuclei, and I is the nuclear spin. The intensity of the peaks follow Pascal’s triangle, for example, a triplet will have an intensity ratio of 1:2 :1. Highfrequency EPR (HFEPR) can be used to determine many physical parameters for transition metal complexes; however, typical parameters obtained for singlemolecule magnets are ground state spin, S, the zero field splitting parameters , which are the s ame axial ZFS parameter in the spin Hamiltonian of Equation 24 with an additional the rhombic zerofield splitting parameter, E , and exchange couplings, J. Equation 24 becomes Equation 221 with the additional term for the rhombic zerofield splitting p arameter, E . = + + (2 21) The analysis of EPR spectra for highspin complexes can provide precise information such as the exact value of the groundstate spin the magnitude and sign of D 60, 61 the location in energy of excited spin states relative to the ground state 62, 63 and most importantly, information concerning transverse spin Hamiltonian parameters e.g., the rhombic E term 64. However, the (2 S+1) fold energy level structure associated with a large molecular spin S necessitates EPR spectroscopy spanning a wide frequency range . Furthermore, large ZFS due to the significant anisotropy and large ST values demand the use of frequencies and magnetic fields considerably higher ( 50 GHz to several hundred GHz, up to 10 T) than those typically used by th e majority of EPR spectroscopists.

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56 2.3 X Ray Crystallography Single crystal x ray crystallography is a powerful tool for the identification of the arrangement of atoms contained within a crystal and ultimately the structure of the individual molecules wi thin the crystal. X ray crystallography is a method where a beam of xrays bombard a crystal and diffracts into many specific directions. A simple schematic of a x ray diffractometer is shown in Figure 216. A crystallographer can use the intensity and angles of the diffracted beam to produce a three dimensional picture of the electron density within the crystal. By mapping these electron densities, the average positions of the atoms can be determined as well as their connectivity (bonds), disorder, and ot her crystallographic information. In order for the method to work, it must follow Bragg’s law, meaning that constructive interference only occurs for certain values of theta correlating to a (hkl) plane, specifically when the path difference is equal to n wavelengths (Figure 217). Mathematically, it is as follows that (using definitions from Figure 2 17): AC + BC = n (2 22) sin = ( 223) Therefore, after substitution the previous become Equation 224 = sin (2 24) And for diffraction to occur Equation 226 must be true. 2 = (2 25) = 2 sin (2 26) X ray diffraction experiments or measurements are made by mounting a crystal on a goniometer and systematically rotating the crystal whil e it is being bombarded by xrays produced by either a molybdenum or copper source. The spots that make up the diffraction

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57 pattern are known as reflections. The reflections collected from different rotations are converted to a three dimensional model of el ectron density data and chemical data known about the sample using Fourier transforms. Crystal quality and size are very important to the resolution of this method. If single crystal quality or size is an issue there are other x ray methods which can be ap plied to gain information albeit much less informative such as powder diffraction, small angle xray scattering and fiber diffraction. Single crystal x ray crystallography has been fundamental in the development of certain research areas due to many types of materials forming crystals such as salts, minerals, metals, and various inorganic, organic and biological molecules. Initially, xray crystallography was used to determine the size of atoms, lengths and types of bonds, and differences in similar materia ls, for example, different alloys. This method has revealed the structure and function of many biomolecules such as DNA and the activesite of the oxygenevolving center (OEC). As will be found throughout this dissertation, xray crystallography is the main method for atomic structure determination of new materials and subtle differences in similar materials that otherwise would not be seen in other experiments. X ray crystal structures can be useful for understanding observable physical properties. 2.4 Ele mental (or CHN) Analysis Carbon, Nitrogen, and Hydrogen percentages were determination through combustion analysis at the in house spectroscopic service facilities at the University of Florida. A sample of known mass (~ 13 mg) is placed in the furnace and heated in the presence of oxygen gas (Figure 216). Through combustion the carbon, hydrogen, and nitrogen present in the sample react with molecular oxygen and form carbon dioxide (CO2), water (H2O), and nitrogen dioxide (NO2), respectively. The resulting gases pass through a series of absorption columns which selectively trap CO2, H2O, and NO2. Once these gases are trapped, the columns are heated in series to allow

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58 the captured amount of each substance to be measured separately for determination of the mass percent of each component present in the sample. Using the mass percent components present in the sample, it is possible to determine the exact composition of powder samples used for magnetization experiments which relies on a precise calculation of the molecular weight. 2.5 Fourier Transform Infrared Spectroscopy (FT IR) Fourier transform infrared (FT IR) spectroscopy, in the middle of the light spectrum, measures the absorbance of infrared light by investigating how the light interacts with the sample (matter) between 4000 cm1 and 400 cm1.65 As with all spectroscopic methods, FT IR spectroscopy is sensitive to transitions between discrete energy levels of materials being irradiated with light. The energy levels can correspond to either electronic or vibrational modes; how ever, vibrational modes are the main focus of this work due to their accessibility and interest. When the frequency of the infrared is same as the vibrational frequency of a bond then an absorption occurs. All measurements were performed on a midinfrared Nicolet Nexus 670 FT IR spectrometer with an OMNIC software interface located in CLB Room 400. Crystal samples were lightly ground with a mortar and pestle with potassium bromide (KBr) and pressed into KBr pellets. Infrared spectrometers are based on interferometers which consist of a broad band source, beam splitter, fixed mirror, movable mirror, sample and detector, Figure 2 17. The spectral range of 4000 cm1 to 400 cm1 is largely a function of the movable mirror. Fourier transform spectroscopy consists of sending a pulsedsource of radiation (i.e. laser) with many frequency components through the sample which is detected as a time domain or the movable mirror position domain. The spectrum is finally obtained in the frequency domain once a Fourier transform is performed on the time domain data. Typically, FTIR spectra are used to determine if ligand incorporation occurred; however, the area of interest is system specific such as a sharp

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59 band at ~2100 for azides and cyanides, broad stretch ~3300 for alcohol or carboxylate containing ligands, and complexity of the metal oxo region 600400 cm1. 2.6 Ultr aviolet and V isible (UV VIS) Spectroscopy Ultraviolet and visible (UV Vi s) spectroscopy uses the region of the electromagnetic spectrum (200 nm – 800 nm) where the energy is concomitant with electron transitions of molecules and complexes. Transition metal complexes usually show d d transitions, ligand to metal charge transfer (LMCT) or metal to ligand charge transfer (MLCT) bands in their UV Vis spectrum. UV Vis spectroscopy probes energy scales of approximately 6.21 to 1.24 eV which is the range typically related to the energy separating multi electron energy levels.66 A typi cal spectrophotometer comprises a source, monochromator, sample space, photodetector, and computer interface, Figure 2 18. All absorption spectra were acquired using a JASCO V 570 UV/VIS/NIR spectrophotometer (Figure 2 19) with a halogen lamp and a deuteri um lamp and a single monochromator which covers a wavelength range from 1902500 nm. The monochromator features duel gratings that are automatically exchanged, 1200 groves/mm for the UV/VIS region and 300 grooves/mm for the near infrared (NIR) region. A photomultiplier (PM) tube detector is used for the UV VIS region and PbS detector is used for the NIR region. Both gratings and detectors are automatically exchanged within a selectable 750 900 nm range. Step compensation is used to smooth the transition to the baseline during grating/detector changes. Spectral Manager is the software interface used for experiment setup and data collection. This instrument is a double beam instrument which allows for easy background subtraction due to one cuvette holding the “blank” which is the exact sample preparation as the sample of interest minus the species of interest. For example, the “blank ” cuvette holds only solvent and the “sample” cuvette holds the solvent and the material of interest. The data were collected at r oom temperature and measured in one centimeter length quartz cuvettes. The main use of UV VIS

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60 spectroscopy in the Christou lab is to determine if our complexes decompose in solution or remain intact. Three or more concentrations of the complex in solution are measured and the absorbance of the signal is compared for all concentrations according to the Beer Lambert Law, Equation 227. A = bc ( 227) Where A is absorbance, e is the extinction coefficient, b is the path length, and c is the concentr ation. For example, if solutions of concentrations of 1, 2, 4, and 8 mM were measured, if the complex stayed intact then the absorbance would be expected to double as the concentration doubled (i.e. 1 mM to 2 mM, 2 mM to 4 mM, ect.).

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61 Figure 21. Schematic of a SQUID magnetometer.

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62 Figure 22. Photographs of sample preparation stepwise (a d) and a completely prepared sample in a straw (e). Not shown: needle holes being poked into the straw and the action of taping gelatin capsule and the end of t he straw.

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63 Figure 23. Schematic of centering a sample in the coils (top) and photograph of software after performing automated centering of a sample (bottom).

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64 Figure 24. Examples of MT vs T plots, (left) demonstrates predominate antiferromagnetic in teractions and (right) demonstrates predominate ferromagnetic interactions. Figure 25. Example of an E(STa triangular Fe3+ 3 complex.

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65 Figure 26. Plot s of reduced magnetization ( M / NB) vs H / T . The solid lines are the fit of the data . Figure 27. Energy diagram of two states with increasing field.

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66 Figure 28. Schematic of the oscillating field with the lagging magnetic moment from the material (i.e. single molecule magnet) . Figure 29. Examples of inphase M T vs T plots, (left) wellisolated ground state and (right) not a well isolated ground state.

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67 Figure 210. Examples of out of phase M vs T plots, (left) peaks in the out of phase just beginning resulting in a “tails” and (right) full outof phase peaks. Figure 211. Example of an Arrhenius plot.

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68 Figure 212. Argand (or Cole Cole) plots of vs for wet crystals of the complexes [Mn12O12(O2CC6F5)16(H2O)4]z+ : z = 0 at 4.0 K (top), z = 1 at 3.4 K (m iddle), z = 2 at 2.2 (bottom) . The dashed line in each is the least squares fit of the data to a single relaxation process as described in the text. The solid line is the fit to a distribution of single relaxation processes also described in the text. Rep rinted with permission from Royal Society of Chemistry.16

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69 Figure 213. Example of a ln " plot. 1/T (K-1) 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 ln ( M"/ M') -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 1000 Hz 500 Hz 250 Hz 100 Hz 50 Hz 10 Hz 5 Hz

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70 Figure 214. Plot showing the allowed, quantized spin states, Ms, of the spin vector of a molecule with S = 10 like Mn12O12(O2CR)16(H2O)4 (top left). An alternate figure which depicts a similar situation to the previous incorporating the barrier to spin reversal, U, and includes the relative energies of each state (bottom left). Magnetization ( M ) hyster esis loops for a single crystal of [Mn12O12(O2CC6F5)16(H2O)4]3CH2Cl2 showing the dependence at a fixed sweep rate (top right) and the sweep rate dependence at a fixed temperature (bottom right). Reprinted with permission from the Royal Society of Chemistr y. 16

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71 Figure 215.Energy level diagram for the Zeeman and hyperfine splittings of an S = spin on a nucleus with I = 1. Selection rules require that only one quantum number changes during the transition so the ms number changes while the mI number remains constant resulting in the three possible transitions illustrated.

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72 Figure 216. Schematic of a single crystal X ray diffractometer. Figure 217. Bragg’s Law as it relates to x ray diffraction.

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73 Figure 218. CHN combustion analysis instrument illustration. Figure 219. Schematic of the functional parts of an FT IR spectrometer.

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74 Figure 220. Schematic for a double beam UV VIS spectrometer.

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75 C HAPTER 3 SPIN FRUSTRATION EFFECTS AND AN INTERMEDIATE S = 3 GROUND STATE IN AN FE6 CLUSTER: A QUANTITATIVE SPIN FRUSTRATION SCALE 3.1 Introduction Polynuclear complexes of oxobridged Fe3+ ions are relevant to at least two important areas of study: bioinorganic chemistry and nanoscale magnetism. Many proteins a nd enzymes implicated in important biological processes have active sites containing oxo bridged iron ions. Examples include hemerythin, ribonucleotide reductase, and methane monooxygenase, all with diferric active sites6769. In contrast, t he protein ferritin is implicated in iron storage and recovery processes, may contain up to 4500 Fe3+ ions70, 71. Other polynuclear i ron complexes, such as [Fe8O2(OH)12(tacn)6]8+ 72 , 73 and [Fe4(OMe)6(dpm)6]74(tacn = triazacyclononane, dpm = dipivaloylmethane), are single molecule magnets (SMMs) which display slow reversal of magnetization due to large negative zerofield splitting and a high spin ground state. These compounds allow study of magnetism on a quantum scale, and could be used in a variety of applications ranging from nanoscale digital memory storage to quantum computers. For 3d metals with no first order angular momentum, s ingle molecule magnetism requires a large negative zero field splittin g parameter, D, and a nonzero ground state spin, S. Iron(III) seems like a great candidate to form good single molecule magnets (SMMs) because each Fe3+ ion has five unpaired electrons ( S =5/2). However, highspin iron(III) ions display very strong antiferromagnetic coupling which causes an antiparallel alignment of the spins resulting in many complexes with an S = 0 ground state.7581 Iron(III) complexes with high enough Fex nuclearities and topologies that contain triangular subunits can lead to competing exchange interaction s which do not allow the spins to align in their preferred orie ntations and can occasionally result in higher ground spin states. This phenomenon is termed spin frustration and has recently become of great interest in single molecule magnetism, specifically for investigating

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76 the structural and electronic contribution s within a molecule. Previously, there have been many ways to describe a ‘frustrated’ complex or pathway; however, there has not been a clear way to quantify the amount of spin frustration found within a pathway or complex. A universal quantifiable descrip tion of spin frustration has become necessary to be able to clearly compare different pathways and/or molecules , just as it was necessary to find a way to compare nuclear magnetic resonance spectra across research groups and facilities. As was discussed in Chapter 1, theoretical calculations can be used to determine the value of exchange couplings in complexes that are too cumbersome to fit the experimental data. Additionally, expectation values B AS S (where A and B refer to magnetic center s) are calculated for spin states obtained from the Heisenberg Spin Hamiltonian (HSH) . This is useful because the product B A ABS S J 2 is the contribution to the total energy of a spin state made by the A B exchange pathway. Since JAB indicates the preferred alignment of spins while B AS S represents the actual alignment, if they are different in sign, the A B pathway is frustrated. On this basis, spin frustration has been defined as an increase in the energy of a spin state due to a spin alignment across an exchange pathway that is opposite to the preferred alignment. In this chapter, the structure and properties of an Fe6 complex with an S =3 ground state, [Fe6O2(hmp)10(H2O)2](NO3)4 ( 31 ) (where hmpis the anion of 2(hydroxymethyl)pyridine), that inspired this work will be described. The quantitative rationalization of an unusual S = 3 ground state using the results from the ZILSH semiempirical method through analysis of the exchange (J) and spin couplings ( BASS ) , along with the sensitivity of the ground state to subtle changes in the J/J exchange coupling ratio, will be explored . Finally, a new way to quantitate spin frustration and how it can be used will be described. This should prove extreme ly

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77 useful in the future for predicting and/or rationalizing the magnetic properties of new polynuclear Fe(III) complexes, and how those properties might be affected by structural changes. 3.2 Experimental Section 3.2.1 Complexes studied [Fe6O2(hmp)10(H2O)2](NO3)4 ( 3 1 ): Complex 31 is comprised of six Fe3+ ions in a chair confirmation and can be described as two triangular [Fe3( 3O2 -)] units joined together at their bases to form a central rectangle (Figure 3 1) ; e ach connection Fe 2 / Fe 3 and Fe 2 / Fe 3 is by two bridging hmpalkoxo groups. The two Fe3O triangular units are related by an inversion center. Each Fe3O triangular unit is scalene but is almost isosceles with two relatively similar Fe Fe distances and one different Fe Fe distance (Fe1 Fe 2 = 3.064 , Fe 1Fe 2 = 3.030(2) , Fe 2Fe 3 3oxide only slightly out of the Fe3 plane by 0.004 . The two similar sides of each isosceles triangle are each bridged by one hmpalkoxide that chelates to an Fe atom that is at the base of the triangular unit. The local octahedral geometry is completed by a chelating hmpgroup and a terminal H2O on Fe 1 and Fe 14 rectangle is particularly distorted with angles of the cis and trans ligands ranging from 73.2 to 111.6, and 148.7 to 167.6, respectively. It is of great relevance to the magnetic properties of 31 to compare its structure with those of other [Fe6( 3O)2( OR)8]6+ complexes in the literature with the same or very similar core. The dc magnetic susceptibility plot of complex 31 indicates an S = 3 ground state and the ac magnetic susceptibility plot confirms the spin ground state.82 As was previously stated, it is not inherently obvious how to explain the S =3 ground state of this complex. [Fe6O2Cl4(hmp)8](ClO4)2 ( 32 ).83 The structure of complex 32 is similar to that of 31, 31 each possess a chelating hmpand a terminal H2O, whereas these atoms in 32 each possess only two terminal Clions and are thus five -

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78 coordinate. A more complete comparison of these two complexes is provided in Table 31, with reference to Figure 3 1. [Fe6O2(OH)2(O2CBut)10(hep)2] ( 33 ). Complex 33 can be described as two Fe33O) triangular units fused at two apex forming an almost planar core. Each Fe33O) is linked by two bridging carboxylate groups and one hydroxide, the Fe O(H) Fe angle was determined to be 121.6 (Figure 32). E ach oxide in the center of the Fe3 triangular unit is out of the plane by 0.2 are asymmetric linkages in each Fe3 O2CRO2CRalkoxide from the hepligand as 3oxide. The nonplanari ty of the Fe6 core is caused by the presence of intramolcular hydrogen bonds between the hydrogen of the bridging hydroxyl group and one of the oxygen atoms from the distal carboxyl group. [Fe6O2(OH)(O2CBut)9(hep)4] ( 34 ). Complex 34 can be described as a twisted boat Fe6 core made up of two Fe3O triangular units. The triangular units, Fe1Fe2 Fe3 and Fe4Fe5 Fe6, 3oxide is slightly out of the plane in both triangular units, tter. There is a mirror plane, which cuts through the hydroxide bridge between Fe1 and Fe6 and the two carboxylates bridging Fe3 and Fe4, making Fe3 and Fe4, Fe2 and Fe5, and Fe1 and Fe6 equivalent (Figure 33). Fe1 and F2 are bridged by carboxylate s. While these descriptions point out the differences, complexes 33 and 34 are very similar to one another, in complex 33 the alkoxo bride is trans and the alkoxo bridge is cis in complex 34.

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79 3.2.2. Computational Studies Theoretical calculations were carried out on complex 31 with the ZILSH method34 to provide independent estimates of the constituent exchange constants. The complex has fifteen pairwise exchange constants, so together with the spinindependent term E0 there are sixteen unknown parameters to be solved for in E quation 31. = 2 (3 1) Calculations were thus performed for sixteen spin components, including the “high spin” (HS) component with all unpaired spins parallel , and all unique components in which the unpaired spins on two metal ions were reversed (antiparallel) relative to all others (i.e., spins of Fe1 and Fe2 reversed, spins of Fe1 and Fe3 reversed, etc.). Calculated energies and local spin densities found for these components are given i n Table 32. The HS component is substantially higher in energy than the other components, indicating the presence of antiferromagnetic interactions in the complex. The spin densities are close to the formal value of five expected for highspin d5 Fe3+ io ns but are reduced below this number by spin delocalization, as found with ZILSH for other complexes of Fe3+ ions.81, 8487 The signs of the local spin densities indicate the relative directions of spin moments of the iron ions, and demonstrate that correct spin distributions were obtained for each spin component. The spin couplings BAS S UHF found from ZILSH wavefunctions with the local spin operator (Table 3 3) also have values close to 5, similar to those obtained from ZILSH calculations on other polynuclear Fe3+ complexes.81, 8488 3.2.3 Method for Calculating Percent Spin Compensation Initially only the exchange interactions between two Fe3+ ions were considered due to the commonly occurring antiferromagnetic interactions and the common triangular units. The range of possible spin couplings obtained from all allowed spin orientations fr om completely frustrated

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80 to completely satisfied is 15 for two Fe3+ or any high spin d5 metal ion. However, the midpoint (50% frustration) is not at absolute zero as seen in Figure 3 4. To overcome the asymmetric distribution of the values about the midpoint, the B AS S calc is divided by the maximum BAS S max. The ratio is divided by two because this only represents half of the total range. The decimal is then multiplied by 100 to express the value as a percentage. These steps are represented in E quation 33 for percent frustration. Equation 34 can be used to calcula te the percent frustration and E quation 35 can be used to calculate the percent satisfaction . Regardless of the equation used the same results are obtained. The midpoint issue is eliminated by addressing one side at a time and using the ratio of the calculated spin coupling, BAS S calc over the absolute value of the maximum spin coupling, BASS max. The decision as to which val ue to use is based on the sign of BASS calc. If the value is positive, B AS S max is equal to +6.25 and if the value is negative, BASS max is 8.75. % = = + % (3 3) Simplifying E quation 33, we are left with E quation 34. % = = | | + % (3 4) In addition, the sign of B AS S calc resolves the issue of whether the second half should be added or subtracted in each E quations 34 and 35. % = = % | | (3 5)

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81 It is the author’s belief that the majority of the time the quantification will be represented as percent frustration; however, due to the nature of the equation it is possible to also state the values as percent satisfaction. 3.3 Results and Discussion 3.3.1 Summary of Experimental Studies The structure of 31 is shown in Figure 35 along with the exchange pathways with significant magnetic interactions. C omplex 31 is centrosymmetric with an inversion center. The exchange constants can thus be appropriately grouped into J1, J2, J3, and J4 as shown in Figure 35. The structure comprises six Fe atoms in a chair conformation. It is of great relevance to the magnetic properties of 31 discussed previously to compare its structure with those of other [Fe6( 3O)2( OR)8]6+ complexes in the literature with the same or a very similar core ( Table 3 4). In fact, there are several structural classes of FeIII 6 clusters that have been reported to date, differing in the Fe6 structural topology. These have been conveniently referred to as (a) planar, (b) twisted boat , (c) chairlike, (d) parallel triangles, (e) octahedral, (f) fused or extended butterflies, (g) cyclic, and (h) linkedtriangles. As can be anticipated, and as will be of interest to the magnetic arguments to follow, these different Fe6 topologies have le d to a variety of ground state spin S values among these complexes. In order to allow for a convenient structural and magnetochemical comparison, these data for FeIII 6 complexes are collected in Table 3 4, together with their cores, the structural class they belong to, and their resultant ground state S values. As can be seen in Table 3 2 , there are only two known examples of FeIII 6 complexes of class c), i.e. possessing a chair like Fe6 topology; these ar e complex 31 and [Fe6O2Cl4(hmp)8](ClO4)2 ( 3 2).83 The structure of complex 32 is similar to that of 31, except that the end Fe atoms Fe 1 and Fe 1 of 31 each possess a chelating hmpand a terminal H2O, whereas these atoms in 32 each possess only two terminal Clions and are thus five coordinate.

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82 Examination of Table 3 2 shows that an S = 3 ground state for an FeIII 6 complex is very rare. By far, m ost of the complexes for which the ground state spin has been determine d have an S = 0 or S = 5 ground state. In fact, it is not intuitively obvious how an S = 3 ground state could arise for an FeIII 6 complex, since it is clearly not the resultant of simple considerations of spin up and spindown alignment possibilities . The usual qualitative rationalization in such cases is to say that spin frustration effects must be operative within the Fe3 triangular subunits. Spin frustration is here defined in the more general, chemical sense as the presence of competing exchange inter actions of comparable magnitudes that prevent (frustrate) the spin alignments preferred from the nature (ferro or antiferromagnetic) of the exchange interactions between them. Thus, the qualitative argument would say that intermediate spin alignments ( MS = 2 3 , 21 for highspin FeIII) are present at some number of the Fe atoms and this gives the observed S = 3 ground state. While such qualitative arguments are undoubtedly correct, they are less than satisfying. The other complex in class c), [Fe6O2Cl4(hmp)8](ClO4)2 ( 32 ), was also found to have an S = 3 ground state.83 Seeking to understa nd the origin of this ground state, the authors carried out computational studies using irreducible tensor methods to obtain the various pairwise Jij exchange parameters for each FeiFej pair and thus rationalize the S = 3 ground state. However, these calculations led to a predicted S = 0 ground state for 3 2, in conflict with the experimental data. The authors suggested several reasons for this discrepancy, but the bottom line is that the origin of the unusual S = 3 gr ound state for this class of FeIII 6 complex has yet to be satisfactorily explained at a quantitative level. In order to do so for our present complex 31, and by extension for 32, we have carried out computational studies on complex 31 using the ZILSH me thod.

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83 3.3.2 Computational Studies Nonzero exchange constants obtained from the data of Table 31 are presented in Table 35. Trends in the 3oxo bridged triangular subunits of 31 (J1, J2, and J3) follow magnetostructural correlations established for oxomediated interactions between Fe3+ ions,89 with stronger antiferromagnetic coupling accompanying larger Fe O Fe bond angles and shorter Fe O bonds in the oxobridged pathways ( Tab le 3 5). This is especially evident for the J3 pathway, which has a much larger bond angle and shorter average bond distance than the J1 and J2 pathways, and hence a much larger exchange constant. The J4 pathway which is mediated exclusively by alkoxide moieties of hmp does not follow this trend, having a larger exchange constant despite its smaller average bond angle and longer average bond distance than the J1 and J2 pathways. This could indicate that the ZILSH method treats exchange interactions media ted by substituted oxide ligands less accurately than it treats interactions mediated by unsubstituted oxide ligands. Whether that eventually proves to be the case or not, the J4 interaction does not influence the ground state spin of 31 or 33, as thor oughly discussed in reference 30.90 These calculations were first carried out with exchange constants obtained from ZILSH as the initial step in fitting the MT data which gave the ground state spin of 31 as S = 3, in accord with, along with the ground s tate spin of 33 as S = 5 and ground state spin of 34 as S=0.90 Repeating the spin eigenstate calculations with the exchange constants obtained empirically gave the same result: complex 31 has a S = 3 ground state, while complex 33 and 34 have a S = 5 and S = 0 ground state, respectively and in agreement with all relevant experimental magnetic data on the complexes. Ground state properties computed for 31, 33,

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84 and 34 with exchange constants obtained from either ZILSH calculations or empirical fits are gi ven in Table 3 5. In previous work our group has considered the spin couplings BASS found for the ground state of a complex by diagonalizing the HSH as an indicator of spin frustration.91 The spin coupling for a pathway indicates the alignment of spins in that pathway in the ground state, and is positive for parallel alignment and negative for antiparallel alignment. Spin coupling values are hel pful in determining the spin alignment in different ST due to the unique values for every combination of Ms for a given system. For example, any combination of two spins aligned antiparallel will give an ST = 0; however, the BASS value wi ll be distinctly different (Figure 3 6). The exchange constant, on the other hand, indicates the preferred alignment of spins. Under the –J (or –2J) convention, a negative exchange constant describes antiferromagnetic coupling and hence a preferred antiparallel spin alignment, while a positive e xchange constant describes ferromagnetic coupling and a preferred parallel alignment. Thus a pathway with B AS S and J with opposite signs is frustrated. Previously we have used this argument qualitatively as a simple indicator of the pre sence or absence of spin frustration. We have also discussed the product –2JAB B AS S as a more quantitative measure of spin frustration,92 as it represents the contribution of the A B path way to the total energy of the ground state. Spin frustrated pathways thus increase the energy of the state, while pathways that are not frustrated decrease the energy. Viewed in this way, spin frustration occurs in spite of increasing the ground state energy because the resulting alignment of spins allows greater decreases in energy in other pathways that are not frustrated.

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85 The two views of spin frustration just described are both useful for understanding magnetic interactions between metal centers, but are both formulated on the basis of the simple presence or absence of spin frustration, i.e., a pathway is either frustrated, resulting in parallel alignment of the spins (assuming antiferromagnetic coupling), or is not frustrated, resulting in antiparallel alignment of spins. Although the idea of “partial spin frustration” is often invoked in cases of intermediate spin ground states that cannot result from fully parallel or antiparallel spin alignments, as in triangular Fe3 complexes in which the ground state can have ST = 21 , 23 , or 2 5 ,28 it has not previously been discussed on a quantitative basis. A more quantitative understanding of spin frustration in such cases would clearly be useful. This is amply illustrated by the initial report of complex 32,83 in which a fit of the magnetic susceptibility with a model assuming J1 = J2 failed to reproduce the ground state spin of S = 3, giving instead S = 0. Several qualitative arguments were given to explain this discrepancy, including the absence of zero field splitting in the model, the possibility that J1 2, the magnetic field used in obtaining M vs. H dat a perturbed the ground state, and the observed ground state spin actually represented an average over several thermally populated states. The second argument proves to be the crucial point ( vide infra ), but this is unclear without a quantitative view of s pin interactions in the complex. The following discussion presents a quantitative description of spin interactions that thoroughly explains the origin of the intermediate spin ground states observed for 31 and 32. There are three alternate definitions or types of frustration described by Baker et.al called type I, type II, and type III.93 Type I systems obey . Physically, they must have an odd number of electrons and result in a degenerate, spin active ground state, i.e., multiple S = 1/2 levels. The spin number of the ground states will be lower than can be reached by regarding the quantum spins of the system classically. Structurally this will require a very regular geometry and the presence of oddnumbered circuits —either triangles, pentagons

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86 (as in the Keplerates), or larger rings. Type II frustration is where the single ground state has a spin value lower than can be achieved by treating the molecule as having classical spins. The degenerate ground state required for type I frustration is not evident in type II systems. Structurally, a type II system is likely to contain oddnumbered circuits of spin center s, but with some structural distortion. Type III frustration is found in cases where the ground state could be derived from a classical treatment of spin, but where there are competing antiferromagnetic exchange interactions.93 While the authors go into qualitative detail regarding the different types of frustration, we are focused on quantifying the extent of frustration within different pathw ays regardless of the type of frustration. The central concept of our quantitative view of spin frustration is again that the spin coupling B AS S reflects the actual alignment of the spins across the A B pathway. In principle, then, this quantity directly reflects the “partially frustrated” spin alignments indicated for 31 in Table 3 7 in which, e.g., Fe1 and Fe1 both have M1 = + 23 . It is immediately apparent when comparing 2 1 S S for 31 and 3 3, in which MX = MY = + 25 , that the value of YXS S is distinctly different in the two cases. Before proceeding in analyzing this difference, it is necessary to first consider a point of terminology. The Fe1Fe3 pathway in 31 is clearly partially frustrated, with M1 = M3 = + 23 , but no similar term has been used previously to describe the interaction of Fe1 and Fe2, which have M1 = + 23 and M2 = – 23 . The 12 interaction thus appears to be “partially not frustrated.” We introduce the term “spin satisfaction” to avoid this awkward phrasing; the 12 pathway would thus be “partially satisfied.” Spin frustration and spin satisfaction are opposite senses of the sa me phenomenon, which we henceforth refer to as spin compensation. We next introduce a quantitative scale of spin compensation based on the spin coupling that ranges from fully frustrated through fully satisfied and encompasses both partially frustrated an d partially satisfied interactions.

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87 In 31, the sides of the two triangles have J's of 17 and 22 cm1. The sides with J = 17 cm1 are partially frustrated, all spins are roughly + 2 3 , and the frustration causes them to align to a net of S = 3 in the ground state. In the case of nonequivalent J's which have largely differing values, the results are more or less complete satisfaction in one side and frustration in the other, local spin components of + 2 5 , and alignments leading to the net spin of 5. If those J's are changed slightly to be equivalent, then the ground state changes dramatically. The ground state becomes S = 0, all spins average to zero (combinations of spin components pointing in opposite directions on e ach metal), and none of the pathways are completely frustrated. The pathways are only slightly satisfied but they are not frustrated. Both slightly satisfied and slightly frustrated pathways are present in complex [Fe 6O2(hmp)10(H2O)2](NO3)4 ( 31 ). As expected, all of the exchange couplings are negative, indicating antiferromagnetic coupling. However, the most interesting results are the spin couplings for each pair of FeIII ions because all of the pathways except for the interaction between Fe2 and Fe3 (as well as the symmetry equivalent Fe1 and Fe3 ) have values of 3.69 which is indicative of two FeIII ions with Sz = 2 3 with opposite spin direction (antiparallel alignment), Figure 3 7. The pathway between Fe2 and Fe3 (Fe2 and Fe3 ) is frustrated as expected because it has a negative exchange coupling that is the smallest within the complex and has a positive spin coupling, BASS = +2.23 which is similar to the calculated spin coupling of + 2.25 for two spins of 23 aligned parallel to one another. In Figure 3 7, the spin alignments are shown; therefore, S = 6 – 3 = 3 explains the S = 3 ground state. As has been discussed before, when the competing exchange interactions are comparable in strength the re is a balance established and the spin ground state is very sensitive to the relative magnitudes of the exchange couplings. This can be demonstrated for complexes 31 and 32 and

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88 is part of the explanation for why the literature example, complex 32, gave an S = 0 ground state when the data were fit to an isosceles triangle. The S = 3 ground state was explained assuming a scalene triangle for each triangular unit when calculating the exchange couplings of 17, 22, 60 cm1. When we assumed an isosceles triangle for the triangular units and used J = 19.5, 19.5, and 60 cm1, an S = 0 ground state was predicted. The influence of lower symmetry on the ground state S is f urther demonstrated in Table 3 6 where the ground state varies from S = 0 to S = 5 w ith only slight changes in the value of J23 (and it s symmetry equivalent) and holding all other exchange pathways constant at 22, 33 and 60 cm1 pathway nu mbering according to Figure 37. The results found in Table 3 6 show how the spin ground state can vary from S = 0 to S = 5 with only subtle changes to one pathway of a triangular unit. The plot found in Figure 38 shows how the ratio of J13 and J23 can change the spin ground state drastically. These values were calcu lated varying the ratios of J13 and J23 (and their symmetry equivalents) and holding all other exchange parameters constant. The yellow dot represents the ratio of J13 and J23 for complex 31, it has been shown that subtle changes in the symmetry change the ground state of the complex. When the pathways have approximately equal or equal values the S = 0 ground state prevails which was the problem with the isosceles symmetry assumption made in effort to explain the S = 3 spin ground state of 32. In contras t to complex 3 1, which has spin couplings of the order of 32, in [Fe6O2(OH)2(O2CBut)10(hep)2] ( 33 ) and [Fe6O2(OH)(O2CBut)9(hep)4] ( 34) , two similar complexes previously reported, the spin couplings are all larger than 5.0 in magnitude. All Sz values are close to 25 in magnitude. Both complexes, 33 and 34 (Figure 3 9), have competing antiferromagnetic exchange interactions; however, they are not all comparable in strength which

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89 forces the pairs of spins with the weakest interactions to align parallel to one another i.e. the weakest interactions are completely frustrated in both complexes . The placement of the weakest interactions within each complex ultimately is responsible for the difference in the ground state (i.e. complex 33 and 34 having S = 0 and S =5, respectively.) 3.3.3 A Spin Frustration Quantification Method When the quantification method was being developed, it became obvious that it would be most convenient to express spin compensation as a percen tage as mentioned earlier . I will use the being in terms of spin frustration rather than spin satisfaction, the spin satisfaction percentage will be denoted by s and the spin frustration percentage will be denoted by just with no subscript. The initial test for our method for calculating percent compensation was how the values compared for all possible spin alignments for two Fe3+ ions. These results are impressive b ecause there is a symmetric distribution about the 50% satisfied/frustrated as shown in Figure 3 10. Only the percent frustration values were calculated; however, when the percent satisfaction is calculated the values have a similar distribution around 50% (included at the end in the supplementary information for completeness). T hree Fe3+ 6 clusters will be used as test cases because all three cases contain exchange pathways which are antiferromagnetic and are comprised of two triangular units. These two conditions always result in at least some degree of spin frustration as shown in all of these complexes. The success of these results led to the implementation of our method to quantify spin compensation on complex 31, which clearly has two frustrated pathways. For both complexes 31 and 32, none of the pathways are completely satisfied or completely frustrated. Starting with

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90 the Fe1 Fe2 exchange pathway in complex 31 which has a J = 22 cm1 and a BASS calc = 3. s) of this pathway wit hin the compound. = . | . | % + % = % ( 36) = % . | . | % = % ( 37) Then, Fe1Fe3 exchange pathway which has a J = 17cm1 and BASS calc = +2.23 = . | . | % + % = % ( 38) = % . | . | % = % ( 39) This method was carried out with every pathway in both complexes which makes it possible to discuss the amount of spin compensation contained for each interaction. The amount of spin frustration as well as the spin dependent energy contribution for each exchange pathway is shown in Table 37. Focusing on complex 31, it is possible to see that by only two pathways being 68% frustrated and the ot hers being 71% satisfied, actually lowers the total spin dependent energy. The many definitions used to qualitatively describe spin frustration are in agreement with the first way to quantitate spin satisfaction , as is shown in Table 3 7. 3.5 Conclusions The unusual S = 3 ground state for an FeIII 6 complex has been explained by intermediate spin states orientation at each metal. The intermediate spin states were identified by examining the exchange interactions and the spin couplings f or each pathway. There are two partially frustrated pathways due to the par allel alignment and the balance are partially satisfied by aligning antiparallel of the intermediate spins on each metal. Since the two FeIII 6 complexes with

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91 the S = 3 ground states were discovered there has been a new complex with an S = 4 ground state that can be added to the FeIII 6 family.94 The decision to make assumptions to simplify fitting the data or calculations is a very important one as the influence of lower symmetry was shown to have drastic effects on the spin ground state. By only varying J12 slightly, we were able to show that only subtle changes can have large effects on the spin ground state. The assumption of higher symmetry doesn’t allow the explanation of unusual ground states in all cases. With the discovery of new FeIII complexes with unusual spin ground states, it is i mportant to have a quantitative scale to be able to compare frustrated pathways from complex to complex as well as within a single complex. As thermometers allow the quantitative measurement of temperature so we know exactly how hot or how cold something i s instead of using vague words such as hot and hotter, t his work allows not only a more specific way to discuss spin compensation but also a way to identify trends in these pathways that are not completely satisfied or completely frustrated. Equations 3 4 and 35 are also effective for describing systems with smaller numbers of unpaired electrons. For completeness, two figures have been included to describe the complete range from completely satisfied to completely frustrated spin alignments for two high spin d4 metals (Figure 3 11) and two d3 metals (Figure 3 12). The percentages for each intermediate spin state are symmetric around the 50% mark and describe the 50% mark in the case of two high spin d4 metals. In the future, it may be possible to use magne tostructural parameters and spin compensation parameters to develop a correlation method to predict spin compensation based on structural information. This would allow information to be obtained without employing

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92 computational methods on large complexes that are potentially too large and cumbersome to obtain theoretical results without huge expenses.

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93 Table 3 1. Structural Parameters and Magnetic Properties for the Two Chair like Complexes with the [FeIII 6( 3O)2( OR)8]6+ Core Complex a ( o ) ( o ) ( o ) ( o ) Fe ( 3 O) Fe ( o ) FeFe () Fe ( 3 O) b () J i (cm 1 ) S Ref (3 -2 ) 100.2 101.3 105.2 105.4 150.7 104.1 104.9 3.040 3.054 3.688 3.165c 1.907 1.905 1.947 J 1 = 18d J2 = 18d J3 = 52d J4 = -3d 0 83 ( 3 1 ) 97.7 99.4 104.9 105.2 100.7 102.6 156.7 3.030 3.064 3.671 3.166c 1.967 1.962 1.874 J 1 = 17 J2 = -22 J3 = -60 J4 = -33 3 t.w . a See Figure 3 2 for the definition of the structural parameters given in this table. b Average FeO distance. c Neighboring FeFe distances between the apices of the two triangular [Fe3( 3O)]7+ units. d From theoretical calculations, assuming an isosceles FeIII 3O triangle, and applying a 3J model ( J1 = J2, see Figure 3 2).

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94 Table 3 2. Results of ZILSH calculations on complex 31. See text for discussion. Componenta Energy (cm1) M1 b M2 M3 M4 M5 M6 high spin 4328.44 c ( 854.41034573) d 4.37 4.35 4.30 4.37 4.35 4.30 1,2 2337.89 4.35 4.34 4.29 4.36 4.34 4.30 1,3 2252.74 4.31 4.31 4.30 4.37 4.34 4.30 1,4 0.00 4.31 4.30 4.29 4.31 4.30 4.29 1,5 1332.65 4.32 4.31 4.29 4.33 4.31 4.30 1,6 1431.90 4.31 4.31 4.29 4.36 4.34 4.29 2,3 2155.51 4.32 4.30 4.29 4.36 4.35 4.30 2,4 1332.74 4.33 4.31 4.30 4.32 4.31 4.29 2,5 191.22 4.31 4.30 4.30 4.31 4.30 4.30 2,6 1527.70 4.33 4.30 4.30 4.35 4.35 4.29 3,4 1431.84 4.36 4.34 4.29 4.31 4.31 4.29 3,5 1527.39 4.35 4.35 4.29 4.33 4.30 4.30 3,6 2870.34 4.36 4.35 4.29 4.36 4.35 4.29 4,5 2337.83 4.36 4.34 4.30 4.35 4.34 4.29 4,6 2252.52 4.37 4.34 4.30 4.31 4.31 4.30 5,6 2155.23 4.36 4.35 4.30 4.32 4.30 4.29 a Indices indicate metals with unpaired spins reversed to all other unpaired spins. See Figure 31 for numbering scheme. “HS” indicates component with all unpaired spins aligned. b local spin density for Fe1 from ZILSH calculations. c Relative energy (cm1). d Absolute energy of HS component (a.u.).

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95 Table 33. Spin couplings BASS UHF compu ted from ZILSH UHF wavefunctions for spin components of compound 31. Componenta S1S2 S1S3 S1S1' S1S2' S1S3' S2S3 S2S1' S2S2' S2S3' S3 S1' S3 S2' S3 S3' S1' S2' S1' S3' S2' S3' high spin 4.75 4.70 4.77 4.75 4.70 4.68 4.75 4.74 4.69 4.70 4.69 4.63 4.75 4.70 4.68 1,2 4.72 4.66 4.73 4.72 4.68 4.65 4.73 4.71 4.67 4.66 4.65 4.61 4.73 4.68 4.67 1,3 4.65 4.63 4.71 4.68 4.64 4.63 4.70 4.68 4.64 4.69 4.66 4.62 4.74 4.70 4.67 1,4 4.64 4.63 4.64 4.63 4.62 4.61 4.63 4.62 4.61 4.62 4.61 4.60 4.64 4.63 4.61 1,5 4.66 4.64 4.67 4.65 4.64 4.62 4.66 4.64 4.63 4.64 4.62 4.61 4.66 4.64 4.63 1,6 4.65 4.63 4.70 4.68 4.61 4.62 4.70 4.68 4.62 4.68 4.65 4.60 4.73 4.67 4.65 2,3 4.65 4.64 4.70 4.70 4.65 4.61 4.68 4.68 4.63 4.67 4.67 4.62 4.74 4.68 4.68 2,4 4.66 4.64 4.67 4.66 4.64 4.63 4.65 4.64 4.62 4.64 4.63 4.61 4.66 4.64 4.62 2,5 4.64 4.63 4.65 4.64 4.63 4.62 4.64 4.62 4.61 4.63 4.61 4.61 4.64 4.63 4.62 2,6 4.65 4.64 4.70 4.70 4.63 4.62 4.67 4.67 4.60 4.67 4.67 4.60 4.73 4.66 4.66 3,4 4.73 4.67 4.70 4.70 4.68 4.65 4.68 4.68 4.65 4.61 4.62 4.60 4.65 4.63 4.62 3,5 4.73 4.66 4.70 4.67 4.67 4.66 4.70 4.67 4.67 4.63 4.60 4.60 4.65 4.64 4.62 3,6 4.74 4.67 4.75 4.74 4.67 4.66 4.74 4.73 4.66 4.67 4.66 4.59 4.74 4.67 4.66 4,5 4.73 4.68 4.73 4.73 4.66 4.67 4.72 4.71 4.65 4.68 4.67 4.61 4.72 4.66 4.65 4,6 4.74 4.70 4.71 4.70 4.69 4.67 4.68 4.68 4.66 4.64 4.64 4.62 4.65 4.63 4.63 5,6 4.74 4.68 4.70 4.68 4.67 4.68 4.70 4.68 4.67 4.65 4.63 4.62 4.65 4.64 4.61 a All spins on the indicated metals reversed relative to others; see Figure 2 for numbering scheme.

