Florida State University Libraries
Electronic Theses, Treatises and Dissertations The Graduate School
2006 Magnetic and High-Field EPR Studies of New Spin-Frustrated Systems Saritha Nellutla
Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES
Magnetic and High-Field EPR Studies of New Spin-Frustrated Systems
By SARITHA NELLUTLA
A dissertation submitted to the Department of Chemistry and Biochemistry in partial fulfillment of the requirements for the degree of Doctorate of Philosophy
Degree Awarded: Spring Semester, 2006 The members of the Committee approve the dissertation of Saritha Nellutla defended on January 9, 2006.
Naresh Dalal Professor Directing Dissertation
James Brooks Outside Committee Member
Johan van Tol Committee Member
Oliver Steinbock Committee Member
Igor Alabugin
Committee Member
Approved:
Naresh Dalal, Chair, Department of Chemistry and Biochemistry
The office of Graduate Studies has verified and approved the above named committee members.
ii ACKNOWLEDGEMENTS
I dedicate this manuscript to my beloved parents Kishan Rao and Rama Devi Nellutla and sisters Swetha Nellutla and Shobitha Nellutla, whose never-ending love and support have been my joy and stabilizing force not only these past five years but also through out my life. Though an adequate list of all my friends to whom I owe my gratitude is long, I would like to acknowledge Shivdas, Stephanie, Vijay and Seshu for their friendship, hospitality, knowledge, and wisdom. Their constant encouragement has helped me to keep my goals in perspective. I would also like to thank the Dalal group members who have provided a great amount of assistance over the past few years. I would like to acknowledge all my high school and undergraduate teachers for influencing the outcome of my education. I would not have been in Chemistry were it not for my high school teacher Mr. Naresh Ankaraju, whose patience allowed a young mind to mature. I express my deepest admiration to my research advisor, mentor and friend, Prof. Naresh Dalal, whose optimistic attitude and scientific talent has been a continuous inspiration through out my graduate school and will remain as the high standard by which I will judge my professional development. Further acknowledgement goes to Dr. Ulrich Körtz’s group at International University of Bremen, Germany for his synthetic expertise and Dr. Johan van Tol at National High Magnetic Field Laboratory, Florida, for helping with the High-Field EPR instruments. Last but not least, I would like to thank all the staff members of Department of Chemistry and Biochemistry at Florida State University for their help with all aspects of technical assistance.
iii TABLE OF CONTENTS
List of Tables……………………………………………………………………viii List of Figures……………………………………………………………………..x Abstract………………………………………………………………………….xiv
1. INTRODUCTION…………………………………………………………….1 1.1 Introduction……………………………………………………………….1 1.2 Overview………………………………………………………………….5 1.3 Organization……………………………………………………………...19 2. MAGNETIZATION AND EPR CHARACTERIZATION OF A TRI- COPPER(II) COMPLEX: A MODEL SPIN-FRUSTRATED TRIANGULAR SYSTEM…………………………………………………………………………20 2.1. Introduction……………………………………………………………...21 2.2. Synthesis and Experimental Details……………………………………..22 2.2.1. Synthesis………………………………………………………….22 2.2.2. X-ray Crystallography……………………………………………22 2.2.3. dc Magnetic Susceptibility measurements……………………….23 2.1.1. Powder and Single crystal EPR measurements…………………..23 2.3. Molecular Structure……………………………………………………...24 2.4. Magnetic Susceptibility………………………………………………….27 2.4.1. Theoretical Model………………………………………………...27 2.4.2. Experimental Data Analysis……………………………………...31 2.5. EPR Spectroscopy……………………………………………………….33 2.6. Summary………………………………………………………………...38 2+ 3. EPR AND MAGNETISM OF A (Cu )4 SUBSTITUTED GERMANO TUNGSTATE: A TRIPLET GROUND STATE…..………………………...40 3.1. Introduction……………………………………………………………...41 3.2. Experimental Details…………………………………………………….42