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96 T able 3 4. Structural Classes and Ground State S Values of Known FeIII 6 Clusters Complex a,b Core Class c S Ref. [Fe 6 O 2 (OH) 2 (O 2 CMe) 10 (C 7 H 11 N 2 O) 2 ] [Fe 6 ( 3 O) 2 ( OH) 2 ( OR) 2 ] a 5 83 [Fe 6 O 2 (OH) 2 (O 2 CPh) 10 (dipaH 2 ) 2 ] [Fe 6 ( 3 O) 2 ( OH) 2 ( OR) 2 ] a 5 95 [Fe 6 O 2 (OH) 2 (O 2 CBu t ) 10 (hep) 2 ] ( 3 3 ) [Fe 6 ( 3 O) 2 ( OH) 2 ( OR) 2 ] a 5 96 [Fe 6 O 2 (OH) 2 (O 2 CMe) 10 (Me hmp) 2 ] [Fe 6 ( 3 O) 2 ( OH) 2 ( OR) 2 ] a 5 96 [Fe 6 O 2 (OH) 2 (O 2 CPh) 10 (hep) 2 ] [Fe 6 ( 3 O) 2 ( OH) 2 ( OR) 2 ] a 5 90 [Fe 6 O 2 (OH)(O 2 CPh) 9 (hep) 4 ] [Fe 6 ( 3 O) 2 ( OH)( OR) 4 ] a 0 90 [Fe 6 O 2 (OH ) 4 Cl 2 (O 2 CR) 6 (4 NCC 5 H 4 N) 4 ] [Fe 6 ( 3 O) 2 ( OH) 4 ( OR) 2 ] a n.r. 97 [Fe 6 O 2 (OH) 2 (O 2 CMe) 10 (C 10 H 13 N 4 O) 2 ] [Fe 6 ( 3 O) 2 ( OH) 2 ( OR) 2 ] a 5 28 [Fe 6 O 2 (OH)(O 2 CBu t ) 9 (hep) 4 ] ( 3 4 ) [Fe 6 3 O) 2 OR) 4 ] b 0 96 [Fe 6 O 2 (OH) 2 (O 2 CBu t ) 12 (THF) 2 ] [Fe 6 ( 3 O) 2 ( OH) 2 ] b 0 98 [Fe 6 O 2 (OH) 2 (O 2 CPh) 12 (H 2 O) 2 ] [Fe 6 ( 3 O) 2 ( OH) 2 ] b 0 98 [Fe 6 O 2 (O 2 CH 2 )(O 2 CCH 2 Bu t ) 12 (py) 2 ] [Fe 6 ( 3 O) 2 ( 4 O 2 CH 2 )] b 0 99 [Fe 6 O 2 (OH) 2 (O 2 CPh) 12 (py) 2 ] [Fe 6 ( 3 O) 2 ( OH) 2 ] b 0 100 [Fe 6 O 2 (OH) 2 (O 2 CPh) 12 (H 2 O)(diox)] [Fe 6 ( 3 O) 2 ( OH) 2 ] b 0 101 [Fe 6 O 2 (O 2 )(O 2 CPh) 12 (H 2 O) 2 ] [Fe 6 ( 3 O) 2 ( 4 O 2 )] b n.r. 102 [Fe 6 O 2 (O 2 )(O 2 CBu t ) 12 (L) 2 ] [Fe 6 ( 3 O) 2 ( 4 O 2 )] b n.r. 103 [Fe 6 O 2 (hmp) 10 (H 2 O) 2 ] 4+ ( 3 1 ) [Fe 6 ( 3 O) 2 ( OR) 8 ] c 3 t.w. [Fe 6 O 2 Cl 4 (hmp) 8 ] 2+ ( 3 2 ) [Fe 6 ( 3 O) 2 ( OR) 8 ] c 3 83 [Fe 6 O 2 (O 2 CCH 2 Cl) 6 (moe) 6 ] 2+ [Fe 6 ( 3 O) 2 ( OR) 6 ] d 0 99 [Fe 6 O 2 (O 2 CBu t ) 6 (hmp) 6 ] 2+ [Fe 6 ( 3 O) 2 ( OR) 6 ] d 0 77 [Fe 6 O 2 (O 2 CPh) 6 (hmp) 6 ] 2+ [Fe 6 ( 3 O) 2 ( OR) 6 ] d 0 77 6 O 3 (hpidaH) 6 ]} + [Fe 6 ( O) 3 ( OR) 3 ]} d 0 104

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97 Table 3 4. Continued Complex a,b Core Class c S Ref. [Fe 6 O 2 (O 2 ) 3 (O 2 CMe) 9 ] [Fe 6 ( 3 O) 2 ( 4 O 2 ) 3 ] d 1 84 [Fe 6 (L ) 6 ] [Fe 6 ( 3 OR) 6 ] d n.r. 85 [F e 6 O 2 (OH) 6 (ida) 6 ] 4 [Fe 6 ( 3 O) 2 ( OH) 6 ] d n.r. 105 [Fe 6 O(OMe) 18 ] 2 [Fe 6 ( 6 O)( OMe) 14 ] e n.r. 106 [Fe 6 O{CH 3 C(CH 2 O) 3 } 6 ] 2 [Fe 6 ( 6 O)( OR) 12 ] e n.r. 88 [Fe 6 OCl 6 (OMe) 3 (thmeH 3 ) 3 ] 2 [Fe 6 ( 6 O)( OR) 12 ] e 0 107 [Fe 6 OCl 6 (OMe) 12 ] 2 [Fe 6 ( 6 O)( OMe) 12 ] e n.r. 108 [Fe 6 O 2 (OPr i ) 8 (O 2 CPh) 6 ] [Fe 6 ( 3 O) 2 ( OPr i ) 6 ] f 3 100 [Fe 6 O 2 (OH) 6 (O 2 CR) 4 Cl 4 (2 Ph 2 P(O)py) 2 ] [Fe 6 ( 4 O) 2 ( OH) 6 ] f n.r. 109 [Fe 6 O 2 Cl 4 (OMe) 6 (L 1 ) 2 ] [Fe 6 ( 4 O) 2 ( OMe) 6 ] f 3 110 [Fe 6 O 3 (O 2 CMe) 9 (OEt) 2 (bpy) 2 ] + [Fe 6 ( 4 O) ( 3 O) 2 ( OEt) 2 ] f 0 111 [Fe 6 O 3 (O 2 CMe) 9 (OPh) 2 (bpy) 2 ] + [Fe 6 ( 4 O)( 3 O) 2 ( OPh) 2 ] f 0 91 [Fe 6 O 2 (OH) 2 (O 2 CPh) 6 (hmbp) 4 ] 2+ [Fe 6 ( 3 O) 2 ( OH) 2 ( OR) 4 ] f 5 86 [Fe 6 O 2 (OH) 4 (O 2 CBu t ) 8 (dmem) 2 ] [Fe 6 ( 3 O) 2 ( OH) 4 ( OR) 2 ] f 5 8 7 [Fe 6 O 2 (OMe) 12 (tren) 2 ] 2+ [Fe 6 ( 4 O) 2 ( OMe) 8 ] f 5 112 [Fe 6 O 6 (O 2 CPh) 3 (L 3 ) 3 (H 2 O) 2 ] 3+ [Fe 6 ( 3 O) 4 ( O) 2 ] f 0 78 [Fe 6 O 4 Cl 4 (O 2 CPh) 4 (L 3 ) 2 ] 2+ [Fe 6 ( 3 O) 4 ] f 0 113 [Fe 6 O 3 (OH)( p NO 2 C 6 H 4 CO 2 ) 11 L 4 ] [Fe 6 ( 3 O) 3 ( OH)] f n.r. 114 [Fe 6 O 4 (OH) 2 (ami) 4 (phen) 8 ] 8+ [Fe 6 ( O) 4 ( OH) 2 ] g 0 115 [Fe 6 Br 6 (L 5 ) 6 ] [Fe 6 ( OR) 12 ] g n.r. 116 [Fe 6 (ashz) 6 (MeOH) 6 ] [Fe 6 ( OR) 12 ] g 0 117

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98 Table 3 -4. Continued Complex a,b Core Class c S Ref. [Fe 6 Cl 6 (Rda) 6 ] [Fe 6 ( OR) 12 ] g n.r. 118 [Fe 6 (L 6 ) 6 ] [Fe 6 ( OR) 12 ] g 0 119 [Fe 6 O 3 (O 2 CMe) 8 (L 4 ) 4 ] [Fe 3 ( 3 O)]( O)[Fe 3 ( 3 O)] h n.r. 120 [Fe 6 O(OH) 3 (O 2 CMe) 3 (O 2 PPh) 4 (py) 9 ] 2+ {[Fe 3 ( 3 O)][Fe 3 ( OH) 3 ]} h n.r. 121 [Fe 6 O 2 (O 2 CPh) 10 (salox) 2 (H 2 O) 2 ] [Fe 6 ( 3 O) 2 ( OR) 2 ] h 0 122 a Counterions and solvate molecules are omitted. b Abbreviations: n.r. = not reported; t.w. = this work; dipaH3 = diisopropanolamine; hepH = 2(2 hydroxyethyl)pyridine; Me hmpH = 6methyl 2(hydroxymethyl)pyridine; THF = tetrahydrofuran; py = pyridine; diox = 1,4dioxane; L = various terminal solvent molecules; moeH=2 methoxyethanol; hpidaH3 = N (2 hydroxypropyl)im inodiacetic acid; (L’)3 = di paratolyl malonate; ida2 = dianion of iminodiacetic acid; thmeH3 = 1,1,1tris(hydroxymethyl)ethane; H2L1 = N,N’ bis( nbutylcarbamoyl)pyridine 2,6dicarboxamide; bpy = 2,2’ bipyridine; hmbpH = 6 hydroxymethyl 2,2’ bipyridine; dmemH = 2 {[2 (dimethylamino)ethyl]methylamino}ethanol; tren = 2,2’,2’’ triaminotriethylamine; L3 = 1,2bis(2,2’ bipyridyl 6yl)ethane; ami = amphoteric ion of alanine; phen = 1,10phenanthroline; H2L5 = N (2,5 dimethylbenzyl)iminodiethanol; ashzH3 = N propionylsalicylhydrazide; bicH3 = bicine; RdaH2 = various N substituted diethanolamines; H3L6 = N (2 hydroxy5nitrobenzyl)iminodiethanol; L4 = N (2 methylthiazole 5yl) thiazole 2carboxamide; saloxH2 = salicylaldehyde oxime. c a = planar, b = twisted boat, c = chair like, d = parallel triangles, e = octahedral, f = fused or extended butterflies, g = cyclic, and h = linked triangles.

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99 Table 3 5. Nonzero exchange constants ( 2J convention) obtained for compounds 31, 33, and 3 4 with ZILSH calcu lations and empirical fits of magnetic susceptibility data. All values given in cm1. Interactiona 31 33 34 Method ZILSH b FIT b ZILSH c FIT c FIT d FIT b J 1 16.8 15.9 3.5 18 J 2 22.0 39.0 29.9 18 J 3 60.0 55.6 39.1 52 J 4 33.3 28.5 17.4 3 a Numbering scheme as in Figure3 1.b This work.c Reference22.d Reference 23.

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100 Table 3 6. Calculated spin ground states holding all J constant except J23. J 23 J 13 S 18.5 22.0 0 18.0 22.0 1 17.5 22.0 2 17.0 22.0 3 16.5 22.0 4 16.0 22.0 5

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101 Table 3 7. Exchange couplings (J, cm1), spin couplings ( ), (cm1) and % Frustration ) for 31, 3 3, and 34. Note: Fe2F3’ and Fe3Fe2’ values for complex 34 correspond to Fe2Fe5 and Fe3Fe4 pathways, respectively. 3 1 3 3 3 4 J % ) J % ) J % ) Fe1 Fe2 22 3.69 162.4 29 7.5 6.16 92.4 93 16 5.34 37.3 99 Fe1 Fe3 17 2.23 +75.8 68 34 7.13 485 9 31 7.17 444.5 9 Fe2 Fe3 60 3.69 442.8 29 47 7.47 702 9 33 7.11 469.3 7 Fe2 Fe3’ 33 3.69 243.5 29 17 6.17 210 15 7.5 7.57 113.6 15 Fe3 Fe2’ 33 3.69 243.5 29 17 6.17 210 7 21 6.15 258.3 15

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102 Figure 31. Schematic of [Fe6O2(hmp)10(H2O)2](NO3)4 , complex 31. Figure 32. Schematic of [Fe6O2(OH)2(O2CBut)10(hep)2], complex 33.

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103 Figure 33. Schematic of [Fe6O2(OH)(O2CBut)9(hep)4], complex 34. S 1z = +5/2 S 1z = +5/2 S 1z = +5/2 S 1z = +5/2 S 1z = +5/2 S 1z = +5/2 S 2z = 3/2 S 2z = 1/2 S 2z = +3/2 S 2z = +1/2 S 2z = +5/2 S 2z = 5/2 S 1 S 2 = 8.75 S 1 S 2 = 5.25 S 1 S 2 = 1.75 S 1 S 2 = 1.25 S 1 S 2 = 3.75 S 1 S 2 = 6.25 S T = 0 S T = 1 S T = 2 S T = 3 S T = 4 S T = 5 S 1z = +1/2 S 2z = 1/2 S 1 S 2 = 0.75 S T = 0 S 1z = +1/2 S 2z = +1/2 S 1 S 2 = 0.25 S T = 1 S 1z = +3/2 S 1z = +3/2 S 1z = +3/2 S 1z = +3/2 S 2z = 3/2 S 2z = 1/2 S 2z = +3/2 S 2z = +1/2 S 1 S 2 = 3.75 S 1 S 2 = 1.25 S 1 S 2 = 0.75 S 1 S 2 = 2.25 S T = 0 S T = 1 S T = 2 S T = 3 complete spin satisfaction spin satisfied spin frustrated complete spin frustration J <0 Figure 34. The alignments of the z component of two FeIII ions ranging from completely satisfied to completely frustrated.

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104 Figure 35. The core of complex 31, defining the structural and magnetic parameters listed in Table 3 1. Figure 36. Multiple ways that ms states can combine to give ST = 0; however, all combinations give unique B AS S values.

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105 Figure 37. Schematic of complex 31 with J values, values, and spin alignments.

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106 Figure 38. Plot of J23 versus J13 show ing how their relative magnetudes affect the spin ground state. The dashed line is the J23 = J13 situation .

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107 Figure 39. Schematic of complex 33 (top) and 34 (bottom) showing J values, values, and spin alignments. The frustrated pathways are indicated with dashed lines.

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108 S Az = +5/2 S Az = +5/2 S Az = +5/2 S Az = +5/2 S Az = +5/2 S Az = +5/2 S Bz = 3/2 S Bz = 1/2 S Bz = +3/2 S Bz = +1/2 S Bz = +5/2 S Bz = 5/2 S A S B = 8.75 S A S B = 5.25 S A S B = 1.75 S A S B = 1.25 S A S B = 3.75 S A S B = 6.25 S T = 0 S T = 1 S T = 2 S T = 3 S T = 4 S T = 5 S Az = +1/2 S Bz = 1/2 S A S B = 0.75 S T = 0 S Az = +1/2 S Bz = +1/2 S A S B = 0.25 S T = 1 S Az = +3/2 S Az = +3/2 S Az = +3/2 S Az = +3/2 S Bz = 3/2 S Bz = 1/2 S Bz = +3/2 S Bz = +1/2 S A S B = 3.75 S A S B = 1.25 S A S B = 0.75 S A S B = 2.25 S T = 0 S T = 1 S T = 2 S T = 3 complete spin satisfaction spin satisfied spin frustrated complete spin frustration J<0 0% Frustrated 46% Frustrated 52% Frustrated 80% Frustrated 40% Frustrated 60% Frustrated 100% Frustrated 20% Frustrated 29% Frustrated 43% Frustrated 56% Frustrated 68% Frustrated Figure 310. Percent Frustration ( ) calculated for all values of for two FeIII (S = 5/2) ions .

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109 S 1z = +2 S 2z = 2 S 1 S 2 = 4 S T = 0 S 1z = +2 S 2z = 1 S 1 S 2 = 2 S T = 1 S 1z = +2 S 2z = +1 S 1 S 2 = 2 S T = 3 S 1z = +2 S 2z = +2 S 1 S 2 = 4 S T = 4 S 1z = +1 S 2z = 1 S 1 S 2 = 1 S T = 0 The calculated values of < S 1 S 2 > for all possible spin alignments for S = 2 S 1z = + 2 S 2z = +1 S 1 S 2 = 0 S T = 2 S 1z = +1 S 2z = +1 S 1 S 2 = 1 S T = 2 S 1z = +1 S 2z = 0 S 1 S 2 = 0 S T = 1 S 1z = 0 S 2z = 0 S 1 S 2 = 0 S T = 0 0% Frustrated 50% Frustrated 62.5% Frustrated 50% Frustrated 37.5% Frustrated 25% Frustrated 50% Frustrated 75% Frustrated 100 % Frustrated Figure 311. All possible spin alignments for two high spin d4 metals (i.e. MnIII).

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110 S 1z = +3/2 S 2z = 3/2 S 1 S 2 = 2.25 S T = 0 S 1z = +3/2 S 2z = 1/2 S 1 S 2 = 0.75 S T = 1 S 1z = +3/2 S 2z = +1/2 S 1 S 2 = 0 .75 S T = 2 S 1z = +3/2 S 2z = +3/2 S 1 S 2 = 2.25 S T = 3 S 1z = +1/2 S 2z = 1/2 S 1 S 2 = 0.25 S T = 0 S 1z = +1/2 S 2z = +1/2 S 1 S 2 = 0.25 S T = 1 The calculated values of < S 1 S 2 > for all possible spin alignments for S = 3/2 0% Frustrated 33% Frustrated 67% Frustrated 100 % Frustrated 44% Frustrated 56% Frustrated Figure 3 12. All possible spin alignments for two d3 metals (i.e. MnIV).

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111 CHAPTER 4 DINUCLEAR MANGANESE(III) COMPLEXES WITH UNUSUALLY STRONG FERROMAGNETIC COUPLING 4.1 Introduction Transition metal compounds can have interesting magnetic properties caused by large spin moments. These properties are important in understanding enzymatic processes such as water oxidation in photosynthesis, in which the changes in the magnetic moment of a manganesecalcium cluster active site accompany changes in oxidation state during the catalytic cycle.123 125 When transition me tal compounds can be fixed in two different distinct magnetic states they are called "singlemolecule magnets" (SMMs). SMMs have the potential for applications in molecular scale digital memory storage126 and quantum computing.127, 128 The size of the energy barrier between two distinct magnetic states depends on the coupling of the transition metal ion spin moments.129 Higher energy barriers are needed to ensure data integrity by limiting thermally assisted switching between magnetic.12 Single molecule magnet behavior in most 3d metals results from a large ground state spin ( S) and a large and negative (Ising or easy axis type) magnetic anisotropy, as gauged by the zero field splitting parameter ( D ). This combination leads to a significant barrier for magnetization reversal, whose upper limit is given by S2| D | for integer S values and ( S2 – 1/4)| D | for halfinteger S values. It is thus important to establish a comprehensive understanding of spin mo ment coupling in transition metal compounds. Over the last twenty years, manganese(III) based single molecule magnets have been the main focus of many research groups due to the inherent axial anisotropy from JahnTeller axes and relatively large spin ( S) in each MnIII ion ( S = 2, d4). These properties are also important in magnetocalorics where large spin ground states are necessary. The main issue with MnIII ions is that they tend to have weak coupling regardless of the type (antiferromagnetic or ferroma gnetic) and when they do display strong coupling it tends to be antiferromagnetic. Weak

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112 exchange interactions cause small energy gaps between spin states which is an issue when a well isolated, large ground state spin is desired to optimize the previously mentioned important physical properties. The exchange constant , J , for a dinuclear complex can be determined by fitting variable temperature magnetic susceptibility data to the appropriate Van Vleck Equation 4 1. This allows the sign and magnitude of J. Experimental determination of J values in complexes with more than two metals is carried out in the same way, but becomes more difficult as the number of metals in the complex increases. = ( ) ( ) ( ) ( ) ( ) (4 1) The increased number of interactions in a larger metal cluster can lead to problems with obtaining a unique set of fitting parameters , with heavy dependence on the initial parameter values assumed in the fit. For this reason, ther e is no direct link between experiment and exchange constants in some larger complexes. Computational modeling can in principle be used to assess magnetic interactions between transition metal ions, either to independently provide corroboration for result s of fits of experimental data or to provide estimates of exchange constants in large, asymmetric complexes. Thus, a strong interest in the synthesis and study of small nuclearity MnIII and/or MnIV complexes remains. For example, a series of [Mn3O4(O2CR)4( bpy)2]130 (R = Me, Et) complexes containing the V shaped [Mn3 O)4] unit and new procedures to dinuclear MnIV complexes containing terminal Clligands have been published in the past.131 Many groups are developing a number of new procedures to access MnIII and/or MnIV species, as well as oxidizing MnII io ns in complexes to higher oxidation states.

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113 A common route to manganese clusters is the oxidation of a MnII salt in the presence of a carboxylic acid and often a chelating ligand. In aqueous acetic acid, KMnO4 has been used to synthesize the dodecanuclear cluster [Mn12O12(O2CMe)16(H2O)4],132 octanuclear [Mn8O10(O2CMe)6(H2O)2(bpy)6](ClO4)4 133 and dinuclear [Mn2O2(bpy)4](ClO4)3 134, just to name a few. The use of NnBu4M nO4 135 was introduced by our group as a powerful oxidizing agent soluble in most common organic solvents, and this has led to the synthesis of a variety of polynuclear MnIII complexes. An alternate oxid i zing agent, (NH4)2[Ce(NO3)6], has been used in the synthesis of several MnIV containing complexes such as [Mn2O2(O2CMe)(bpy)2Cl(H2O)](ClO4)2 10 and [Mn3O4(bpy)4(H2O)2](NO3)2(ClO4)2,5 and more recently to a variety of mixedmetal Mn/Ce complexes.136141 The pr esent work explores the use of oxone as an oxidizing agent in Mn chemistry. Oxone is a peroxymonosulfate (SO5 2 -), a very powerful oxidizing agent with E0 = 1.79 V vs NHE.142 The use of oxone in manganese coordination chemistry is very limited: for example, it was used in the synthesis of a MnIIIMnIV complex [Mn2O2(terpy)2(H2O) 2](NO3)2 143 (where terpy is 2, 2’, 6, 6’ terpyridine). Our group has investigated many reactions of MnII salts with oxone in the presence of a chelating ligand and carboxylic acid. The chel at es for th e present study are 2,2' bipyridine (bpy) and 1,2bis(2,2' bipyrididyl 6yl)ethane (bbe), shown in Figure 41. The former is a commonly used ligand in many inorganic reactions and the latter is a bis chelating ligand commonly employed in supramolecular chemistry ,144151 and which has previously yielded some tetranuclear complexes in Mn chemistry , [Mn4O2(O2CR)4(bbe)2](ClO4)2 and [Mn4O2(OMe)3(O2CR)2(bbe)2(MeOH)](ClO4)2 (R = Me, Et, Ph).152 Although bbe has not been used much in manganese chemistry, it has been explored in V153, Cr,152 Fe76, 78, Co154, Ni155, and

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114 Cu152 chemistry. The synthesis, structure, physical properties and DFT calculations of two ferromagnetically coupled dinuclear manganese(III) carboxylate/sulfate containing compounds with bpy or bbe will be discussed. These are the first SO4 2 bridged species in MnIII chemistry. Also reported is a synthetic attempt to isolate a carboxylate and bbe containing dimer without the use of oxone , which resulted in a tetranuclear species, and a study of the magnetic properties of this complex. 4.2 Experimental Section 4.2.1 S yntheses All manipulations were performed under aerobic conditions, except the synthesis of the organic compound bbe. All chemicals and solvents were used as received. The compound 1,2bis(2,2' bipyridyl 6yl)ethane156 (bbe), Mn(O2CEt)24H2O157 [Mn2O (SO4)2(bpy)2(H2O)2]158 (4 1), and [Mn2O(O2CMe)(SO4)(bbe)(MeOH)2](PF6)158 (4 2) were synthesized as described elsewhere. [Mn2O(SO4)2(bpy)2(H2O)2] ( 41): The synthesis of complex 41 was confirmed by elemental analysis, infrared spectroscopy, and crystal unit cell comparison with the unit cell comparison with the authentic material . Elemental analysis: (%) calculated (found) for 41 3H2O: C 33.38 (33.78); H 3.64 (3.59); N 7.78 (7.72). Selected IR data of the crystals (KBr pellet, cm1): 1644 (w), 1601 (s), 1566 (m), 1495 (m), 1471 (m), 1445 (s) 1314 (m), 1282 (w), 1251 (m), 1113 (vs ), 1030 (vs), 965 (vs), 774 (s), 730 (s), 658 (s), 612 (s). The sample crystallized in the monoclinic space group P21/n. [Mn2O(O2CMe)(SO4)(bbe)(MeOH)2](PF6)158 ( 42): The synthesis of complex 42 was confirmed by elemental analysis, infrared spectroscopy, and crystal unit cell comparison with the unit cell comparison with the authentic material . Elemental analysis: Elemental analysis: (%) calculated (found) for 22 H2O C 36.12 (35.63), H 3.85 (3.83), N 6.66 (6.48) %. Selected

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115 IR data (cm1): 1602 (m), 1565 (m), 1530 (m), 1494 (m), 1453 (s), 1314 (w), 1264 (w ), 1227 (w), 1187, (w), 1171 (w), 1153 (w), 1059 (s), 1032 (s), 1011 (m), 984 (m), 844 (s), 779 (s), 726 (w), 672 (w), 657 (w), 639 (w), 602 (w) 557 (s). The sample crystalized in the space group P 21/n. [Mn4O2(O2CMe)4(bbe)2] ( 43): To a stirred solution of bbe (0.1g, 0.3 mmol) was added Mn(O2CMe)2 (0.35 g, 2.0 mmol) and NaIO4 (0.028g, 0.15mmol) followed by HAc (5 mL, 87 mmol). The yellow slurry was stirred for one hour, during which time, the solution changed to a deep red. The so lution was filtered and set up for slow evaporation. Single crystals formed on the sides of the vial after three days, the yield was 68 %. Elemental analysis: (%) calculated (found) for 43 4H2O: C 36.11 (36.11); H 3.83 (3.67); N 5.61 (5.85). Selected IR data (cm1): 3429 (b), 3121 (m), 1600 (m), 1578 (m), 1566 (m), 1455 (m), 1402(s), 1314 (w), 1094 (s), 1031 (m), 780 (s), 724 (m), 657 (m), 623 (m ). This complex crystallized in the space group P1 .A similar compound has been isolated by other methods.159 4.2.2 Physical Measurements Infrared spectra were recorded in the solid state (KBr pellets) on a Nicolet Nexus 670 FTIR spectrometer in the 400 4000 cm1 range. Elemental analyses (C, H, and N) were performed by the in house fa cilities of the University of Florida, Chemistry Department. Variabletemperature dc and ac magnetic susceptibility data were collected at the University of Florida using a Quantum Design MPMS XL SQUID susceptometer equipped with a 7 T magnet and operating in the 1.8 300 K range. Samples were embedded in solid eicosane to prevent torqueing. Magnetization vs field and temperature data were fit using the program MAGNET. Pascal’s constants were used to estimate the diamagnetic correction, which was subtracted from M).

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116 4.2.3 Computational Studies The exchange constants in complex 41 and 42 were estimated with the ZILSH method34 and density functional theory (DFT) calculations. For the ZILSH calculations, unrestricted Hartree Fock molecular orbital wavefunctions were obtained with the INDO/S method of Zerner160 167 for various spin components of the complex. These wavefunctions were assumed to follow an effective Heisenberg spin Hamiltonian given in Equation 4 2, BABAABeffSSJHH20 (4 2) where A and B label metal centers and 0 contains all spin ind ependent terms in the electronic Hamiltonian. The expectation value of eff i is given in Equation 43, BAiUHFBAABiUHFSSJEE,0,2 (4 3) where E0 contains all spin independent contributions to the energy. Spin couplings BASS UHF were calculated with the semiempirical local spin operator of Davidson and O’Brien.168 170 Given energies and spin couplings for the appropriate number of spin components, Equation 43 were solved simultaneously for the parameters E0 and JAB for all unique combinations of A and B. The spin components used were those wi th all unpaire d spins aligned parallel (“high spin”), and the component with unpaired spins on one of the two metal ions reversed. Since the identity of the two metals was the same reversing the spins on either metal was acceptable. A similar strategy was used in the DFT calculations by assuming that energies of unrestricted KohnSham determinants representing the spin components also follow Equation 4 3. Following our standard procedure, ZILSH spin couplings were used with DFT energies to obtain estimates of the exchange constants. Spin couplings computed with the ZILSH method are

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117 generally similar to those obtained from DFT densities.170 172 The B3LYP functional173 , 174 was used for all DFT calculations, which were performed with the Gaussian03 program.175 One basis set, the triple zeta TZVP basis set of Alrichs176 was employed o n all atoms. An important quantity obtained from both ZILSH and DFT calculations was the local spin density for each metal atom, equal to the number of unpaired electrons (Ni) on metal atom ‘i’.170 The signs of the Ni indicate the spin alignments within the complex for a particular spin component. The local spin densities were used to check that the correct spin component wavefunctions (or densities, in the case of DFT calculations) were obtained from the calculations ( vide infra ). Once the exchange constants ( JAB) were obtained, wavefunctions and energies of the spin eigenstates described by the Heisenberg spin model could be obtained by substituting the JAB into the Heisenberg spin Hamiltonian (Equation 4 5 with 0 = 0) and diagonalizing the operator in the basis of spin components i N 2 1 iM M M , where MA is the formal local z component of spin of metal ‘A’ (i.e. MA = 2 for high spin d4 MnIII ions). The wavefunctions of the spin eigenstates are then linear com binations of the basis functions i, iiNiiiiISMMMCC21 (4 4) as given by Equation 44. In the case of a ground state with nonzero spin, the component making the leading contribution to the wavefunction (i.e., that with t he largest weighting coefficient Ci) indicates the spin alignments in the ground state. Both complexes were small enough to be treated with full diagonalization. The positions of the added protons were optimized using the MM+ forcefield with the Hyperchem program,177 while keeping all other atoms in fixed positions.

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118 4.3 Results and Discussion 4.3.1 Structure Descriptions 4.3.1.1 Complex 41 T he treatment of MnCl24H2O and 2,2 bipyridine in aqueous MeCO2H with oxone resulted in the formation of a black solution, from which a new product, [Mn2O(SO4)2(bpy)2(H2O)2] ( 1) was obtained in the form of black crystals after the addition of THF (Equation 45). 2 MnCl2 + 2 bpy + SO5 2 + 2 H2O + SO4 2 [Mn2O(SO4)2(bpy)2(H2O)2] + 4 Cl(4 5) Complex 41 crystalizes in the monoclinic space group P21/n, and contains a dinuclear MnIII 2 core bridged by a 2O2 and two 11SO4 2 ions . The octahedr al coordina tion sphere is complete by a chelating 2,2 bipyridine (bpy) and a terminal water molecule. The two bpy units are nearly perpendicular to one another, as is ususlly the case for Mn2( O)( O2R)2(bpy)2]2+ units.135 Bond valence sum calculations confirm that the two Mn centers are MnIII ions and that the two terminal ligands are water molecules. This in in agreement with the Jahn Teller (JT) axial elongation clearly present in the molecules , as expected for MnIII with nearly octahedral geometry. The labeled core of 41 is shown in Figure 4 2 and selected intermolecular distances and angles can be found in Table A 1. The JT axes are O(3) Mn(1) O(7) and O(4) Mn(2) O(13). Thus, at each Mn, one MnIIIO(SO4) bond is ~ 2.14 , significantly longer than the other one (~ 1.96 ). The JT elongated MnOH2 bonds are 2.218 (2) and 2.186 (2) shorter than those in [Mn2O(O2CMe)2(bpy)2(H2O)2]2+ 135 (2.293(6) and 2.331(6) ) but longer t han those in [Mn4O2(O2CPh)9 (H2O)]172 (2.102(3)). The two JT axes are essentially perpendicular. The sulfate groups are tetrahedral, with all O S O angles in a narrow range of 108111. The coordinated water molecules are involved in hydrogenbonding to two of

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119 the H2O molecules in the lattice (O(79) O(81)), the distances being 2.689 (2) (O(79)O(3)) and 2.653 (O(80)O(4)). The O atoms of the SO4 2 groups are also involved in hydrogenbonding with a lattice molecule, (O(9)O(81) = 2.783 (2) ) and this water molecule also forms hydrogenbonds to the neighboring dinuclear unit. There are also additional intermolecular stac king of bpy rings (~3.4 ). 4.3.1.2 Complex 42 Addition of oxone to Mn(O2CMe)24H2O and bbe in MeOH produced a red solution with a light precipitate. After addition of MeCO2H, filtration , and addition of TBAPF6 to the filtrate, the compound [Mn2O(O2CMe)(S O4)(bbe)(MeOH)2](PF6) (42 ) was obtained as dark red crystals (Equation 4 6). 2 Mn(O2CMe)2 + bbe + SO5 2 + 2 MeOH [Mn2O(O2CMe)(SO4)(bbe)(MeOH)2]+ + 3MeCO2 (4 6) Complex 42, Figure 43, has a similar topology to complex 41 with slightly different ligands such as a bridging acetate, two terminal methanols, and a tetradentate bbe bridging chelate. Both complexes are described elsewhere.158 Complex 42 crystallizes in the monoclinic space group P21 O2 -, a syn, syn MeCO2 and one 11, SO4 2 ion. . Selected intermolecular distances and angles of 42 can be found in Table A 2. Octahedral coordination at each metal center is completed by a MeOH molecule and a chelating bipyridyl unit from the ligand bbe. The MnIII oxidation states and the protonated nature of the MeOH groups was established by BVS calculations on both the Mn and O atoms. However, the expected axial elongation of a MnIII JT distortion was not obvious. For each Mn center, the shortest bond is the Mn oxide bond (Mn(1) O(1) 1.780 (2) and Mn(2) O(1) 1.774 ). The Mn(1)Mn(2) distance is 3.178 (20) and the Mn(1) O(1) Mn(2) angle is 126.83o. Figure 43 shows the parallel arrangement of the two bipyridyl halves of the bbe, necessitated by

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120 their linkage via the ethylene bridge. This parallel arrangement is in contrast to the perpendicular arrangement of two bpy groups about [Mn2( O)( O2CR)2]+ core. The Mn(1) O(5) Mn(1) angle of 127.82(9)o in 41 is very similar to that of 42. The Mn centers in 4 1 are both clearly Jahn Teller (JT) axially elongated along the O(3)Mn(1) O(7) and O(4) Mn(2) O(13) trans bonds, as expected for highspin MnIII in near octahedral geometry. The Mn coordination geometries in 4 2 are also clearly distorted, although this di stortion does not take the form of the usual axial elongation. As can be seen in Figure 43, the two bonds undergoing the main elongation are cis to each other, involving atoms N(2) and O(4) at Mn(1), and N(4) and O(7) at Mn(2). This is an unusual pattern of bond elongation at a JT susceptible metal ion. The pattern in 41 is the normal situation in dinuclear MnIII systems with a bridging oxide. The naturally short MnO2 bond already removes the degeneracy of the d orbitals of an octahedral, highspin MnI II ion. Taking this direction as the z axis, then the axial elongation of two trans bonds in the xy plane causes additional stabilization of the singlyoccupied dx 2 y 2 orbital and thus increases the overall ligand field stabilization energy of the molecule. Note that, as expected, each JT elongation is along the axis containing the neutral solvent molecule, the poorest donor of the ligand set. It is possible that the ve ry short Mn O bond is also causing some of the asymmetric elongation of two bonds (i.e. 2.13 vs 2.21 for the two JT elongated bonds. The unusual bond elongation pattern in 4 2 can be rationalized as follows: the naturally short Mn O2 bond destabilizes the dz2 over the dx2y2 orbital, and elongation of bonds in the xy plane would again lead to further stabilization of the molecule. Elongation of the MnMeOH bond is understandable. The unusual elongation of the bond cis rather than trans to the MeOH is due, we believe, to an additional benefit of the former over the latter, and that is a relief of strain in the molecule due to the limited flexibility of the bis pyridyl ligand bbe.

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121 4.3.1.3 Complex 43 When NaIO4 was added to a mixture containing bbe, Mn(O2CMe)2 aqueous acetic acid, the yellow slurry changed to a dark red solution. Complex 43 was prepared from the following 4 Mn(O2CMe)2 + 2 bbe + O2 [Mn4O2(O2CMe)4(bbe)2]+ (4 7) Complex 43 (Figure 4 4) is a dimer of dimers and consists of two [Mn2O(O2CCH3)2(bbe)]+ fragments held together by Mn1O3 and Mn1 O3 interfragment linkages . Selected intermolecular distances and angles for 43 can be found in Table A 3. The cation is centrosymmetric and mixed valent containing two MnII and two MnIII ions where the MnII ions are five coordinate and the MnIII ions are six coordinate. Each resulting MnIIMnIII pair is quadruply bridged by O3, two syn, synH3CCO2 groups and the bbe ligand, which is attached to both metals. All bipyridine rings are essentially para llel, providing additional interfragment interactions through stacking as well as intramolecular stacking. 4.3.2 Magnetochemistry Variabletemperature magnetic susceptibility studies were performed on microcrystalline samples of 4 1, 42, and 43, restrained in eicosane to prevent torqueing. 4.3.2.1 Magnetochemical s tudies for c omplex 4 1 The magnetic susceptibilities were examined at a 0.1 T (1 kG) field in the 2.0 to 300 K temperature range for 41. Diamagnetic corrections were applied to the magnetic susceptibilities using Pascal's constants.178 The solid MT of 41 (Figure 4 5) shows a smooth increase from 7.2 cm3 K mol1 at 300 K to a platea u at 9.0 cm3 K mol1 between 10.0 and 35.0 K and then sharply decreases to 4.8 cm3 K mol1 at 2.00K . This is a good indication that the ground state of the complex is ferromagnetic because the 300K value is a little higher than the spin only (g = 2.0) value of 6 cm3 K mol1 that would be expected for two noninteracting MnIII ions. The

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122 plateau value of 9.0 cm3 K mol1 suggests the presence of ferromagnetic interactions in the dinuclear MnIII complex of ST = 4 ground state. The sharp decrease in the signal is most probably due to changes in the population of the components of the spin ground state multiplet which are split by ZFS and antiferromagnetic intermolecular interactions caused by the solvent molecules within the lattice. It is important to collect magnetism data below 0.5 T to know whether a sharp decrease in signal at low temperature is due to intermolecular exchange interactions mediated by the solvent molecules in the lattice ( vide supra ) and Zeeman effects from the applied field or if it is an artifact. The data were fit to the theoretical expression, based on the spin Hamiltonian = BAABSSJ2 , MT of a dinuclear MnIII complex (S1 = S2 = 2).179 MT at the lowest temperatures is due to the factors mentioned above that are not included in the model. A temperature independent paramagnetism (TIP) term was held constant at 300 x 106 cm3 mol1. The best fit is shown as the solid line in Figure 4 5, and the fit parameters were J = +11.4(3) cm1 and g = 1.86(1). The net ferromagnetic interaction between the two MnIII ions in 41 gives an S = 4 ground state separated from the S = 3 first excited state by |8J| = 91.2 cm1. In order to assess if the fit obtained was the superior fit and also to ensure it was the global minimum was located, a root mean square J vs g error surface was calculated, which calculates the relative difference between the experimental MT data and the calculated values for various combinations of J and g. The error surface is shown in Figure 46 as a two dimensional contour plot and clea rly shows only one minimum, confirming a good fit to the data. To confirm the indicated ST = 4 ground state of complex 41 and to estimate the magnitude of the zerofield splitting parameter D, magnetization vs dc field measurements were made on restrained samples at applied magnetic fields and temperatures in the 1 70 kG and 1.8-

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123 10.0 K ranges, respectively. The resulting data for 41 are shown in Figure 47 as a reduced magnetization ( M / N B) vs H/T plot, where M is the magnetization, N is Avogadro’s number, B is the Bohr magneton, and H is the magnetic field. The data were fit using the program MAGNET,180 by diagonalization of the spin Hamiltonian matrix assuming only the ground state is populated, incorporating the axial anisotropy ( 2zS D ) and Zeeman terms, and employing a full powder average. The corresponding spin Hamiltonian is given by Equation 48, = + (4 8) where zS is the easy axis spin operator, g is the Land g factor and 0 is the vacuum permeability. The best fit for 41 is shown as the solid lines in Figure 47 and was obtained with S = 4 and either of the two sets of parameters: g = 1.86 and D = +1.6 cm1, or g = 1.82(2) and D = 0.63 cm1. Alternate fits with S = 3 were rejected because they gave unreasonable values o f g. It is common to obtain two acceptable fits of the magnetization data for a given S value, one with D > 0 and one with D < 0, since magnetization fits are not very sensitive to the sign of D . In order to assess which is the superior fit and also to ensure the global minimum was located, a root mean square D vs g error surface was calculated using the GRID181 program, which calculates the relative difference between the experimental M / NB data and the calculated values for various combinations of D and g. The error surface is shown in Figure 4 8 as a two dimensional contour plot and clearly shows only two minima, wi th positive and negative D values. While both appear to be equally good fits of the data, it is not possible on the basis of these magnetization fits to conclude the more likely sign of the axial anisotropy parameter, D. However, the zero field splitting of the ground state of a polynuclear MnIII complex is largely due to the vector addition of the single ion ZFS tensors. Jahn Teller elongations are typically

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124 seen in octahedral MnIII ions where two MnL bonds opposite one another are noticeably longer creating a unique axis that usually defines the magnetic structure. Electron paramagnetic resonance experiments have shown that s ingle ion ZFS can be very large. F or example, Mn(acac)3 (acac = 2,4 pentanedione) and Mn(taa) (taa = tris(1 (2 azolyl) 2azabuten 4yl)amine have D values of 4.52 cm1 and 5.90 cm1, respectively. When all JT axes are aligned essentially parallel, the net ZFS is relatively large as in the case of the Mn12 family where D ~ 0.5 cm1. Using chemical intuition, the J T elongations tend to give negative ZFS parameters so the fit with the negative ZFS parameter is most likely correct. An additional, independent assessment of the ground state S value can be determined with an ac s usceptibility measurement. An ac experiment was collected on 41 in the 1.8 10 K range using a 3.5 G ac field oscillating at a frequency of 997 Hz. If the magnetization vector can relax fast enough to keep up with the oscillating field, then there is no imaginary (out of phase) suscept ibility signal (M), and the real (inphase) susceptibility (M ) is equal to the dc susceptibility. However, if the barrier to magnetization relaxation is significant compared to thermal energy (kT), then there is a nonzero M signal and the inphase s ignal decreases. In addition, the M and M signals will be frequency dependent if the complex is a singlemolecule magnet. The obtained inphase M signal for 41 is plotted as M T vs T in Figure 49 ( top ) and can be seen to quickly decreasing from 10K down to 1.8 K. Extrapolating to 0 K the data from above 4K (to avoid lower temperature effects from the slight anisotropy and weak intermolecular interactions) gives a value in the 7 cm3Kmol1 range, which is low for an S = 4 ground state and g < 2 but as was mentioned previously when looking at the MT vs T plot, there is plateau and a steep drop at low temperature due to intermolecular interactions from the pipi stacking. Our

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125 hypothesis that complex 41 may be a single molecule magnet proved to be wr ong as there is no M signal in the out of phase plot (Figure 4 9, bottom ). 4.3.2.2 Magnetochemical s tudies for complex 4 2 The solid state MT of 42 shows only a slight increase from 8.1 cm3 K mol1 at 300 K to 9 cm3 K mol1 at 50.0 K , which appears to almost be temperature independent. This is a good indication that the ground state of the complex is ferromagnetic because the 300K value is a little higher than the spinonly (g = 2.0) value of 6 cm3 K mol1 that would be expected for tw o noninteracting MnIII ions. The plateau value of 9 cm3 K mol1 suggests the presence of ferromagnetic interactions in the dinuclear MnIII complex of ST = 4 ground state. The sharp decrease in the signal is probably due to changes in the population of the components of the spin ground state multiplet which are split by ZFS and antiferromagnetic intermolecular interactions caused by the solvent molecules within the lattice. The data were fit to the theoretical expression, based on the spin Hamiltonian = B A ABS S J 2 , for the temperature dependence of the MT of a dinuclear MnIII complex (S1 = S2 = 2).179 Data below 8 K were neglected because the MT at the lowest temperatures is due to the factors mentioned above that are not included in the model. A temperature indepe ndent paramagnetism (TIP) term was held constant at 300 x 106 cm3 mol1. The best fit is shown as the solid line in Figure 4 5, and the fit parameters were J = 46( 2) cm1 and g = 1.86(4). The net ferromagnetic interaction between the two MnIII ions in 42 gives an S = 4 ground state separated from the S = 3 first excited state by |8J| = 350.4 cm1. In order to assess if the fit obtained was the superior fit and also to ensure the global minimum was located, a root mean square J vs g error surface was calculated, which calculates the relative difference between the experimental MT data and the calculated values for various combinations of J and g. The error surface is shown in Figure 4 10 as a two -

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126 dimensional contour plot and clearly shows only one minimum, confirming a good fit to the data. However, t he fit looked slightly insensitive to the value of J with an uncertainty in the value from 44< J <48. Magpack182 was used to simulate the data with J ranging from 44 to 46 cm 1 and the simulations plotted with the experimental data (Figure 4 11) and confirmed the insensitivity to the value in the range of 4446cm 1 for complex 42. To confirm the indicated ST = 4 ground state of complex 42 and to estimate the magnitude of the zero field splitting parameter D, magnetization vs dc field measurements were made on restrained samples at applied magnetic fields and temperatures in the 1 70 kG and 1.810.0 K ranges, respectively. The resulting data for 42 are shown in Figure 412 as a reduced magnetization ( M / N B) vs H/T plot, where M is the magnetization, N is Avogadro’s number, B is the Bohr magneton, and H is the magnetic field. The best fit for 42 is shown as the solid lines in Figure 4 12 and was obtained with S = 4 and either of the two sets of parameters: g = 1.80(2) and D = +0.92(3) cm1, or g = 1.84(1) and D = 0.80(2) cm1. Alternative fits with S =3 were rejected because they gave unreasonable values of g. The error surface for 42 is shown as the two dimensional contour plot in Figure 413 and shows only two minima with positive and negative D values, with the latter being of superior quality thus suggesting the true sign of D is negative. A lternating current s usceptibility studies were performed on complex 42 (Figure 4 1 4) to determine if it displayed single molecule magnet behavior. There were no indications that the in phase data would allow for confirmation of the ground state due to relatively strong intermolecular interaction s from pi pi stacking. The obtained inphase M signal for 4 2 is plotted as M T vs T in Figure 414 ( top) and decreases quickly from 10K down to 1.8 K. Extrapolating to 0 K the data from above 4K (to avoid lower temperature effects from the slight

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127 anisotropy and weak intermolecular interactions) gives a value around 4 cm3Kmol1 range, which is low for an S = 4 ground state and g < 2. There is no M signal in the out of phase plot (Figure 4 14 , bottom ). 4.3.2.3 Magnetochemical s tudies for complex 4 3 The solid state MT of 43 has a value of ~5.9 cm3 K mol1 and appears temperature independent from 300 K down to 40 K where is slowly decreases to a value of 5.5 before decreasing rapidly to 3.5 cm3Kmol1 at 5 K (Figure 4 15). The value of ~ 6 cm3Kmol1 at 300 K is much lower than the spinonly value of 14.75 cm3Kmol1 expected for four noninteracting manganese (2 MnIII and 2 MnII) ions which is an indication of antiferromagnetic interactions. The sharp decrease in the signal is most probably due to changes in the population of the components of the spin ground state which are split by ZFS and intermolecular interactions. The metal ions are thus clearly involved in magnetic exchange interactions, and the data were fit to the theoretical MT vs T expres sion derived from the spin Hamiltonian appropriate for a Mn4 butterfly; given in Equation 48, = 2Jwb12 12 1 2 1 2 ) – 2Jbb11 ) – 2Jww2 2) (4 8) Where Si refers to the spin of metal Mni, and Jwb and Jbb are the pairwise exchange parameters for wingtip body and bodybody metals of the butterfly topology, respectively; the Mn labeling scheme of Figure 44 was employed. However, it is reasonable to simplify Equation 48 to Equation 49 based on structural considerations. = 2Jwb12 12 1 2 1 2 ) – 2Jbb11 ) (4 9) This Hamiltonian can be transformed into an equivalent form (Equation 4 9) by using the A 1 B 2 T A B where the ST is the resultant spin of the complete molecule.

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128 = 2JwbT 2 – A 2– B 2) – 2JbbA 2 – 1 2 – 2) (4 10) From Equation 410 can be obtained the energy expression (Equation 4 11) for the energies, E(ST), of each ST state; constant terms contributing equally to all states have been omitted from E quation 410. E(ST, SA, SB) = Jwb[ST(ST+1) – SA(SA+1) – SB(SB+1)] – Jbb[SA(SA+1)] (4 11) An expression for the molar paramagnetic susceptibility, M, was derived using the above and the Van Vleck equation, and assuming an isotropic g tensor. The derived equation was then used to fit the experimental M vs T data in Figure 416 as a function of the two exchange parameters Jwb and Jbb, and the g factor. Good fits were obtained with fit parameters of Jwb = 4.6 + 0.3 cm1, Jbb = 2.4 + 0.1 cm1, and g = 1.85 + 0.03, with temperature independent paramagnetism (TIP) held constant at 600 x 106 cm3 mol1. Using these values, an energy ladder (Figure 4 17 ) c an be created to further confirm the S =1 ground state with a |1, 4> and the first excited state is |2, 4>, located 18.4 cm1 above the ground state. There is a cluster of 5 excited states within 36.8 cm1 shows that there are many low lying excited states which helps explain the following magnetic results. By using the energy ladder and the exchange couplings it is possible to see how the S T changes with the ratio of Jwb/Jbb in a spin frustrated system (Figure 4 18). To confirm the indicated ST = 1 ground state of complex 43 and to estimate the magnitude of the zerofield splitting parameter D, magnetization vs dc field measurements were made on restrained samples at applied magnetic fields and temperatures in the 0.1 70 kG and 1.810.0 K ranges, respectively. The resulting data for 43 are shown in Figure 419 as a reduced magnetization ( M / N B) vs H/T plot, where M is the magnetization, N is Avogadro’s number, B is the Bohr magneton, and H is the magnetic field. However, a reasonable fit was not obtained

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129 for any ground state S = 0 4. The splitting between the isofield lines indicates either a relatively large ZFS parameter or relatively strong intermolecular interactions. Strong intermolecular interactions are common with complexes containing large aromatic rings due to pi pi stacking. An additional, independent assessment of the ground state S value, ac s usceptib ility data, were collected on 43 in the 1.8 10 K range using a 3.5 G ac field oscillating at a frequency of 997 Hz. If the magnetization vector can relax fast enough to keep up with the oscillating field, then there is no imaginary (out of phase) susceptibility signal (M), and the real (in phase) susceptibility ( M ) is equal to the dc susceptibility. However, if the barrier to magnetization relaxation is significant compared to thermal energy (kT), then there is a non zero M signal and the in phase signal decreases. In addition, the M and M signals will be frequency dependent if the complex is a single molecule magnet. The main advantage of ac s tudies in the present case is that no dc field is used. This precludes problems arising from a dc field, such as the stabilization of Ms levels of low lying excited states with S greater than that of the ground state. The obtained inphase M signal for 43 is plotted as M T vs T in Figure 420 ( top ) and can be seen to quickly decreasing from 10 K down to 1.8 K. Extrapolating to 0 K the data from above 4K (to avoid lower temperature effects from the slight anisotropy and weak intermolecular interactions) gives a value around the 2 cm3Kmol1 range, which is consistent with an S = 1 ground state and g ~ 2. As can be seen in Figure 420 (bottom) , there is no out of phase signal. 4.3.3 Computational S tudies Theoretical calculations were carried out on complex 41 and 42 using semiemperical ZILSH method and with DFT calculations (vide infra). The single exchange constant is obtained by computing energies and spin couplings for the ferromagnetic (F, parallel) and

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130 antiferromagnetic (AF, antiparallel) spin components, and then solving Equation 4 3 for J and E0 using Equation 412. = (4 12) Energies and local spin densities of the Mn ions for each component are presented in Table 4 3. To summarize these results, the F component is quite low in energy relative to the other component. This indicates the exchange interactions between the two Mn3+ ions are ferromagnetic in nature. The spin densities are close to the formal values of four expected for highspin Mn3+ (d4) ions but are reduced below these numbers by spin delocalization, as found with ZILSH for other co mplexes.34, 90, 92, 183 The signs of the local spin densities indicate the relative direction of the spin mom ents of the manganese ions and show that the correct spin distributions were obtained for all spin components considered. Exchange constants were obtained from the information in Table 44 by simultaneous solution of Equation 48. The interactions between the two MnIII ions in both 41 and 42 are weakly antiferromagnetic with J12 = 4.8 cm1. ZILSH calculations indicate that the exchange constants in both complexes are equivalent and antiferromagnetic which is contrary to experimental evidence. Refinement of the exchange constants with more accurate DFT calculations showed that these interact ions were in fact different. Complexes 41 and 42 are small enough to be treated with DFT without fragmentation. The single exchange coupling, J12, is obtained by computing the DFT energies of both spin components along with spin couplings obtained with t he semiempirical ZILSH method and solving Equation 49 for J12 and E0. The obtained exchange constant, J12 are 16.4 cm1 and 45.7 cm1 for 41 and 42, respectively, which are in excellent agreement with the values of 16.4 cm1 and 43.8 cm1 obtained from the fit of the magnetization data.

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131 4.4 Conclusions and Future Work Peroxymonosulfate used in Mn chemistry in aqueous or mixed aqueous organic reaction matrices can be simply an oxidizing agent or can be used as an oxide or sulfate ion source. The use of peroxymonosulfate yielded two new species, [Mn2O(SO4)2(bpy)2(H2O)2] ( 41 ) and [Mn2O(O2CMe)(SO4)(bbe)(MeOH)2](PF6) (42 ), which are strongly ferromagnetically coupled. Species 41 and 42 display ferromagnetic coupling between the MnIII centers, with a resul ting groundstate spin of S = 4. The unusually strong ferromagnetic coupling in 42 is assigned to the net sum of its unusual structural distortions and two different tri atomic bridges. Clearly, the obtained results demonstrate that strong ferromagnetic c oupling is possible between two MnIII ions in the common structural type [MnIII 2O(X)2(bbe)2] where X is a polyatomic bridging group and bbe a chelating ligand. This unusually strong coupling found in complexes 41 and 42 were validated by DFT calculations. A similar mixed valent Mn4 tetramer has been synthesized and fully characterized. Contrary to the dimeric complexes, complex 43 displays antiferromagnetic coupling with an S = 1 ground state and can be rationalized usi ng the concept of spin frustration. Future work is to investigate how the strain of the bbe ligand effects the exchange interactions within the complex. The investigation will have the angle between the bipyridine units of the bbe ligand systematically va ried in 5 increments with geometry optimization before the exchange couplings are calculated through computational methods. Further attempts need to be made to isolate the [Mn2O(H3CCO2)2(bbe)(H3CCO)2]+ complex to determine if the sulfate bridges play a ro le or if our hypothesis is correct that there is a correlation between the strain of the ligand on the molecule and the magnetic interactions.

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132 Table 4 1. Exchange Interactions and Selected Structural Parameters for [MnIII 2OXY]n+ Complexes. Complex Mn .. Mn, Mn O, Mn O Mn, o J , cm 1 Ref [Mn 2 O(O 2 CMe) 2 (bpy) 2 Cl 2 ] 3.353(3) 1.788(11) 1.777(12) 124.3 (7) 4.1 184 [Mn 2 O(O 2 CPh) 2 (bpy) 2 (N 3 ) 2 ] 3.253(4) 1.802(4) 122.0(5) +8.8 184 [Mn 2 O(O 2 CMe) 2 (bpy) 2 (H 2 O) 2 ](ClO 4) 3.132(2) 1.781(5) 1.784(5) 122.9(4) 3.4 158 [Mn 2 O(O 2 CMe) 2 (HB(pz) 3 ) 2 ] a 3.159(1) 1.780(2) 125.0(3) 0.5 179 [Mn 2 O(O 2 CMe) 2 (Me 3 TACN) 2 ] b na 1.810(4) 120.9(1) +9 185 [Mn 2 O(O 2 CMe) 2 (TMIP) 2 ](ClO 4 ) 2 3.164(5) 1.797(11) 1.781(11) 124.4(6) 0.5 186 4 2 3.17 8(2) 1.780(3) 1.774(3) 126.83(16) +43.8 t.w. 4 1 3.2157(5) 1.7947(16) 1.7858(17) 127.82(9) +11.4 t.w. a HB(pz)3 = hydridotris ((1 pyrazol)borate). b Me3TACN = 1,4,7 trimethyl 1,4,7 triazacyclononane. t.w. = this work.

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133 T able 4 2. Crystallographic data for [Mn2O(SO4)2(bpy)2(H2O)2] ( 41), [Mn2O(O2CMe)(SO4)(bbe)(MeOH)2](PF6) (42 ) and [Mn4O2(O2CMe)4(bbe)2](ClO4) (4 3) . aFo| | Fc Fo|. b w (| Fo| | Fc|)2 w |Fo|2]1/2 where w 2(| Fo|). 4 1 H 2 O 4 2 4 3 MeCNH 2 O Empirical Formula C 20 H 26 Mn 2 N 4 O 14 S 2 C 26 F 6 H 29 Mn 2 N 4 O 9 PS C 32 H 40 Mn 4 N 6 O 21 FW, g mol 1 720.45 828.47 1064.44 Crystal System Monoclinic monoclinic triclinic Space Group P 21/n P 2 1 /n P1 Temperature 116 K 193 K 193 K 8.6849(3) 7.5946(6) 12.7443(6) 37.7372(15) 16.129(2) 13.0561(7) 17.0389(7) 27.531(2) 13.7098(7) 90 90 81.539(2) 101.1080(10) 91.849(2) 89.482(2) 90 90 80.227(2) Z 8 4 2 0.71073 0.71073 0.71073 Calculated density, g cm3 1.568 1.660 1.686 Linear absorption coefficient, cm1 11.506 9.48 12.90 R b or R1, % a 3.51 a 5.44 a 4.55 a R w or wR2 c , % b 8.65 b 13.10 c 12.88 c

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134 Table 4 3. B ond valance sum table for complex for 43. Mn(II) Mn(III) Mn(IV) M n 1 2.93 2.91 2.83 M n 2 1.81 Atom BVS Assignment group Atom BVS Assignment group O1 RO H 3 CO 2 O 4 1.98 RO H 3 CO 2 O2 RO H 3 CO 2 O RO H 3 CO 2 O3 1. O 2 oxide The underlined value is the one closest to the charge for which it was calculated. The oxidation state of a particular atom can be taken as the nearest whole number to the underlined value. The BVS values for O atoms of O2 -, OH-, and H2O groups are typica lly 1.82.0, 1.01.2, and 0.20.4, respectively. Table 4 4. Computational results for complexes 41 and 42. 4 1 ZILSH DFT Component Ferromagnetic Antiferromagnetic Ferromagnetic Antiferromagnetic E (cm 1 ) b ( a ( a +243.61 b Mn1 3.84 3.83 Mn2 +3.89 +3.83 +3.89 +3.83 +3.691 4 2 ZILSH DFT Component Ferromagnetic Antiferromagnetic Ferromagnetic Antiferromagnetic E (cm 1 ) +299.38 b ( a ( a b Mn1 3.84 +3.91 3.83 Mn2 +3.84 +3.82 a a.u. b cm1

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135 Figure 41. Structure of ligands: 2,2' bipyridine (bpy) and 1,2 bis(2,2' bipyrididyl 6 yl)ethane (bbe).

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136 Figure 42. The structure of complex 41 (top), a stereopair (middle), and the labeled core. Hydrogen atoms have been omitted for clarity. Color code: MnIII green; O red; N blue; S magenta; C gray.

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137 Figure 43. The structure of complex 42 (top), a stereopair (middle), and the labeled core. Hydrogen atoms have been omitted for clarity. Color code: MnIII, green; O , red; N , blue; S , magenta; C , gray.

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138 Figure 44. The structure of complex 43 (top), a stereopair (middle), and the labeled core. Hydrogen atoms have been omitted for clarity. Color code: MnII, yellow; MnIII, green; O , red; N blue; C , gray.

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139 050100150 200 250 300 350 MT (cm3 mol -1 K) 0 2 4 6 8 10 T (K) Figure 45. Plots of MT vs T for complexes 41 4 2 lines are fits to the data, see text for details.

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140 J (cm-1) 05101520 g 1.801.821.841.861.881.90 Figure 46. J vs g root mean square error surface for 41.

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141 H/T (kG/K) 01020304050 M/NB 0 2 4 6 8 0.1 T 0.5 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit Figure 47. Plot of reduced magnetization for 4 1; see text for fit parameters.

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142 Figure 48. D vs. g root mean square error surface for 41. g 1.801.851.901.952.002.052.102.15 D (cm-1) -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0.84 0.87 0.90 0.93 0.96 0.99 1.02 1.05 1.08 1.11 1.14 1.17 1.20 1.23 1.26 1.29 1.32 1.35 1.38 1.41 1.44 1.47 1.50 1.53 1.56 1.59 1.62 1.65 1.71 1.68 1.65 1.62 1.59 1.56 1.53 1.50 1.47 1.44 1.41 1.38 1.35 1.32 1.29 1.26 1.23 1.20 1.17 1.14 1.11 1.08 1.05 1.02 0.99 0.96 0.93 0.90 0.87 0.84 0.81 0.78 0.75 0.72 0.69 0.66 0.63 0.60 0.57 0.54 0.51 0.48 0.45 0.42 0.39 0.36 0.81 0.33 0.78 0.75 0.72 0.30 0.30 0.69 0.66 0.63 0.27 0.60 0.57 0.33 0.54 0.24 0.51 0.48 0.36 0.45 0.42 0.21 0.39 0.39 0.36 0.18 0.42 0.33 0.30 0.45 0.27 0.24 0.15 0.48 0.21 0.51 0.18 0.54 0.15 0.12 0.12 0.57 0.60 0.09 0.63 0.06 0.09 0.66 0.69 0.09 0.12 0.72 0.75 0.15

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143 T (K) 024 6 8 10 12 M'T (cm3 K mol-1) 0 2 4 6 8 T (K) 0 2 4 6 8 10 12 '' (cm3 mol-1) -1 0 1 2 3 Figure 49. Plots of inphase M (as M T) vs T ( left) and outof phase M vs T (right) ac s usceptibility for complex 41.

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144 J 35404550556065 g 1.801.821.841.861.881.901.921.941.961.98 1.40 1.39 1.38 1.37 1.36 1.35 1.34 1.33 1.32 1.31 1.30 1.30 1.29 1.29 1.28 1.28 1.27 1.27 1.26 1.26 1.25 1.25 1.24 1.24 1.23 1.23 1.22 1.22 1.21 1.21 1.20 1.20 1.19 1.19 1.18 1.18 1.17 1.17 1.16 1.16 1.15 1.15 1.14 1.14 1.13 1.13 1.12 1.12 1.11 1.11 1.10 1.10 1.09 1.09 1.08 1.08 1.07 1.07 1.06 1.06 1.05 1.05 1.04 1.04 1.03 1.03 1.02 1.02 1.01 1.01 1.00 1.00 0.99 0.99 0.98 0.98 0.97 0.97 0.96 0.96 0.95 0.95 0.94 0.94 0.93 0.93 0.92 0.92 0.91 0.91 0.90 0.90 0.89 0.89 0.88 0.88 0.87 0.87 0.86 0.86 0.85 0.85 0.84 0.84 0.83 0.83 0.82 0.82 0.81 0.81 0.80 0.80 0.79 0.79 0.78 0.78 0.77 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73 0.73 0.72 0.72 0.71 0.71 0.70 0.70 0.69 0.69 0.68 0.68 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.58 0.57 0.57 0.56 0.56 0.55 0.55 0.54 0.54 0.53 0.53 0.52 0.52 0.51 0.51 0.50 0.50 0.49 0.49 0.48 0.48 0.47 0.47 0.46 0.46 0.45 0.45 0.44 0.44 0.43 0.43 0.42 0.42 0.41 0.41 0.40 0.40 0.39 0.39 0.38 0.38 0.37 0.37 0.36 0.36 0.35 0.35 0.34 0.34 0.33 0.33 0.32 0.32 0.31 0.31 0.30 0.30 0.29 0.29 0.28 0.28 0.27 0.27 0.26 0.26 0.25 0.25 0.24 0.24 0.23 0.23 0.22 0.22 0.21 0.21 0.20 0.20 0.19 0.19 0.18 0.18 0.17 0.17 0.20 0.20 0.19 0.19 0.18 0.18 0.17 0.17 0.27 0.27 0.26 0.26 0.25 0.25 0.24 0.24 0.23 0.23 0.22 0.22 0.21 0.21 0.36 0.36 0.35 0.35 0.34 0.34 0.33 0.33 0.32 0.32 0.31 0.31 0.30 0.30 0.29 0.29 0.28 0.28 0.45 0.45 0.44 0.44 0.43 0.43 0.42 0.42 0.41 0.41 0.40 0.40 0.39 0.39 0.38 0.38 0.37 0.37 0.54 0.54 0.53 0.53 0.52 0.52 0.51 0.51 0.50 0.50 0.49 0.49 0.48 0.48 0.47 0.47 0.46 0.46 0.16 0.16 0.16 0.16 0.55 0.55 0.15 0.15 0.15 0.15 0.56 0.56 0.14 0.14 0.14 0.57 0.57 0.13 0.13 0.13 0.12 0.12 0.58 0.58 0.59 0.11 0.11 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 Figure 410. J vs g root mean square error surface for 42.

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145 T (K) 050100 150 200 250 300 350 MT (cm3 K mol-1) 0 2 4 6 8 10 0.1 T data J = 44 J = 45 J = 46 J = 47 J =48 Figure 411. Magpack simulations f or complex 42 with varying values of J.

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146 Figure 412. Plot of the r educed magnetization for 42; see text for fit parameters. Figure 413. D vs g root mean square error surface for 42. H/T (kG/K) 01020304050 M/NB 02468 2 T 3 T 4 T 5 T 6 T 7 T Fit

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147 T (K) 024 6 8 10 12 M'T (cm3 K mol-1) 0 2 4 6 8 T (K) 0 2 4 6 8 10 12 '' (cm3 mol-1) -1 0 1 2 3 Figure 414. Plots of in phase M (as M T) vs T ( top) and out of phase M vs T ( bottom ) ac s usceptibility for complex 42.

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148 T (K) 050100150200250300350 MT (cm3Kmol-1) 01234567 Figure 415. Plot of M T vs T for complex 43. T (K) 0 50 100 150 200 250 300 350 M (cm3 mol-1) 0.0 0.2 0.4 0.6 0.8 1.0 0.1 T fit Figure 416. Plot of M vs T for complex 43, solid black line is the fit to the data, see text for details

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149 ST 0123456789 Energy (cm-1) 0100200300400500 Figure 417. Energy ladder for Complex 43. Jbb/Jwb -4 -2 0 2 4 E/Jbb -200 -100 0 100 200 300 Figure 418. Plot of Energy/Jbb vs Jbb/Jwb for complex 43.

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150 H/T (kG/K) 01020 30 40 50 M/NB 0 1 2 3 4 5 6 0.1 T 0.5 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Figure 419. Plot of the r educed magnetization for complex 43.

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151 T (K) 02468 10 12 14 16 M'T (cm3 K mol-1) 01234 5 6 T (K) 0 2 4 6 8 10 12 14 16 M" (cm3 mol-1) -1.0-0.50.00.51.0 Figure 420. Plots of in phase M (as M T) vs T (top ) and out of phase M vs T ( bottom ) ac s usceptibility for complex 43.

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152 CHAPTER 5 A FAMILY OF MN7 DISKLIKE COMPLEXES WITH AN UNUSUAL GROUND STATE SPIN OF S = 9 5.1 Introduction The pursuit of novel mixedvalent high nuclearity manganese clusters has been continued for a plethora of reasons for which range from their aesthetically pleasing architecture to their ability to act as mimics for Mnx sites within biomolecules.187 192 Moreover, many of them display interesting magnetic properties such as large ground spin states, S , and sometimes behave as single molecule magnets (SMMs). SMMs are individual molecules that function as singledomain nanoscale magnetic particles below their blocking temperature, TB.16, 138, 193 This behavior arises from the combination of a large groundstate spin, S, and Isingtype magnetoanisotropy (negative zerofield splitting parameter, D), which leads to a significant energy barrier to the thermal relaxation of the molecular magnetic moment.194 The upper limit of the ener gy barrier to the relaxation of the magnetization can be calculated by S2|D| or (S21/4)|D| for integer and half integer spins, respectively. Experimentally, an SMM exhibits frequencydependent out of phase ac magnetic susceptibility signals, and hysteresis in a plot of magnetization vs applied dc magnetic field. Various families of SMMs have been discovered, and the largest Mn SMM is a Mn84 torus. SMMs have be known to display interesting quantum phenomena such as quantum tunneling of magnetization,195201 spin parity effects,57, 202 and quantum phase interference.57, 202 , 203 Thus, they have been implicated for possible use in quantum computing and as components in molecular spintronic devices, among others.204209 Thus, much of the allure of inorganic synthetic chemistry is to try to synthesize these interesting complexes for potential applications; however, part of this attraction is no doubt related to the unpredictable and sometimes serendipitous products produced from different types of reactions.

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153 Our group has reported the successful synthesis and isolation of two [Mn10O4(N3)4(hmp)12]2+ cations with T symmetry and a ground state spin, S = 22.210212 After a thorough investigation, it was established that the [Mn10O4(N3)4(hmp)12]2+ cations are not SMMs due to their small D . Following up on this project, the same synthetic route was used with the initial goal of substituting the azide ligands with other pseudohalides and halides to potentially change the symmetry or orientation of the JahnTeller axes to isolate a g ood single molecule magnet by taking advantage of the large ground state spin. However, the substitution of azide for other pseudohalides and halides has instead led to the preparation of a [Mn7(OH)3(hmp)9X3]2+ (where X = SCN-, OCN-, Br-, Cl-, I-) family of complexes. Herein the syntheses, crystal structures, and physical properties of this family of Mn7 clusters will be de scribed . The thiocyanate version is a new member of the whole integer spin SMM family of Mn7 wheels. 5.2 Experimental Section 5.2.1 Syntheses All preparations were performed under aerobic conditions using reagents and solvents as received unless otherwise specified. Safety note : Perchlorate salts are potentially explosive; such compounds should be synthesized and used in small quantities, and treated with utmost care at all times. [Mn7(OH)3(SCN)3(hmp)9] (ClO4)2 ( 51) : To a stirred solution of hmpH (0.20 ml, 2 .0 mmol) and NEt3 (0.28mL, 2.0 mmol) in MeCN/MeOH (19/1, v/v) was added tetrabutylammonium thiocyanate ( NBun 4SCN) (0.155g, 2 mmol) and Mn(ClO4)2 x H2O (0.50g, 2.0 mmol). Immediately following the addition of Mn(ClO4)2, Bromine water (1.7 mL, 2 .0 mmol) was added. The resulting red brown solution was stirred for 30 minutes , filtered and the filtrate layered with diethyl ether and left undisturbed at room temperature. After two days, X -

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154 ray quality crystals of 51MeCN were obtained. They were collected by filtration, washed with Et2O, and dried under vacuum; the yield was 82 %. Anal. Calculated (Found) for 51 (solvent free): C 39.31 (39.25); H 3.41 (3.29); N 10.52 (10.49). Selected IR data (cm1): 3487 (b), 2839 (m), 2064 (vs), 1605 (s), 1569 (m), 1480 (m), 1437(s), 1384 (w), 1363 (m), 1281 (m), 1223 (w), 1154 (m), 1063 (s), 1044 (s), 1017 (m), 762 (s) , 719 (m), 670 (m), 565 (s), 525 (m), 480 (m), 448 (m). [Mn7(OH)3(NCO)3(hmp)9] (ClO4)2 ( 52) : To a stirred solution of hmpH ( 0.2 ml, 2 .0 mmol) and NEt3 (0.28 mL, 2 .0 mmol) in MeCN/MeOH (19/1, v/v) was added NaNCO (0.14 g, 2.0 mmol) and Mn(ClO4)2 x H2O (0.50 g, 2.0 mmol). The resulting red brown solut ion was stirred for 30 minutes, filtered and the filtrate layered with diethyl ether and left undisturbed at room temperature. After two days, X ray quality crystals of 52MeCN were obtained. They were collected by filtration, washed with Et2O, and dried under vacuum; the yield was 76 %. Anal ysis: Calc ulate d (Found) for 52 MeCN: C 36.856 (36.95); H 3.596 (3.361); N 9.001 (8.937). Selected IR data (cm1): 3439 (b), 2840 (m), 2196 (vs), 1606 (s), 1570 (m), 1481 ( s), 1439 (s), 1366 (m), 1324 (w), 1288 (m), 1225 (w), 1156 (s), 1068 (s), 1017 (s), 823 (w), 763 (s), 720 (m), 669 (s), 624 (s), 566 (s), 527 (m), 481 (w). [Mn7(OH)3 (hmp)9 (I)2(H2O)] (ClO4)3 ( 53 ) : To a stirred solution of hmpH ( 0.2 ml, 2 mmol) and NEt3 (0.28mL, 2 mmol) in MeCN/MeOH (19/1, v/v) was added TEAI (0.514g, 2 mmol) and Mn(ClO4)2 x H2O (0.50g, 2 mmol) The resulting redbrown solution was stirred for 30 minutes, filtered , the filtrate was layered with diethyl ether , and left undisturbed at room temperature . After two days, X ray quality crystals of 53MeCN were obtained. They were collected by filtration, washed with Et2O, and dried under vacuum; the yield was 74 %. Anal ysis: Calc ulate d (Found) for 53 (solvent free): C 34.51 (34.37); H 3.16 ( 2.93); N 6.71

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155 (6.57). Selected IR data (cm1): 3400 (b), 3059 (m), 3024 (m), 2832 (m), 2246 (m), 1606 (s), 1569 (m), 1480 (s), 1438 (s), 1365 (m), 1223 (w), 1156 (m), 1065 (s), 1016 (m), 824 (w), 760 (s), 720 (m), 669 (m), 640 (s), 561 (m), 525 (m), 447 (m ). [Mn7(OH)3(Br)3(hmp)9] (ClO4)2 ( 54) : To a stirred solution of hmpH ( 0.20 ml, 2 .0 mmol) and NEt3 (0.28 mL, 2 .0 mmol) in MeCN/MeOH(19/1, v/v) was added TBABr (0.65 g, 2.0 mmol) and Mn(ClO4)2 x H2O (0.50 g, 2 mmol). The resulting red brown solution was sti rred for 30 minutes, filtered , the filtrate was layered with diethyl ether , and left undisturbed at room temperature. After two days, X ray quality crystals of 54MeCN were obtained. They were collected by filtration, washed with Et2O, and dried under vacuum; the yield was 85 %. Anal ysis: Calc ulate d (Found) for 543MeCN: C 36.57 (36.54); H 3.38 (3.38); N 8.53 (8.43). Selected IR data (cm1): 3398 (b), 2840 (m), 1606 (s), 1569 (s), 1482 (s), 1439 (s), 1365 (m), 1289 (s), 1259 (w), 1224 (m), 1157 (m), 1066 (s), 1015 (s), 885 (w), 825 (m), 761 (s), 721 (m), 670 (s), 562 (s), 525 (m), 484 (m) 448 (w). [Mn7(OH)3(Cl)3(hmp)9] (ClO4)2 ( 55): To a stirred solution of hmpH ( 0.20 ml, 2 .0 mmol) and NEt3 (.28mL, 2.0 mmol) in MeCN/MeOH(19/1, v/v) was added TEACl (0.36g, 2.0 mmol) and Mn(ClO4)2 x H2O (0.50g, 2.0 mmol). The resulting redbrown solution was stirred for 30 minutes , filtered , the filtrate layered with diethyl ether, and left undisturbed at room temperature. After two days, X ray quality crystals of 54 MeCN were obtained. They were collected by filtration, washed with Et2O, and dried under vacuum; the yield was 78 %. Anal ysis: Calc ulate d (Found) for 54 H2O: C 38.57 (38.42); H 3.85 (3.84); N 6.98 (7.03). Selected IR data (cm1): 3398 (b), 2840 (m), 1606 (s), 1569 (s), 1482 (s), 1439 (s), 1365 (m), 1289 (s), 1259 (w), 1224 (m), 1157 (m), 1066 (s), 1015 (s), 885 (w), 825 (m), 761 (s), 721 (m), 670 (s), 562 (s), 525 (m), 484 (m) 448 (w).

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156 5.2.2 X ray Crystallography X Ray Intensity data were collected at 100 K on a Bruker DUO diffractometer using MoK radiation ( ) and an APEXII CCD area detector. Raw data frames were read by program SAINT1 and integrated using 3D profiling algorithms. The resulting data were reduced to produce hkl reflections a nd their intensities and estimated standard deviations. The data were corrected for Lorentz and polarization effects and numerical absorption corrections were applied based on indexed and measured faces. The structure of 51 was solved and refined in SH ELXTL6.1 using direct methods and full matrix least squares refinement. The nonH atoms were refined with anisotropic thermal parameters and all of the H atoms were placed in calculated , idealized positions and refined as riding on their parent atoms. The asymmetric unit consists of one third of a Mn7 cluster, two 1/3 perchlorate anions and two acetonitrile solvent molecules. The Mn7 and perchlorates are located on 3fold rotation axes while the solvent molecules are in general positions. Each of the solvent molecules was disordered and was refined in three parts each. The H atom , H4, on the bridging atom O4 was obtained from a difference Fourier map and refined freely. In the final cycle of refinement, 6607 reflections (of which 6382 are observed with I > 2(I)) were used to refine 386 parameters and the resulting R1, wR2 and S (goodness of fit) were 3.01%, 8.54% and 1.061, respect ively. The refinement was carried out by minimizing the wR2 function using F2 rather than F values. R1 is calculated to provide a reference to the conventional R value but its function is not minimized. The structure of 52 was so lved and refined in SHE LXTL6.1 using direct methods and full matrix least squares refinement. The nonH atoms were refined with anisotropic thermal parameters and all of the H atoms were calculated in idealized positions and refined as riding on

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157 their parent atoms. The asymmetric unit consist of a third of a Mn7 cluster (located on a 3 fold rotation axis, a 1/3 perchlorate anion (also located on the same 3 fold rotation axis ) , a 1/3 perchlorate anion in general position, an acetonitrile solvent molecule and two one third methanol solvent molecules each located on 3 fold rotational axes. The H atom on the bridging O1 atom was obtained from a difference Fourier map and refined freely w hile the protons of the methanol solvent molecules could not be located and thus were not included in the final refinement cycle. In the final cycle of refinement, 5243 reflections (of which 4629 are observed with I > 2(I)) were used to refine 357 paramet ers and the resulting R1, wR2 and S (goodness of fit) were 4.83 %, 13.70% and 1.069 , respectively. The refinement was carried out by minimizing the wR2 function using F2 rather than F values. R1 is calculated to provide a reference to the conventional R value but its function is not minimized. The structure of 54 was solved and refined in SHELXTL6.1 using direct and fullmatrix least squares refinement. The nonH atoms were refined with anisotropic thermal parameters and all of the H atoms were calculated in idealized positions and refined riding on their parent atoms. The asymmetric unit consists of a Mn7Br3 cluster, one perchlorate anion, one Brdisordered against a perchlorate anion, and five acetonitri le solvent molecules. The Br/Cl O4 ratio was fixed at 90/10 after refinement. Three of these perchlorate or Brdisordered anions interact strongly with the three bridging OH ligands , whose H atoms were obtained from a difference Fourier map and refined freely. In the final cycle of refi nement, 17929 reflections (of which 14761 are observed with I > 2(I)) were used to refine 988 parameters and the resulting R1, wR2 and S (goodness of fit) were 2.07 %, 5.05 % and 1.019, respectively. The refinement was carried out by minimizing the wR2 f unction using F2 rather than F values. R1 is calculated to provide a reference to the conventional R value but its function is not minimized.

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158 5.2.3 Physical Measurements Infrared spectra were recorded in the solid state (KBr pellets) on a Nicolet Nexus 67 0 FTIR spectrometer in the 400 4000 cm1 range. Elemental analyses (C, H, and N) were performed by the in house facilities of the University of Florida, Chemistry Department. Variabletemperature dc and ac magnetic susceptibility data were collected at the University of Florida using a Quantum Design MPMS XL SQUID susceptometer equipped with a 7 T magnet and operating in the 1.8 300 K range. Samples were embedded in solid eicosane to prevent torqueing. Magnetization vs field and temperature data were fit using the program MAGNET. Pascal’s constants were used to estimate the diamagnetic correction, which was subtracted from the experimental susceptibility to give the molar paramagnetic susceptibility M). 5.3 Results and Discussion 5.3.1 Syntheses Some of the most common routes to highnuclearity Mnx clusters are reactions of simple manganese salts in the presence of potentially bridging or chelating ligands. The exact identity and nuclearity of the isolated products depend on a variety of factors such as pH, reagent ratios, solvent, carboxylate and chelate, among others. Reaction of Mn(ClO4)26H2O with equimolar amounts of hmpH, NEt3, and Xsalts (X= Br-, I-, Cl-, OCN-) in MeCN/MeOH (20:1 v/v) resulted in dark reddish brown solutions from which were subsequently isolated [Mn7(OH)3(hmp)9X3](ClO4)2 in good yields (7485 %). The thiocyanate (SCN-) version with the same formula was isolated with the addition of bromine water to the previous reaction. O nly the full structure of 51, 52, 53, and 54 were solved because unit cell determinations, infrared spectra, and elemental analyses indicated compound 55 was the same a previously published compound. Formation of 51, 52, 54, and 55 is summarized i n Equation 51: 4Mn2+ + 3Mn3+ + 9hmpH + 6NEt3 + 3/2 O2 + 3X

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159 [Mn7(OH)3(hmp)9X3]2+ + 6HNEt3 + ( 51) And the formation of 53 is summarized in Equation 52: 14Mn2+ + 18 hmpH + 24 NEt3 + 3/2 O2 + 6H2O 2[Mn7(OH)3(hmp)9I2(H2O)]2+ + 24HNEt3 + ( 52) where atmospheric O2 is assumed to be the oxidizing agent to generate MnIII from MnII, facilitated by the basic conditions provided by NEt3; in the absence of NEt3, longer reaction times are required to get a significant dark coloration and the yields of the isolated products are much lower. However, addition of more than 2 equivalents of NEt3 does not increase the yield of products. 5.3.2 Description of Structures Complexes 51 and 52 are isostructural and crystallize in a rhombohedral space group R3 and have C3 crystallographic symmetry (Figures 5 5 and 5 6) with the JahnTeller elongations of 51 and 52 shown in Figure 57. Selected intermolecular distances and angles for 51 and 52 can be found in Table A 4 and A 5, respectively. The five cation s of 5(1 5) all contain a near planar hexagon of alternating MnII and MnIII ions surrounding a central, seventh MnII ion. Ther e is a perchlorate ion hydrogenbonded to the three 3OH groups (Figure 58, top). The central MnII ion is 0.28 out of the Mn6 hexagon plane (Figure 58, bottom). This Mn7 unit is held together by three 3OH and 9 hmpligands (Figures 5 5 and 56). There are three terminal halides or pseudo halides on each of the MnII ions in the outer hexagon. The manganese ions are all six c oordinate with near octahedral geometry. The oxidation state assignments mentioned above were determined from charge considerations, the metric parameters, bond valence sum (BVS) calculations (Table 5 3), and the identification of JahnTeller distortions expected for MnIII ions; the Mn7 cations of 5( 14 ) are thus mixed valent

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160 4MnII, 3MnIII and they are color coded accordingly in Figures 51 – 56. The protonation levels of the bound O atoms were confirmed by oxygen BVS calculations (Figure 54) to be prot onated in the case of the hydroxides and deprotonated for the hmpoxygen atoms. The MnIII JT elongation axes are O3Mn1Mn351 and 52, respectively. The cores of the structures of 51 – 55 are thus overall very similar to each other, except for the terminal halides or pseudohalides on the MnII ion in the outer wheel (Figures 5(1 4)). Closer inspection of the structures and metric parameters reveal f ew differences. Selected intermolecular distances and angles for 54 can be found in Table A 6. For this reason, direct comparison will be done on complexes 51 and 5 2 because they are isostructural and differ only by three atoms. The Jahn Teller axes are shown for both 51 and 52 in Figure 57 and the core with a perchlorate ion hydrogenbonded to the three hydroxides is shown in 58. In fact, 51 and 52 were overlaid and a root mean square difference was calculated to be only 0.0318 (Figure 5 9). 5.3.3 Magnetochemistry 5.3.3.1 Direct c urrent m agnetic susceptibility studies Solid state, variable temperature dc magnetic susceptibility ( M) measurements were performed on vacuum dried microcrystalline samples of complexes 5(1 5) . The data were collected i n the 5.0300 K range in a 0.1 T (1000 Oe) dc magnetic field, and they are shown as MT vs T plots in Figure 510. Variable temperature magnetic susceptibility studies were performed on microcrystalline samples of 5 1, restrained in eicosane to prevent torqueing. The magnetic susceptibilities were

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161 examined at a 0.1 T (1000 Oe) field in the 5 to 300 K temperature range for 51. Diamagnetic corrections were applied to the magnetic susceptibilities using Pascal's constants.178 For complex 51, MT gradually increases from 24.78 cm3Kmol1 at 300K to a value of ~29 cm3Kmol1 at 100 K and then increases rapidly to 58.06 cm3Kmol1 at 5K (Figure 5 10). The 300K value i s slightly less than the spinonly (g = 2) value of 26.5 cm3Kmol1 for four MnII and three MnIII noninteracting ions, indicating the presence of dominant ferromagnetic exchange interactions. The MT value at low temperature appears to be heading for a final value of ~60 cm3Kmol1, the spin only ( g = 2) value of a species with an S = 11 ground state. For complexes 52, 53, 54, and 55, MT gradually increases from ~26 cm3Kmol1 at 300K to a value of ~29 cm3Kmol1 at 100 K and then increases rapidly to ~ 40.06 cm3Kmol1 at 5K (Figure 510). The 300K value is slightly less than the spinonly (g = 2) value of 26.5 cm3Kmol1 for four MnII and three MnIII noninteracting ions. The MT value at low temperature appears t o be heading for a final value of ~ 40 cm3Kmol1, the spinonly (g = 2) value of a species with an S = 9 ground state. To confirm the indicated S = 11 and S = 9 ground state for complex 51 and 5( 24 ), respectively, and to estimate the magnitude of the zero field splitting parameter, D , magnetization vs dc field measurements were made on restrained samples at applied magnetic fields and temperatures in the 1 – 10 kG and 1.810.0 K ranges, respectively. Attempts to fit the data, using the MAGNET program, by diagonalization of the spin Hamiltonian matrix assuming z 2), Zeeman terms, and employing a full powder average. The corresponding spin Hamiltonian is given by Equation 5 4, z i s the easy B is the Bohr magneton, and 0 is the vacuum permeability.