iv 3.2.1. Synthesis………………………………………………………….42 3.2.2. X-ray Crystallography……………………………………………42 3.2.3. Magnetic and EPR Measurements……………………………….43 3.3. Crystal and Molecular Structure………………………………………...44 3.4. Magnetic Studies…………………………………..…………………….46 3.4.1. Theoretical Model………………………………………………..46 3.4.2. Magnetic Susceptibility and Magnetization……………………...48 3.5. EPR Spectroscopy……………………………………………………….53 3.6. Summary………………………………………………………………...57 4. MAGNETIC AND EPR PROBING OF THE SPIN GROUND STATE OF A COPPER(II) PENTAMER………………………………………………...58 4.1. Introduction……………………………………………………………...59 4.2. Synthesis and Experimental Details……………………………………..61 4.2.1. Synthesis………………………………………………………….61 4.2.2. X-ray Crystallography……………………………………………61 4.2.3. Magnetic Measurements………………………………………….62 4.2.4. Powder EPR measurements………………………………………62 4.3. Molecular Structural Details……………………………………………..62 4.4. dc Magnetic Susceptibility and Magnetization Studies………………….65 4.5. High Frequency EPR Studies……………………………………………72 4.6. Summary………………………………………………………………...77 5. MAGNETIZATION AND EPR STUDIES OF AN IRON(III) HEXAMER: DIAMAGNETIC GROUND STATE WITH LOW LYING EXCITED STATES…………………………………………………………………………..79 5.1. Introduction……………………………………………………………...80 5.2. Synthesis and Experimental Details……………………………………..81 5.2.1. Synthesis………………………………………………………….81 5.2.2. X-ray Crystallography……………………………………………82 5.2.3. dc Magnetic Susceptibility Measurements……………………….82
v 5.2.4. EPR measurements………………………………………………83 5.3. Molecular Structure……………………………………………………..83 5.4. Magnetochemistry………………………………………………………87 5.4.1. Theoretical Model………………………………………………..87 5.4.2. Magnetic Susceptibility Data Analysis…………………………..89 5.5. EPR Spectroscopic Studies……………………………………………...92 5.6. Summary………………………………………………………………...97 2+ 6. MAGNETIC AND HIGH-FIELD CHARACTERIZATION OF A (Co )15 CLUSTER: A TRIANGLE OF TRIANGLES COUPLED SYSTEM…………100 6.1. Introduction……………………………………………………………101 6.2. Synthesis and Experimental Details…………………………………...103 6.2.1. Synthesis………………………………………………………..103 6.2.2. X-ray Crystallography………………………………………….103 6.2.3. dc Magnetic Susceptibility and EPR Measurements…………...103 6.3. Structural Details………………………………………………………104 6.4. Magnetic Studies………………………………………………………108 6.4.1. Theoretical Model………………………………………………108 6.4.2. dc Magnetic Susceptibility Data Analysis…………………...…112 6.5. High-Frequency EPR Studies….………………………………………116 6.6. Summary………………………………………………………………116 7. CONCLUSIONS AND CRITIQUE………………………………………..120 APPENDIX A INSTRUMENTAL DETAILS OF THE HIGH FREQUENCY SET UP………………………………………………………...123 APPENDIX B BASIS FUNCTIONS, EXCHANGE MATRIX AND 2+ EIGENVALUES FOR THE (Cu )5 PENTAMER OF SiCu5…………………125 B.1. Basis Functions…….…………………………………………………..125 B.2. Exchange Matrix and Eigenvalues……………..………………………125 APPENDIX C COMPUTER CODES TO CALCULATE THE SPIN 3+ 2+ EXCHANGE ENERGIES OF (Fe )6 AND (Co )9 CLUSTERS……………..131
vi 3+ C.1. (Fe )6 Hexamer………………………………………………………..131 C.1.1. Review of spin-exchange model………………………………..131 3+ C.1.2. Program Code for (Fe )6 hexamer of GeFe6…………………..133 2+ C.2. (Co )9 Nonamer……………………………………………………….135 C.2.1. Review of spin-exchange model………………………………..135 2+ C.2.2. Computer code for (Co )9 cluster of SiCo15…………………...137 BIBLIOGRAPHY………………………………………………………………139 BIOGRAPHICAL SKETCH…...……………………………………………….151
vii LIST OF TABLES
Table 2.1 Crystal Structure Data for AsCu3……………………………………..23
Table 2.2 Axial and Equatorial Bond Distances and Angles of Copper(II) Triangle…………………………………………………………………………..24
Table 2.3 Possible Spin states and their Energies for Equatorial and Isosceles Exchange Models………………………………………………………………...29
Table 3.1 Crystal Structure Data for GeCu4……………………………………..43
Table 3.2 Selected Bond Distances and Angles for GeCu4……………………...44
Table 3.3 Spin state Energies of Copper Tetramer………………………………48
Table 4.1 Crystal Structure Data for SiCu5……………………………………...61
2+ Table 4.2 Bond Distances and Angles for the (Cu )5 core of SiCu5..…………..65