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162 z 2 + g B0 H (5 4) From past experience, MnII 4MnIII 3 wheel complexes tend to be a case where there are low lying excited states that are consequently populated even at relatively low temperatures and/or excited states that are more separated from the ground state but have S values greater than that of the g round state and thus their larger Ms levels rapidly approach (or even cross) those of the ground state in a strong magnetic field. Such situations are expected for complexes 5( 14 ) because of their high MnII content (exchange interactions involving MnII a re known to be weak and almost always antiferromagnetic, leading to small energy separations between the ground state and the many excited states with larger S values), and will lead to poor fits of the magnetization data since the fitting program assumes only the ground state is populated.213 For complex 51, a satisfactory fit was obtained using data collected in the field range 0.10.8 T. The best fit is shown as the solid lines in the reduced magnetization ( M/NB vs H/T ) plot (Figure 5 11), and was obtained with S = 11, g = 1.83(1), and D = 0.06(1). An equally good fit was also obtained with S = 11, g = 1.82(2), and D = 0.75(1) cm1. It is common to obtain two acceptable fits of magnetization data for a gi ven S value, one with D < 0 and the other with D > 0, since magnetization fits are not very sensitive to the sign of D . Alternative fits with S = 10 were rejected because they gave unreasonable values of g and D . The root mean square D vs g error surface for the fit was generated using the program GRID, and is shown as a 2 D contour plot in Figure 512 for the D = 0.3 to 0.3 cm1 and g = 1.8 2.2 ranges. Two minima are observed; the one for the negative D value is clearly of greater q uality. For complex 52, we were able to obtain a satisfactory fit using all data up to 3 T. This suggests that the ground state of complex 52 is relatively well isolated from the nearest excited

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163 states. The best fit is shown as the solid lines in the reduced magnetization ( M/NB vs H/T ) plot in Figure 5 13 and was obtained with S = 9, g = 1.94(1), and D = 0.03(1) cm1. An equally good fit was also obtained with S = 9, g = 1.94(2), and D = 0.03(1) cm1. It is common to obtain two acceptable fits of magn etization data for a given S value, one with D < 0 and the other with D > 0, since magnetization fits are not very sensitive to the sign of D . Alternative fits with S = 10 and 8 were rejected because they gave unreasonable values of g and D. The root mean square D vs g error surface for the fit was generated using the program GRID, and is shown as a 2 D contour plot in Figure 514 for the D = 0.3 to 0.3 cm1 and g = 1.8 2.2 ranges. Two minima are observed, both are of similar quality thus it is not poss ible on the basis of these fits to determine the more likely sign of the axial anisotropy parameter D for 52. 5.3.3.2 Alternating c urrent m agnetic s usceptibility studies. A c s usceptibility studies are a powerful complement to dc studies for determining t he ground state of a system, because they remove the complications that arise from having a dc field present. The obtained inphase M signal for complex 51 is plotted as MT vs T in Figure 715, and the data appears to be almost temperature independent, confirming a well isolated ground state before decreasing slightly around 3 K, extrapolation to 0 K (to avoid lower temperature effects from the slight anisotropy and weak in termolecular interactions) gives a value of ~ 62 cm3 K mol1, which is consistent with an S = 11 ground state and g ~2, in excellent agreement with the reduced magnetization fit. We conclude that complex 51 does have an S = 11 ground state. There is an ou t of phase ac s usceptibility signal; however, only a partial peak is present down to 1.8 K, the operating limit of our SQUID magnetometer. The obtained inphase M signal for complexes 52, 53, 54 , and 55 are plotted as MT vs T in Figure 515, and the data appears to be almost temperature independent, before

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164 decreasing slightly around 3 K , extrapolation to 0 K gives a value of ~ 43 cm3 K mol1, which is consistent with an S = 9 ground state and g ~2, in excellent agreement with the reduced magnetization fit. We conclude that complex 52 does have an S = 9 ground state. There is no out of phase ac s usceptibility signal down to 1.8 K, the operating limit of our SQUID magnetometer. An S = 11 ground state has been identified for six Mn7 complexes at the MnII 4MnIII 3 oxidation level: 5 1 and the five previously published examples in Table 51. Additionally, an S = 9 ground state has been identified for four complexes reported in the present work. The repeat occurrence of S = 11 is a little surprising due to complexes containing only MnIIMnII and MnIIMnIII interactions, typically all interaction would be expected to be weak and of comparable magnitude.1 , 214, 215 The Mn7 topology is typically described as a Mn6 hexagon with a central manganese ion; however, it also consists of fused Mn3 triangles which are common examples of units suscepti ble to spin frustra tion effects. I t is reasonable to conclude that the ground state would be very sensitive to the relative magnitude of the competing interactions; a MnII 4MnIII 3 species could have a ground state spin of S = 0 16 range, so an intermediate S = 11 or 9 could be rationalized as due to spin frustration.1 Thus, a family of Mn7 complexes could be expected to have a variety of ground states res ulting in slight changes in their structural parameters, from differing ligation, crystal packing, solvation, and so forth. However, the above five Mn7 complexes instead possess S =11 and 9 ground states even though they contain only slight modification of the terminal ligands. To fully understand the role spin frustration effects are playing, it is necessary to examine the exchange interactions between the constituent manganese. Unfortunately, the Mn7 complexes are not amenable to the Kambe method18 and the exchange

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165 couplings are not easily or reliably obtained by fitting the variable temperature magnetization for such a complicated high nuclearity manganese system. However, previous work on similar Mn7 wheel clusters with the same oxidation states of the metals within the same topology has given a foundation to begin to understand the differences in the ground states displayed by the Mn7 family presented herein. Stamatatos et al. reported complexes, {[Na(MeOH)3][MnII 4MnIII 3(N3)6(mda)6]}215 n ( 5 6) and{Na[MnII 4MnIII 3(N3)6(teaH)6]}n ( 57), with S = 11 and 16, respectively (Figure 5 17).213 In complex 56, the MnII ions are labeled as Mn2, Mn3, M n4, and Mn7 and the MnIII ions are labeled as Mn1, Mn5, and Mn6. In complex 57, the MnII and Mn3 and the MnIII S = 16 ground state of complex 57 results from all of the spins alig ning parallel to one another, whereas the S = 11 ground state of complex 56 occurs with all of the outer manganese ions’ spins aligning parallel with one another and the central manganese ion’s spin aligning antiparallel to the outer ring. Theoretical cal culations were performed on both complexes and the estimated exchange couplings are shown in Figure 5 18. The outer ring of manganese ions are coupled relatively strongly compared to the inner wheel couplings. So, the ground state is dependent on the subtl e differences in the magnitude of the coupling of the central MnII ion to the outer ring of Mn ions. In the case of complex 56, the MnIIMnII antiferromagnetic exchange interactions dominate leading to an S =11 ground state, whereas in complex 57, the MnI IMnIII ferromagnetic exchange interactions dominate leading to an S = 16 ground state. Thus, it becomes clear that if the magnitude of the outer MnIIMnIII interactions are of comparable magnitude to the inner MnIIMnII and MnIIMnIII interactions spin frustration effects led to an intermediate ground state spin. A similar example was discussed in Chapter 3.

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166 5.4 Conclusions and Future W ork A new family of Mn7 wheel clusters containing the hmpligand has been prepared and characterized. The use of hmpH and a variety of pseudohalides and halides in manganese cluster chemistry resulted in a new family of Mn7 ( 5 ( 25)) complexes with an unusual ground state spin value of S = 9 and a rare example of a whole integer single molecule magnet ( 51 ). The present work along with past work emphasizes the versatility of hmpas a chelating and bridging ligand and suggests that further work substituting halides and pseud ohalides in place of azide is worth exploring in the future. Further investigation of the exchange couplings within the new Mn7 family with the ground spin state value S = 9 through computational methods could further help explain this unusual ground sta te spin.

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167 Table 5 1. Previously reported Mn7 wheel complexes. Complex R ef S D (cm 1 ) U eff [Mn II 4 Mn III 3 (OH) 3 (hmp) 9 Cl 3 ](Cl)(ClO 4 ) 216, 11 [Mn II 4 Mn III 3 (teaH) 3 (tea) 3 ](ClO 4 ) 2 3MeOH 218 11 [NEt 4 ]{Mn II [Mn II 3 Mn III 3 Cl 6 (mda) 6 ]} 219 {[Na(MeOH) 3 ][Mn II 4 Mn III 3 (N 3 ) 6 (mda) 6 ]} n 11 (NHEt 3 )[Mn II 4 Mn III 3 Cl 6 (mda) 6 ] 213 11 (NHEt 3 )[Mn II 4 Mn III 3 (N 3 ) 6 (mda) 6 213 11 {Na[Mn II 4 Mn III 3 (N 3 ) 6 (teaH) 6 ]} n 16 (NHEt 3 )[Mn II 4 Mn III 3 (N 3 ) 6 (teaH) 6 ] 213 16 [Mn II (pppd) 6 (tea)(OH) 3 ][BF 4 } 2 MeOH2CH 2 Cl 2 [Mn II (paa) 6 (OMe) 6 ][NO 3 ] 2 MeOH [Mn II 3 Mn III 4 (OMe) 12 (dbm) 6 ]CHCl 3 4MeOH 221 [Mn II 3 Mn III 4 NO 2 hbide) 6 2 H 4 Cl 2 119, 222 {Mn II [Mn II 2 Mn III 4 Cl 6 (L 3 ) 6 ]}2CHCl 3 223 [Mn II Mn III 6 (heamp) 6 ](ClO 4 ) 2 CH 2 Cl 2 H 2 O 224 12.9 cm 1 hmpH, 2hydroxymethylpyridine; teaH3, triethanolamine; mdaH2, N methyldiethanolamine; pppdH, 1phenyl 3 (2 pyridyl)propane 1,3dione; paaH, N (2 pyridinyl)acetoacetamide; Hdbm, dibenzoylmethanol; H3(5NO2 hbi de), N (2 hydroxy5nitrobenzyl)iminodiethanol; H2L3, N nbutyldiethanolamine, heampH3, 2[N,N di(hydroxyethyl)aminomethyl]phenol

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168 Table 5 2. Crystallographic data for complexes 51, 52, and 54. complex 1 2 4 formula crystal system Rhombohedral Rhombohedral Triclinic space group R3 R3 P1 3 6361.1 Z 3 3 2 calc, gcm3 1 R1c,d wR2 e Table 5 3. Bondvalence sums for the Mn atoms of complex 51, 52, 53 , and 54. 1 2 3 Mn II Mn III Mn IV Mn II Mn III Mn IV Mn II Mn III Mn IV Mn1 3.32 3.07 3.14 3.34 3.11 3.24 3.34 3.11 3.24 Mn2 1.78 1.92 1.94 1.94 1.99 1.94 1.99 Mn3 1.95 1.82 1.94 1.82 1.94 3 4 Mn II Mn III Mn IV Mn II Mn III Mn IV Mn1 3.21 3.01 3.21 3.31 3.11 3.21 Mn2 1.95 1.98 1.96 1.97 1.94 1.98 Mn3 1.97 1.89 1.86 1.96 The underlined value is the one closest to the charge for which it was calculated. The oxidation state of a particular atom can be taken as the nearest whole number to the underlined value.

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169 Table 5 4. Bondvalence sums for the O atoms of complex 51, 52, 53, and 54. 5 1 5 2 Atom BVS Assignment group Atom BVS Assignment group O1 RO hmp O1 1.349 HO HO O2 RO hmp O2 RO hmp O3 RO hmp O3 1.931 RO hmp O4 HO OH O4 RO hmp 5 3 5 4 Atom BVS Assignment group Atom BVS Assignment group O1 1.213 HO OH O1 HO OH O2 1.214 HO OH O2 HO OH O3 1.214 HO OH O3 1.181 HO OH O4 RO hmp O4 RO hmp RO hmp RO hmp O6 RO hmp O6 RO hmp 1.964 RO hmp 1.864 RO hmp O8 RO hmp O8 RO hmp O9 1.866 RO hmp O9 RO hmp 1.989 RO hmp 1.499 RO hmp O11 1.963 RO hmp O11 1.939 RO hmp O12 1.868 RO hmp O12 1.983 RO hmp O13 H 2 O H 2 O The BVS values for O atoms of O2 -, OH-, and H2O groups are typically 1.82.0, 1.01.2, and 0.20.4, respectively.

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170 Figure 51. Structure of 51, side on view (top); topdown view (middle); labelled stereoview (bottom). Hydrogen atoms have been omitted for clarity. Color code: Mn3+, green; Mn2+, yellow; S, magenta; O, red; N, blue; C, light grey. Mn1” Mn2’ Mn3 Mn2” Mn1’ Mn2’ O4 O4’ O4” O3’ O3 O3” Mn1 Mn2” Mn2” Mn1’ Mn1 Mn3 Mn2’ O 4 O4’ O4” O3’ O3 O3” Mn1”

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171 Figure 52. Structure of 52, side on view (top); topdown view (middle); and labelled stereoview. Hydrogen atoms have been omitted for clarity. Color code: Mn3+, green; Mn2+, yellow; O, red; N, blue; C, light grey. Mn2 Mn2” Mn2’ Mn1 Mn3” Mn3 Mn3’ O 2 O2’ O2” O1’ O1 O1” Mn2 Mn2” Mn2’ Mn3” Mn3 Mn3’ O 2 O2’ O2” O1’ O1 O1” Mn1

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172 Figure 53. Structure of 53, side on view (top); topdown view (middle); and labelled stereoview. Hydrogen atoms have been omitted for clarity. Color code: Mn3+, green; Mn2+, yellow; O, red; N, blue; I, light green; C, light grey.

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173 Figure 54. Structure of 54, side on view (top); topdown view (middle); and labelled stereoview. Hydrogen atoms have been omitted for clarity. Color code: Mn3+, green; Mn2+, yellow; O, red; N, blue; C, light grey; Br, orange.

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174 Figure 55. The stereopair of 51, side on view (top); topdown view with J T axes shown in bright green (bottom). Hydrogen atoms have been omitted for clarity. Color code: Mn3+, green; Mn2+, yellow; O, red; N, blue; C, light grey.

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175 Fi gure 56. The stereopair of 52, side on view (top); topdown view (bottom). Hydrogen atoms have been omitted for clarity. Color code: Mn3+, green; Mn2+, yellow; O, red; N, blue; C, light grey.

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176 Figure 57. The stereopair of 51 (top) and 52 (bottom) wi th J T axes shown in bright green. Hydrogen atoms have been omitted for clarity. Color code: Mn3+, green; Mn2+, yellow; O, red; S, magenta; N, blue; C, light grey.

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177 Figure 58. The core of 52 hydrogenbonding with perchlorate (top); stereoview of 52 hydrogen bonding to the perchlorate counter ion (middle); and side view of Mn6 plane showing the central Mn2+ ion slightly out of the plane. Hydrogen atoms have been omitted for clarity. Color code: Mn3+, green; Mn2+, yellow; O, red; N, blue; C, light gre y.

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178 Figure 59. Weighted root mean square deviation of 51 and 52; stick diagram (top) and stereoview (bottom).

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179 T (K) 050100 150 200 250 300 350 MT (cm3 K mol -1 ) 010203040506070 5-1 5-2 5-3 5-4 5-5 Figure 510. Plots of MT vs T for complexes 51, 52, 53, 54, and 55.

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180 H/T (kG/K) 0 1 2 3 4 5 6 M/NB 0 2 4 6 8 10 12 14 16 18 0.1 T 0.2 T 0.3 T 0.4 T 0.5 T 0.6 T 0.7 T 0.8 T 0.9 T 1.0 T Fit Figure 511. Reduced magnetization plot for complex 51; see the text for fit parameters.

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181 2.6 2.6 2.8 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.0 3.8 3.6 3.4 3.2 3.0 3.0 2.8 2.8 2.6 2.6 2.4 2.4 2.2 2.2 2.0 2.0 1.8 1.8 1.8 1.6 1.6 1.6 1.4 1.4 1.4 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 3.8 2.4 2.4 3.6 2.2 2.2 3.4 2.0 2.0 3.2 1.0 1.0 1.0 1.0 1.0 1.0 1.8 1.8 3.0 1.6 1.6 2.8 1.4 1.4 1.4 1.4 1.4 2.6 0.8 0.8 0.8 0.8 0.8 2.4 1.2 1.2 2.2 1.0 1.0 1.6 1.6 2.0 0.6 0.6 0.6 0.8 0.8 1.8 1.8 1.8 0.6 0.6 1.6 0.4 0.4 1.4 0.4 0.4 2.0 1.2 0.2 2.2 1.0 0.4 0.8 2.4 0.6g 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 D (cm-1) -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Figure 512. Root mean square error surface for D vs g plot for complex 51.

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182 H/T (kG/K) 0.0 0.5 1.0 1.5 2.0 2.5 M/N B 0 2 4 6 8 10 12 14 0.1 T 0.2 T 0.3 T 0.4 T Fit Figure 513. Reduced magnetization plot for complex 52; see text for fit parameters.

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183 1.0 1.1 1.3 1.2 1.1 1.0 0.9 0.8 0.8 0.7 0.7 0.9 0.9 0.6 0.6 0.6 1.1 0.8 0.8 1.0 0.7 0.7 0.9 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.8 0.5 0.5 0.6 0.6 0.6 0.6 0.7 0.4 0.4 0.4 0.4 0.4 0.4 0.6 0.3 0.3 0.5 0.3 0.3 0.3 0.7 0.7 0.7 0.4 0.2 0.2 0.3 0.2 0.2 0.8 0.8 0.8 0.2 0.2 0.1 0.9 0.9 0.2 0.3 0.3 0.1 1.0 1.0 0.2 0.4 0.4 0.5 0.5 1.1 1.1 0.3 0.6 0.6 0.4 1.2 0.7 0.7 0.5 1.3 0.6 0.8 1.4 0.9g 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 D (cm-1) -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Figure 514. Root mean square error surface for D vs g for complex 52.

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184 F T (K) 0 2 4 6 8 10 12 M'T (cm3 K mol-1) 0 10 20 30 40 50 60 70 5-1 5-2 5-3 5-4 5-5 Figure 515. A lternating current s usceptibility studies for 51, 52, 53, 54 , and 55 plotted as M’T vs T.

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185 T (K) 0 2 4 6 8 10 12 14 16 M" (cm3 mol-1) -0.5 0.0 0.5 1.0 1.5 2.0 2.5 1000 Hz 250 Hz 50 Hz Figure 516. Plot of M” vs T for complex 51.

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186 Figure 517. Labelled structures of complexes 56 and 57 Reprinted (adapted) with permission from Stamatatos, T.C.; Foguet Albiol, D.; Poole, K.M.; Wernsdorfer, W.; Abboud, K.A.; O’Brien, T.A.; Christou, G. Inorg. Chem. 2009, 48, 9831. Copyright (2009) American Chemical Society.213 Figure 518. Labelled structures of complexes 56 and 57 with the ground state rationalization based on theoretical calculations of the exchange couplings. A dapted with permission from Stamatatos, T.C.; Foguet Albiol, D.; Poole, K.M.; Wernsdorfer, W.; Abboud, K.A.; O’Brien, T.A.; Christou, G. Inorg. Chem. 2009, 48, 9831. Copyright (2009) American Chemical Society.213

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187 CHAPTER 6 NEW M n5 AND M n18 MANGANESE CLU STERS FROM THE USE OF CYANIDE IN PLACE OF AZIDE IN KNOWN REACTIONS 6.1 Introduction The pursuit for new polynuclear transition metal complexes continues to be of great interest. This is especially due to their exciting magnetic properties, and potential us e for many applications.12, 15, 27, 36 , 138, 193 , 203 Manganese ions are of particular interest due to their variety of oxidation states and their rich redox chemistry. In recent years, the fields of biochemistry and magnetic materials have been particularly focused on the synthesis of manganese complexes. Overall, it is generally accepted that a tetranuclear manganese cluster is located in the active site of photosystem II in green plants to catalyze the light driven water oxidation reaction to generate dioxygen.187189, 191, 192 , 225 231 Currently, many oxygenevolving center (OEC) analogues or near OEC analogues have been reported.26 , 189192, 216 , 226 249 The synthesis and structural characterization of manganese clusters have provided a treasure trove of data to model the photosynthetic water oxidation center.26, 172 , 234238 , 240244 Another focus of manganese cluster chemistry is the rich magnetic pr operties which offer potential in design of molecular magnetic materials, which has been of considerable interest.1 , 15, 250 252 So far, one of the most common strategies to prepare polynuclear manganese complexes relies mostly on the use of carboxylate ligands either with or without a chelating ligand. This chemistry has been explored in the Christou group extensively.6 , 13, 26, 46, 204 , 216 , 233, 236 , 238, 244, 246, 249, 253 , 254 However, many complexes have been reported without the use of carboxylates and the use of exclusively versatile chelating and bridging ligands might foster the formation of higher nuclearity products. Two families of such ligands are pyridyl and nonpyridyl alcohols, which have proved to be versatile chelating and bridging groups that have produced many manganese containing clusters with various metal

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188 topologies .81 , 86, 87, 217, 255 258 Some successfully employed pyridyl alcohol ligands are 2 hydroxymethyl pyridine (hmpH), 2,6pyridine dimethanol (pdmH2), and dipyridyl 2ketone (dpkdH2) and nonpyridyl alcohols are 2,2bis(hydroxymethyl) 2,2 ,2nitrlotriethanol(bis tris) and 1,1,1tris(hydroxymethyl)ethane (thmeH3) (Figure 6 1). Previously, 2,6pyridine dimethanol and 1,1,1, tris (hydroxymethyl)ethane have been employed together in the presence of sodium azide and r esulted in [Mn10O2(N3)6(pdmH)4(thme)4] complex.210 Continuation of the synthetic strategy where pseudohalides are substituted for sodium azide has resulted in two novel mixed valent Mn(II/IV) pentanuclear complexes with a regular trigonal bipyrimidal metal topology and a mixed valent Mn(II/III) octadecanuclear complex with a doubledecker [3X3] grid topology. The synthesis, structures, and magnetic properties of these complexes will be presented. 6.2 Experimental Section 6.2.1 Syntheses All manipulations were performed under aerobic conditions. All chemicals and solvents were used as received. Safety note: Perchlorate salts are potentially explosive and cyanide salts are highly toxic; such compounds should be synthesized and used in small quantities, and treated with utmost care at all times. [Mn5(pdmH)6(thme)2] (ClO4)2 ( 6 1): To a stirred solution of pdmH2 (0.28g, 2.0 mmol), thmeH3 (0.24 g, 2.0 mmol) and triethylamine (0.28ml, 2.0 mmol) in acetonitrile/methanol mixture wa s added potassium cyanide (KCN) (0.130g/ 2.0 mmol) directly followed by Mn(ClO4)2 6H2O (0.72, 2.0 mmol) The dark red solution was filtered, layered with Et2O, and left undisturbed. After three days, x ray quality crystals were obtained. These crystals were collected by filtration, washed with Et2O, and dried in vacuo; the yield was ~89% (Figure 62). Anal. Calc. (Found) for 61 (solvent free): 40.589 (40.601); H, 4.454 (4.48); N, 5.562 (5.519). Selected IR data (cm1): 3431 (b), 2851 (w), 1599 (s), 1506 (w), 1384 (s), 1109 (s), 775 (w), 625

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189 (s). [Mn5(pdmH)6(thme)2](I3)2 ( 62): To a stirred solution of pdmH2 (0.28g, 2.0 mmol), thmeH3 (0.24 g, 2.0 mmol) and triethylamine (0.28ml, 2.0 mmol) in acetonitrile/methanol mixture was added potassium cyanide (0.130g, 2.0 mmol). This slurry was allowed to stir for approximately 15 minutes before the addition of Mn(ClO4)2 6H2O (0.72, 2.0 mmol). After five minutes, iodine (0.255 g, 1.0 mmol) was added to the mixture and stirred furt her for one hour. The dark reddish yellow solution was filtered, layered with Et2O, and left undisturbed. After three days, xray quality crystals were obtained in 83% yield (Figure 6 2). Anal. Calc. (Found) for 62 (solvent free): C, 29.729 (30.121); H, 3.261 (3.258); N, 4.021 (4.041). Selected IR data (cm1): 3429 (b), 2853 (w), 1600 (s), 1504 (w), 1387 (s), 1110 (s), 773 (w), 626 (s). [Mn18O12(hmp)20(H2O)2](ClO4)6 (6 3) : A solution of NEt4 (0.28mL, 2mmol), hmpH (2 hydroxymethylpyridine) (0.20mL, 2mmol), KCN (0.130 g, 2mmol) in MeCN/MeOH (20 mL/1 mL) was treated with Mn(ClO4)2 (0.50 g, 2 mmol). The black slurry was stirred for 45 minutes. After the filtered solution was carefully layered with tertbutanol, and it slowly produced black crystals of [Mn18O12(hmp)20(H2O)2](ClO4)6 ( 6 3) as 6 3MeCN in 45% yield (Figure 63). Vacuum dried solid analyzed as solvent free: C, 32.813 (32.663); H, 3.875 (3.246); N, 6.378 (6.422). Selected IR data (cm1): 3426 (b), 1614 (s), 1592 (s), 1567 (s), 1475 (w), 1443 (w), 1384 (s), 1089 (m), 1048 (m), 1015 (w), 760 (m), 704 (m), 624 (s). 6.2.2 X Ray Crystallography X Ray Intensity data were collected on a Bruker DUO diffractometer using MoK radiation ( = 0.71073 ) and an APEXII CCD area detector. Suitable crystals of 61, 62, and 63 were attached to glass fibers using silicone grease and transferred to a goniostat where they were cooled to 100 K for data collection. Raw data frames were read by program SAINT1 and integrated using 3D profiling algorithms. The resulting data were reduced to produce hkl

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190 reflections and their intensities and estimated standard deviations. The data were corrected for Lorentz and polarization effects and numerical absorption corrections were applied based on indexed and measured faces. The structure of 61 was solved and refined in SHELXTL6.1,259 using full matrix leastsquares refinement. The non H atoms were refined with an isotropic thermal parameters and all of the H atoms were calculated in idealized positions and refined riding on their parent atoms. In the final cycle of refinement, the asymmetric unit consists of a half Mn5 cluster, one heavily disordered perchlorate a nion and disordered water solvent molecules. The first partial perchlorate is resolved in two positions with occupation factors of 0.4 and 0.2 (fixed after several refinement cycles of full refinement). The second perchlorate anion is refined against thr ee partial water molecules with occupation factors of 0.2 for each part. The third perchlorate is also refined against three partial water molecules with occupation factors of 0.2 for each part. The hydroxyl protons were obtained from a Difference Fourie r maps and refined freely. 7480 reflections (of which 5611 are observed with I > 2(I)) were used to refine 459 parameters and the resulting R1, wR2 and S (goodness of fit) were 6.78%, 20.72% and 1.083, respectively. The refinement was carried out by minimizing the wR2 function using F2 rather than F values. R1 is calculated to provide a reference to the conventional R value but its function is not minimized. The structure of 62 was solved and refined in SHELXTL2013,260 using full matrix least squares refinement. The non H atoms were refined with anisotropic thermal parameters and all of the H atoms were calculated in idealized positions and refined riding on their parent atoms. The asymmetric unit consists of a half Mn5 cluster and one I3 counterion. The three hydroxy protons were obtained from a Difference Fourier map and refined freely. The I3 is significantly disordered and was refined in several parts. Judging from the electron density maps, it looks like

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191 the counterions appear more like diffused electron density than discrete electron density peaks. In the final cycle of refinement, 7595 reflections (of which 6165 are observed with I > 2(I)) were used to refine 502 parameter s and the resulting R1, wR2 and S (goodness of fit) were 3.34%, 9.10% and 0.953 , respectively. The refinement was carried out by minimizing the wR2 function using F2 rather than F values. R1 is calculated to provide a reference to the conventional R value but its function is not minimized. Unit cell data and details of the structure refinements for the two complexes are listed in Table 6 1. The structure of 63 was solved and refined in SHEL XTL6.1,259 using full matrix leastsquares refinement. The non H atoms were refined with anisotropic thermal parameters and all of the H at oms were calculated in idealized positions and refined riding on their parent atoms. The asymmetric unit consists of a half Mn18 cluster cations, three perchlorate anions and two ether solvent molecules. The solvent molecules were disordered and could not be modeled properly, thus program SQUEEZE,261 a part of the PLATON262 package of crystallographic software, was used to calculate the solvent disorder area and remove its contribution to the overall intensity data. The coordinated water protons were obtained from a Difference Fourier map but refined ridin g on their o atom. In the final cycle of refinement, 13424 reflections (of which 5367 are observed with I > 2(I)) were used to refine 1000 parameters and the resulting R1, wR2 and S (goodness of fit) were 7.13%, 16.71% and 0.811, respectively. The refinement was carried out by minimizing the wR2 function using F2 rather than F values. R1 is calculated to provide a reference to the conventional R value but its function is not minimized. 6.2.3 Other studies Infrared spectra were recorded in the solid state (KBr pellets) on a Nicolet Nexus 670 FTIR spectrometer in the 400 4000 cm1 range. Elemental analyses (C, H and N) were performed by the in house facilities of the University of Florida, Chemistry Department.

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192 Variabletemperature dc and ac magnet ic susceptibility data were collected at the University of Florida using a Quantum Design MPMS XL SQUID susceptometer equipped with a 7 T magnet and operating in the 1.8 – 300 K range. Samples were embedded in solid eicosane to prevent torqueing. Magnetization vs. field and temperature data was fit using the program MAGNET.53 Pascal's constants were used to estimate the diamagnetic correction, which was subtracted from the experimental susceptibility to give the molar paramagnetic susceptibility (M). 6.3 Results and Discussion 6.3.1 Syntheses The initial attempts to substitute cyanide salts for azide salts in reactions afforded new interesting products. Cyanide was chosen as a good candidate because it tends to behave similarly to azide. The previous azide containing reaction produced the mixedvalent [Mn10O2(N3)6(pdmH)4(thme)4] which contains 6 MnIII ions that have an octahedral topology with 4 MnII ions capping four faces. The addition of cyanide provided access to a lower nuclearity cluster retaining the higher symmetry in the isolation of a Mn5 cluster with trigonal bipyramidal topology. The reaction of pdmH2, thmeH3, KCN, and Mn(ClO4)2 in MeCN/Me OH in the presence of base afforded a dark orangered solution from which was subsequently obtained the new mixedvalent [MnII 3 MnIV 2] complex [Mn5(pdmH)6(thme)2](ClO4)2 ( 61 ). Its formation is summarized in Equation 61. 5 Mn2+ + 6 pdmH2 + 2 thmeH3 + O2 + 12 NEt3 [Mn5(pdmH)6(thme)2]2+ + 12 HNEt3 + (6 1) Complex 61 contains two MnIV and three MnII ions. Generally, it is not easy to obtain MnIV ions by simple aerobic oxidation reactions starting with MnII sources. More common approaches to higher oxidation state manganese clusters is the use of comproportionation

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193 reactions or the use of a strong oxidant in the reaction mixture. Comproportionation reactions typically employ optimum ratios of MnII/MnVII to a chieve a desired average Mnn+ product. While this method could be useful, we employed the method by addition of a non Mn oxidant to the reaction mixture. Our initial attempt was to try and oxidize the MnII ions in 61 to create a MnIII/MnIV mixed valent co mplex; however, using the oxidant in the reaction provided a more direct and potentially more intuitive reaction to the final product [Mn5(pdmH)6(thme)2](I3)2. 5 Mn2+ + 6 pdmH2 + 2 thmeH3 + 3 I2 + 12 NEt3 [Mn5(pdmH)6(thme)2]2+ + 2 I3 + 12 HNEt3 + ( 62) As before, the previous azide containing reaction produced the mixedvalent [Mn10O4(N3)4(hmp)12](ClO4)2 which contains 6 MnIII ions that have an octahedral topology with 4 MnII ions capping four faces. The addition of cyanide provided access to a higher nuclearity cluster with an unprecedented and architecturally beautiful double [3x3] grid topology. The reaction of hmpH, KCN, and Mn(ClO4)2 in MeCN/MeOH in the presence of base afforded a black solution from which was subsequently obtained the new mixedvalent [MnII 4 MnIII 14] complex [Mn18O12(hmp)20(H2O)2](ClO4)6 ( 6 3). The formation of 63 is summarized in Equation 63. 18 Mn2+ + 20 hmpH + 2H2O + 20 NEt3 + 3 O2 [Mn18O12(hmp)20(H2O)2]6+ + 20 HNEt3 + (6 3) The lack of incorporation of cyanide in 61, 62, and 63 was surprising especially in the case of 63 due to the ligation being completed by two water molecules. Thus, the reactions were investigated without the presence of cyanide and no products were isolated. Additionally, cyanide is a weak base so reactions with 1 mmol of potassium hydroxide without cyanide were

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194 performed resulting in the isolation of an unidentifiable oily product. Therefore, we conclude the cyanide is necessary even though its role is still unclear. 6.3.2 Description of Str uctures Complex 61 crystallizes in the monoclinic space group C2/c with one Mn5 unit in the asymmetric unit. The partially labelled structure of the [Mn5(pdmH)6(thme)]2+ cation is shown in Figure 6 3. Selected interatomic distances and angles are listed i n Table A 7. The core of 61 consists of five Mn atoms arranged in a trigonal bipyramidal topology (Figure 63, bottom). The apical positions are occupied by MnIV ions, whereas the equatorial plane positions are occupied by three MnII ions. The MneqMneqMneq, MneqMneqMnap, and MneqMnapMneq angles range from 59.360.3, 57.257.6, and 64.865.5, respectively. Each MnII ion is linked to the other equatorial MnII ions and the apical MnIV ions through six 3OR bridges (O1, O1 , O3, O3 , O8, and O8 ) o f the 2,6dimethanol pyridine ligands. All Mn atoms are six coordinate with distorted octahedral geometry. Charge considerations and an inspection of the metric parameters indicate a 2MnIV, 3MnII description, which was confirmed by BVS calculations (Table 62),263 , 264 which identified Mn2 as MnIV and the other Mn as MnII ions. The protonation levels of the peripheral and bridging ligands were also confirmed by BVS calculations (Table 6 5 ). Complex 62 also crystallizes in the monoclinic space group C2/c with half of a Mn5 unit in the asymmetric unit. The partially labelled structure of the [Mn5(pdmH)6(thme)2]2+ cation is shown in Figure 64. Selected interatomic distances and angles are listed in Table A 8 . The core of 62 consists of five Mn atoms arranged in a trigonal bipyramidal topology (Figure 6 4). The apical positions are occupied by MnIV ions, whereas the equatorial plane positions are occupied by three MnII ions. The MneqMneqMneq, MneqMneqMnap, and MneqMnapMneq angles range

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195 from 59.660.2, 57.357.6, and 64.665.0, respectively. Each MnII ion is linked to the other equatorial MnII ions and the apical MnIV ions through six 3OR bridges (O1, O1 , O3, O3 , O8, and O8 ) of the 2,6dimethanol pyridine ligands. Complexes 61 and 62 are very similar; in fact, the weighted root mean square deviation between the two structures is 0.0235 (Figure 6 5). All Mn atoms are six coordinate with distorted octahedral geometry. Charg e considerations and an inspection of the metric parameters indicate a 2MnIV, 3MnII description, which was confirmed by BVS calculations (Table 6 2),263 , 264 which identified Mn2 as MnIV and the other Mn as MnII i ons. The protonation levels of the peripheral and bridging ligands were also confirmed by BVS calculations (Table 6 3). There are many structural types of Mn5 complexes known in the literature (Table 6 4), the most well known topology is the trigonal bipyramidal. However, the complexes reported here are the first II/IV mixed oxidation state Mn5 complexes reported. The partially labeled structure of [Mn18O12(hmp)20(H2O)2](ClO4)6 ( 6 3) is shown in Figure 66, 67, and 68; selected interatomic distances and angles are listed in Table A 9. Complex 63 crystallizes in the triclinic space group P 9 units bridged by twelve 3O2 ions and 20 hmpligands with the coordination sphere completed with two water molecules. The two l ayers are held together with twelve 3O2 -, twelve 3hmp alkoxide arms and six 2hmp alkoxide arms. There are seven MnIII and two MnII ions in each layer. The manganese ions are all six coordinate with near octahedral geometry. The oxidation state assign ments mentioned above were determined from charge considerations, the metric parameters, bond valence sum (BVS) calculations (Table 6 5), and the identification of JahnTeller distortions expected for MnIII ions; the Mn18 cation of 63 are thus mixed vale nt 4MnII, 14MnIII and they are color coded accordingly in Figures 63. The protonation levels of the bound

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196 O atoms were confirmed by oxygen BVS calculations (Figure 63) to be protonated in the case of the waters and deprotonated for the hmpoxygen atoms. There are 12 virtually parallel Jahn Teller axes and two Jahn Teller axes that are perpendicular (two MnIII ions in the same row as the MnII ions) shown in Figure 69. A single layer of the double decker grid core is shown in Figure 610. The exterior location of the MnII ions suggests that they prefer to be away from the highly negative oxide core whereas the MnIII ions prefer the much more electron rich environment of the oxide core. There are a few examples of Mn grid complexes;265 however, none have shown slow relaxation of their magnetization or spin ground states larger than S = . The largest Mn grid complex reported previously is a Mn16. Dawe and coworkers describe the core as a compartmentalized {4 x [2 x 2]} MnII 16 anitferromagnetically coupled square grid.266 There are some examples of mixed valent Mn9 co mplex containing [3 x 3] topology; however, they are synthesized through self assembly with tritopic picolinic dihydrazone ligands.267, 268 The deprotonated hydrazine oxygen atoms bridge all manganese ions and hold six them almost planar with the other three ions slightly below the plane. The highest MnIII/MnII ratio contained in this topology is 4/5 in [Mn9(2poap2H)6](ClO4)10 ( 6 4). 267, 268 6.3.3 Magnetochemistry 6.3.3.1 Direct c urrent m agnetic s usceptibility. Variable temperature magnetic susceptibility studies were performed on microcrystalline samples of 6 1 and 62, restrained in eicosane to prevent torqueing. The magnetic susceptibilities were examined at a 0.1 T (1 kG) field in the 5 to 300 K temperature range for 61. Diamagnetic corrections were applied to the magnetic susceptibilities using Pascal's constants.178 For complex 61, MT very gradually increases from 17.25 cm3Kmol1 at 300K to a value of ~ 20 cm3Kmol1 at 30 K and then increases rapidly to 32.13 cm3Kmol1 at 5.0K (Figure

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197 611). The 300 K value is slightly larger than the spinonly (g = 2) value of 16.875 cm3Kmol1 for three MnII and two MnIV noninteracting ions . The MT value at low temperature appears to be increasing toward a final value of ~ 35 cm3Kmol1, the spin only (g=2) value of a species with an S = 1 7/2 ground state. The metal ions are thus clearly involved in magnetic exchange interactions, and the data were fit to the theoretical MT vs T expression derived from the spin Hamiltonian appropriate for a Mn5 trigonal bipyramid; given in Equation 6 5, = 12 13 14 25 35 45) – 2J 233424) 2J 15) (6 5) Where Si refers to the spin of metal Mni, and J, J , and J are the pairwise exchange parameters for apical to equatorial and equatorial to equatorial metals of the trigonal bipyramid, respectively; the Mn labeling scheme of Figure 62 was employed. This Hamiltonian can be transformed into an equivalent form (Equa tion 6 2) by using the Kambe coupling method and the A 2 3B A 4C 1 5T B C where the ST is the resultant spin of the complete molecule. = T 2B 2 – C 2) 2J 2 2 – 3 2 – B 2 – 4 2) J ( C 2 – 1 2 – 5 2) (6 6) From E quation 66 can be obtained the energy expression (Equation 6 7) for the energies, E(ST), of each ST state; constant terms contributing equally to all states have been omitted from Equation 66. E(ST) = J [ST(ST+1) – SB(SB+1) – SC(SC+1)] –J [ SB(SB+1)] – J [SC(SC+1)] (6 7) There are a total of 3456 possible ST states ranging in values from to 21/2, where ST is the total spin of the Mn5 complex. The eigenvalue expression (Equation 6 7) and the van Vleck

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198 equation were used to de rive a theoretical MT vs T expression for 61 and this was used to least squares fit the experimental data. The fit (solid line in Figure 6 11) gave J = 1.2(3) cm1, J = 0.8(2) cm1, and g = 2.02(2), with temperature independent paramagnetism (TIP) hel d constant at 500 x 106 cm3 mol1. For complex 62, MT very gradually increases from 18.40 cm3Kmol1 at 300 K to a value of ~21 cm3K mol1 at 20 K before increasing rapidly to 38.34 cm3Kmol1 at 5 K (Figure 6 12). The 300K value is slightly larger than the spin only (g = 2) value of 16.875 cm3Kmol1 for three MnII and two MnIV noninteracting ions. The MT value at low temperature appears to be heading for a final value of ~ 40 cm3Kmol1, the spinonly (g=2) value of a species with an S = 17/ 2 ground state. The metal ions are thus clearly involved in magnetic exchange interactions, and attempts to fit the data were made with the theoretical MT vs T and M vs T expression derived from the spin Hamiltonian appropriate for a Mn5 trigonal bipyramid; given in Equation 65. For complex 63, MT very gradually decreases from 48.4 cm3Kmol1 at 300K to a value of ~30 cm3Kmol1 at 30 K and then decreases more rapidly to 23.55 cm3Kmol1 at 5.0K (Figure 613). The 300K value is much small er than the spinonly (g = 2) value of 59.5 cm3Kmol1 for four MnII and fourteen MnIII noninteracting ions, indicating the presence of dominant antiferromagnetic exchange interactions. The MT value at low temperature appears to be heading for a final val ue of ~24 cm3Kmol1, which is slightly less than the spin only (g=2) value of a species with an S = 7 ground state. It is not possible to fit complex 63 for the exchange parameters due to the complex structure and number of unique exchange interactions. T o confirm the S = 17/2 and 7 ground state for complex 61 and 63, respectively; and to estimate the magnitude of the zero field splitting parameter, D, magnetization vs dc field

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199 measurements were made on restrained samples at applied magnetic fields and t emperatures in the 1 – 70 kG and 1.810.0 K ranges, respectively. Then attempts were made to fit the data, using the MAGNET program, by diagonalization of the spin Hamiltonian matrix assuming only the ground state is populated, incorporating axial anisotroz 2), Zeeman terms, and employing a full powder average. The corresponding spin Hamiltonian is given by Equation 6 z is the easy B is the Bohr magneton, and 0 is the vacuum permeability. z 2 + g B0 H (6 8) For complex 61, we were able to obtain a satisfactory fit using all data up to 3 T. This suggests that the ground state of complex 61 is relatively well isolated from the nearest excited states. The best fit is shown as the solid lines in the reduced magnetization ( M/NB vs H/T ) plot in Figure 6 14 and was obtained with S = 1 7/2, g = 2.02(4), and D = 0.02(1) cm1. An equally good fit was also obtained with S = 1 7/2, g = 2.00(2), and D = 0.25(1) cm1. It is common to obtain two acceptable fits of magnetization data for a given S value, one with D < 0 and the other with D > 0, since magnetization fits are not very sensitive to the sign of D . Alternative fits with S = 1 5/2 and 1 9/2 were rejected because they gave unreasonable values of g and D . The root mean square D vs g error surface for the fit was generated using the pro gram GRID, and is shown as a 2 D contour plot in Figure 615 for the D = 0.3 to 0.3 cm1 and g = 1.8 2.2 ranges. Two minima are observed the one for the negative D value is clearly of greater. For complex 62, initial attempts to fit the reduced magnetization data from 0.1 T to 7T were unsuccessful for a range of S values.

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200 For complex 63, a satisfactory fit was obtained using field data from 0.1 to 3 T. This suggests that the ground state of complex 63 is relatively well isolated from the nearest exc ited states. The best fit is shown as the solid lines in the reduced magnetization ( M/NB vs H/T ) plot in Figure 6 16 and was obtained with S = 7, g = 1.94(4), and D = 0.23(2) cm1. An equally good fit was also obtained with S = 7, g = 1.80(2), and D = 0.13(4) cm1. However, the g = 1.80 is a slightly lower than the expected value for a manganese complex. Though it is common to obtain two acceptable fits of magnetization data for a given S value, the one with D < 0 seems more reasonable even though a dece nt fit was obtained with D > 0 ;however, g of 1.80 is considered very low and unreasonable . Alternative fits with S = 8 and 6 were rejected because they gave unreasonable values of g and D. The root mean square D vs g error surface for the fit was generated using the program GRID, and is shown as a 2D contour plot in Figure 61 7 for the D = 0.3 to 0.3 cm1 and g = 1.8 2.2 ranges. Two minima are observed; the one for the negative D value is clearly of greater quality. 6.3.3.2 Alternating c urrent m agnetic s usceptibility s tudies. A c s usceptibility studies are a powerful complement to dc studies for determining the ground state of a system, because they remove the complications that arise from having a dc field present. The obtained inphase M signal for complex 61 is plotted as MT in Figure 618, and the data increases from 25.5 to 35.7 cm3K mol1 ove r the temperature range 15 to 4 K which is indicative of low lying excited states that are smaller than the ground state. Extrapolation to 0 K from above 3 K to avoid lower temperature effects from the slight anisotropy and we ak intermolecular interactions gives a value of ~ 38 cm3 K mol1, which is consistent with an S = 17/2 ground state and g ~2, in excellent agreement with the reduced magnet ization fit. The obtained inphase M signal for 62 is plotted as MT in Figure 6 1, and the data increases from

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201 31.9 to 42.6 cm3Kmol1 over the temperature range 15 to 4 K which indicates thermal population of the low lying excited states even at very low temperatures. Extrapolation of the data to 0 K above 3 K gives a value of ~ 48 cm3 K mol1, which is consistent with an S = 17/2 ground state and g ~ 2 in agreement with the data from the isostructural complex 61. We conclude that complex 62 does have an S = 17/2 ground state. There is an out of phase ac susceptibility signal; however, only a partial peak is present down to 1.8 K, the operating limit of our SQUID magnetometer. For complex 63, the obtained in phase M signal is plotted as MT in Figure 620, and the data appears to be decreasing slightly from ~ 31 cm3Kmol1 at 15 K to ~ 25 cm3Kmol1 at 5 K, confirming a relatively well isolated ground state before decreasing concomitantly with the increase in the out of phase signal beginning around 4.5 K. To avoid lower temperature effects from slight anisotropy and weak intermolecular interactions and the out of phase signal, extrapolation to 0 K from the data above 5 K gives a value of ~ 24.5 cm3 K mol1, which is consistent with an S = 7 ground state and g ~2, in excellent agreement with the reduced magnetization fit. Multi frequency ac measurements are an excellent tool to probe slow relaxation of the magnetization vector at low temperature. Only complex 6 3 showed such behavior thus data were collected for 63 in the 1.8 – 15 K range at 501000 Hz. At lower temperature, below 4.5 K, a decrease i n M T and the concomitant rise in the out of phase M signal were seen (Figure 6 20, bottom), indicating the slow relaxation of the magnetization vector due to the presence of a spin barrier. However, the ac out of phase plot shows only partial peaks and they appear to be frequency independent which is inconsistent with single molecule magnetism.

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202 6.3.3.3 Single crystal hysteresis studies of 6 3 below 1.8 K. Ac measurements strongly suggest that 63 could be a single molecule magnet (SMM), which was conf irmed by the observations of hysteresis loops in the magnetization vs dc field scans, measured on a singlecrystal of 63 using a microSQUID apparatus. The temperaturedependence at 0.14 Ts1 and the scan rate dependence at 0.03 K of the hysteresis loops are shown in Figure 6 21 and Figure 622, respectively. The coercivities clearly increase with decreasing temperature and increasing scan rate, as expected for the superparamagnet like behavior of SMMs. However, complex 63 has extremely fast tunneling of its magnetization so there are no steps visible in the hysteresis loops. 6.4 Conclusions and Future Work The successful employment of the tridentate O,O,O ligand thme3 and tridentate O,N,O ligand pdmHwith a cyanide salt to isolate novel mixedvalent pe ntanuclear complexes has been presented. Again, it is surprising that the CNgroup does not get incorporated to the complexes. The pentanuclear manganese clusters are the first such complexes reported with the combination of Mn(II)/Mn(IV) ions in a regul ar trigonal bipyramidal geometry. Magnetochemical characterization of these complexes revealed that 61 and by extention 62 ha s ground state spin values of S = 1 7/2. The two clusters display similar magnetic properties. Further attempts to isolate the mixed valent complex with three Mn(III) ions and two Mn(IV ) ion s could prove fruitful for redox applications. A novel manganese double decker [3X3] grid complex was isolated from the substitution of potassium cyanide for sodium azide in a known reaction. The grid structure was obtained by self assembly without a ligand scaffold to force the grid metal topology and is the first nonzero whole integer spin system with a barrier to the reversal of magnetization. The synthesis, structure, and physical properti es have been presented and discussed. Future work will include

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203 trying to grow the grid structure to more layers and/or larger grid layers; however, one obstacle that will need to be overcome is the charge build up as complex 63 has a 6+ charge.

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204 Table 6 1. Crystal data and structure refinement for 61 and 62. ___________________________________61____________________62 _______________ Empirical formula C17.33 H23.33 Cl0.67 Mn1.67 N2 O9.33 C52 H66 I6 Mn5 N6 O18 Formula weight 524.25 2099.20 Temperature 100(2) K 100(2) K Wavelength 0.71073 0.71073 Crystal system Monoclinic Monoclinic Space group C2/c C2/c Unit cell dimensions a = 19.6048(12) a = 19.5974(16) b = 18.3096(11) b = 18.3002(14) c = 20.0246(12) c = 20.2057(16) = 90 = 90 = 115.0140(10). = 114.2034(12). = 90. = 90. Volume 6513.8(7) 3 6609.5(9) 3 Z 12 4 Density (calculated) 1.604 Mg/m3 2.110 Mg/m3 Absorption coefficient 1.113 mm-1 3.802 mm-1 F(000) 3228 4028 Crystal size 0.20 x 0.16 x 0.06 mm3 0.218 x 0.103 x 0.056 mm3 Theta range for data collection 1.60 to 27.50. 1.651 to 27.500. Index ranges Reflections collected 45318 47110 Independent reflections 7480 [R(int) = 0.0440] 7595 [R(int) = 0.0423] Completeness to theta = 27.50 99.9 % = 25.242 100.0 % Absorption correction Integration Analytical Max. and min. transmission 0.9322 and 0.8097 0.8424 and 0.6329 Refinement method Full matrix least squares on F2 Full matrix least squares on F2 Data / restraints / parameters 7480 / 32 / 459 7595 / 0 / 502 Goodness of fit on F2 1.083 0.953 Final R indices [I>2sigma(I)] R1 = 0.0678, wR2 = 0.2072 [5611] R1 = 0.0334, wR2 = 0.0910 [6165] R indices (all data) R1 = 0.0874, wR2 = 0. 2241 R1 = 0.0450, wR2 = 0.0959 Largest diff. peak and hole 2.804 and 0.937 e.3 1.226 and 0.751 e.3 _____________________________________________________________________________________________ R1 = (||F o | |F c |F o |.wR2 = [ w(F o 2 F c 2 ) 2 w F o 2 2 ]] . S = [ w(F o 2 F c 2 ) 2 p)] . w= 2 (F o 2 )+(m*p)2+n*p], p = [max(F o 2 c 2 ____________________________________________________________________________________________

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205 Table 6 2. Bondvalence sum (BVS)a calculations for Mn in complexes 61 and 62. 6 1 6 2 Mn(II) Mn(III) Mn(IV) Mn(II) Mn(III) Mn(IV) Mn1 1.71 1.61 1.62 1.74 1.45 1.52 Mn2 4.17 3.81 4.00 4.45 4.16 4.22 Mn3 1.76 1.67 1.67 1.72 1.62 1.63 The underlined value is the one closest to the charge for which it was calculated. The oxidation state of a particular atom can be taken as the nearest whole number to the underlined value. Table 6 3. Bondvalence sums for the O atoms of complex 61, 62, and 6 3. 6 1 6 2 Atom BVS Assignment group Atom BVS Assignment group O1 ROH pdmH O1 ROH pdmH O2 RO pdm O2 RO pdm O3 ROH pdmH O3 ROH pdmH O4 ROH pdmH O4 ROH pdmH RO pdm RO pdm O6 RO pdm O6 1.81 RO pdm 6 3 Atom BVS Assignment group Atom BVS Assignment group O1 O 2 O 2 RO hmp O2 1.919 O 2 O 2 O11 1.886 RO hmp O3 O 2 O 2 O12 H 2 O H 2 O O4 RO hmp O13 1.944 O 2 O 2 RO hmp O14 1.921 RO hmp O6 RO hmp O 2 OH 1.941 RO hmp O16 1.896 RO hmp O8 1.812 RO hmp O 2 O 2 O9 1.942 RO hmp The BVS values for O atoms of O2 -, OH-, and H2O groups are typically 1.82.0, 1.01.2, and 0.20.4, respectively.

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206 Table 6 4. Structural types and ground state S values for pentanuclear manganese clusters. Complex Core Type S Ref [Mn II 5 (Htrz) 2 (SO 4 ) 4 (OH) 2 ] [Mn 5 ( 3 OH) 2 ] 8+ c n.r. 269 [Mn II 5 (p3oapH) 6 ] 4+ [Mn 5 ( OR) 6 ] 4+ d 5/2 270 [Mn II 5 (poapH) 6 ] 4+ [Mn 5 ( OR) 6 ] 4+ d 5/2 270 [Mn II 5 (L) 2 (O 2 CMe) 2 (ClO 4 ) 2 ] 2+ [Mn 5 ( OR) 6 ( OClO 3 ) 2 ] 2+ e n.r. 271 [Mn II 5 (phaapH) 6 ] 4+ [Mn 5 ( OR) 6 ] 4+ d 5/2 272 [Mn III 5 O 3 (t BuPO 3 ) 2 (MeCO 2 ) 5 (H 2 O)(phen) 2 ] [Mn 5 ( 3 O) 3 ] 9+ i 2 273 [Mn III 5 O 3 ( t BuPO 3 ) 2 (PhCO 2 ) 5 (phen) 2 ] [Mn 5 ( 3 O) 3 ] 9+ i 2 273 [Mn III 5 ( 3 O) 2 1 ) 4 (O 2 CMe) 3 (CH 3 OH)] [Mn 5 ( 3 O) 2 ( OR) 5 ] 6+ i 2 274 [Mn III 5 ( 3 O) 2 1 ) 4 (O 2 CPh) 3 (CH 3 OH)] [Mn 5 ( 3 O) 2 ( OR) 5 ] 6+ i 2 274 [Mn II Mn III 4 2 ) 2 2 ) 2 (O 2 CMe) 4 )] [Mn 5 ( OR) 6 ] 8+ e 2 274 [Mn II Mn III 4 2 ) 2 2 ) 2 (O 2 CPh) 4 )] [Mn 5 ( OR) 6 ] 8+ e 2 274 [Mn II Mn III 4 (shi) 4 (O 2 CMe)(DMF) 6 ] [Mn 5 ( 3 ON) 4 ] 10+ f n.r. 27 5 [Mn II Mn III 4 (shi) 4 (O 2 CPh) 2 (MeOH) 6 ] [Mn 5 ( 3 ON) 4 ] 10+ f n.r. 276 [Mn II 2 Mn III 3 O(salox) 3 Cl 2 (N 3 ) 6 ] 3 [Mn 5 ( 3 O)( ON) 3 ( N 3 ) 6 ] 2+ d 11 277 [Mn II 2 Mn III 3 (LH 2 ) 3 (LH 5 )(MeOH) 3 ] 4+ [Mn 5 ( OR) 7 ] 6+ d 2 278 [Mn II 3 Mn III 2 (fsatren) 2 (H 2 O) 4 ] [Mn 5 ( OR) 8 ] 4+ g 7/2 279 [Mn II 3 Mn III 2 (tmphen) 6 (CN) 12 ] Mn 5 ( NC) 6 ] 6+ d 11/2 280 [Mn II 3 Mn IV 2 (thme) 2 (pdm) 4 (pdmH) 2 ] 2+ ( 7 1 ) [Mn 5 ( OR) 6 ] 6+ d 15/2 t.w. [Mn II 3 Mn IV 2 (thme) 2 (pdm) 4 (pdmH) 2 ] 2+ ( 7 2 ) [Mn 5 ( OR) 6 ] 6+ d 15/2 t.w. [Mn II 4 Mn III (cat) 4 (O 2 CCMe 3 ) 2 (py) 8 ] + [Mn 5 ( 3 OR) 4 ( OR) 4 ] 3+ e n.r. 281 a Abbreviations: n.r.= not reported; t.w.= this work; Htrz = triazole; phaapH = ditopic, diazine ligands; LH2 =a [2 + 2] macrocycle; H2L1 3,5 dibromosalicylidene 2 ethanolamine 2H2 = 3 (2 hydroxy 3,5 dibromobenzylideneamino)propane 1,2diol; shiH3 = salicylhydroxamic acid; DMF = dimethylformamide, saloxH2 = salicylaldoxime; fsatrenH6 = 3 formylsalicylic acid; tmphen = 3,4,7,8 tetramethyl 1,10 phenanthroline; catH2 = catechol; py =pyridine. b Counterions and solvate molecules are omitted. c Edge sharing MnO6 octahedra. d Trigonal bipyramid. e Four Mn around a central Mn. f [12 metallac rown g Linear array. h basket like cage. i incomplete cubane extended at one face by an incomplete adamatane unit.

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207 Table 6 5. Bond valence sum calculations for 63. Mn(II) Mn(III) Mn(IV) Mn1 3.14 2.87 3.02 Mn2 3.79 3.47 3.64 Mn3 1.98 1.83 1.89 Mn4 1.94 1.81 1.85 Mn5 3.26 2.98 3.13 Mn6 3.26 3.05 3.09 Mn7 3.14 2.90 2.96 Mn8 3.20 2.97 3.05 Mn9 3.23 3.01 3.08 The underlined value is the one closest to the charge for which it was calculated. The oxidation state of a particular atom can be taken as the nearest whole number to the underlined value. N OH N OH OH HO OH HO Figure 61. Structure of ligands: (left) 2 hydroxymethyl pyridine (hmpH), (center) 2,6pyridine dimethanol (pdmH2) and (right) 1,1,1 tris(hydroxymethyl)ethane (thmeH3).

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208 Figure 62. Structure of 61 (top), stereoview (middle), and partially labeled core (bottom). Color scheme: MnIV, purple; MnII, yellow; O, red; N, blue; C, gray. .

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209 Figure 63. Structure of 62 (top), stereoview (middle), and partially labeled core (bottom). Color scheme: MnIV, purple; MnII, yellow; O, red; N, blue; C, gray.

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210 Figure 64. The Mn5 topology of complex 61, emphasizing the trigonal bipyramidal description (left) and top down view of the core of 61 (right). Color scheme: MnIV, purple; MnII, yellow; O, red.

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211 Figure 65. Weighted root mean square deviation between complexes 61 and 62.

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212 Figure 66. Structure of 63 (top), stereoview (middle), and partially labeled core (bottom). Color scheme: MnIII, green; MnII, yellow; O, red; N, blue; C, gray.

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213 Figure 67. Stereoview of 63 from the top down view. Color scheme: MnIII, green; MnII, yellow; O, red; N, blue; C, gray.

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214 Figure 68. Spacefilling stereoview structures of complex 63. Hydrogens are omitted for clarity. Color scheme: MnIII, green; MnII, yellow; O, red; N, blue; C, gray.

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215 Figure 69. Core of 63 with JahnTeller axes highlighted in cyan. Color scheme: MnIII, green; MnII, yellow; O, red; N, blue.

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216 Figure 610. A single [3X3] layer of the core of complex 63. Color scheme: MnIII, green; MnII, yellow; O, red; N, blue.

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217 T (K) 050100150200 250 300 350 MT (cm3 K mol-1) 0 5 10 15 20 25 30 35 data Figure 611. Plot of MT vs T for complexes 61 ; see text for fit parameters. T (K) 050100 150 200 250 300 350 MT (cm3 K mol-1) 0 10 20 30 40 50 Figure 612. Direct current magnetic susceptibility studies plotted as MT vs T for complex 62.

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218 Figure 613. Direct current susceptibility studies plotted at MT vs T for complex 63 H/T (kG/K) 024 6 8 10 12 14 16 18 M/NB 0246810 12 14 0.1 T 0.5 T 1 T 2 T 3 T Fit Figure 614. Plot of reduced magnetization ( M/NB) vs. H/ T for complex 61 at applied fields of 0.1 7.0 T in the 1.8 10 K temperature range. The solid lines are the fit of the data; see the text for the fit parameters. T (K) 050100150200250300350 MT (cm3 K mol-1) 0102030405060

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219 1.0 1.4 1.4 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.6 0.4 0.4 1.2 0.8 1.0 0.6 0.2 0.2 0.2 0.8 0.4 0.4 0.4 0.6 0.6 0.6 0.6 0.4 0.4 0.8 0.8 0.4 1.0 1.0 0.6 0.6 1.2 0.8 1.4 0.8 1.0g 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 D (cm-1) -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Figure 615. Root mean square error surface of D vs. g for complex 61. H/T (T/K) 024681012141618 M/NB 02468101214 0.1 T 0.5 T 1 T 2 T 3 T Fit Figure 616. Plot of reduced magnetization ( M/NB) vs. H/ T for complex 63 at applied fields of 0.1 7.0 T in the 1.8 10 K temperature range. The solid lines are the fit of the data; see the text for the fit parameters.

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220 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.1 1.1 0.4 1.5 1.0 1.0 1.0 0.4 0.4 0.4 0.4 1.5 1.0 1.0 0.4 1.4 0.9 0.9 0.4 0.4 0.3 0.3 1.4 0.9 0.9 0.3 1.3 0.9 0.8 0.3 0.3 1.3 0.8 0.8 0.3 0.3 1.2 0.8 0.8 0.3 0.3 1.2 0.7 0.7 0.2 0.2 1.1 0.7 0.7 0.2 0.2 1.1 0.7 0.2 0.2 1.0 0.6 0.6 0.2 1.0 0.6 0.6 1.0 0.6 0.5 0.2 0.9 0.5 0.1 0.9 0.5 0.5 0.1 0.1 0.8 0.5 0.8 0.4 0.4 0.1 0.1 0.7 0.4 0.7 0.4 0.4 0.1 0.1 0.7 0.3 0.6 0.3 0.1 0.1 0.1 0.6 0.3 0.5 0.3 0.0 0.2 0.5 0.3 0.2 0.2 0.4 0.2 0.0 0.2 0.4 0.4 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.3 0.3 0.3 0.1 0.3 0.4 0.2 0.4 0.4 0.2 0.0 0.1 0.4g 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 D (cm-1) -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Figure 617. Root mean square error surface of D vs. g for complex 63.

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221 T (K) 0246810121416 M'T (cm3 K mol-1) 01020304050 T (K) 0 2 4 6 8 10 12 14 16 M''T (cm3 mol-1) -1 0 1 2 3 4 5 Figure 618. Plots of in phase M' (as M T ) vs. T (top) and out of phase M vs. T (bottom) alternating current signals or complex 61 at the indicated frequencies.

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222 T (K) 0246810121416 M'T (cm3 K mol-1) 0 10 20 30 40 50 T (K) 0 2 4 6 8 10 12 14 16 M" (cm3 mol-1) -1 0 1 2 3 4 5 Figure 619. Plots of in phase M' (as M T ) vs. T (top) and out of phase M vs. T (bottom) alternating current signals or complex 62 at the indicated frequencies.

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223 T (K) 0 2 4 6 8 10 12 14 16 M'T (cm3 K mol-1) 0 5 10 15 20 25 30 35 50 Hz 250 Hz 997 Hz T (K) 0246810121416 M" (cm3 mol-1) -0.10.00.10.20.30.40.5 250 Hz 250 Hz 997 Hz Figure 620. Plots of in phase M' (as M T ) vs. T (top) and out of phase M vs. T (bottom) a lternating current signals or complex 63 at the indicated frequencies.

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224 Figure 621. Magnetization ( M ) vs. direct current field hysteresis loops for a single crystal of 63 at the indicated field sweep rate. The magnetization is normalized to its saturation value, MS. -1-0.500.5 1 -0.5 0 0.5 0.03 K 0.2 K 0.4 K 0.7 K 1.0 K 1.3 K M/Ms 0H (T) 0.14 T/s

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225 Figure 622. Magnetization ( M ) vs. dc field hysteresis loops for a single crystal of 63 at the indicated temperature. The magnetization is normalized to it s saturation value, MS. -1-0.500.51-0.500.5 0.280 T/s 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 0.001 T/s M/Ms 0H (T) 0.03 K

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226 APPENDIX A S ELECTED I NTERATOMIC D ISTANCES AND A NGLES T able A 1. Selected Interatomic Distances () and Angles (o) for Complex 41. Mn(1) Mn(2) 3.2157(5) O(8) Mn(2) N(39) 168.37(8) Mn(2) O(5) 1.7858(17) Mn(1) O(5) 1.7947(16) Mn(2) O(8) 1.9645(17) Mn(1) O(12) 1.9640(16) Mn(2) N(28) 2.072(2) Mn(1) N(27) 2.069(2) Mn(2) N(39) 2.092(2) Mn(1) N(16) 2.074(2) Mn(2) O(13) 2.1388(16) Mn(1) O(7) 2.1381(18) Mn(2) O(4) 2.1867(18) Mn(1) O(3) 2.2187(19) N(28) Mn(2) N(39) 77.81(7) Mn(2) O(5) Mn(1) 127.82(9) O(5) Mn(2) O(13) 93.68(7) O(5) Mn(1) O(12) 98.99(7) O(8) Mn(2) O(13) 93.68(7) O(5) Mn(1) N(27) 167.75(8) N(28) Mn(2) O(13) 86.97(7) O(12) Mn(1) N(27) 92.69(7) N(39) Mn(2) O(13) 93.07(7) O(5) Mn(1) N (16) 89.80(8) O(5) Mn(2) O(4) 95.69(7) O(12) Mn(1) N(16) 167.59(8) O(8) Mn(2) O(4) 87.72(8) N(27) Mn(1) N(16) 78.10(8) N(28) Mn(2) O(4) 83.96(7) O(5) Mn(1) O(7) 96.83(7) N(39) Mn(2) O(4) 87.44(8) O(12) Mn(1) O(7) 90.55(7) O(13) Mn(2) O(4) 170.60(7) N( 27) Mn(1) O(7) 86.67(7) N(16) Mn(1) O(7) 97.12(7) O(5) Mn(1) O(3) 96.26(7) O(12) Mn(1) O(3) 87.51(8) N(27) Mn(1) O(3) 80.50(8) N(16) Mn(1) O(3) 82.81(8) O(7) Mn(1) O(3) 166.91(7) O(5) Mn(2) O(8) 99.99(8) O(5) Mn(2) N(28) 168.82(8) O(8) Mn(2) N(28) 91.17(8) O(5) Mn(2) N(39) 91.01(8)

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227 Table A 2. Selected Interatomic Distances () and Angles (o) for the Cation of Complex 42. Mn(1)••Mn(2) 3.178(3) Mn(1) O(1) 1.780(3) Mn(1) O(3) 2.008(3) Mn(1) N(1) 2.045(4) Mn(1) O(2) 2.074(3) Mn(1) N(2) 2.141(4) Mn(1) O(4) 2.198(3) Mn(1) Mn(2) 3.178(2) Mn(2) O(1) 1.774(3) Mn(2) O(6) 1.985(3) Mn(2) N(3) 2.041(4) Mn(2) O(5) 2.089(3) Mn(2) N(4) 2.136(4) Mn(2) O(7) 2.232(3) S(1) O(8) 1.439(4) S(1) O(2) 1.472(3) S(1) O(9) 1.475(3) S(1) O(5) 1.475(3) Mn(1) O(1) Mn(2) 126.85(15) O(1) Mn(1) O(3) 94.98(13) O(1) Mn(1) N(1) 169.81(14) O(3) Mn(1) N(1) 91.14(14) O(1) Mn(1) O(2) 97.26(12) O(3) Mn(1) O(2) 91.55(13) N(1) Mn(1) O(2) 90.69(13) O(1) Mn(1) N(2) 94.84(15) O(3) Mn(1) N(2) 166.72(14) N(1) Mn(1) N(2) 77.92(16) O(2) Mn(1) N(2) 96.05(15) O(1) Mn(1) O(4) 85.71(12) O(3) Mn(1) O(4) 86.75(13) N(1) Mn(1) O(4) 86.51(13) O(2) Mn(1) O(4) 176.70(13) N(2) Mn(1) O(4) 85.09(14) O(1) Mn(2) O(6) 94.64(13) O(1) Mn(2) N(3) 171.83(15) O(6) Mn(2) N(3) 90.72(15) O(1) Mn(2) O(5) 97.62(13) O(6) Mn(2) O(5) 93.63(14) N(3) Mn(2) O(5) 88.18(14) O(1) Mn(2) N(4) 94.56(15) O(6) Mn(2) N(4) 168.12(16) N(3) Mn(2) N(4) 79.37(17) O(5) Mn(2) N(4) 92.58(15) O(1) Mn(2) O(7) 88.24(13) O(6) Mn(2) O(7) 87.71(13) N(3) Mn(2) O(7) 85.81(14) O(5) Mn(2) O(7) 173.86(12) N(4) Mn(2) O(7) 85.07(14)

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228 Table A 3. Selected interatomic distances () and angles () for 43. Mn1O1 1.8466(12) Mn2O1 2.0324(12) Mn1O1#1 1.8873(11) Mn2O4 2.0798(12) Mn1O5 2.0313(12) Mn2O2 2.1146(13) Mn1N1 2.0679(14) Mn2N4 2.1782(15) Mn1O3 2.2352(12) Mn2N3 2.2643(14) Mn1N2 2.3303(14) O1 Mn1#1 1.8873(11) O1 Mn1O1#1 82.69(5) O3 Mn1N2 157.09(5) O1 Mn1O5 102.40(5) O1 Mn2O4 107.70(5) O1#1Mn1O5 174.82(5) O1 Mn2O2 94.48(5) O1 Mn1N1 168.72(5) O4 Mn2O2 91.35(5) O1#1Mn1N1 87.43(5) O1 Mn2N4 130.52(5) O5 Mn1N1 87.59(5) O4 Mn2N4 121.46(5) O1 Mn1O3 94.11(5) O2 Mn2N4 89.98(5) O1#1Mn1O3 98.32(5) O1 Mn2N3 96.23(5) O5 Mn1O3 80.51(5) O4 Mn2N3 96.17(5) N1 Mn1O3 92.69(5) O2 Mn2N3 164.38(5) O1 Mn1N2 100.65(5) N4 Mn2N3 74.42(5) O1#1Mn1N2 100.85(5) Mn1O1 Mn1#1 97.31(5) O5 Mn1N2 79.27(5) Mn1O1 Mn2 112.65(6) N1 Mn1N2 75.82(5) Mn1#1O1 Mn2 135.34(6) Table A 4. Selected interatomic distances () and angles () for 51. Mn1O1 1.8608(19) Mn2O3 2.2279(19) Mn1O2 1.8826(18) Mn2O1#1 2.2405(18) Mn1O4 1.9942(19) Mn3O3 2.1576(18) Mn1N1 2.073(2) Mn3O3#2 2.1577(17) Mn1N2 2.187(2) Mn3O3#1 2.1577(17) Mn1O3 2.1925(18) Mn3O4#2 2.2060(18) Mn2N4 2.110(2) Mn3O4#1 2.2060(18) Mn2O2 2.1804(18) Mn3O4 2.2060(18) Mn2O4#1 2.2017(19) O1 Mn2#2 2.2405(18) Mn2N3 2.226(2) O4 Mn2#2 2.2018(18) Mn1O1 Mn2#2 104.39(8) Mn1O2 Mn2 107.65(8) Mn3O3 Mn1 95.16(7) Mn3O3 Mn2 99.09(8) Mn1O3 Mn2 95.97(8) Mn1O4 Mn2#2 101.37(8) Mn1O4 Mn3 99.62(8) Mn2#2O4 Mn3 98.43(8)__________________________________

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229 Table A 5. Selected interatomic distances () and angles () for 52. Mn1O2#1 2.159(3) Mn2O1 2.193(4) Mn1O2#2 2.159(3) Mn2N1 2.214(5) Mn1O2 2.159(3) Mn2O2 2.266(4) Mn1O1 2.208(3) Mn2O3 2.287(4) Mn1O1#2 2.208(3) Mn3O3 1.851(4) Mn1O1#1 2.208(3) Mn3O4 1.882(4) Mn1Mn3#2 3.1991(7) Mn3O1 1.974(4) Mn1Mn3#1 3.1991(7) Mn3N2 2.067(4) Mn1Mn3 3.1992(7) Mn3O2#1 2.199(4) Mn2N4 2.068(5) Mn3N3 2.201(4) Mn2O4#2 2.181(4) O4 Mn2#1 2.181(4) Mn1O2 Mn3#2 94.48(14) Mn1O2 Mn2 99.15(14) Mn3#2O2 Mn2 95.07(14) Mn3O3 Mn2 103.20(15) Mn3O4 Mn2#1 108.08(16) ____________________________________________________________

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230 Table A 6. Selected interatomic distances () and angles () for 54. ___________________________________________________ Mn1O12 2.1317(11) Mn4N4 2.0523(14) Mn1O6 2.1333(11) Mn4O9 2.2180(11) Mn1O9 2.1613(11) Mn4N5 2.2345(14) Mn1O2 2.2108(12) Mn5O8 2.1527(11) Mn1O3 2.2213(12) Mn5O3 2.2046(12) Mn1O1 2.2395(12) Mn5O10 2.2046(11) Mn2O4 1.8746(11) Mn5N6 2.2159(14) Mn2O5 1.8895(11) Mn5O9 2.2618(11) Mn2O1 1.9438(12) Mn5Br2 2.5667(3) Mn2N1 2.0559(14) Mn6O10 1.8705(11) Mn2O6 2.2485(11) Mn6O11 1.8921(11) Mn2N2 2.2519(14) Mn6O3 1.9513(12) Mn3O5 2.1384(11) Mn6N7 2.0587(14) Mn3O7 2.1942(11) Mn6O12 2.2274(11) Mn3O2 2.2402(13) Mn6N8 2.2430(14) Mn3O6 2.2558(11) Mn7O11 2.1640(12) Mn3N3 2.2582(15) Mn7O4 2.1853(12) Mn3Br1 2.5600(3) Mn7O1 2.2328(12) Mn4O7 1.8831(11) Mn7N9 2.2337(14) Mn 4O8 1.8939(11) Mn7O12 2.2593(11) Mn4O2 1.9409(12) Mn7Br3 2.5615(3) Mn2O1 Mn7 101.05(5) Mn1O6 Mn3 101.09(5) Mn2O1 Mn1 99.66(5) Mn2O6 Mn3 93.90(4) Mn7O1 Mn1 98.08(5) Mn4O7 Mn3 104.42(5) Mn4O2 Mn1 100.47(5) Mn4O8 Mn5 109.94(5) Mn4O2 Mn3 100.82(5) Mn1O9 Mn4 93.73(4) Mn1O2 Mn3 99.21(5) Mn1O9 Mn5 97.94(4) Mn6O3 Mn5 102.00(5) Mn4O9 Mn5 95.53(4) Mn6O3 Mn1 100.57(5) Mn6O10 Mn5 104.73(5) Mn5O3 Mn1 97.89(5) Mn6O11 Mn7 108.19(5) Mn2O4 Mn7 105.13(5) Mn1O12 Mn6 94.99(4) Mn2O5 Mn3 109.46(5) Mn1O12 Mn7 100.52(4) Mn1O6 Mn2 93.87(4) Mn6O12 Mn7 94.30(4) _____________________________________________________________

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231 Table A 7. Selected interatomic distances () and angles () for 61. Mn1O4 1.873(6) Mn4N6 2.247(7) Mn8O16 2.103(5) Mn1O1 1.900(6) Mn5O15 1.897(6) Mn9O3 1.871(6) Mn1O5 1.927(6) Mn5O10 1.905(5) Mn9O17 1.915(5) Mn1N1 2.059(9) Mn5O2 1.906(5) Mn9O13' 1.924(6) Mn1N2 2.222(7) Mn5O7 1.927(6) Mn9O16 1.931(5) Mn1O6 2.334(5) Mn5O11 2.152(5) Mn9N10 2.272(7) Mn2O8 2.035(6) Mn5O3 2.444(5) Mn9O15 2.369(5) Mn2O5 2.140(5) Mn6O13 1.895(6) Mn7O1 Mn1 150.6(3) Mn2O2 2.154(6) Mn6O1 1.903(5) Mn7O1 Mn6 98.3(3) Mn2N3 2.248(9) Mn6O6 1.918(6) Mn1O1 M n6 110.4(3) Mn2O6 2.285(5) Mn6O11 1.938(5) Mn5O2 Mn8 96.2(2) Mn2O7 2.320(5) Mn6O2 2.265(5) Mn5O2 Mn2 103.6(2) Mn3O8 2.105(5) Mn6N8 2.273(7) Mn8O2 Mn2 156.3(3) Mn3O3 2.166(6) Mn7O1 1.867(6) Mn5O2 Mn6 98.4(2) Mn3O9 2.201(6) Mn7O17' 1.883(6) Mn8O2 Mn6 98.1(2) Mn3O7 2.231(5) Mn7O13 1.925(5) Mn2O2 Mn6 91.9(2) Mn3N5 2.256(7) Mn7N9 2.070(7) Mn9O3 Mn4 95.9(3) Mn3N4 2.274(9) Mn7O14 2.199(5) Mn9O3 Mn3 163.5(3) Mn4O17 1.877(6) Mn7O12 2.322(6) Mn4O3 Mn3 99.3(2) Mn4O3 1.913(5) Mn8O14 1.877(5) Mn9O3 Mn5 95.0(2) Mn4O9 1.925(7) Mn8O15 1.900(5) Mn4O3 Mn5 95.0(2) Mn4N7 2.130(6) Mn8O2 1.908(6) Mn3O3 Mn5 90.0(2) Mn4O10 2.168(5) Mn8O15' 1.947(6)

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232 Table A 8. Selected interatomic distances () and angles () for 62. Mn1O4 1.8770(11) Mn6O4 1.8791(11) Mn5O2 Mn6 87.83(4) Mn1O10 1.8884(11) Mn6O1 1.9381(11) Mn2O2 Mn6 89.45(4) Mn1O1 1.9258(11) Mn6O15 1.9602(12) Mn4O2 Mn6 165.85(5) Mn1O11 1.9604(11) Mn6O17 1.9750(12) Mn5O3 Mn4 98.68(5) Mn1O13 2.1827(12) Mn6O14 2.1831(12) Mn1O4 Mn6 97.32(5) Mn1O5 2.3712(11) Mn6O2 2.2170(11) Mn1O4 Mn2 108.49(5) Mn2O7 1.8817(10) Mn7O7 1.8880(10) Mn6O4 Mn2 101.09(5) Mn2O8 1.9095(11) Mn7O7' 1.9125(10) Mn2O5 Mn1 82.83(4) Mn2O4 1.9237(11) Mn7O1 0' 1.9143(11) C37 O5 Mn5 125.30(9) Mn2O2 1.9466(10) Mn7O9 1.9314(10) Mn2O5 Mn5 85.03(4) Mn2O18 2.2442(11) Mn7O20 2.2054(11) Mn1O5 Mn5 83.46(4) Mn2O5 2.2904(11) Mn7O28 2.4674(11) Mn2O7 Mn7 128.70(5) Mn3O9 1.8941(10) Mn8O10' 1.8632(11) Mn2O7 Mn7' 131.50(6) Mn3O8 1.9012(10) Mn8O9 1.8646(10) Mn7O7 Mn7' 99.03(5) Mn3O19 1.9074(11) Mn8O23 1.9597(11) Mn3O8 Mn2 107.10(5) Mn3O22 1.9586(11) Mn8O12' 1.9750(11) Mn3O8 Mn9 117.28(5) Mn3O26 2.1507(12) Mn8O21 2.2461(12) Mn2O8 Mn9 121.00(5) Mn3O18 2.4280(11) Mn8O25 2.3078(13) Mn3O8 Mn4 99.98(4) Mn4O30 2.1027(12) Mn9O8 2.1043(11) Mn2O8 Mn4 96.53(4) Mn4O19 2.1243(11) Mn9O29 2.1229(12) Mn9O8 Mn4 111.00(4) Mn4O2 2.1960(11) Mn9O27 2.1945(12) Mn8O9 Mn3 126.53( 6) Mn4O3 2.2094(11) Mn9O6 2.2007(12) Mn8O9 Mn7 95.67(5) Mn4N2 2.2476(14) Mn9N3 2.2689(15) Mn3O9 Mn7 136.00(6) Mn4O8 2.2689(10) Mn9O28 2.3227(11) Mn8' O10 Mn1 131.13(6) Mn5O2 1.8636(11) Mn5O1 Mn1 113.48(5) Mn8' O10 Mn7' 96.30(5) Mn5O3 1.8899(12) Mn5O1 Mn6 95.07(5) Mn1O10 Mn7' 132.55(6) Mn5O1 1.9139(11) Mn1O1 Mn6 93.75(5) Mn2O18 Mn3 81.90(4) Mn5N1 2.0379(14) Mn5O2 Mn2 114.61(5) Mn3O19 Mn4 105.08(5) Mn5O16 2.1711(12) Mn5O2 Mn4 99.97(5) Mn9O28 Mn7 109.94(4) Mn5O5 2.4514(11) Mn2O2 Mn4 97.85(5)

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233 Table A 9. Selected interatomic distances ( ) and angles ( ) for 63. _____________________________________________________ Mn1O4 1.873(6) Mn9O13#1 1.924(6) Mn1O1 1.900(6) Mn9O16 1.931(5) Mn1O5 1.927(6) Mn9N10 2.272(7) Mn1N1 2.059(9) Mn9O15 2.369(5) Mn1N2 2.222(7) O13 Mn9#1 1.924(6) Mn1O6 2.334(5) O15 Mn8#1 1.947(6) Mn2O8 2.035(6) O17 Mn7#1 1.883(6) Mn2O5 2.140(5) O2 Mn6Mn2 42.65(14) Mn2O2 2.154(6) N8 Mn6Mn2 138.96( 18) Mn2N3 2.248(9) Mn7O1 Mn1 150.6(3) Mn2O6 2.285(5) Mn7O1 Mn6 98.3(3) Mn2O7 2.320(5) Mn1O1 Mn6 110.4(3) Mn3O8 2.105(5) Mn5O2 Mn8 96.2(2) Mn3O3 2.166(6) Mn5O2 Mn2 103.6(2) Mn3O9 2.201(6) Mn8O2 Mn2 156.3(3) Mn3O7 2.231(5) Mn5O2 Mn 6 98.4(2) Mn3N5 2.256(7) Mn8O2 Mn6 98.1(2) Mn3N4 2.274(9) Mn2O2 Mn6 91.9(2) Mn4O17 1.877(6) Mn9O3 Mn4 95.9(3) Mn4O3 1.913(5) Mn9O3 Mn3 163.5(3) Mn4O9 1.925(7) Mn4O3 Mn3 99.3(2) Mn4N7 2.130(6) Mn9O3 Mn5 95.0(2) Mn4O10 2.168(5) Mn4O3 Mn5 95.0(2) Mn4N6 2.247(7) Mn3O3 Mn5 90.0(2) Mn5O15 1.897(6) Mn1O5 Mn2 110.5(2) Mn5O10 1.905(5) Mn6O6 Mn2 97.8(2) Mn5O2 1.906(5) Mn6O6 Mn1 94.0(2) Mn5O7 1.927(6) Mn2O6 Mn1 92.75(19) Mn5O11 2.152(5) Mn5O7 Mn3 103.4(2)

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234 Mn5O3 2.444(5) Mn5O7 Mn2 97.1(2) Mn6O13 1.895(6) Mn3O7 Mn2 93.06(19) Mn6O1 1.903(5) Mn2O8 Mn3 105.9(2) Mn6O6 1.918(6) Mn4O9 Mn3 97.7(2) Mn6O11 1.938(5) Mn5O10 Mn4 104.9(2) Mn6O2 2.265(5) Mn6O11 Mn5 101.3(2) Mn6N8 2.273(7) Mn6O13 Mn9#1 165.7(3) Mn7O1 1.867(6) Mn6O13 Mn7 96.6(3) Mn7O17#1 1.883(6) Mn9#1O13 Mn7 95.8(3) Mn7O13 1.925(5) Mn8O14 Mn7 104.5(2) Mn7N9 2.070(7) Mn5O15 Mn8 96.7(2) Mn7O14 2.199(5) Mn5O15 Mn8#1 155.6(3) Mn7O12 2.322(6) Mn8O15 Mn8#1 97.2(2) Mn8O14 1.877(5) Mn5O15 Mn9 96.8(2) Mn8O15 1.900(5) Mn8O15 Mn9 95.8(2) Mn8O2 1.908(6) Mn8#1O15 Mn9 101.7(2) Mn8O15#1 1.947(6) Mn9O16 Mn8 104.1(2) Mn8O16 2.103(5) Mn4O17 Mn7#1 154.6(3) Mn9O3 1.871(6) Mn4O17 Mn9 95.6(3) Mn9O17 1.915(5) Mn7#1O17 Mn9 97.5(2)

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235 Table A 10. Selected interatomic distances and angles for D 1. Mn1—O13 1.866 (6) Mn4—O16 1.852 (7) Mn1—O1 1.887 (6) Mn4—O2 1.886 (7) Mn1—O21 1.918 (7) Mn4—O24 1.907 (6) Mn1—N13 1.996 (8) Mn4—N16 2.003 (8) Mn1—O17 2.100 (7) Mn4—O18 2.141 (10) Mn1O2 2.787(6) Mn4O13 2.907(6) Mn2—O11 1.867 (7) Mn5—O1 2.455 (6) Mn2—O1 1.869 (6) Mn5—O2 1.874 (5) Mn2—O22 1.936 (7) Mn5—O14 1.890 (6) Mn2—N11 1.992 (9) Mn5—O25 1.996 (8) Mn2—O27 2.171 (7) Mn5—N14 2.003 (10) Mn2—O14 2.429 (7) Mn5—O2E 2.236 (7) Mn3—O12 1.862 (7) Mn6—O15 1.872 (8) Mn3—O1 1.924 (7) Mn6—O26 1.898 (7) Mn3—O23 1.946 (6) Mn6—O2 1.918 (7) Mn3—N12 1.988 (8) Mn6—N15 2.002 (9) Mn3—O1E 2.193 (6) Mn6—O28 2.163 (7) Mn3—O25 2.272 (7) Mn6O23 2.550(7) Mn1—Mn2 3.1926 (17) Mn5—Mn6 3.217 (2) Mn4—Mn6 3.176 (3) O13 —Mn1—O1 159.6 (3) O16 —Mn4—N16 90.0 (3) O13 —Mn1—O21 90.5 (3) O2 —Mn4—N16 89.5 (3) O1 —Mn1—O21 88.4 (3) O24 —Mn4—N16 169.0 (3) O13 —Mn1—N13 86.2 (3) O16 —Mn4—O18 92.5 (4) O1 —Mn1—N13 91.1 (3) O2 —Mn4—O18 94.4 (3) O21 —Mn1—N13 169.1 (3) O24 —Mn4—O18 98.2 (3) O13 —Mn1—O17 103.9 (3) N16 —Mn4—O18 92.8 (3) O1 —Mn1—O17 96.5 (3) O2 —Mn5—O14 160.1 (3) O21 —Mn1—O17 90.7 (3) O2 —Mn5—O25 90.5 (3)

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236 N13 —Mn1—O17 100.1 (3) O14 —Mn5—O25 95.2 (3) O11 —Mn2—O1 169.9 (3) O2 —Mn5—N14 89.2 (3) O11 —Mn2—O22 88.7 (3) O 14—Mn5—N14 88.0 (3) O1 —Mn2—O22 91.8 (3) O25 —Mn5—N14 171.3 (3) O11 —Mn2—N11 90.3 (3) O2 —Mn5—O2E 100.4 (2) O1 —Mn2—N11 88.6 (3) O14 —Mn5—O2E 98.9 (3) O22 —Mn2—N11 176.3 (3) O25 —Mn5—O2E 86.2 (3) O11 —Mn2—O27 99.6 (3) N14 —Mn5—O2E 85.3 (3) O1 —Mn2—O27 90.4 (2) O2 —Mn5—O1 85.4 (2) O22 —Mn2—O27 94.7 (3) O14 —Mn5—O1 77.9 (2) N11 —Mn2—O27 89.0 (3) O25 —Mn5—O1 74.5 (2) O11 —Mn2—O14 91.0 (3) N14 —Mn5—O1 114.2 (3) O1 —Mn2—O14 78.9 (2) O2E —Mn5—O1 160.0 (3) O22 —Mn2—O14 90.8 (3) O15 —Mn6—O26 89.4 (3) N11 —Mn2—O14 85.7 (3) O15 —Mn6—O2 172.1 (3) O27 —Mn2—O14 168.2 (2) O26 —Mn6—O2 90.7 (3) O12 —Mn3—O1 168.9 (3) O15 —Mn6—N15 86.9 (4) O12 —Mn3—O23 89.2 (3) O26 —Mn6—N15 173.8 (4) O1 —Mn3—O23 90.1 (3) O2 —Mn6—N15 92.2 (3) O12 —Mn3—N12 89.5 (3) O15 —Mn6—O28 96.3 (3) O1 —Mn3—N12 92.0 (3) O26 —Mn6—O28 96.8 (3) O23 —Mn3—N12 175.9 (3) O2 —Mn6—O28 91.6 (3) O12 —Mn3—O1E 97.6 (3) N15 —Mn6—O28 88.6 (3) O1 —Mn3—O1E 93.5 (2) Mn2—O1 —Mn1 116.4 (3) O23 —Mn3—O1E 92.8 (3) Mn2—O1 —Mn3 118.8 (3) N12 —Mn3—O1E 83.6 (3) Mn1—O1 —Mn3 117.9 (3) O12 —Mn3—O25 88.6 (3) Mn2—O1 —Mn5 100.3 (2) O1 —Mn3—O25 80.3 (2) Mn1—O1 —Mn5 96.2 (2) O23 —Mn3—O25 90.7 (2) Mn3—O1 —Mn5 99.8 (2)

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237 APPENDIX B LIST OF COMPLEXES [Fe6O2(hmp)10(H2O)2](NO3)4 ( 31 ) [Fe6O2Cl4(hmp)8](ClO4)2 ( 32 ) [Fe6O2(OH)2(O2CBut)10(hep)2] ( 33 ) [Fe6O2(OH)(O2CBut)9(hep)4] ( 34 ) [Mn2O(SO4)2(bpy)2(H2O)2]158 (4 1) [Mn2O(O2CMe)(SO4)(bbe)(MeOH)2](PF6) (4 2) [Mn4O2(O2CMe)4(bbe)2] ( 43) [Mn7(OH)3(SCN)3(hmp)9] (ClO4)2 ( 51) [Mn 7(OH)3(NCO)3(hmp)9] (ClO4)2 ( 52) [Mn7(OH)3 (hmp)9 (I)2(H2O)] (ClO4)3 ( 53 ) [Mn7(OH)3(Br)3(hmp)9] (ClO4)2 ( 54) [Mn7(OH)3(Cl)3(hmp)9] (ClO4)2 ( 55) [Mn5(pdmH)6(thme)2] (ClO4)2 ( 6 1) [Mn5(pdmH)6(thme)2](I3)2 ( 62 ) [Mn18O12(hmp)20(H2O)2](ClO4)6 (6 3) [Mn6Ca4O4Cl6(pd)6(MeOH)10] ( C 1 ) [Mn6O2(naphthsao)6(MeCO 2)2(EtOH)(H2O)]•xEtOH•yH2O ( D 1)

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238 APPENDIX C M N6C A4 COMPLEX Description of Structure [Mn6Ca4O4Cl6(pd)6(MeOH)10 ] ( C 1): Complex C 1 was synthesized by Constantina “Ninetta” Papatriantafyllopoulou in Cyprus. Complex C 1 crystalizes in C1 2/c1 and can be described as a MnIII 6 octahedron inside a tetrahedron of CaII ions , shown in Figure C 1 . Complex C 1 is similar to the tetra facecapped octahedral topology of the [MnIII 6MnII 4O4(N3)4(hmp)12]2+ cation and the [Mn6Na4O(N3)(O2CMe)5(thme)4(H2O)4] with the CaII taking the place of the MnII and Na+ ions , respectively .210 , 282 The structure is comprised of a MnIII 6 octahedron within a tetrahedron of CaII ions with four 4O2 ions bridging three MnIII ions and one CaII ions each to form the Mn6Ca4 core. The Mn atoms are all six coordinate with near octahedral geometry. The oxidation states are obvious from charge considerations, the metric parameters, bond valence sum (BVS)263 264 calculations, and the Jahn–Teller (JT) distortions expected for highspin MnIII ions; the Mn6 octahedral unit of C 1 is thus 6MnIII. The protonation levels of the bound pdO atoms and MeOH molecules III JT elongation axes are Cl (1) –Mn(1) – Cl ( 2), Cl (1) –Mn(2) –Cl ( 2), Cl (1) –Mn(3) –Cl ( 2 ), and Cl (1) – Mn(4) –Cl ( 2 ), each involving the 3Clions . Magnetochemistry Variable temperature magnetic susceptibility studies were performed on microcrystalline a sample of C 1, restrained in eicosane to prevent torqueing. The magnetic susceptibilities were examined at a 0.1 T (1 kG) field in the 5 to 300 K temperature range for C 1. Diamagnetic corrections were applied to the magnetic susceptibilities using Pascal's constants.178 For complex C 1, MT gradually increases from 25.55 cm3Kmol1 at 300K to a near plateau value of ~79 cm3Kmol1 at 4020 K and then decreases to 67.79 cm3Kmol1 at 5.0K

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239 (Figure C 2 ). The 300K value is much larger than the spin only (g = 2) value of 18 cm3Km ol1 for six MnIII noninteracting ions, indicating the presence of dominant ferromagnetic exchange interactions. The MT near plateau value in the 2040K range appears to be heading for a final value of ~79 cm3Kmol1, the spin only (g=2) value of a specie s with an S = 12 ground state, before exhibiting the final decrease at temperatures below 10K. The latter decrease is likely due to a combination of zero field splitting (ZFS), Zeeman effects, and any weak intermolecular interactions. The metal ions are th us clearly involved in magnetic exchange interactions, and the data were fit to the theoretical MT vs T expression derived from the spin Hamiltonian appropriate for a Mn6 octahedron; given in E quation C 1, = 2Jcis12 13 14 16 23 25 26 34 35 45 + 46 56) – 2Jtrans15 24 36) ( C 1) Where Si refers to the spin of metal Mni, and Jcis and Jtrans are the pairwise exchange parameters for adjacent and opposite metals of the octahedron, respectively; the Mn labeling scheme of Figure C 3 was employed. This Hamiltonian can be transforme d into an equivalent form (E quation C 2) by using the Kambe coupli A 1 5, B 2 4C 3 6T A B C where the ST is the resultant spin of the complete molecule. = 2Jcis12 13 14 16 23 25 26 34 35 45 + 46 56) – 2Jtrans15 24 36) ( C 2)

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240 From E quation C 2 can be obtained the energy expression (E quation C 3) for the energies, E(ST), of each ST state; constant terms contributing equally to all states have been omitted from E quation C 3. E(ST) = Jcis[ST(ST+1) – SA(SA+1) – SB(SB+1) – SC(SC+1)] – Jtrans[SA(SA+1) + SB(SB+1) + SC(SC+1)] ( C 3) An expression for the molar paramagnetic susceptibility, M, was derived using the above and the Van Vleck equation, and assuming an isotropic g tensor. The derived equation was then used to fit the experimental MT vs T data in Figure C 2 as a function of the two exchange parameters Jcis and Jtrans, and the g fac tor. Only data for the 20.0 – 300K range were used, since the model does not incorporate ZFS and other minor effects and therefore cannot reproduce the decrease at lower temperatures. Good fits were obtained with fit parameters of Jcis = 3.8 + 0.2 cm1, J trans = 1.2 + 0.8 cm1, and g = 2.02 + 0.002, with temperature independent paramagnetism (TIP) held constant at 600 x 106 cm3 mol1. The fit indicates that Mn 6Ca4 complex has an ST = 12 ground state. In the notation | ST, SA, SB, SC> this is the |12, 4, 4, 4> state in which all six MnIII spins are aligned parallel. The first excited state is a triply degenerate set of ST = 11 states comprising the |11, 3, 4, 4>, |11, 4, 3, 4>, and |11, 4, 4, 3> states at 366 cm1 above the ground state. Thus, the S = 12 ground state is well isolated from the nearest excited state. To confirm the S = 12 ground state for complex C 1 and to estimate the magnitude of the zero field splitting parameter, D, magnetization vs dc field measurements were made on restrained samples at applied magnetic fields and temperatures in the 1 – 70 kG and 1.910.0 K ranges, respectively. We then attempted to fit the data, using the MAGNET program, by diagonalization of the spin Hamiltonian matrix assuming only the ground state is populated, incorpz 2), Zeeman terms, and employing a full powder average. The

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241 corresponding spin Hamiltonian is given by equation C z is the easy axis spin B is the Bohr magneton, and 0 is the vacuum permeability. z 2 + g B0 H (C 4) For complex C 1, we were able to obtain a satisfactory fit using all data up to 7 tesla. This suggests that the ground state of complex C 1 is relatively well isolated from the nearest excited states, as su ggested from the obtained J values (vide supra). The best fit is shown as the solid lines in the reduced magnetization ( M/NB vs H/T ) plot in Figure C 4 and was obtained with S = 12, g = 2.07, and D = 0.051 cm1. An equally good fit was also obtained with S = 12, g = 2.05, and D = 0.058 cm1. It is common to obtain two acceptable fits of magnetization data for a given S value, one with D < 0 and the other with D > 0, since magnetization fits are not very sensitiv e to the sign of D . Alternative fits with S = 11 were rejected because they gave unreasonable values of g and D . The root mean square D vs g error surface for the fit was generated using the program GRID, and is shown as a 2D contour plot in Figure C 5 fo r the D = 0.6 to 0.6 cm1 and g = 1.8 2.2 ranges. Two minima are observed and are of essentially equal quality which makes it impossible based on these magnetization fits to conclude the more likely sign of the axial anisotropy parameter D . The ZFS of the ground state of polynuclear MnIII complexes is largely a consequence of the vectorial addition of the single ion ZFS tensors. Octahedral MnIII ions typically undergo a large Jahn Teller (JT) distortion to remove orbital degeneracy which can be visualiz ed as a unique axis formed by two noticeably longer MnL bond distances. This axis often defines the unique axis of the magnetic structure of the MnIII ion. When all JT axes are oriented parallel, the resultant ZFS of a MnIII x complex can be very large; for example, the essentially parallel JT axes in the 8 MnIII ions contained in [Mn12O12(O2CR)16(H2O)4] complexes (8 MnIII and 4 MnIV)

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242 result in a fairly large ZFS of the molecule (D ~ 0.5 cm1). Conversely, when the JT axes do not align parallel, the resu ltant ZFS will be small due to the individual contributions cancelling each other out. This is common in Mn6 octahedron complexes such as complex C 1 because of the high symmetry of the molecule, the vectorial addition of single ion anisotropies sums to zero. This clearly explains the experimental observation of D ~ 0 for complex C 1. A c s usceptibility studies are a powerful complement to dc studies for determining th e ground state of a system, because they remove the complications that arise from having a dc field present. The obtained inphase ’M signal for complex C 1 is plotted as ’MT in Figure C 6, and the data appears to be almost temperature independent, confi rming a well isolated ground state before decreasing slightly just before 5 K (to avoid lower temperature effects from the slight anisotropy and weak intermolecular interactions) gives a value of ~ 79 cm3 K mol1, which is consistent with an S = 12 ground state and g ~2, in excellent agreement with the reduced magnetization fit. We conclude that complex C 1 does have an S = 12 ground state. There is no out of phase ac s usceptibility signal down to 1.8 K, the operating limit of our SQUID magnetometer.

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243 Figure C 1. Stereoview of complex C 1 (top), stereoview of the core of C 1 (middle) and partially labeled core of C 1 (bottom). Hydrogens have been omitted for clarity. Color scheme: Ca, pink; MnIII, green; O, red; C, grey.

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244 T (K) 0 50 100 150 200 250 300 MT (cm3 K mol-1) 0 20 40 60 80 100 fit Figure C 2. Plot of MT vs T for complex C 1. The solid line is the fit of the data; see text for the fit parameters.

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245 Figure C 3. Labeling scheme employed in Equation C 1. H/T (kG/K) 010203040 M/NB 051015202530 0.1 T 0.5 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T Fit Figure C 4. Plot of reduced magnetization ( M/NB vs H/T ) for complex C 1. The solid lines are the fit of the data; see text for the fit parameters.

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246 g 1.801.851.90 1.95 2.00 2.05 2.10 2.15 D (cm-1) -0.20-0.15-0.10-0.050.000.050.100.150.20 0.18 0.22 0.20 0.18 0.18 0.20 0.22 0.24 0.20 0.26 0.28 0.18 0.18 0.30 0.20 0.32 0.34 0.22 0.20 0.36 0.24 0.38 0.26 0.22 0.40 0.28 0.42 0.24 0.30 0.44 0.26 0.32 0.46 0.34 0.28 0.48 0.30 0.36 0.50 0.38 0.52 0.32 0.40 0.54 0.34 0.42 0.56 0.36 Figure C 5. Two dimensional contour plot of the root mean square error surfa ce for the D vs g fit for complex C 1.

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247 T (K) 0 2 4 6 8 10 12 14 16 M'T (cm3 K mol-1) 0 20 40 60 80 100 997 Hz 250 Hz 50 Hz Figure C 6. Inphase susceptibility ( M’ data plotted as M’T) of complex C 1 in a 3.5 G ac field oscillating at the indicated frequencies.

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248 APPENDIX D [Mn6O2(naphthsao)6(MeCO2)2(EtOH)(H2O)]•xEtOH•yH2O D.1 I ntroduction In the frenzy of single molecule magnet development, flexible organic bridging ligands were employed in a self assembly processes with manganese ions,283 which led to the exploration and development of oxime bridged [Mn6O2] core complexes. The family began with the employment of salicylaldoxime (saoH2) and resulted in [Mn6O2(sao)6(O2CR)2(EtOH)4] family with an S = 4 ground states.247 The development and characterization of the initial membe rs of [Mn6O2] family resulted in the realization the complexes possess very weak exchange interactions, normally a disadvantage due to the inevitable low lying excited states; however, it means that slight structural modifications could easily switch the interactions from antiferromagnetic to ferromagnetic in nature. The idea of creating a ‘twisted’ torsion angle of the bridging sao ligand between manganese(III) ions (i.e. Mn N O Mn) by derivatizing the sao ligand was hypothesized and proved to be effectiv e when analogous complexes were synthesized with bulkyderivatives of salicylaldoxime (i.e. Me saoH2, Ph saoH2) which were more sterically “hindered” and had an S =12 ground state.246 , 284 For example, [Mn6O2(Et sao)6(O2CPh(CH3)2)2(EtOH)6] held the record for the largest effective barrier to magnetization reversal (Ueff) of 86.4 K for a while.246 , 284 This family containing the [Mn6O2] core with various saoH2 ligands have provided insight into the physical characteristics and are well characterized in terms of magnetostructural correlations.285288 The classic examples are the [MnIII 6O2(Et sao)6(O2CPh)2(EtOH)4(H2O)2]45 and [MnIII 6O2(Et sao)6(O 2CPh(Me)2)2(EtOH)6]246 clusters follow the “magic angle theory”.45, 246 Since the discovery of this family of compounds numerous modifications, mainly addressing the terminal part of the complexes, have been reported.289292 Moreover, Brechin et al. introduced new members with different structural types, through the

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249 addition of bridging ligands and mixedvalent [MnIII 4MnIV 2] cores.285, 286 Due to the ease and highyield of the syntheses of this family along with the interesting magnetic properties, there has been continued interest in the development of new saoderivatives and new Mn6 compounds. Previously the naphthsaoH2 ligand was introduced and produced a series of its [Mn3] complexes.293 Also a [Mn9] defect supertetrahedron species, displaying enhanced energy barriers, was constructed.294 A standard procedure developed by Brechin et al .285 288 in combination with naphthsoaH2 results in the isolation of a new Mn6 complex with a surprising new modification of the classic [Mn6O2] core. The synthesis, structure, and magnetic and highfrequency electron paramagnetic resonance measurements are reported for a new Mn6 complex, [Mn6O2(naphthsao)6(MeCO2)2(EtOH)(H2O)] xEtOH yH2O. D .2 Experimental Section D .2.1 Syntheses General. HPLC grade absolute ethanol and a 25% solution of tetraethylammonium hydroxide (TEAOH) in methanol stored under argon atmosphere were used. T he organic ligand (1 (1 hydroxynaphthalen2yl) ethanone oxime, naphthsaoH2) was synthesized as reported elsewhere.293 Other chemicals (manganese(II) acetate tetrahydrate) were used as obtained commercially, without further purification. [Mn6O2(naphthsao)6(MeCO2)2(EtOH)(H2O)]•xEtOH•yH2O (D 1). Original synthesis of D 1 was carried out by Malgorzata solution of 1(1 hydroxynaphthalen 2yl) ethanone oxime (naphthsaoH2, 0.4 g, 2 mmol) ) and manganese(II) acetate (0.49 g, 2.0 mmol) i n ethanol (50 mL) was added tetraethylammonium hydroxide (2 mL) which resulted a color change to a black mixture. The mixture was stirred for 1 h, subsequently filtered and left for slow evaporation. Black crystals of D 1 (Figure D 1) were obtained after D 14 days at 78% yield. Elemental analysis f or sample dried under: Air –

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250 A nalysis: D 16H2O % Calc ulate d (Found): C 50.44(50.99), H 4.88(4.21), N 4.53(3.86); Vacuum – analy sis: D 1 3H2O % Calc ulate d (Found): C 51.95(51.57), H 4.70(4.27), N 4.66(4.01). IR ba nds (cm1): 382.06 (s), 391.66 (s), 422.07 (s), 443.55 (s), 481.23 (s), 521.89 (vs), 562.19 (s), 575.10 (s), 601.18 (s), 618.01 (vs), 636.44 (vs), 658.47 (vs), 736.57 (s), 795.32 (s), 897.31 (s), 991.17 (s), 1022.25 (s), 1034.13 (s), 1087.94 (m), 1136.47 (w), 1151.64 (w), 1209.79 (w), 1236.67 (w), 1251.50 (w), 1297.75 (w), 1345.92 (m), 1384.17 (s), 1419.64 (m), 1450.73 (w), 1516.79 (m), 1556.65 (m), 1618.98 (vw). D .2.2 X Ray X ray diffraction data for D 1 were collected at 100(2) K on a Stoe IPDS2295 diffractometer equipped with an image plate detector and with graphite monochromatized MoK radiation (Table D X crystallographic data). The crystal structure was solved by direct methods in SHELXS97 and refined in SHELXL97 software.296 C bonded H atoms were placed in their calculated positions with Ueq = 1.2/1.5Ueq (parent C atom) for aromatic/methyl H atoms, respectively. SIMU/EADP restraints were used for displacement facto rs of some disordered atoms. Extensive disorder of solvent molecules occupying structure voids had to be treated with SQUEEZE procedure.261 The affected solvent occupied 32 voids, out of which 8 largest were of about 705 3 volume. In total, electron density c orresponding to ~70 e/asymmetric unit (7 water molecules or about 3 ethanol molecules) was thus removed. Some difference Fourier maxima still present after further refinement cycles were interpreted as disordered water molecules: cooperatively disordered O 1W/O2W (refined occupancies of 0.54(2)/0.46(2), respectively), O3W/O4W (refined occupancies of 0.61(2)/0.39(2), respectively), O5W/O6W (refined occupancies of 0.41(2)/0.59(3), respectively) and O7W, O8W with occupancies refined as free variables to 0.49(4) , 0.33(3), respectively. On

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251 the final difference Fourier map the highest peak of 0.78 e/3 is located at 1.08 from Mn5 atom. D .2.3 High frequency Electron Paramagnetic Resonance (HFEPR) High frequency electron paramagnetic resonance (HFEPR) data were col lected for a finely ground dried sample of [Mn6O2] that was incorporated into a KBr pellet in order to avoid field alignment of the micro crystallites within the powder. Measurements have been performed at high frequencies of 50 – 441.6 GHz in the temperat ure range of 2.525 K. HFEPR spectra were collected at the U.S. National High Magnetic Field Laboratory Electron Magnetic Resonance facility, using a transmission probe in which microwaves are propagated through cylindrical lightpipes. Highfrequency microwaves were generated by a phaselocked Virginia Diodes solid state source operating at 13 1 GHz followed by a chain of multipliers and amplifiers. Microwaves detection was provided by a bolometer. High magnetic fields were provided by a 17 T superconducti ng magnet 297. D .2.4 Other Physical Methods Infrared spectra were recorded in the solid state (KBr pellets) on a Nicolet Nexus 670 FTIR spectrometer in the 400 4000 cm1 range. Elemental analyses (C, H, and N) were performed by the in house facilities of the University of Florida, Chemistry Department. Variabletemperature dc and ac magnetic susceptibility data were collected at the Univer sity of Florida using a Quantum Design MPMS XL SQUID susceptometer equipped with a 7 T magnet and operating in the 1.8 300 K range. Samples were embedded in solid eicosane to prevent torqueing. Magnetization vs field and temperature data were fit using the program MAGNET. Pascal’s constants were used to estimate the diamagnetic correction, which was subtracted from M).

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252 Powder diffractograms were collected on a Bruker StadiVari device at 5 100 2 range using CuK radiation. The simulation of a theoretical pattern was carried out in Mercury software.298 T hermogravimetric diagram was recorded for a 9.2 mg sample of D 1 on a NETZSCH STA 409 CD device at temperature range of 25 1200C and scanning rate of 5 K/min . A 3 step decomposition pattern was observed with first stages apparently corresponding to the release of interstitial solvent. D .3 Results and Discussion D .3.1 Syntheses. Some of th e most common routes to highnuclearity Mnx clusters are reactions of simple manganese salts in the presence of potentially bridging or chelating ligands. The exact identity and nuclearity of the isolated products depend on a variety of factors such as pH, reagent ratios, solvent, carboxylate and chelate, among others. Reaction of Mn(MeCO2)2 with equimolar amounts of naphthsaoH2, TEAOH in EtOH resulted in black solution from which were subsequently isolated 6Mn3+ + 6 naphthsaoH2 + 2 MeCO2 + O2 + EtOH + 11 TEAOH [Mn6O2(naphthsao)6(MeCO)2(EtOH)(H2O)] + 11 H2O (D 1) where atmospheric O2 is assumed to be the oxidizing agent to generate MnIII from MnII, facilitated by the basic conditions provided by TEAOH; in the absence of TEAOH, longer reaction times are required to get a significant dark coloration and the yields of the isolated products are much lower. When the reaction is carried out in methanol, the previously reported triangular [Mn3O(naphthsao)3(CH3OH)5(CH3COO)] complex is isolated.293

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253 D .3.2 Description of structures The complex core contains two well known oxime bridged [MnIII 3O] units, which are bound together in an unusual way. In the classical example of an [Mn6O2] core45, 288 the two [Mn3O] units are antiparallel and joined through MnOoxime bonds at one edge. In D 1, these units are almost parallel and linked through two stronger Mn Ooxo/oxime bonds, along with two weaker Mn Ooxime/oxo bonds (Table A 7, Figure D 2, D 3). Thus, an unusual cage like unit can be distinguished (Figure D 2, bottom) with stacking of tilted “Mn(Ooxo)(NO)oximeMn” rings. The “classical” and “modified” [Mn6O2] cores might be conveniently distinguished by the criterion of MnMn distances, involving Mn atoms from different units, where, as expected, higher maximum distances are observed fo r the “classical core” compounds (see Table D X, comparison mn6s). Similar considerations may lead to detection of other structural types within the [Mn6O2] family. The possibility of the related [Mn6O2] isomers formation was already proved by Milios et al.299 An interesting compound with a novel modification was introduced, being a co crystal of the classical core complex. No detailed magnetic properties characterization was undertaken due to the presence of the two individuums in one crystal structure. D .3.3 Magnetochemistry D .3.3.1 Direct current magnetic susceptibility studies Solid state, variable temperature dc magnetic susceptibility ( M) measurements were performed on vacuum dried, air dried (dry) and pristine (wet), microcrystalline samples of D 1, restrained in eicosane to prevent torqueing. The data were collected in the 5.0 300 K range in a 0.1 T (1000 Oe) dc magnetic field and they are shown as M T vs T plots in Figure D 4. Diamagnetic corrections were applied to the magnetic susceptibilities using Pascal's constants.178

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254 For the vacuum dried sample of co mplex D 1, MT gradually decreases from 17.25 cm3Kmol1 at 300K to a value of ~15 cm3Kmol1 at 100 K and then increases rapidly to 8.25 cm3Kmol1 at 5.0K (Figure D 11). The 300K value is slightly less than the spinonly (g = 2) value of 18 cm3Kmol1 for six MnIII noninteracting ions, indicating the presence of dominant antiferromagnetic exchange interactions. The MT value at low temperature appears to be heading for a final value of ~8 cm3Kmol1, the spinonly (g=2) value of a species with an S = 4 ground state. Similar results were obtained regardless of sample preparation (Figure D 4). To confirm the indicated S = 4 ground state for complex D 1, and to estimate the magnitude of the zero field splitting parameter, D , magnetization vs dc field measurements were made on restrained samples at applied magnetic fields and temperatures in the 1 – 70 kG and 1.8 10.0 K ranges, respectively. Attempts to fit the data were made using the MAGNET program, by diagonalization of the spin Hamiltonian matrix assuming only the ground state is populated, incorporating axial anisotropy ( z 2), Zeeman terms, and employing a full powder average. The corresponding spin Hamiltonian is given by Equation D z is the easy axis spin or, B is the Bohr magneton, and 0 is the vacuum permeability. z 2 + g B0 H (D 2) However, a satisfactory fit was not obtained regardless of the parameters and data used for the fit attempts. D .3.2.2 Alternating current magnetic susceptib ility studies Solid state, variable temperature dc magnetic susceptibility ( M) measurements were performed on vacuum dried, air dried (dry) and pristine (wet), microcrystalline samples of D 1, restrained in eicosane to prevent torqueing. The data were collected in the 1.815 K range in a

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255 3.5 G ac magnetic field and data for vacuum dried, dry, and wet are shown in plots in Figure D 5, D 7, and D 8, respectively. Diamagnetic corrections were applied to the magnetic susceptibilities using Pascal's constant s.178 Ac susceptibility studies are a powerful complement to dc studies for determining the ground state of a system, because they remove the complications that arise from having a dc field present. The obtained inphase ’M signal for the vacuum dried preparation of complex D 1 is plotted as MT in Figure D 5 (top), and the data decreases from 9.34 to 7.34 cm3 K mol1 at 15K to 4K, respectively, which is indicat ive of low lying excited states. Extrapolation to 0 K to avoid lower temperature effects from the slight anisotropy and week intermolecular interactions gives a value of ~ 7 cm3 K mol1, which is consistent with the spin only value for an S = 4 ground stat e. There is a decrease in the in phase ac susceptibility concomitant with an increase in the out of phase ac susceptibility beginning at 4 K (Figure D 5). The out of phase signal is frequency dependent which is consistent with SMM behavior. These data suggest that D 1 is an SMM with significant relaxation barriers, and thus their magnetization vector cannot relax fast enough to stay in phase with the oscillating ac field. The ac M vs T plots can be used as a source of relaxation data for determining the t rue or effective energy barrier (Ueff) to magnetization relaxation, because at the M peak maximum the relaxation rate (1/ , where is the relaxation time) is equal to the angular frequency (2 ) of the field. The obtained data for D 1 are shown as Arrhenius plots in Figure D 6, based on the Arrhenius Law of Equation D 3, where k is the Boltzmann constant and 0 is the pre exponential factor. The fit of the data for D 1 gave Ueff ~ 35.8 K and t0 ~ 2 x 107 s1. = 0 exp(Ueff/ k T) (D 3) SMMs tend to have 0 in the range of 107109 s1.

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256 AC susceptibility studies confirm that D 1 is an SMM. The most striking observation concerns the out of M vs. T plot for the pristine sample (Figure D 7), where two peaks at 2 and 6 K are observed. These peaks could correspond to different relaxation processes with the energy barriers of 19 and 69 K, respectively, calculated based on the relevant Arrhenius plots. The high temperature Ar rhenius plot is shown in Figure D 8 has fit parameters of Ueff and 0 values of 69 K and 4.5x109s1, respectively . The 0 for the high temperature data is more consistent with single molecule magnet relaxation rates. The two peaks are observed independent of the sample preparation method. The intensity of the higher temperature component is higher for a sample filtered fresh from the mother solution. It seems that two out of phase peaks are still observed when a dry sa mple is examined (see Figure D 9). Howe ver, an unambiguous proof cannot be achieved due to the presence of considerable experimental error. However, it appears that the double relaxation results from different solvation environments with in the crystal lattice due to the elimination of the high temperature peak after the sample is placed under vacuum for 6 hours. A previous investigation by Redler et al. showed that the anisotropy of the system does not change but desolvation influences the quantum tunnelling interactions and reduction of the Ueff.300 Thus, the experiment showing a double relaxation in the pristine sample because regardless of the care t aken there will be some solvent loss in sample preparation. The solvent loss over time was evaluated by thermogravametric methods with the results shown in Figure D 10. X ray powder diffraction data was collected and simulated to ensure only one type of pr oduct was iso lated in the sample (Figure D 11). A double relaxation observed in the [Mn12] complexes was explained in terms of the so called Jahn Teller isomerism. However, there is no indication in the crystal structure to support such an explanation in t he case of D 1.

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257 D .4 High frequency electron paramagnetic resonance studies The analysis of EPR spectra for high spin complexes can provide precise information such as the exact value of the groundstate spin the magnitude and sign of D 60, 61 the location in energy of excited spin states relative to the ground state 62, 63 and most importantly, information concerning transverse spin Hamiltonian parameters e.g., the rhombic E term 64. However, the (2 S+1) fold energy level structure associated with a large molecular spin S necessitates EPR spect roscopy spanning a wide frequency range. Furthermore, large ZFS due to the significant anisotropy and large ST values demand the use of frequencies and magnetic fields considerably higher (50 GHz to several hundreds of GHz, up to 10 T) than those typically used by the majority of EPR spectroscopists. Temperature dependence of spectra recorded at two different frequencies, 416 GHz and 208 GHz are shown in Figure D 11(a) and (b), respectively. Spectra recorded at 416 GHz show a series of peaks that are at low er field than the g = 2 (14.86 T) position, i.e. they have higher gvalues. The first peak, at ~ 0.5 T, grows with decreasing temperature which is indicative of a transition from the ground state. The other peaks emerge at elevated temperature indicating t hat they are transitions from excited states. On the other hand, spectra that were recorded at 208 GHz show a series of peak throughout the entire field range. The dips (labeled as 3 T and 5.2 T are attributed to paramagnetic oxygen impurities trappe d in the KBr pellet. The sharp large features (labeled by ) observed at g = 2 (7.4 T) are attributed to isotropic paramagnetic impurities (MnII) on sample holder. This was observed at the lowest temperature (2.5 K) ; the largest feature is at a high field (12.2 T). This feature becomes smaller as the temperature increasing which is indicative of a transition from the ground state. All other features grow larger with increasing temperature indicating that they are excited state transitions. For an axial system, the parallel (B//z) component of the powder spectrum typically extends about twice as far from

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258 being directly proportional to the magnitude of the D axial p arameter. On this basis, the low field features in 416 GHz spectra can be attributed to parallel excitations. The spectrum recorded at 416 GHz and 20 K revealed at least three resolved peaks that correspond to the following fine structure transitions within the ground state S = 4 spin multiplet: ms Z4 > 3), ms Z3 > 2) and ms Z2 > 1 buried in the noise and the remaining transitions are beyond the field range). The fact that the spectral weight associated with the parallel spectrum shifts to the low field ms transitio n upon cooling provides confirmation of the negative sign of D , i.e., the ms lowest in energy when B//z. Some features are labelled in the spectra recorded at 218 GHz to show the corresponding energy transitions (Figure D 11 (b)). The feature at the very low field is caused by z component transition from ms ms Z2 > 1), meanwhile the very high field feature is a y component transition of ground state to first excited state ( Y4 > 3) within S = 4 spin multiplet. Both temperature d ependence spectra have simulated by employing the following Hamiltonian: 22200 44 (-)B zxyHBgSDSESSBO ( D 4) where S , zS , xS , and yS are spin operators, B is the applied magnetic field vector, g is the Land g tensor, B is the Bohr magneton, D and E are the second order axial and rhombic zero field splitting parameter respectively, a nd the final term represents axial fourth order zero field splitting 301. The parameters used for the simulation were S = 4, D = 2.12 cm1, | E | = 0.52 cm1, 04B = 4.67 104 cm1, and gx = gy = gz = 2.00. The relevant parallel and perpendicular portions

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259 of the simulations agree with the experiments in every respect. Gaussian distributions of the D and E parameters (fwhm of ~ 0.02 cm1) were employed in these simulations. In order to obtain tighter constraints on the spin Hamiltonian parameter for complex D 1, frequencydependent powder EPR experiments were carried out with frequencies in the range 50 – 441.6 GHz. The positions of the parallel and parallel component peaks were plotted versus frequency, as seen in Figure D 13.Th data were simulated with the Hamiltonian shown in Equation D 4. The solid lines represent the best simulation of the frequencydependent data using the same parameters used to simulate Figure D 12. In addition, the kinetic barrier to magnetization relaxation (Ueff) of 33.92 cm1 or 48.80 K was estimated from these parameters. This value is consistent value of 35K acquired by AC susceptibility studies prepared similarly to the HFEPR sample. D .5 Conclusions and Future Work In conclusion, a new isomer of the classical oximebridged [Mn6O2] core complexes is introduced. The complex shows SMM behavior and signs of a double relaxation of magnetization process with mild solvent loss. All results of other studies are in favor of this postulate, although unambiguous proof is still unavailable. A possible explanation would be based on desolvation of the crystal. Future studies will aim at getting further insight into this phenomenon in solid state and in solution. It could be expected that even more isomeric forms of the classical [Mn6O2] core may be synthesized, leading to unexplored magnetic properties and new insight into the magnetostructural correlations in this family of compounds. A careful design of the bridging oxime ligand should be the path to their successful isolation. Moreover, chara cterization of more complexes with a core related to D 1 should enable a magnetostructural correlation to be developed in this class of compounds.

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260 Table D 1. Selected X ray data for D 1. D 1 Formula C 78 H 68 Mn 6 N 6 O 20 .82(H 2 O) Formula weight 1807.85 Temperature [K] 100(2) 0.71073 Crystal system Orthorhombic Space group Fdd2 a [] 69.882 (6) b [] 26.962 (5) c [] 17.639 (4) V [ 3 ] 33235 (10) calc [g cm 3 ] 16, 1. 445 1 ] 0.96 F(000) 14819 Crystal size [mm] 0.07 0.06 0.04 1.41 25.00 rflns: total/unique 35403 / 14328 R(int) 0.130 Abs. corr. numerical Min., max. transmission factors 0.684, 0.960 Data/restraints/params 14328 /627/1023 GOF on F 2 1.00 0.075 wR2 (all data) 0.181 elect [e 3 ] 0.78, 0.56 Table D 2. Results of the BVS calculations for D 1. Mn1 Mn2 Mn3 Mn4 Mn5 Mn6 Mn II 3.62 3.32 3.03 3.26 3.08 3.11 Mn III 3.22 3.26 3.20 3.20 3.02 3.17 Mn IV 3.46 3.17 3.11 3.11 2.94 2.97

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261 Table D 3. MnMn distances in D 1 and in the reported example of “classical” [Mn6O2] core compounds in ascending order. Ref codes from the CCDC database302 are cited. The corresponding distances are quoted as retrieved from the CCDC database. EKELAI – related compound (1st molecule) reported by Milios et al._ENREF_16299299 299 299 299 299– see the main Article. Labels from D 1 D 1 EKELAI AGABOA AGACAN CEYMAV FUSQOA VIVFIQ 1 molec. 2 molec. Mn1 Mn5 3.254(2) 3.323 3.259 3.323 3.23 3.254 3.29 3.154 Mn2 Mn5 3.341(2) 3.343 3.771 3.693 3.798 3.784 3.762 3.647 Mn3 Mn5 3.366(3) 3.601 3.771 3.693 3.798 3.784 3.762 3.647 Mn1 Mn4 3.551(2) 3.694 4.938 4.998 4.96 5.009 4.941 5.018 Mn3 Mn6 3.691(2) 4.258 4.938 4.998 4.96 5.009 4.941 5.018 Mn1 Mn6 4.080(3) 4.889 6.22 6.141 6.29 6.292 6.208 6.148 Mn3 Mn4 5.385(3) 5.217 6.22 6.186 6.29 6.301 6.208 6.242 Mn2 Mn4 5.727(2) 5.527 6.242 6.186 6.31 6.301 6.24 6.242 Mn2 Mn6 5.748(2) 6.083 7.716 7.739 7.749 7.804 7.69 7.837

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262 MnMnONCH3O MnMnMnONCH3O Figure D 1. Coordination modes of the ligand in complex D 1. Figure D 2. S tructure of D 1 (top); Stereoview of complex D 1 (middle); the complex core (bottom).

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263 Figure D 3. Complex D 1 core with cagemotif highlighted with black bonds (left) and an overlap diagram (right) of D 1 and a “classical core” (dashed lines) example.2a Fitted atoms are labeled. Figure D 4. Plot of MT vs T for complex D 1. The solid line is the fit of the data; see text for the fit parameters. T (K) 050100 150 200 250 300 350 MT (cm3 K mol-1) 02468 10 12 14 16 18 wet vacuum dry

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264 T (K) 0246810121416 M'T (cm3 K mol-1) 0246810 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K) 024 6 8 10 12 14 16 M" (cm3 mol-1) 0.00.10.20.30.40.5 0.6 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz Figure D 5. Alternating current magnetic susceptibility studies for D 1 in phase plotted as M (top) and out of phase plotted as M (bottom).

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265 1/T (K-1) 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 ln(1/ ) 2 3 4 5 6 7 8 9 10 data fit Figure D 6. Arrhenius plot for the vacuum dried sample of D 1.See text for fit parameters.

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266 T (K) 024 6 8 10 12 14 16 M'T (cm3 K mol-1) 0 2 4 6 8 10 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K) 0 2 4 6 8 10 12 14 16 M" (cm3 mol-1) -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz Figure D 7. Alternating current magnetic susceptibility studies for D 1 (pr i stine sample) in phase plotted as M of phase plotted as M (bottom).

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267 1/T (1/K) 0.160.180.20 0.22 0.24 0.26 ln() 1 2 3 4 5 6 7 8 Figure D 8. Arrhenius plot for the hightemperature pristine sample of D 1.See text for fit parameters.

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268 T (K) 0246810121416 M" (cm3 mol-1) 0.00.10.20.30.4 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz T (K) 0246810121416 M'T (cm3 K mol-1) 0246810 1500 Hz 1000 Hz 500 Hz 250 Hz 50 Hz 25 Hz 10 Hz 5 Hz Figure D 9. Alternating current magnetic susceptibility studies for D 1 (dry) in phase plotted as Md out of phase plotted as M (bottom).

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269 Figure D 10 . Thermogravimetric diagram obtained for a sample of D 1. Figure D 11 . Simulated and experimental powder diagram recorded for a powdered sample of D 1.

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270 Figure D 12 . Temperature dependent of HFEPR spectra of complex [Mn6O2] (experimental (a) and (b) and simulated (c) and (d)), recorded in field derivative mode at 416 GHz [(a) and (c)] and 208 GHz [(b) and (d)] in the temperature range 2.525 K collected on a powder sample restrained in KBr. The features in (a) and (b) are labeled according to the scheme described in the main text. 0 2 4 6 8 10 12 14 Z-2-> -1Z-3 -> -2 dI/dB (arb. units)Magnetic Field (T) 25 K 20 K 15 K 10 K 5 K 2.6 KZ-4 -> -3 (a) 0 2 4 6 8 10 12 14 (c) 25 K 20 K 15 K 10 K 5 K 2.6 K dI/dB (arb. units, offset)Magnetic Field (T) 0 2 4 6 8 10 12 14 (b) Z-2-> -1 Y-4-> -3 15 K 10 K 8 K 5 K 2.5 K dI/dB (arb. units, offset)Magnetic Field (T) 0 2 4 6 8 10 12 14 (d) 15 K 10 K 8 K 5 K 2.5 K dI/dB (arb. units, offset)Magnetic Field (T)

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271 Figure D 13 . (a) Easy axis ( z axis) and (b) hard plane (xyplane) frequency dependent EPR data for complex [Mn6O2 ]. The solid lines are a simulation of the data employing the parameters: S = 4, D = 2.12 cm1, | E | = 0.52 cm1, 04B = 4.67 104 cm1, and gx = g y = gz = 2.00. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 200 400 600 800 Frequency (GHz)Magnetic Field (T) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 100 200 300 400 500 Frequency (GHz)Magnetic Field (T) (b)

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272 APPENDIX E VAN VLECK EQUATIONS 4 -1 and 4 -2 : Mn2 Van Vleck Equation: num= + 180.0000 *exp( 20.0000 *l) + 84.0000 *exp( 12.0000 *l) + 30.0000 *exp( 6.0000 *l) + 6.0000 *exp( 2.0000 *l) den= + 9.0000 *exp(20.0000 *l) + 7.0000 *exp( 12.0000 *l) + 5.0000 *exp( 6.0000 *l) + 3.0000 *exp( 2.0000 *l) + 1.0000 l=J/0.695052552/x C=0.1250415518 TIP=2.0e -4 f=(C*g^2/x)*num/den+TIP k=f*x fit k to XmT 61: Mn5(pdmH)6(thme)2 k=0.695052552 C=0.1250415518 TIP=5.0e 4 l=Jap/k/T m=Jeq/k/T n=0 Num=2656.5*exp( 45*l+63.75*m+12*n) +1995.0*exp( 24*l+63.75*m+12*n) +1995.0*exp( 30*l+63.75*m+6*n) +1995.0*exp( 39.0*l+48.75*m+12*n) +1453.5*exp( 5*l+63.75*m+12*n) +1453.5*exp( 11*l+63.75*m+6*n) +1453.5*exp( 14*l+63.75*m+2*n) +1453.5*exp( 20*l+48.75*m+12*n)

PAGE 273

273 +1453.5*exp( 26*l+48.75*m+6*n) +1453.5*exp( 33*l+35.75*m+12*n) +1020.0*exp(+12*l+63.75*m+12*n) +1020.0*exp(+6*l+63.75*m+6*n) +1020.0*exp(+2*l+63.75*m+2*n) +1020.0*exp( 0*l+63.75*m+0*n) +1020.0*exp( 3*l+48.75*m+12*n) +1020.0*exp( 9*l+48.75*m+6*n) +1020.0*exp( 13*l+48.75*m+2*n) +1020.0*exp( 16*l+35.75*m+12*n) +1020.0*exp( 22*l+35.75*m+6*n) +1020.0*exp( 27*l+24.75*m+12*n) +682.5*exp(+27*l+63.75*m+12*n) +682.5*exp(+21*l+63.75*m+6*n) +682.5*exp(+17*l+63.75*m+2*n) +682.5*exp(+12*l+48.75*m+12*n) +682.5*exp( 1*l+35.75*m+12*n) +682.5*exp( 7*l+35.75*m+6*n) +682.5*exp(+6*l+48.75*m+6*n) +682.5*exp(+2*l+48.75*m+2*n) +682.5*exp( 0*l+48.75*m+0*n) +682.5*exp( 11*l+35.75*m+2*n) +682.5*exp( 12*l+24.75*m+12*n) +682.5*exp( 18*l+24.75*m+6*n) +682.5*exp( 21*l+15.75*m+12*n) +429.0*exp(+40.*l+63.75*m+12*n) +429.0*exp(+34*l+63.75*m+6*n) +429.0*exp(+19*l+48.75*m+12*n) +429.0*exp(+13*l+48.75*m+6*n) +429.0*exp(+9*l+48.75*m+2*n) +429.0*exp(+12*l+35.75*m+12*n)

PAGE 274

274 +429.0*exp(+6*l+35.75*m+6*n) +429.0*exp(+2*l+35.75*m+2*n) +429.0*exp( 0*l+35.75*m+0*n) +429.0*exp(+1*l+24.75*m+12*n) +429.0*exp( 5*l+24.75*m+2*n) +429.0*exp( 9*l+24.75*m+2*n) +429.0*exp( 8*l+15.75*m+12*n) +429.0*exp( 14*l+15.75*m+6*n) +429.0*exp( 15*l+8.75*m+12*n) +247.5*exp(+51*l+63.75*m+12*n) +247.5*exp(+36*l+48.75*m+12*n) +247.5*exp(+30*l+48.75*m+6*n) +247.5*exp(+23*l+35.75*m+12*n) +247.5*exp(+17*l+35.75*m+6*n) +247.5*exp(+13*l+35.75*m+2*n) +247.5*exp(+12*l+24.75*m+12*n) +247.5*exp(+6*l+24.75*m+6*n) +247.5*exp(+2*l+24.75*m+2*n) +247.5*exp( 0*l+ 24.75*m+0*n) +247.5*exp(+3*l+15.75*m+12*n) +247.5*exp( 3*l+15.75*m+6*n) +247.5*exp( 7*l+15.75*m+2*n) +247.5*exp( 4.0*l+8.75*m+12*n) +247.5*exp( 10*l+8.75*m+6*n) +247.5*exp( 9*l+3.75*m+12*n) +126.0*exp(+32*l+35.75*m+12*n) +126.0*exp(+26*l+35.75*m+6*n) +126.0*exp(+21*l+24.75*m+12*n) +126.0*exp(+15*l+24.75*m+6*n) +126.0*exp(+11*l+24.75*m+2*n) +126.0*exp(+12*l+15.75*m+12*n)

PAGE 275

275 +126.0*exp(+6*l+15.75*m+6*n) +126.0*exp(+2*l+15.75*m+2*n) +126.0*exp( 0*l+15.75*m+0*n) +126.0*exp(+5*l+8.75*m+12*n) +126.0*exp( 1*l+8.75*m+6*n) +126.0*exp( 5*l+8.75*m+2*n) +126.0*exp( 0*l+3.75*m+12*n) +126.0*exp( 6*l+3.75*m+6*n) +126.0*exp( 3*l+15.75*m+12*n) +52.5*exp(+39*l+35.75*m+12*n) +52.5*exp(+28*l+24.75*m+12*n) +52.5*exp(+22*l+24.75*m+6*n) +52.5*exp(+19*l +15.75*m+12*n) +52.5*exp(+13*l+15.75*m+6*n) +52.5*exp(+9*l+15.75*m+2*n) +52.5*exp(+12*l+8.75*m+12*n) +52.5*exp(+6*l+8.75*m+6*n) +52.5*exp(+2*l+8.75*m+2*n) +52.5*exp(0*l+8.75*m+0*n) +52.5*exp(+7*l+3.75*m+12*n) +52.5*exp(+1*l+3.75*m+6*n) +52.5*exp( 3*l+3.75*m+2*n) +52.5*exp(+4*l+0.75*m+12*n) +52.5*exp( 2*l+0.75*m+6*n) +15.0*exp(+33*l+24.75*m+12*n) +15.0*exp(+24*l+15.75*m+12*n) +15.0*exp( 18*l+15.75*m+6*n) +15.0*exp(+17*l+8.75*m+12*n) +15.0*exp(+11*l+8.75*m+6*n) +15.0*exp(+7*l+8.75*m+2*n) +15.0*exp(+12*l+3.75*m+12*n)

PAGE 276

276 +15.0*exp(+6*l+3.75*m+6*n) +15.0*exp(+2*l+3.75*m+2*n) +15.0*exp(0*l+3.75*m+0*n) +15.0*exp(+3*l+0.75*m+6*n) +15.0*exp( 1*l+0.75*m+2*n) +1.50*exp(+27*l+15.75*m+12*n) +1.50*exp(+20*l+8.75*m+12*n) +1.50*exp(+14*l+8.75*m+6*n) +1.50*exp(+9*l+3.75*m+6*n) +1.50*exp(+5*l+3.75*m+2*n) +1.50*exp(+2*l+0.75*m+2*n) +1.50*exp(0*l+0.75*m+0*n) Den=22*exp( 45.0*l+63.75*m+12*n) +20*exp( 24*l+63.75*m+12*n) +20*exp( 30*l+63.75*m+6*n) +20*exp(39*l+48.75*m+12*n) +18*exp( 5*l+63.75*m+12*n) +18*exp( 11*l+63.75*m+6*n) +18*exp( 14*l+63.75*m+2*n) +18*exp( 20*l+48.75*m+12*n) +18*exp( 26*l+48.75*m+6*n) +18*exp( 33*l+35.75*m+12*n) +16*exp(+12*l+63.75*m+12*m) +16*exp(+6*l+63.75*m+6*n) +16*exp(+2*l+63.75*m+2*n) +16*exp( 0*l+63.75*m+0*n) +16*exp( 3*l+48.75*m+12*n) +16*exp( 9*l+48.75*m+6*n) +16*exp( 13*l+48.75*m+2*n) +16*exp( 16*l+35.75*m+12*n) +16*exp( 22*l+35.75*m+6*l)

PAGE 277

277 +16*exp( 27*l+24.75*m+12*n) +14*exp(+27*l+63.75*m+12*n) +14*exp(+21*l+63.75*m+6*n) +14*exp(+17*l+63.75*m+2*n) + 14*exp(+12*l+48.75*m+12*n) +14*exp( 1*l+35.75*m+12*n) +14*exp( 7*l+35.75*m+6*n) +14*exp(+6*l+48.75*m+6*n) +14*exp(+2*l+48.75*m+2*n) +14*exp(0*l+48.75*m+0*n) +14*exp( 11*l+35.75*m+2*n) +14*exp( 12*l+24.75*m+12*n) +14*exp( 18*l+24.75*m+6*n) +14*exp( 21*l+15.75*m+12*n) +12*exp(+40*l+63.75*m+12*n) +12*exp(+34*l+63.75*m+6*n) +12*exp(+19*l+48.75*m+12*n) +12*exp(+13*l+48.75*m+6*n) +12*exp(+9*l+48.75*m+2*n) +12*exp(+12*l+35.75*m+12*n) +12*exp(+6*l+35.75*m+6*n) +12*exp(+2*l+35.75*m+2*n) +12*exp( 0*l+35.75*m+0*n) +12*exp(+1*l+24.75*m+12*n) +12*exp( 5*l+24.75*m+6*n) +12*exp( 9*l+24.75*m+2*n) +12*exp( 8*l+15.75*m+12*n) +12*exp( 14*l+15.75*m+6*n) +12*exp( 15*l+8.75*m+12*n) +10*exp(+51*l+63.75*m+12*n) +10*exp(+36*l+48.75*m+12*n)

PAGE 278

278 +10*exp(+30*l+48.75*m+6*n) +10*exp(+23*l+35.75*m+12*n) +10*exp(+17*l+35.75*m+6*n) +10*exp(+13*l+35.75*m+2*n) +10*exp(+12*l+24.75*m+12*n) +10*exp(+6*l+24.75*m+6*n) +10*exp(+2*l+24.75*m+2*n) +10*exp( 0*l+24.75*m+0*n) +10*exp(+3*l+15.75*m+12*n) +10*exp( 3*l+15.75*m+6*n) +10*exp( 7*l+15.75*m+2*n) +10*exp( 4*l+8.75*m+12*n) +10*exp( 10*l+8.75*m+6*n) +10*exp( 9*l+3.75*m+12*n) +8*exp(+32*l+35.75*m+12*n) +8*exp(+26*l+35.75*m+6*n) +8*exp(+21*l+24.75*m+12*n) +8*exp(+15*l+24.75*m+6*n) +8*exp(+11*l+24.75*m+2*n) +8*exp(+12*l+15.75*m+12*n) +8*exp(+6*l+15.75*m+6*n) +8*exp(+2*l+15.75*m+2*n) +8*exp(0*l+15.75*m+0*n) +8*exp(+5*l+8.75*m+12*n) +8*exp( 1*l+8.75*m+6*n) +8*exp( 5*l+8.75*m+2*n) +8*exp(0*l+3.75*m+12*n) +8*exp( 6*l+3.75*m+6*n) +8*exp( 3*l+15.75*m+12*n) +6*exp(+39*l+35.75*m+12*n) +6*exp(+28*l+24.75*m+12*n)

PAGE 279

279 +6*exp(+22*l+24.75*m+6*n) +6*exp(+19*l+15.75*m+12*n) +6*exp(+13*l+15.75*m+6*n) +6*exp(+9*l+15.75*m+2*n) +6*exp(+12*l+8.75*m+12*n) +6*exp(+6*l+8.75*m+6*n) +6*exp(+2*l+8.75*m+2*n) +6*exp(0*l+8.75*m+0*n) +6*exp(+7*l+3.75*m+12*n) +6*exp(+1*l+3.75*m+6*n) +6*exp( 3*l+3.75*m+2*n) +6*exp(+4*l+0.75*m+12*n) +6*exp( 2*l+0.75*m+6*n) +4*exp(+33*l+24.75*m+12*n) +4*exp(+24*l+15.75*m+12*n) +4*exp( 18*l+15.75*m+6*n) +4*exp(+17*l+8.75*m+12*n) +4*exp(+11*l+8.75*m+6*n) +4*exp(+7*l+8.75*m+2*n) +4*exp(+12*l+3.75*m+12*n) +4*exp(+6*l+3.75*m+6*n) +4*exp(+6*l+3.75*m+6*n) +4*exp(+2*l+3.75*m+2*n) +4*exp(0*l+3.75*m+0*n) +4*exp(+3*l+0.75*m+6*n) +4*exp( 1*l+0.75*m+2*n) + 4*exp(+27*l+15.75*m+12*n) +2*exp(+20*l+8.75*m+12*n) +2*exp(+14*l+8.75*m+6*n) +2*exp(+9*l+3.75*m+6*n) +2*exp(+5*l+3.75*m+2*n)

PAGE 280

280 +2*exp(+2*l+0.75*m+2*n) +2*exp( 0*l+0.75*m+0*n) C 1: Mn6Ca4O4Cl6(pd)6(MeOH)10 Num=+0.0000*exp(0.0000*m+0.0000*n) +18.0000*exp(0.0000*m+2.0000*n) +150.0000*exp(0.0000*m+6.0000*n) +504.0000*exp(0.0000*m +12.0000*n) +3780.0000*exp(0.0000*m+20.0000*n) +0.0000*exp( 4.0000*m+4.0000*n) +18.0000*exp( 2.0000*m+4.0000*n) +90.0000*exp(2.0000*m+4.0000*n) +36.0000*exp( 6.0000*m+8.0000*n) +180.0000*exp( 2.0000*m+8.0000*n) +504.0000*exp(4.0000*m+8.0000*n) +450.0000*exp( 8.0000*m+14.0000*n) +1260.0000*exp( 2.0000*m+14.0000*n) +2160.0000*exp(6.0000*m+14.0000*n) +504.0000*exp( 10.0000*m+22.0000*n) +1080.0000*exp( 2.0000*m+22.0000*n) +1980.0000*exp(8.0000*m+22.0000*n) +0.0000*exp( 12.0000*m+12.0000*n) +18.0000*exp( 10.0000*m+12.0000*n) +90.0000*exp( 6.0000*m+12.0000*n) +540.0000*exp(8.0000*m+12.0000*n) +54.0000*exp( 16.0000*m+18.0000*n) +330.0000*exp( 12.0000*m+18.0000*n) +840.0000*exp( 6.0000*m+18.0000*n) +1620.0000*exp(2.0000*m+18.0000*n) +2640.0000*exp(12.0000*m+18.0000*n)

PAGE 281

281 +450.0000*exp( 20.0000*m+26.0000*n) +1260.0000*exp( 14.0000*m+26.0000*n) +2700.0000*exp( 6.0000*m+26.0000*n) +4950.0000*exp(4.0000*m+26.0000*n) +6552.0000*exp(16.0000*m+26.0000*n) +0.0000*exp( 24.0000*m +24.0000*n) +72.0000*exp( 22.0000*m+24.0000*n) +540.0000*exp( 18.0000*m+24.0000*n) +2016.0000*exp( 12.0000*m+24.0000*n) +4320.0000*exp( 4.0000*m+24.0000*n) +5940.0000*exp(6.0000*m+24.0000*n) +6552.0000*exp(18.0000*m+24.0000*n) +72.0000*exp( 30.0000*m+32.0000*n) +450.0000*exp( 26.0000*m+32.0000*n) +1512.0000*exp( 20.0000*m+32.0000*n) +3780.0000*exp( 12.0000*m+32.0000*n) +5940.0000*exp( 2.0000*m+32.0000*n) +8190.0000*exp(10.0000*m+32.0000*n) +10080.0000*exp(24.0000*m+32.0000*n) +0.0000*exp( 40.0000*m+40.0000*n) +18.0000*exp( 38.0000*m+40.0000*n) +90.0000*exp( 34.0000*m+40.0000*n) +252.0000*exp( 28.0000*m+40.0000*n) +540.0000*exp( 20.0000*m+40.0000*n) +990.0000*exp( 10.0000*m+40.0000*n) +1638.0000*exp(2.0000*m+40.0000*n) +2520.0000*exp(16.0000*m+40.0000*n) +3672.0000*exp(32.0000*m+40.0000*n) +18.0000*exp( 4.0000*m+6.0000*n) +270.0000*exp( 4.0000*m+10.0000*n) +756.0000*exp( 4.0000*m+16.0000*n)

PAGE 282

282 +0.0000*exp( 6.0000*m+6.0000*n) +36.0000*exp( 8.0000*m+10.0000*n) +504.0000*exp(2.0000*m+10.0000*n) +180.0000*exp( 10.0000*m+16.0000*n) +1080.0000*exp(4.0000*m+16.0000*n) +84.0000*exp(6.0000*m+6.0000*n) +0.0000*exp( 10.0000*m+10.0000*n) +540.0000*exp(10.0000*m+10.0000*n) +18.0000*exp( 14.0000*m+16.0000*n) +990.0000*exp(14.0000*m+16.0000*n) +54.0000*exp( 12.0000*m+14.0000*n) +540.0000*exp( 14.0000*m+20.0000*n) +1512.0000*exp( 8.0000*m+20.0000*n) +1512.0000*exp( 16.0000*m+28.0000*n) +3240.0000*exp( 8.0000*m+28.0000*n) +5940.0000*exp(2.0000*m+28.0000*n) +0.0000*exp( 14.0000*m+14.0000*n) +72.0000*exp( 18.0000*m+20.0000*n) +3960.0000*exp(10.0000*m+20.0000*n) +360.0000* exp( 22.0000*m+28.0000*n) +6552.0000*exp(14.0000*m+28.0000*n) +990.0000*exp(16.0000*m+14.0000*n) +0.0000*exp( 20.0000*m+20.0000*n) +3276.0000*exp(22.0000*m+20.0000*n) +36.0000*exp( 26.0000*m+28.0000*n) +5040.0000*exp(28.0000*m+28.0000*n) +54.0000*exp( 24.0000*m+26.0000*n) +540.0000*exp( 28.0000*m+34.0000*n) + 1512.0000*exp( 22.0000*m+34.0000*n) +3240.0000*exp( 14.0000*m+34.0000*n) +5940.0000*exp( 4.0000*m+34.0000*n)

PAGE 283

283 +9828.0000*exp(8.0000*m+34.0000*n) +0.0000*exp( 26.0000*m+26.0000*n) +72.0000* exp( 32.0000*m+34.0000*n) +10080.0000*exp(22.0000*m+34.0000*n) +2520.0000*exp(30.0000*m+26.0000*n) +0.0000*exp( 34.0000*m+34.0000*n) +7344.0000*exp(38.00000*m+34.0000*n) +54.0000*exp( 40.0000*m+42.0000*n) +270.0000*exp( 36.0000*m+42.0000*n) +756.0000*exp( 30.0000*m+42.0000*n) +1620.0000*exp( 22.0000*m+42.0000*n) +2970.0000*exp( 12.0000*m+42.0000*n) +4914.0000*exp(0.0000*m+42.0000*n) +7560.0000*exp(14.0000*m+42.0000*n) +0.0000*exp( 42.0000*m+42.0000*n) +7344.0000*exp(30.0000*m+42.0000*n) +5130.0000*exp(48.0000*m+42.0000*n) +0.0000*exp( 18.0000*m+18.0000*n) +546.0000*exp(24.0000*m+18.0000*n) +2520.0000*exp(32.0000*m+24.0000*n) +0.0000*exp( 32.0000*m+32.0000*n) +3672.0000*exp(40.0000*m+32.0000*n) +450.0000*exp( 24.0000*m+30.0000*n) +1260.0000*exp( 18.0000*m+30.0000*n) +2700.0000*exp( 10.0000*m+30.0000*n) +2520.0000*exp( 26.0000*m+38.0000*n) +5400.0000*exp( 18.0000*m+38.0000*n) +9900.0000*exp( 8.0000*m+38.0000*n) +54.0000*exp( 28.0000*m+30.0000*n) +3960.0000*exp(0.0000*m+30.0000*n) +720.0000*exp( 32.0000*m+38.0000*n)

PAGE 284

284 +13104.0000*exp(4.0000*m+38.0000*n) +0.0000*exp( 30.0000*m+30.0000*n) +4914.0000*exp(12.0000*m+30.0000*n) +108.0000*exp( 36.0000*m+38.0000*n) +15120.0000*exp(18.0000*m+38.0000*n) +5040.0000*exp(26.0000*m+30.0000*n) +0.0000*exp( 38.0000*m+38.0000*n) +14688.0000*exp(34.0000*m+38.0000*n) +3672.0000*exp(42.0000*m+30.0000*n) +10260.0000*exp(52.0000*m+38.0000*n) +450.0000*exp( 40.0000*m+46.0000*n) +1260.0000*exp( 34.0000*m+46.0000*n) +2700.0000*exp( 26.0000*m+46.0000*n) +4950.0000*exp( 16.0000*m+46.0000*n) +8190.0000*exp( 4.0000*m+46.0000*n) +54.0000*exp( 44.0000*m+46.0000*n) +10080.0000*exp(10.0000*m+46.0000*n) +0.0000*exp( 46.0000*m+46.0000*n) +11016.0000*exp(26.0000*m+46.0000*n) +10260.0000*exp(44.0000*m+ 46.0000*n) +6930.0000*exp(64.0000*m+46.0000*n) +588.0000*exp( 24.0000*m+36.0000*n) +3780.0000*exp( 24.0000*m+44.0000*n) +150.0000*exp( 30.0000*m+36.0000*n) +1080.0000*exp( 16.0000*m+36.0000*n) +1512.0000*exp( 32.0000*m+44.0000*n) +5940.0000*exp( 14.0000*m+44.0000*n) +18.0000*exp( 34.0000*m+36.0000*n) +1650.0000*exp( 6.0000*m+36.0000*n) +450.0000*exp( 38.0000*m+44.0000*n) +8190.0000*exp( 2.0000*m+44.0000*n)

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285 +0.0000*exp( 36.0000*m+36.0000*n) +2184.0000*exp(6.0000*m+36.0000*n) +54.0000*exp( 42.0000*m+44.0000*n) +10080.0000*exp(12.0000*m+44.0000*n) +2520.0000*exp(20.0000*m+36.0000*n) +0.0000*exp( 44.0000*m+44.0000*n) +11016.0000*exp(28.0000*m+44.0000*n) +2448.0000*exp(36.0000*m+36.0000*n) +10260.0000*exp(46.0000*m+44.0000*n) +1710.0000*exp(54.0000*m+36.0000*n) +6930.0000*exp(66.0000*m+44.0000*n) +1764.0000*exp( 40.0000*m+52.0000*n) +3780.0000*exp( 32.0000*m+52.0000*n) +6930.0000*exp( 22.0000*m+52.0000*n) +450.0000*exp( 46.0000*m+52.0000*n) +9828.0000*exp( 10.0000*m+52.0000*n) +54.0000*exp( 50.0000*m+52.0000*n) +12600.0000*exp(4.0000*m+52.0000*n) +0.0000*exp( 52.0000*m+52.0000*n) +14688.0000*exp(20.0000*m+52.0000*n) +15390.0000*exp(38.0000*m+52.0000*n) +13860.0000*exp(58.0000*m+52.0000*n) +9108.0000*exp(80.0000*m+52.0000*n) +1620.0000*exp( 40.0000*m+60.0000*n) +588.0000*exp( 48.0000*m+60.0000*n) +2640.0000*exp( 30.0000*m+60.0000*n) +150.0000*exp( 54.0000*m+60.0000*n) +3822.0000*exp( 18.0000*m+60.0000*n) +18.0000*exp( 58.0000*m+60.0000*n) +5040.0000*exp( 4.0000*m+60.0000*n) +0.0000*exp( 60.0000*m+60.0000*n)

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286 +6120.0000*exp(12.0000*m+60.0000*n) +6840.0000*exp(30.0000*m+60.0000*n) +6930.0000*exp(50.0000*m+60.0000*n) +6072.0000*exp(72.0000*m+60.0000*n) +3900.0000* exp(96.0000*m+60.0000*n) Den=+1.0000*exp(0.0000*m+0.0000*n) +9.0000*exp(0.0000*m+2.0000*n) +25.0000*exp(0.0000*m+6.0000*n) +42.0000*exp(0.0000*m+12.0000*n) +189.0000*exp(0.0000*m+20.0000*n) +3.0000*exp( 4.0000*m+4.0000*n) +9.0000*exp( 2.0000*m+4.0000*n) +15.0000*exp(2.0000*m+4.0000*n) +18.0000*exp( 6.0000*m+8.0000*n) +30.0000*exp( 2.0000*m+8.0000*n) +42.0000*exp(4.0000*m+8.0000*n) +75.0000*exp( 8.0000*m+14.0000*n) +105.0000*exp( 2.0000*m+14.0000*n) +108.0000*exp(6.0000*m+14.0000*n) +42.0000*exp( 10.0000*m+22.0000*n) +54.0000*exp( 2.0000*m+22.0000*n) +66.0000*exp(8.0000*m+22.0000*n) +3.0000*exp( 12.0000*m+12.0000*n) +9.0000*exp( 10.0000*m+12.0000*n) +15.0000*exp( 6.0000*m+12.0000*n) +27.0000*exp(8.0000*m+12.0000*n) +27.0000*exp( 16.0000*m+18.0000*n) +55.0000*exp( 12.0000*m+18.0000*n) +70.0000*exp( 6.0000*m+18.0000*n) +81.0000*exp(2.0000*m+18.0000*n)

PAGE 287

287 +88.0000*exp(12.0000*m+18.0000*n) +75.0000*exp( 20.0000*m+26.0000*n) +105.0000*exp( 14.0000*m+26.0000*n) +135.0000*exp( 6.0000*m+26.0000*n) +165.0000*exp(4.0000*m+26.0000*n) +156.0000*exp(16.0000*m+26.0000*n) +6.0000*exp( 24.0000*m+24.0000*n) +36.0000*exp( 22.0000*m+24.0000*n) +90.0000*exp( 18.0000*m+24.0000*n) +168.0000*exp( 12.0000*m+24.0000*n) +216.0000*exp( 4.0000*m +24.0000*n) +198.0000*exp(6.0000*m+24.0000*n) +156.0000*exp(18.0000*m+24.0000*n) +36.0000*exp( 30.0000*m+32.0000*n) +75.0000*exp( 26.0000*m+32.0000*n) +126.0000*exp( 20.0000*m+32.0000*n) +189.0000*exp( 12.0000*m+32.0000*n) +198.0000*exp( 2.0000*m+32.0000*n) +195.0000*exp(10.0000*m+32.0000*n) +180.0000*exp(24.0000*m+32.0000*n) +3.0000*exp( 40.0000*m+40.0000*n) +9.0000*exp( 38.0000*m+40.0000*n) +15.0000*exp( 34.0000*m+40.0000*n) +21.0000*exp( 28.0000*m+40.0000*n) +27.0000*exp( 20.0000*m+40.0000*n) +33.0000*exp( 10.0000*m+40.0000*n) +39.0000*exp(2.0000*m+40.0000*n) +45.0000*exp(16.0000*m+40.0000*n) +51.0000*exp(32.0000*m+40.0000*n) +9.0000*exp( 4.0000*m+6.0000*n) +45.0000*exp( 4.0000*m+10.0000*n)

PAGE 288

288 +63.0000*exp( 4.0000*m+16.0000*n) +1.0000*exp( 6.0000*m+6.0000*n) +18.0000*exp( 8.0000*m+10.0000*n) +42.0000*exp(2.0000*m+10.0000*n) +30.0000*exp( 10.0000*m+16.0000*n) +54.0000*exp(4.0000*m+16.0000*n) +7.0000*exp(6.0000*m+6.0000*n) +3.0000*exp( 10.0000*m+10.0000*n) +27.0000*exp(10.0000*m+10.0000*n) +9.0000*exp( 14.0000*m+16.0000*n) +33.0000*exp(14.0000*m+16.0000*n) +27.0000*exp( 12.0000*m+14.0000*n) +90.0000*exp( 14.0000*m+20.0000*n) +126.0000*exp( 8.0000*m+20.0000*n) +126.0000*exp( 16.0000*m+28.0000*n) +162.0000*exp( 8.0000*m+28.0000*n) +198.0000*exp(2.0000*m+28.0000*n) +3.0000*exp( 14.0000*m+14.0000*n) +36.0000*exp( 18.0000*m+20.0000*n) +132.0000*exp(10.0000*m+20.0000*n) +60.0000*exp( 22.0000*m+28.0000*n) +156.0000*exp(14.0000*m+28.0000*n) +33.0000*exp(16.0000*m+14.0000*n) +6.0000*exp( 20.0000*m+20.0000*n) +78.0000*exp(22.0000*m+20.0000*n) +18.0000*exp( 26.0000*m+28.0000*n) +90.0000*exp(28.0000*m+28.0000*n) +27.0000*exp( 24.0000*m+26.0000*n) +90.0000*exp( 28.0000*m+34.0000*n) +126.0000*exp( 22.0000*m+34.0000*n) +162.0000*exp( 14.0000*m+34.0000*n)

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289 +198.0000*exp( 4.0000*m+34.0000*n) +234.0000*exp(8.0000*m+34.0000*n) +3.0000*exp( 26.0000*m+26.0000*n) +36.0000*exp( 32.0000*m+34.0000*n) +180.0000*exp(22.0000*m+34.0000*n) +45.0000*exp(30.0000*m+26.0000*n) +6.0000*exp( 34.0000*m+34.0000*n) +102.0000*exp(38.0000*m+34.0000*n) +27.0000*exp( 40.0000*m+42.0000*n) +45.0000*exp( 36.0000*m+42.0000*n) +63.0000*exp( 30.0000*m+42.0000*n) +81.0000*exp( 22.0000*m+42.0000*n) +99.0000*exp( 12.0000*m+42.0000*n) +117.0000*exp(0.0000*m+42.0000*n) +135.0000*exp(14.0000*m+42.0000*n) +3.0000*exp( 42.0000*m+42.0000*n) +102.0000*exp(30.0000*m+42.0000*n) +57.0000*exp(48.0000*m+42.0000*n) +1.0000*exp( 18.0000*m+18.0000*n) +13.0000*exp(24.0000*m+18.0000*n) +45.0000*exp(32.0000*m+24.0000*n) +3.0000*exp( 32.0000*m+32.0000*n) +51.0000*exp(40.0000*m+32.0000*n) +75.0000*exp( 24.0000*m+30.0000*n) +105.0000*exp( 18.0000*m+30.0000*n) +135.0000*exp( 10.0000*m+30.0000*n) +210.0000*exp( 26.0000*m+38.0000*n) +270.0000*exp( 18.0000*m+38.0000*n) +330.0000*exp( 8.0000*m+38.0000*n) +27.0000*exp( 28.0000*m+30.0000*n) +132.0000*exp(0.0000*m+30.0000*n)

PAGE 290

290 +120.0000*exp( 32.0000*m+38.0000*n) +312.0000*exp(4.0000*m+38.0000*n) +3.0000*exp( 30.0000*m+30.0000*n) +117.0000*exp(12.0000*m+30.0000*n) +54.0000*exp( 36.0000*m+38.0000*n) +270.0000*exp(18.0000*m+38.0000*n) +90.0000*exp(26.0000*m+30.0000*n) +6.0000*exp( 38.0000*m+38.0000*n) +204.0000*exp(34.0000*m+38.0000*n) +51.0000*exp(42.0000*m+30.0000*n) +114.0000*exp(52.0000*m+38.0000*n) +75.0000*exp( 40.0000*m+46.0000*n) +105.0000*exp( 34.0000*m+46.0000*n) +135.0000*exp( 26.0000*m+46.0000*n) +165.0000*exp( 16.0000*m+46.0000*n) +195.0000*exp( 4.0000*m+46.0000*n) + 27.0000*exp( 44.0000*m+46.0000*n) +180.0000*exp(10.0000*m+46.0000*n) +3.0000*exp( 46.0000*m+46.0000*n) +153.0000*exp(26.0000*m+46.0000*n) +114.0000*exp(44.0000*m+46.0000*n) +63.0000*exp(64.0000*m+46.0000*n) +49.0000*exp( 24.0000*m+36.0000*n) +189.0000*exp( 24.0000*m+44.0000*n) +25.0000*exp( 30.0000*m+36.0000*n) +54.0000*exp( 16.0000*m+36.0000*n) +126.0000*exp( 32.0000*m+44.0000*n) +198.0000*exp( 14.0000*m+44.0000*n) +9.0000*exp( 34.0000*m+36.0000*n) +55.0000*exp( 6.0000*m+36.0000*n) +75.0000*e xp( 38.0000*m+44.0000*n)

PAGE 291

291 +195.0000*exp( 2.0000*m+44.0000*n) +1.0000*exp( 36.0000*m+36.0000*n) +52.0000*exp(6.0000*m+36.0000*n) +27.0000*exp( 42.0000*m+44.0000*n) +180.0000*exp(12.0000*m+44.0000*n) +45.0000*exp(20.0000*m+36.0000*n) +3.0000*exp( 44.0000*m+44.0000*n) +153.0000*exp(28.0000*m+44.0000*n) +34.0000*exp(36.0000*m+36.0000*n) +114.0000*exp(46.0000*m+44.0000*n) +19.0000*exp(54.0000*m+36.0000*n) +63.0000*exp(66.0000*m+44.0000*n) +147.0000*exp( 40.0000*m+52.0000*n) +189.0000*exp( 32.0000*m+52.0000*n) +231.0000*exp( 22.0000*m+52.0000*n) +75.0000*exp( 46.0000*m+52.0000*n) +234.0000*exp( 10.0000*m+52.0000*n) +27.0000*exp( 50.0000*m+52.0000*n) +225.0000*exp(4.0000*m+52.0000*n) +3.0000*exp( 52.0000*m+52.0000*n) +204.0000*exp(20.0000*m+52.0000*n) +171.0000*exp(38.0000*m+52.0000*n) +126.0000*exp(58.0000*m+52.0000*n) +69.0000*exp(80.0000*m+52.0000*n) +81.0000*exp( 40.0000*m+60.0000*n) +49.0000*exp( 48.0000*m+60.0000*n) +88.0000*exp( 30.0000*m+60.0000*n) +25.0000*exp( 54.0000*m+60.0000*n) +91.0000*exp( 18.0000*m+60.0000*n) +9.0000*exp( 58.0000*m+60.0000*n) +90.0000*exp( 4.0000*m+60.0000*n)

PAGE 292

292 +1.0000*exp( 60.0000*m+60.0000*n) +85.0000*exp(12.0000*m+60.0000*n) +76.0000*exp(30.0000*m+60.0000*n) +63.0000*exp(50.0000*m+60.0000*n) +46.0000*exp(72.0000*m+60.0000*n) +25.0000*exp(96.0000*m+60.0000*n)

PAGE 293

293 APPENDIX F HIGHFREQUENCY ELECTRON PARAMAGNETIC RESONANCE

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294

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295

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296

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297 Complex 51:

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298

PAGE 299

299

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300 Complex 52:

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301

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303

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304

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305 APPENDIX G PERMISSION TO REPRODUCE COPYRIGHTED MATERIAL ROYAL SOCIETY OF CHEMISTRY LICENSE TERMS AND CONDITIONS order details, the terms and conditions provided by Royal Society of Chemistry, and the payment terms and conditions. All payments must be made in full to CCC. For payment instruc tions, please see information listed at the bottom of this form. Licensed content publisher: Royal Society of Chemistry Licensed content publication: Chemical Society Reviews Licensed content title: The Drosophila of singlemolecule magnetism: [Mn12O12(O2CR)16(H2O)4] Licensed content author: Rashmi Bagai,George Christou Volume number: 38 Issue number: 4 tional Format: electronic Will you be translating? no Order reference number: None

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306 TRANSITION -DERIVED LIGANDS AND THEIR MAGNETIC PROPERTIES Soci ety of Chemistry (“RSC”) provided by the Copyright Clearance Center (“CCC”). The license consists of your order details, the terms and conditions provided by the Royal Society of Chemistry, and the payment terms and conditions. I NTRODUCTION The publisher for this copyrighted material is The Royal Society of Chemistry. By clicking “accept” in connection with completing this licensing transaction, you agree that the following terms and conditions apply to this transaction (along wit h the Billing and Payment terms and conditions established by CCC, at the time that you opened your RightsLink account and that are available at any time at . LICENSE GRANTED The RSC hereby grants you a non -exclusive license to use the aforementioned mater ial anywhere in the world subject to the terms and conditions indicated herein. Reproduction of the material is confined to RESERVATION OF RIGHTS The RSC reserves all rights not specifically g ranted in the combination of (i) the license details provided by your and accepted in the course of this licensing transaction; (ii) these terms and conditions; and (iii) CCC’s Billing and Payment terms and conditions. REVOCATION The RSC reserves the right to revoke this license for any reason, including, but not limited to, advertising and promotional uses of RSC content, third party usage, and incorrect source figure attribution. THIRD If part of the material to be used (for example, a figure) has appeared in the RSC publication with credit to another source, permission must also be sought from that source. If the other source is another RSC publication these details should be included in your RightsLink request. If the other sour ce is a third party, permission must be obtained from the third party. The RSC disclaims any responsibility for the reproduction you make of items owned by a third party.

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309 Intranet If the licensed material is being posted on an Intranet, the Intranet is to be password -protected and made available only to bona fide students or employees only. All content posted to the Intranet must material and include a hypertext link as specified above. Copies of Whole Articles All copies of whole articles must maintain, if available, the copyright information line on the bottom of each page. Other Conditions v1.2 reference. No payment is required. If you would like to pay for this license now, please remit this license along with yourpayment made license date. Payment should be in the form of a check or money order referencing you r account number and this invoice number {Invoice Number}. Once you receive your invoice for this order, you may pay your invoice by credit card. Please follow instructions provided at that time. Make Payment To: Copyright Clearance Center P.O. Bo For suggestions or comments regarding this order, contact Rightslink Customer Support: customercare@copyright.com or +1 --622--646If you would like to pay for this license now, please remit this license along with your payment made payable to "COPYRIGHT CLEARANCE CENTER" otherwise you will be invoiced within 48 hours of the license date. Payment should be in the form of a check or money order referencing your account number and this invoice number 501323523. Once you receive your invoice for this order, you may pay your invoice by credit card. Please follow instructions provided at that time. Make Payment To: Copyright Clearance Center Dept 001 P.O. Box 843006

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311 Title: Spin Maximization from S = 11 to S = 16 in Mn7 Disk Like Clusters: Spin Frustration Effects and Their Computational Rationalization Author: Theocharis C. Stamatatos, Dolos Foguet Albiol, Katye M. Poole, Wolfgang Wernsdorfer, Khalil A. Abboud, Ted A. O’Brien, and George Christou Publication: Inorganic Chemistry Publisher: American Chemical Society Date: Oct 1, 2009 Copyright 2009, American Chemical Society Logged in as: Katye Poole Account #: 3000799459 PERMISSION/LICENSE IS GRANTED FOR YOUR ORDER AT NO CHARGE This type of permission/license, instead of the standard Terms & Conditions, is sent to you because no fee is being charged for your order. Please note the following: Permission is granted for your request in both print and electronic formats, and translations. If figures and/or tables were requested, they may be adapted or used in part. Please print this page for your records and send a copy of it to your publisher/graduate school. Appropriate credit for the requested material should be given as follows: "Reprinted (adapted) with permission from (COMPL ETE REFERENCE CITATION). Copyright (YEAR) American Chemical Society." Insert appropriate information in place of the capitalized words. One time permission is granted only for the use specified in your request. No additional uses are granted (such as deriv ative works or other editions). For any other uses, please submit a new request. If credit is given to another source for the material you requested, permission must be obtained from that source.

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312 LIST OF REFERENCES (1) Kahn, O. Molecular Magnetism ; VCH: Weinheim, Germany, 1993. (2) Jiles, D. 1991. (3) Smart, L. M., E. Solid State Chemistry: An Introduction ; Chapman and Hall: New York, 1992. (4) Janutka, A. J Phys: Condens. Matter 2003, 15, 8561. (5) Aromi, G. A., S. M. J.; Bolcar, M. A.; Christou, G.; Eppley, H. J.; Folting, K.; Hendrickson, D. N.; Huffman, J. C.; Squire, R. C.; Tsai, H. L.; Wang, S.: Wemple, M. W. Polyhedron 1998, 17, 3005. (6) Aubin, S. M. W., M.W.; Adams, D. M.; Tsai, H.L.; Christou, G.; Hendrickson, D.N. J. Am. Chem. Soc. 1996, 118, 7746. (7) Eppley, H. J. T., H. L.; de Vries, N.; Folting, K.; Christou, G.; Hendrickson; D.N. J. Am. Chem. Soc. 1995, 117, 301. (8) Arai, N. S., M.; Suga, H.; Seki, S. J. Phys. Chem. Solids 1977 , 38, 1341. (9) Wickman, H. H. J. Chem. Phys. Rev. 1972, 56, 976. (10) Wickman, H. H. T., A. M.; Williams, H. J.; Hull, G. W.; and Merritt, F. R. Phys. Rev. 1967, 155, 563. (11) Nakatani, K. C., J.Y.; Journaux, Y.; Kahn, O.; Lloret, F.; Renard; J.P.; Pei, Y.; Sletten, J.; Verdaguer, M. J. Am. Chem. Soc. 1989, 111, 5739. (12) Christou, G.; Gatteschi, D.; Hendrickson, D. N.; Sessoli, R. MRS Bull 2000, 25, 66. (13) Sessoli, R. G., D.; Caneschi, A.; Novak, M. A. Nature 1993, 365, 141. (14) Christou, G. Polyhedron 2005, 24, 2065. (15) Gatteschi, D. S., R.; Villain, J. Molecular Nanomagnets ; Oxford University Press, 2006. (16) Bagai, R. C., G. Chem. Soc. Rev. 2009, 38, 1011. (17) F riedman, J. R. S., M.P.; Tejada, J.; Ziolo, R. Phys. Rev. Lett. 1996, 76, 3830. (18) Kambe, K. J. Phys. Soc. Jpn. 1950, 5, 48. (19) Van Vleck, J. H. The Theory of Electronic and Magnetic Susceptibilities ; Oxford Press: London, 1932.

PAGE 313

313 (20) Espinosa Fuentes, E. A. P.L., L.C.; HidalgoSantiago, M.; Vivas Reyes, R.; Hernandez Rivera, S.P. J. Phys. Chem. A. 2013, 117, 10753. (21) Aldabbagh, F. A., J.H.; Bentley, T.W.; Bowman, W.R.; Canle Lopez, M.; Fischer, U.; Hammerich, O.; Hungerbuhler, K.; LloydJones, G.C.; Maskill, H.; Santaballa Lopez; J.A.; Schreiner, P.R.; Storey, J.M.D.; and I.F. Watt; 5th ed.; Maskill, H., Ed.; WileyBlackwell: Oxford, UK, 2008. (22) Davidson, E. R. Chem. Rev. 2000, 100, 351 and references found therein. (23) Rudra, I. W., Q.; and T.V. Voorhis J. Chem. Phys. 2006, 124, 24103. (24) de Visser, S. P. Q., M.G.; Martin, B.; Comba, P.; and U. Ryde Chem. Comm. 2014, 50, 262 and references therein. (25) Zeng, Z. D., Y.; Guenzburger, D. Phys. Rev. B 1997, 55, 12522. (26) Libby, E. M., J. K.; Schmitt, E. A.; Folting, K.; Hendrickson, D. N.; Christou, G. Inorg. Chem. 1991, 30, 3486. (27) McCusker, J. K. S., E. A.; Hendrickson, D. N. In Magnetic Molecular Materials ; Gatteschi, D., Ed; Kluwer Academic Publishers: Dordech t, 1991. (28) McCusker, J. K.; Christmas, C. A.; Hagen, P. M.; Chadha, R. K.; Harvey, D. F.; Hendrickson, D. N. Journal of the American Chemical Society 1991, 113 , 6114. (29) Wemple, M. W.; Coggin, D. K.; Vincent, J. B.; McCusker, J. K.; Streib, W. E.; H uffman, J. C.; Hendrickson, D. N.; Christou, G. Journal of the Chemical Society Dalton Transactions 1998, 719. (30) Armstrong, W. H.; Roth, M. E.; Lippard, S. J. Journal of the American Chemical Society 1987, 109, 6318. (31) Chaudhuri, P. W., M.; Fleischhauer, P.; Haase, W.; Florke, U.; Haupt, H.J. Inorg. Chem. 1993, 212, 241. (32) Wu, L. P., M.; Coppens, P.; DeMarco, M. J. Acta. Crystallogr. Sect. C 1993, 49, 1255. (33) Gorun, S. M.; Lippard, S. J. Inorganic Chemistry 1988, 27, 149. (34) O'Brien, T. A.; Davidson, E. R. Int. J. Quantum Chem. 2003, 92, 294. (35) Lampropoulos, C. M., M.; Harter, A.G.; Wernsdorfer, W.; Hill, S.; Dalal, N.S.; Reyes, A.P.; Kuhns, P.L.; Abboud, K.A.; Christou, G. Inorg. Chem. 2013, 52, 258. (36) Nguyen, T. N. W., W.; Abboud, K.A.; Christou, G. J. Am. Chem. Soc. 2011, 133, 20688.

PAGE 314

314 (37) Nguyen, T. N. A., K.A.; Christou, G. Polyhedron 2013, 66, 171. (38) Mowson, A. M. N., T.N.; Abboud, K.A.; Christou, G. Inorg. Chem. 2013, 2013, 12320. (39) Mukherjee, S. A., K.A.; Wernsdorfer, W.; Christou, G. Inorg. Chem. 2013, 52, 873. (40) Gatteschi, D. S., R.; Cornia, A. Chem. Comm. 2000, 725. (41) Sun, Z. M. G., C.M.; Castro, S.L.; Hendrickson, D.N.; Christou, G. Chem. Comm. 1998, 721. (42) Yang, E. C . H., D.N.; Wernsdorfer, W.; Nakano, M.; Zakharov, L.N.; Sommer, R.D.; Rheingold, A.L.; Ledezma Gairaud, M.; Christou, G. J. Appl. Phys. 2002, 91, 7382. (43) Andres, H. B., R.; Blake, A.J.; Cadiou, C.; Chaboussant, G.; Grant, C.M.; Gudel, H.U.; Murrie, M. ; Parsons, S.; Paulsen, C.; Semadini, F.; Villar, V.; Wernsdorfer, W.; Winpenny, R.E.P. Chem. Eur. J. 2002, 8, 4867. (44) DendrinouSamara, C. A., M.; Zaleski, C.M.; Kampf, J.W.; Kirk, M.L.; Kessissoglou, D.P.; Pecoraro, V.L. Angew. Chem. Int. Ed. 2003, 42, 3763. (45) Milios, C. J. R., A.; Terzis, A.; Lloret, R.; Vicente, R.; Perlepes, S.P.; and Escuer, Angew. Chem. Int. Ed. 2004, 43, 210. (46) Miyasaka, H. C., R.; Wernsdorfer, W.; Lecren, L.; Bonhomme, C.; Sugiura, K.; Yamashita, M Angew. Chem. Int. Ed. 2004, 43, 2801. (47) Clark, J.; Scientific American 271, #2: 1994, p 46. (48) Simpson, R. E.; 2nd ed.; Allyn and Bacon: 1987. (49) Ashcroft, N. W. a. M., N.D.; Saunders: 1976. (50) Batlogg, B. Physics Today 1991, 44, 44. (51) Blackwood, O. H. K., W.C.; and Bell, R.M.; 4th ed.; Wiley: 1973. (52) Quantum Design: San Diego, CA, 2000. (53) Quantum Design: San Diego, CA, 2000. (54) Quantum Design: http://www.qdusa.com , 2014; Vol. 2014. (55) Wu, D. G., D.; Song, Y.; Huang, W.; Duan, C.; Meng, Q.; Sato, O. Inorg. Chem. 2009, 48, 854.

PAGE 315

315 (56) Chakov, N. E. S., M.; Wernsdorfer, W.; Abboud, K.A.; Christou, G. Inorg. Chem. 2005, 44, 5304. (57) Wernsdorfer, W. A.A., N.; Hendrickson, D.N.; Christou, G . Nature 2002, 416, 406. (58) Drago, R. S.; 2nd ed.; Saunders: 1992. (59) Wertz, J. E. a. B., J.R. Electron spin resonance: Elementary theory and practical applications ; McGraw Hill: New York, 1972. (60) Edwards, R. S.; Maccagnano, S.; Yang, E.C.; Hill, S.; Wernsdorfer, W.; Hendrickson, D.; Christou, G. Journal of Applied Physics 2003, 93, 7807. (61) Inglis, R.; Jones, L. F.; Milios, C. J.; Datta, S.; Collins, A.; Parsons, S.; Wernsdorfer, W.; Hill, S.; Perlepes, S. P.; Piligkos, S.; Brechin, E. K. Dalton Transactions 2009, 3403. (62) Petukhov, K.; Hill, S.; Chakov, N. E.; Abboud, K. A.; Christou, G. Physical Review B 2004, 70, 054426. (63) Zipse, D.; North, J. M.; Dalal, N. S.; Hill, S.; Edwards, R. S. Physical Review B 2003, 68, 184408. (64) Hil l, S.; Edwards, R. S.; Jones, S. I.; Dalal, N. S.; North, J. M. Physical Review Letters 2003, 90, 217204. (65) Harris, D. C. a. B., M.D. Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy. ; Oxford University Press: New Y ork, 1978. (66) Denney, R. C. a. S., R.; Mowthorpe, D., Ed.; John Wiley and Sons: New York, 1987. (67) Kurtz, D. M., Jr. Chem. Rev. 1990, 90, 585. (68) Lippard, S. J. Angew. Chem. Int. Ed. Engl. 1988, 27, 344. (69) Toftlund, H. M., K. S.; Zwack, P. R.; Taylor, L. F.; Anderson, O. P. J. Chem. Soc., Chem. Commun. 1986, 191. (70) Theil, E. C. Annu. Rev. Biochem. 1987, 57, 289. (71) Xu, B. C., N. D.; J. Biol. Chem. 1991, 266, 19965. (72) Wieghardt, K. P., K.; Jibril, I.; Huttner, G. Angew. Chem. Int. Ed. Engl. 1984, 23, 77. (73) Delfs, D. G., D.; Pardi, L.; Sessoli, R.; Wieghardt, K.; Hanke, D. Inorg. Chem. 1993, 32, 3099.

PAGE 316

316 (74) Barra, A. L. C., A.: Cornia, A.; Fabizi de Biani, F.; Gattesc hi, D.; Sangregorio, C.; Sessoli, R.; Sorace, L. J. Am. Chem. Soc. 1999, 121, 5302. (75) Grant, C. M. K., M. J.; Huffman, J. C.; Hendrickson, D. N.; Christou, G Chem. Comm. 1998, 1753. (76) Grant, C. M. K., M. J.; Huffman, J. C.; Hendrickson, D. N.; Chri stou, G Inorg. Chem. 1998, 37, 6065. (77) Brechin, E. K. K., M. J.; Huffman, J. C.; Hendrickson, D. N.; Christou, G. Inorg. Chim. Acta. 2000, 297, 389. (78) Seddon, E. J. Y., J.; Folting, K.; Huffman, J. C.; Hendrickson, D. N.; Christou, G. Dalton Trans. 2000, 3640. (79) Canada Vilalta, C. O. B., T.A.; Pink, M.; Davidson, E.R.; Christou, G. Inorg. Chem. 2003, 42, 7819. (80) Foguet Albiol, D. A., K.A.; Christou, G. Chem. Comm. 2005 , 4282. (81) Taguchi, T. S., T. C.; Abboud, K. A.; Jones, C. M.; Poole, K. M.; O'Brien, T. A.: Christou, G. Inorg. Chem. 2008, 47, 4095. (82) Taguchi, T. Dissertation, University of Florida, 2009. (83) Christmas, C. A.; Tsai, H. L.; Pardi, L.; Kesselman, J. M.; Gantzel, P. K.; Chadha, R. K.; Gatteschi, D.; Harvey, D. F.; Hendrickson, D. N. Journal of the American Chemical Society 1993, 115, 12483. (84) Shweky, I. P., L. E.; Papaefthymiou, G. C.; Sessoli , R.; Yun, J. W.; Bino, A.; Lippard, S. J. J. Am. Chem. Soc. 1997, 119, 1037. (85) Saalfrank, R. W. G., H.; Demleitner, B.; Hampel, F.; Chowdhry, M. M.; Schunemann, V.; Trautwein, A. X.; Vaughan, G. B. M.; Yeh, R.; Davis, A. V.; Raymond, K. N. Chem. Eur. J. 2002, 8, 493. (86) Bagai, R. A., K. A.; Christou, G. Inorg. Chem. 2007, 46, 5567. (87) Bagai, R. D., S.; Betancur Rodriguez, A.; Abboud, K. A.; Hill, S.; Christou, G. Inorg. Chem. 2007, 46, 4535. (88) Hegetschweiler, K. S., H. W.; Streit, H. M.; Schneider, W. Inorg. Chem. 1990, 29, 3625. (89) Weihe, H.; Gdel, H. U. Journal of the American Chemical Society 1997, 119, 6539.

PAGE 317

317 (90) Canada Vilalta, C.; O'Brien, T. A.; Brechin, E. K.; Pink, M.; Davidson, E. R.; Christou, G. Inorganic Chemistry 2004, 43, 5505. (91) Canada Vilalta, C.; O'Brien, T. A.; Pink, M.; Davidson, E. R.; Christou, G. Inorganic Chemistry 2003, 42, 7819. (92) O'Brien, T. A. P., K. M.; Canada Vilalta, C.; Christou, G.; Davidson, E. R.; IUPUI: Indianapolis, 2007. (93) Baker, M. L. T., G.A.; Piligkos, S.; Mathieson, J.S.; Mutka, H.; Tuna, F.; Kozlowski, P.; Antkowiak, M.; Guidi, T.; Gupta, T.; Rath, H.; Woolfson, R.J.; Kamieniarz, R.; Pritchard, R.G.; Weihe, H.; Cronin, L.; Rajaraman, G.; Collison, D.; McInnes, E.J.L.; Whinpenny, R.E.P. PNAS 2012, 109, 19113. (94) Bagai, R., University of Florida, 2008. (95) Jones, L. F.; Jensen, P.; Moubaraki, B.; Cashion, J. D.; Berry, K. J.; Murray, K. S. Journal of the Chemical Society Dalton Transactions 2005, 3344. (96) Canada Vilalta, C.; Rumberger, E.; Brechin, E. K.; Wernsdorfer, W.; Folting, K.; Davidson, E. R.; Hendrickson, D. N.; Christou, G. Journal of the Chemical Society Dalton Transactions 2002, 4005. (97) Yoon, S. L., S. J. J. Am. Chem. Soc. 2005, 127, 8386. (98) Smith, A. A. C., R. A.; Harrison, A.; Helliwell, M.; Parsons, S.; Winpenny, R. E. P. Polyhedron 2004, 23, 1557. (99) Murugesu, M. A., K. A.; Christou, G. Polyhedron 2004, 23, 2779. (100) Ammala, P. S.; Batten, S. R.; Cashion, J. D.; Kepert, L. M.; Moubaraki, B.; Murray, K. S.; Spiccia, L.; West, B. D. Inorganica Chimica Acta 2002, 331 , 90. (101) Micklitz, W. L., S. J. J. Am. Chem. Soc. 1988, 27, 3067. (102) Micklitz, W. B., S. G.; Bentse n, J. G.; Lippard, S. J. J. Am. Chem. Soc. 1989, 111, 372. (103) Celenligil Cetin, R. S., R. J.; Stavropoulos, P. Inorg. Chem. 2000, 39, 5838. (104) Schneppensieper, T. L., G.; van Eldik, R.; Ensling, J.; Gutlich, P. Inorg. Chem. 2000, 39, 5565. (105) Harding, C. J.; Henderson, R. K.; Powell, A. K. Angewandte Chemie International Edition English 1993, 32 , 570.

PAGE 318

318 (106) Hegetschweiler, K. S., H. W.; Streit, H. M.; Gramlich, V.; Hund, H. U.; Erni, I. Inorg. Chem. 1992, 31, 1299. (107) Cornia, A. G., D.; He getschweiler, K.; Hausherr Primo, L.; Gramlich, V. Inorg. Chem. 1996, 35, 4414. (108) Spandl, J. K., M.; Brudgam, I. Z. Anorg. Allg. Chem. 2003, 629, 968. (109) Carson, E. C. L., S. J. Inorg. Chem. 2006, 45, 837. (110) Burkill, H. A.; Robertson, N.; Vilar, R.; White, A. J. P.; Williams, D. J. Inorganic Chemistry 2005, 44, 3337. (111) Seddon, E. J. H., J. C.; Christou, G. J.Chem. Soc., Dalton Trans. 2000, 4446. (112) Nair, V. S.; Hagen, K. S. Inorganic Chemistry 1992, 31, 4048. (113) Grant, C. M.; Knapp, M. J.; Streib, W. E.; Huffman, J. C.; Hendrickson, D. N.; Christou, G. Inorganic Chemistry 1998, 37, 6065. (114) Trettenhahn, G. N., M.; Neuwirh, N.; Arion, V. B.; Jary, W.; Pochlauer, P.; Schmid, W. Angew. Chem. Int. Ed. 2006, 45, 2794. (115) Tokii, T. I., K.; Nakashima, M.; Koikawa, M. Chem. Lett. 1994, 441. (116) Saalfrank, R. W. B., I.; Chowdhry, M. M.; Hampel, F.; Vaughan, G. B. M. Chem. Eur. J. 2001, 7, 2765. (117) Lin, S. L., S.X.; Lin, B.Z. inorg. Chim. A cta. 2002, 328, 69. (118) Saalfrank, R. W. D., C.; Sperner, S.; nakajima, T.; Ako, A. M.; Uller, E.; Hampel, F.; Heinemann, F. W. Inorg. Chem. 2004 , 43, 4372. (119) Koizumi, S. N., M.; Nakano, M.; Oshio, H. Inorg. Chem. 2005, 44, 1208. (120) Saalfrank, R. W. R., U.; Gritz, M.; Hampel, F.; Scheurer, A.; Heinemann, F. W.; Bschel, M.; Daub, J.; Schnemann, V.; Trautwein, A. X. Chem. Eur. J. 2002, 8, 3614. (121) Tolis, E. I. H., M.; Langley, S.; Raftery, J.; Winpenny, R. E. P. Angew. Chem. Int. Ed. 2003, 42, 3804. (122) Raptopoulou, C. P. B., A. K.; Sanakis, Y.; Psycharis, V.; Clemente Juan, J. M.; Fardis, M.; Diamantopoulos, G.; Papavassiliou, G. Inorg. Chem. 2006, 45, 2317. (123) Joliot, B. B., G.; Cahbaud, R. Photochem. Photobiol. 1969, 10 , 369.

PAGE 319

319 (124) Kok, B. F., B.; McGloin, M Photochem. Photobiol. 1970, 11, 457. (125) Limburg, J. S., V.A.; Brudvig, G.W.J. J Chem. Soc. Dalton Trans. 1999, 1353. (126) Leunenberger, M. N.; Loss, D. 2001, Nature , 789. (127) Troiani, F.; Affronte, M.; Carretta, S.; Santini, P.; Amoretti, G. Phys. Rev. Lett. 2005, 94 , 190501. (128) Troiani, F.; Ghirri, A.; Affronte, M.; Carretta, S.; Santini, P.; Amoretti, G.; Piligkos, S.; Timco, G.; Wimpenny, R. E. P. Phys. Rev. Lett. 2005, 94, 207208. (129) Beltran, L. M. C.; Long, J. R. Acc. Chem. Res. 2005, 38, 325. (130) Bhaduri, S. P., M.; Christou, G. Chem. Commun. 2002, 2352. (131) Bhaduri, S. T., A. J.; Bolcar, M. A.; Abboud, K. A.; Streib, W. E.; Christou, G. Inorg. Chem. 2003, 42, 1483. (132) Lis, T. Acta. Cryst. B 1980, 36. (133) Tasiopoulos, A. J. A., K. A.; Christou, G. Chem. Commun. 2003, 580. (134) Cooper, S. R. C., M. J. J. Am. Chem. Soc. 1977, 99, 6623. (135) Vincent, J. B. C., H. R.; Folting, K.; Huffman, J. C.; Christ ou, G.: Hendrickson, D. N. J. Am. Chem. Soc. 1987, 109, 5703. (136) Tasiopoulos, A. J. O. B., T. O.; Abboud, K. A.; Christou, G. Angew. Chem. Int. Ed. 2004, 43 345. (137) Tasiopoulos, A. J. M., P. L., Jr.; Abboud, K. A.; O'Brien, T. A.; Christou, G. Inorg. Chem. 2007, 46, 9678. (138) Sessoli, R. T., H. L.; Schake, A. R.; Wang, S.; Vincent, J. B.: Folting, K.; Gatteschi, D.; Christou, G.; Henderickson, D. N. J. Am. Chem. Soc. 1993, 115, 1804. (139) Mishra, A. T., A. J.; Wernsdorfer, W.; Abboud, K. A.; Christou, G. Inorg. Chem. 2007, 46, 3105. (140) Mishra, A. T., A. J.; Wernsdorfer, W.; Moushi, E. E.; Moulton, B.; Zaworotko, M. J.; Abboud, K. A.; Christou, G. Inorg. Chem. 2008, 47, 4832. (141) Milos, C. J. W., P. A.; Parsons, S.; Foguet Albiol, D.; Lampropoulos, C.; Christou, G.; Perlepes, S. P. Brechin, E. K. inorg. Chim. Acta. 2007, 360, 3932.

PAGE 320

320 (142) Limburg, J. B., G. W.; Crabtree, R. H. J. Am. Chem. Soc. 1997, 119, 2761. (143) Limburg, J. V., J. S.; Liable Sands, L. M.; Rheingold, A. L.; Crabt ree, R. H.; Brudvig, G. W. Science 1999, 283, 1524. (144) Lehn, J. N. Supramolecular Chemistry ; VCH Publishers: New York, 1995. (145) Ferrere, S. E., C.M. Inorg. Chem. 1995, 35. (146) Youinou, M. T. Z., R.; Lehn, J. M. Inorg. Chem. 1991, 30, 2144. (147) Piguet, C. B., G.; Hopfgartner, G. Chem. Rev. 1997, 97, 2005. (148) Constable, E. C. Chem. Commun. 1997, 1703. (149) Baxter, P. L., J. M.; De Cian, A.; Fischer, J. J. Angew. Chem., Intl. Ed. Engl. 1993, 32, 69. (150) Hasenknopf, B. L., J. M.; Boum ediene, N.; Dupont Gervais, A.; Van Dorsselaer, A.; Kneisel, B.; Fenske, D. J. Am. Chem. Soc. 1997, 119, 10956. (151) Berl, V. H., I.; Khoury, R. G.; Lehn, J.M. Eur. J. Chem. 2001 , 7, 2798. (152) Sanudo, E. C. G., V. A.; Knapp, M. J.; Bollinger, J. C.; H uffman, J. C.; Hendrickson, D. N.; Christou, G. Inorg. Chem. 2002, 41, 2441. (153) Grant, C. M. S., B. J.; Knapp, M. J.; Folting, K.; Huffman, J. C.; Hendrickson, D. N.; Christou, G J Chem. Soc. Dalton Trans. 1999, 3399. (154) Grillo, V. A. S., Z.; Folting, K.; Hendrickson, D. N.; Christou, G. Chem. Commun. 1996, 2233. (155) Saudo, E. C. C., G. unpublished results . (156) Garber, T. V. W., S.; Rillema, D. P.; Kirk, M.; Hatfield, W. E.; Welch, J. H. Inorg. Chem. 1990, 29, 2863. (157) Aromi, G. B., S.; Artus, P.; Huffman, J. C.; Hendrickson, D. N.; Christou, G. Polyhedron 2002, 21, 1779. (158) Sanudo, E. C. Dissertation, Indiana University, 2003. (159) Sanudo, E. C. G., V. A.; Yoo, J.; Huffman, J. C.; Bollinger, J. C.; Hendric kson, D. N.; Christou, G. Polyhedron 2001, 20, 1269.

PAGE 321

321 (160) Zerner, M. C. L., G. H.: Kirchner, R. F.; Muellerwesterhoff, U. T. J. Am. Chem. Soc. 1980, 102, 589. (161) Ridley, J. E. Z., M. C. Theor. Chim. Acta 1973, 32 , 111. (162) Kotzian, M. R., N.; Zerner, M. C. Theor. Chim. Acta 1992, 81 , 201. (163) Culberson, J. C. K., P.; Rosch, N.; Zerner, M. C. Theor. Chim. Acta 1987, 71, 21. (164) Cory, M. G. K., S.; Kotzian, M.; Rosch, N.; Zerner, M. C. J. Chem. Phys. 1994, 100, 1353. (165) Bacon, A. D. Z., M. C. Theor. Chim. Acta 1979, 53 , 21. (166) Anderson, W. P. C., T. R.; Zerner, M. C. Int. J. Quantum Chem. 1991, 39, 31. (167) Anderson, W. P. C., T. R.; Drago, R. S.; Zerner, M. C. Inorg. Chem. 1990 , 29, 1. (168) Davidson, E. R. C., A. E. Mol. Phys. 2002, 100, 373. (169) Clark, A. E. D., E. R. J. Chem. Phys. 2001, 115, 7382. (170) Libby, E. W., R. J.; Streib, W. S.; Folting, K.; Huffman, J. C.; Christou, G. Chem. Commun. 1989, 1411. (171) Davidson, E. R. C., A. E. J. Chem. Phys. A. 2002, 106, 7456. (172) Wemple, M. W. W., S.; Tsai, H. L.; Claude, J. P.; Streib, W. E.; Huffman, J. C.; Hendrickson, D. N.; Christou, G. Inorg. Chem. 1996, 35, 6437. (173) Lee, C. Y., W.: Parr, R. G. Phys. Rev. B 1988, 37, 785. (174) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (175) Frisch, M. J. T., G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adam o, C.; Jaramillo, J.; Gomperts, R.; Stratman, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomell, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C .; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al Laham, M. A.; Peng, C. Y.; Nanayakkara,

PAGE 322

322 A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. ; Gaussian, Inc: Pittsburgh, PA, 2003. (176) Tamasi, G. C., R. Dalton Trans. 2003, 2928. (177) Hypercube, Inc: Gainesville, FL, 1997. (178) CRC Handbook of Chemistry and Physics ; 64th ed.; CRC Press: Weast, 1984. (179) O'Connor, C. J. Prog. Inorg. Chem. 1982, 29, 203. (180) Davidson, E. R.; MAGNET, Ed. Indiana Univeristy: Bloomington, IN, 1999. (181) Davidson, E. R.; GRID, Ed.; Indiana University: Bloomington, IN.: 1999. (182) J.J. Borras Almenar, J. M. C.J. E. C., B. Tsukerblat, Departamento de Quimica, Universidad de Calencia, Valencia, Spain, 2000. (183) Stamatatos, T. C. C., A.G.; Jones, C.M.; O'Callaghan, B.J.; Abboud, K.A.; O'Brien, T.A.; Christou, G. J. Am. Chem. Soc. 2007, 129, 9840. (184) He, H. G., V.; Spingler, B.; Lippard, S.J. Inorg. Chem. 2000, 37, 4188. (185) Wieghardt, K. B., U.; Ventur, D.; Weiss, J. J.Chem.Soc. Chem. Commun 1985, 6, 347. (186) Vincent, J. B.; Tsai, H. L.; Blackman, A. G.; Wang, S.; Boyd, P. D. W.; Folting, K.; Huffman, J. C.; Lobkocsky, E. B.; Hendrickson, D. N.; Christou, G. J. Am. Chem. Soc. 1993, 115, 12353. (187) Mukhopadhyay, S. M., S.K.; Bhaduri, S.; Armstrong, W.H Chem. Rev. 2004, 104, 3981. (188) Nugent, J., Ed.; Biochim. Biophys. Acta 2001, 1. (189) Hanley, J. S., J.; Petrouleas, V. Biochemistry 2000, 39, 15441. (190) Mukherjee, S. S., J.A.; Yano, J.; Stamatatos, T.C.; Pringouri, K.; Stich, T.A.; Abboud, K.A.; Britt, R.D.; Yachandra, V.K.; Christou, G. Proc. Nat. Acad. Sci. USA 2012, 109, 2257. (191) Yachandra, V. K. S., K.; Klein, M. P. Chem. Rev. 1996, 2927. (192) Peloquin, J . M. C., K. A.; Randall, D. W.; Evanchik, M. A.; Pecoraro, V. L.; Armstrong, W. H.; Britt, R. D. J. Am. Chem. Soc. 2000, 122, 10926. (193) Christou, G. G., D.; Hendrickson, D.N.; Sessoli, R. MRS Bulletin 2000, 25 , 66.

PAGE 323

323 (194) Bircher, R. C., G.; Dobe, D.; Gudel, H.U.; Oshsenbein, S.T.; Sieber, A.; Waldmann, O. Adv. Funct. Mater. 2006 , 16, 209. (195) Morello, A. B., O.N.; Brom, H.B; de Jongh, L.J. Polyhedron 2003, 22, 1745. (196) Caneschi, A. O., T.; Paulsen, C.; Rovai, D.; Sa ngregorio, C.; Sessoli, R.J. J. Magn. Magn. Mater. 1998, 177181. (197) Brechin, E. K. B., C.; Wernsdorfer, W.; Yoo, J.; Yamaguchi, A.; Sanudo, E.C.; Concolino, T.R.; Rheingold, A.L.; Ishimoto, H.; Hendrickson, D.N.; Christou, G. J. Am. Chem. Soc. 2002, 124, 9710. (198) Gatteschi, D. S., R. Angew. Chem. Int. Ed. 2003, 42, 268. (199) Ruiz, D. S., Z.; Albela, B.; Folting, K.; Ribas, J.; Christou, G.; Hendrickson, D.N. Angew. Chem. Int. Ed. 1998, 37, 300. (200) del Barco, E. K., A.D.; Hill, S.; North, J.M.; Dalal, N.S.; Rumberger, E.M.; Hendrickson, D.N.; Chakov, N.; Christou, G. Low Temp. Phys. 2005, 140, 119. (201) Stamp, P. C. E. Nature 1996, 383, 125. (202) Wernsdorfer, W. C., N.E.; Christou, G. Phys. Rev. Lett. 2005 , 95, 037203 (1. (203) Wernsdorfer, W. S., R. Science 1999, 284, 133. (204) Hill, S. E., R.S.; Aliaga Alcalde, N.; Christou, G. Science 2003, 302, 1015. (205) Perenboom, J. B., J.S.; Hill, S.; Hathaway, T.; Dalal, N.S. Phys. Rev. B 1998, 58, 330. (206) Macia, F. L., J.; Hill, S.; Hernadez, J.M.; Tejada, J.; Santos, P.V.; Lampropolous, C.; Christou, G. Phys. Rev. B. 2008, 77, 030403. (207) Park, K. N., M.A.; Dalal, N.S.; Hill, S.; Rikvold, P.A. Phys. Rev. B 2002, 65, 014426. (208) Harter, A. G. C., N.E.; Achey, R.; Reyes, A.; Kuhns, P.; Christou, G.; Dalal, N.S. Polyhedron 2005, 24, 2346. (209) Harter, A. G. L., C.; Murugesu, M.; Kuhns, P.; Reyes, A.; Christou, G.; Dalal, N.S. Polyhedron 2007, 2320. (210) Stamatatos, T. C. P., K.M.; Abboud, K.A.; Wernsdorfer, W.; O'Brien, T.A.; and Christou, G. Inorg. Chem. 2008, 47, 5006. (211) Stamatatos, T. C. A., K.A.; Wernsdorfer, W.; Christou, G. Angew. Chem. Int. Ed. 2006, 45, 4134.

PAGE 324

324 (212) Stamatatos, T. C. A., K.A.; Wernsdorfer, W.; Christou, G. Polyhedron 2007, 26, 2042. (213) Stamatatos, T. C. F.A., D.; Poole, K.M.; Wernsdorfer, W.; Abboud, K.A.; O'Brien, T.A. and Christou, G. Inorg. Chem. 2009, 48, 9831. (214) Que, J., L.; True, A.E. Prog. Inorg. Chem. 1990, 38, 97. (215) Stamatatos, T. C. C., G. Philos. Trans. R. Soc. A. 2008, 366, 113 and references cited therein. (216) Harden, C. N. B., M.A.; Wernsdorfer, W.; Abboud, K.A.; Streib, W.E.; Christou, G. Inorg. Chem. 2003, 42, 7067. (217) Bolcar, M. A. A., S.M.J.; Folting, K.; Hendrickson, D.N.; Christou, G. Chem. Comm. 1997, 1485. (218) Pilawa, B. K., M.T.; Wanka, S.; Geisselmann, A.; Barra, A.L. Europhys. Lett. 1998, 43 , 7. (219) Saalfrank, R. W. N., T.; Mooren, N.; Scheurer, A.; Maid, H.; Hampel, F.; Trieflinger, C.; Da ub J. Eur. J. Inorg. Chem. 2005, 1149. (220) Langley, S. K. C., N.F.; Massi, M.; Moubaraki, B.; Berry, K.J.; Murray, K.S. Dalton Trans. 2010, 39, 7236. (221) Abbati, G. L. C., A.; Fabretti, A.C.; Caneschi, A.; Gatteschi, D. Inorg. Chem. 1998, 37, 3759. (222) Koizumi, S. N., M.;Shiga, T.; Nakano, M.; Npkiri, H.; Bircher, R.; Waldmann, O.; Ochsenbein, S.T.; Gudel, H.U.; Fernandez Alonso, F.; Oshio, H. Chem. Eur. J. 2007, 13, 8445. (223) Saalfrank, R. W. S., A.; Prakash, R.; Heinemann, F.W.; Nakajima, T.; Hampel, F.; Leppin, R.; Pilawa, B.; Rupp, H.; Muller, P. Inorg. Chem. 2007, 46, 1586. (224) Chen, S.Y. B., C.C.; Gan, P R.; Lee, G H.; Hill, S.; Yang, E.C. Inorg. Chem. 2012, 51, 4448. (225) !!! INVALID CITATION !!! (226) Kulik, L. V. E., B.; Lubitz, W.; Messinger, J. J. Am. Chem. Soc. 2005, 127, 2392. (227) Koulougliotis, D. S., J.R.; Ioannidis, N.; Petrouleas, V. Biochemistry 2003, 42, 3045. (228) de Paula, J. C. B., W.F.; Brudvig, G.W. J. Am. Chem. Soc. 1986, 108, 4002. (229) Hasegawa, K. O., T.A.; Inoue, Y.; Kusunoki, M. Chem. Phys. Lett 1999, 200 , 9.

PAGE 325

325 (230) Randall, D. W. S., B.E.; Ball, J.A.; Lorigan, G.A.; Chan, M.K.; Klein, M.P.; Armstong, W.H.; Britt, R.D. J. Am. Chem. Soc. 1995, 117, 11780. (231) McEvoy, J. P. B., G.W. C hem. Rev. 2006, 108, 4455. (232) Zheng, M. D., G.C. Inorg. Chem. 1996, 35, 15441. (233) Wang, S. T., H L.; Libby, E.; Folting, K.; Streib, W.E.; Hendrickson, D.N.; Christou, G. Inorg. Chem. 1996, 35, 7578. (234) Philouze, C. B., G.; Girerd, J.J.; Guilh em, J.; Pascard, C.; Lexa, D. J. Am. Chem. Soc. 1994, 116, 8557. (235) Chan, M. K. A., W.H. J. Am. Chem. Soc. 1990, 112, 4985. (236) Wemple, M. W. T., H.L.; Folting, K.; Hendrickson, D.N.; Christou, G. Inorg. Chem. 1993, 32, 2025. (237) Kirk, M. L. C., M.K.; Armstrong, W.H.; Solomon, E.I. J. Am. Chem. Soc. 1992, 114, 10432. (238) Wemple, M. W. A., D.M.; Folting, K.; Hendrickson, D.N.; Christou, G. J. Am. Chem. Soc. 1995, 117, 7275. (239) Ruettinger, W. F. C., C.; Dismukes, G.C. J. Am. Chem. Soc. 1997, 119, 6670. (240) Dube, C. E. W., D.W.; Pal, S.; Bonitatebus, P.J.; Armstrong, W.H. J. Am. Chem. Soc. 1998, 120, 3704. (241) Gedye, C. H., C.; McKee, V.; Nelson, J. Patterson, J. J. Chem. Soc., Chem. Commun. 1992, 392. (242) Chandra, S. K. C., P.; Chakravorty, A.J. J.Chem. Soc., Dalton Trans. 1993, 863. (243) Wang, S. F., K.; Streib, W.E.; Schmitt, E.A.; McCusker, J.K.; Hendrickson, D.N.; Christou, G. Angew. Chem. Int. Ed. 1991, 20, 305. (244) Vincent, J. B. C., C.; Chang, H . R.; Li, Q.; Boyd, P.D.W.; Huffman, J. C.;Hendrickson, D. N.; Christou, G. J. Am. Chem. Soc. 1989, 111, 32086. (245) Canada Vilalta, C. O. B., T.A.; Brechin, E.K.; Pink, M.; Davidson, E.R.; Christou, G. Inorg. Chem. 2004, 43, 5505. (246) Milios, C. J. V., A.; Wernsdorfer, W.; Moffach, S.; Parsons, S.; Perlepes, S.P.; Christou, G. J. Am. Chem. Soc. 2007, 129, 2754.

PAGE 326

326 (247) Milios, C. J. V., A.; Whittaker, A.G.; Parsons, S.; Wernsdorfer, W.; Christou, G.; Perlepes, S.P.; Brechin, E.K. Inorg. Chem. 2006, 45, 5272. (248) Lecren, L. W., W.; Li, Y.,G.; Vindigni, A.; Miyasaka, H.; Clerac, R. J. Am. Chem. Soc. 2007, 129, 5045. (249) Kanady, S. T., E.; Day, M.; Agapie, T. Science 2011, 333, 733. (250) Miller, J. S. D., M. Eds.; Magnetism: Molecules to Materials ; Wiley VCH: Weinheim, Germany, 2002. (251) Tejada, J. C., E.M.; del Barco, E.; Hernandez, J.M.; Spiller, T.P. Nanotechnology 2001, 12, 181. (252) Zhou, B. T., R.; Shen, S.Q.; Liang, J.Q. Phys. Rev. A 2002, 66, 10301. (253) Canada Vilalta, C.; O'Brie n, T. A.; Brechin, E. K.; Pink, M.; Davidson, E. R.; Christou, G. Inorganic Chemistry 2004, 43, 5505. (254) Mishra, A. W., W.; Abboud, K. A.; Christou, G. J. Am. Chem. Soc. 2004, 126, 15648. (255) Yoo, J. Y., A.; Nakano, M.; Krzystek, J.; Streib, W.E.; B runel, L.C.; Ishimoto, H.; Christou, G.; Hendrickson, D.N. Inorg. Chem. 2001, 40, 4604. (256) Stamatatos, T. C. A., K.A.; Wernsdorfer, W.; Christou, G. Angew. Chem. Int. Ed. 2007, 46, 884. (257) Boskovic, C. B., E.K.; Streib, W.E.; Folting, K.; Hendrickson, D.N.; Christou, G. Chem. Comm. 2001 , 467. (258) L ampropoulos, C. R., G.; Data, S.; Abboud, K.A.; Hill, S.; Christou, G. Inorg. Chem. 2010, 49, 3077. (259) Bruker AXS Madison, WI , USA, 2008. (260) Bruker AXS: Madison, W.. (261) van der Sluis, P. a. S., A.L. Acta. Cryst. 1990, A46 , 194. (262) Spek, A. L. Acta. Cryst. 2009, D65 , 148. (263) Brown, I. D. A., D. Acta. Cryst. B 1985, 41, 244. (264) Liu, W. T. T., H.H. Inorg. Chem. 1993, 32, 4102.

PAGE 327

327 (265) Dawe, L. N. S., Konstantin V.; and Thompson, Laurence K. Chem. Soc. Rev. 2009, 38, 2334. (266) Dey, S. K. T., Laurence K.; and Dawe, Louise N. Chem. Commun. 2006, 4967. (267) Thompson, L. K. K., Timothy L.; Dawe, Louise N.; Grove, Hilde; and Lemaire, Martin T. Inorg. Chem. 2004, 43, 7605. (268) Waldmann, O. G., Hans U.; Kelly, Timothy L.; and Thompson, Laurence K. Inorg. Chem. 2006, 45, 3295. (269) Quellette, W. P., A.V; Vale ich, J.; Dunbar, K.R.; and Zubieta, J. Inorg. Chem. 2007, 46, 9067. (270) Matthews, C. J. T., L.K.; Parsons, S.R.; Xu, Z.; Miller, D.O.; and S.L. Heath Inorg. Chem. 2001, 40, 4048. (271) Brooker, S. M., V.; and Metcalfe, T. Inorg. Chim. Acta. 1996, 246, 171. (272) Matthews, C. J. X., Z; Mandal, S.K.; Thompson, L.K.; Biradha, K.; Poirier, K. and Zaworotko, M.J. Chem. Comm. 1999 , 347. (273) Wang, M. M., C.B.; Yuan, D.Q.; Wang, H.S.; Chen, C.N.; and Liu, Q.T. Inorg. Chem. 2008, 47, 5580. (274) Yang, P.P. S., X.Y.; Liu, R.N.; Li, L. C.; and Liao, D.Z. Dalton Trans. 2010, 39, 6285. (275) Lah, M. S. a. P., V.L. J. Am. Chem. Soc. 1989, 111, 7258. (276) DendrinouSamara, C. P., A.N.; Malamatari, D.A.; Tarushi, A.; Raptopoulou, C.P.; Terzis, A.; Samaras, E.; and Kessissoglou, D.P. J. Inorg. Biochem. 2005, 99, 864. (277) Yang, C.I. W., W.; Lee, G.H.; and Tsai, H.L.; J. Am. Chem. Soc. 2007, 129, 456. (2 78) Stamatatos, T. C. F.A., D.; Wernsdorfer, W.; Abboud, K.A.; and Christou, G. Chem. Comm. 2009 , 41. (279) Shiga, T. a. O., H. Polyhedron 2007, 26, 1881. (280) Berlinguette, C. P. V., D.; Canada Vilalta, C.; Galan Mascaros, J.R; and Dunbar, K.R. Angew . Chem. Int. Ed. 2003, 42, 1523. (281) Reynolds, R. A. a. C., D. Inorg. Chem. 1998, 37, 170. (282) Stamatatos, T. C. A., K.A.; Christou, G. J. Clust. Sci. 2010, 21 , 485.

PAGE 328

328 (283) Aromi, G. a. B., E.K. Struct. Bonding 2006, 122, 1 and references therein. (284) Milios, C. J. V., A.; Wood, P.; Parsons, S.; Wernsdorfer, W.; Christou, G.; Perlepes, S.P.; Brechin, E.K. J. Am. Chem. Soc. 2007, 129, 8. (285) Milios, C. J. G., I.A.; Vinslava, A.; Budd, L.; Parsons, S.; Wernsdorfer, W.; Perlepes, S.P.; Christou, G .; and E.K. Brechin Inorg. Chem. 2007, 46, 6215. (286) Jones, L. F. I., R.; Cochrane, M.E.; Mason, A.; Parsons, S.; Perlepes, S.P.; and E.K. Brechin Dalton Trans. 2008, 6205. (287) Inglis, R. J., L.F.; Milios, C.J.; Datta, S.; Collins, A.; Parsons, S.; Wernsdorfer, W.; Hill, S.; Perlepes, S.P.; Piligkos, S.; and E.K. Brechin Dalton Trans. 2009, 3403. (288) Milios, C. J. I., R.; Vinslava, A.; Bagai, R.; Wernsdorfer, W.; Parsons, S.; Perlepes, S.P.; Christou, G.; and Brechin J. Am. Chem. Soc. 2007, 129, 12505. (289) Jones, L. F. C., M.E.; Koivisto, B.D.; Leigh, D.A.; Perlepes, S.P.; Wernsdorfer, W. and E.K. Brechin Inorg. Chim. Acta. 2008, 361, 3420. (290) Prescimone, A. M., C.J.; Sa nchez Benitez, J.; Kamenev, V.; Loose, C.; Kortus, J.; Moggach, S.; Murrie, M.; Warren, J.E.; Lennie, A.R.; Parsons, S.; and E.K. Brechin Dalton Trans. 2009, 4858. (291) Martinez Lillo, J. C., L.M.; Proust, A.; Verdaguer, M.; and Gouzerh, P.C.R. Chimie 2012, 15. (292) Martinez Lillo, J. T., A.R.; Li, Y.; Chamoreau, L.M.; Cremades, E.; Ruiz, E.; Barra, A.L.; Proust, A.; Verdaguer, M.; and Gouzerh, P.C.R. Dalton Trans. 2012, 41, 13668. (293) Holynska, M. F., N. and Dehnen, S.Z Anorg. Allg. Chem. 2012, 638. (294) Holynska, M. F., N. Pichon, C.; Jeon, I.R.; Clerac, R.; and Dehnen, S.Z Inorg. Chem. 2013, 52, 7943. (295) Cie, S. Darmstadt, Germany, 2002. (296) Sheldrick, G. M.; Bruker, AXS Inc.: 6300 Enterprise Lane, Madison, WI 537191173, USA, 1997. (297) Hassan, A. K.; Pardi, L. A.; Krzystek, J.; Sienkiewicz, A.; Goy, P.; Rohrer, M.; Brunel, L. C. Journal of Magnetic Resonance 2000, 142, 300. (298) CCDC 2001 2009, M. v.

PAGE 329

329 (299) Kozoni, C. M., E.; Siczek, M.; Liz, T.; Brechin, E.K. and Milios, C J. D alton Trans. 2010, 39, 7943. (300) Redler, G. L., C.; Datta, S.; Koo, C.; Stamatatos, T.C.; Chakov, N.E.; Christou, G.; and S. Hill Phys. Rev. B 2009, 80, 94408(1. (301) Stoll, S.; Schweiger, A. Journal of Magnetic Resonance 2006, 178, 42. (302) Brown, I. D.; Brockhouse Institute for Materials Research, McMaster University: Hamilton, Ontario, Canada.

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330 BIOGRAPHICAL SKETCH Katherine Poole was born in Oklahoma City, OK in 1979. She entered Indiana University Purdue University Indianapolis in 2004 and received Bachelor of Sicence degrees in chemistry and psychology in 2008. During her b achelor ’ s, she worked in the research group of Dr. Ted A. O’Brien where she used computational methods to calculate magnetic interaction in transition metal complexes. One focus of her research was the comparison of density functional theory (DFT) and semiempirical methods for estimating magnetic exchange interaction strengths in manganese complexes to optimize the semiempirical methods to better estimate t he exchange interactions in manganese clusters. She participated in collaboration to aid in the interpretation of magnetic studies of newly synthesized transition metal complexes. Upon completion of her undergraduate work, she joined the research group of Prof. George Christou in the Department of Chemistry in the Department of Chemistry at the University of Florida. During her doctoral research, she was awarded the prestigious National Science Foundation Graduate Research Fellowship. Her doctoral researc h primarily involves theoretical and experimental exploration of physical properties of new polynuclear oxobridged Mn and Fe clusters, some of which behave as singlemolecule magnets. .