Table 4.3 Spin Exchange Hamiltonian Eigenvalues for SiCu5………………….69
Table 5.1 Crystal Structure Data for GeFe6……………………………………..82
3+ Table 5.2 Bond Distances and Angles for the (Fe )6 core of GeFe6……………85
Table 5.3 Intra- and inter-trimer Fe···Fe Distances in GeFe6…………………....88
3+ Table 5.4 Various Spin state Energies and their Degeneracies for (Fe )6 cluster…………………………………………………………………………….90
Table 6.1 Crystal Structure Data for SiCo15……………………………………104
2+ Table 6.2 Bond Distances and Angles of Co ions in SiCo15…………………107
Table 6.3 Intra- and inter-trimer Co···Co Distances in SiCo15………………...107
2+ Table 6.4 Various Spin state Degeneracies for (Co )9 cluster………………...110
2+ Table 6.5 Spin Exchange Energy levels for (Co )9 cluster……………………111
2+ Table B.1 Eigenfunctions set for (Cu )5 pentamer of SiCu5…………………..126
viii 2+ Table B.2 Exchange Eigenvalues of (Cu )5 pentamer of SiCu5……………....130
3+ Table C.1 Sample output file of (Fe )6 hexamer of GeFe6……………………134
Table C.2 Sample list of (Co2+)9 exchange energies generated by the code…...138
ix LIST OF FIGURES
Figure 1.1 Diagram of a Spin-frustrated Equilateral Triangle………………….....3
Figure 1.2 Structures of Complete and Tri-lacunary Keggin Moieties…………...4
Figure 1.3 Structure of {Na3Cu3(H2O)9O12} unit of AsCu3………………………7
Figure 1.4 Combined Polyhedral and Ball and Stick representation of AsCu3 molecule…………………………………………………………………...8
Figure 1.5 Polyhedral representation of GeCu4 molecule………………………...9
Figure 1.6 Ball and Stick representation of {Cu4(H2O)4O4} moiety of GeCu4….10
Figure 1.7 Polyhedral representation of SiCu5 molecule………………………...11
Figure 1.8 Ball and Stick representation of {Cu5(OH)4(H2O)2} unit of SiCu5…..12
Figure 1.9 Polyhedral representation of GeFe6………………………………….13
Figure 1.10 Ball and Stick representation of {Fe6(OH)9} fragment of GeFe6…..14
Figure 1.11 Polyhedral representation of SiCo15………………………………...15
Figure 1.12 Ball and Stick representation of {Co9Cl2O21(OH)3(H2O)9} unit of SiCo15…………………………………………………………………….16
Figure 2.1 Molecular Structure of AsCu3………………………………………..25
Figure 2.2 Structure of the Central belt of AsCu3……………………………….26
Figure 2.3 Spin Exchange Coupling models for AsCu3…………………………27
2+ Figure 2.4 Spin Arrangement schematic for (Cu )3 triangle of AsCu3…………30
2+ Figure 2.5 Spin Exchange energies for (Cu )3 triangle of AsCu3…...... 30
Figure 2.6 Plot of χmT vs T for AsCu3…………………………………………...31
2+ Figure 2.7(a) Zeeman energies (B || c-axis) of (Cu )3 triangle of AsCu3…….....34
Figure 2.7(b) Powder EPR spectrum for AsCu3 at 34 GHz and 4 K……………34
x Figure 2.8 Angular Dependence of 34 GHz EPR Spectra of AsCu3..…………...35
Figure 2.9 Experimental and Simulated 95 GHz EPR spectra of AsCu3………..37
Figure 2.10 Temperature Dependence of 95 GHz EPR spectrum of AsCu3….....38
Figure 3.1 Molecular Structure of GeCu4……………………………………….45
Figure 3.2 Structure of Central Cu4O16 unit of GeCu4…………………………..46
Figure 3.3 Diagram of the Spin Exchange coupling in GeCu4………………….47
Figure 3.4 χmT vs T plot of GeCu4………………………………………………49
2+ Figure 3.5 Orientation of 3dx2-y2 orbitals of Cu ions in GeCu4………………..50
Figure 3.6 E/|J1| vs J2/J1 for GeCu4……………………………………………..51
Figure 3.7 Schematic of Ground state Spin configuration of GeCu4…………....51
Figure 3.8 M/Nβ vs B/T plot of GeCu4…………………………………………..52
Figure 3.9 Experimental and Simulated 9.5 GHz EPR spectra of GeCu4……….54
Figure 3.10 Temperature Dependence of 9.5 GHz EPR spectrum of GeCu4……56
Figure 3.11 95 GHz EPR spectrum of GeCu4 ……..……………………………56
Figure 4.1 SiCu5 Molecular Structure…………………………………………...63
Figure 4.2 Central fragment structure of SiCu5………………………………….64
Figure 4.3 Magnetization as a function of field at 1.8 K………………………...66
Figure 4.4 χmT as a function of Temperature at 0.1 Tesla……………………….67
Figure 4.5 Spin-Exchange coupling scheme for SiCu5………………………….68
Figure 4.6 Exchange Energies Relative to the Ground state for SiCu5………….70
Figure 4.7 Relative Orientation of Equatorial and Axial bonds of Cu2+ ions in SiCu5……………………………………………………………………..71
Figure 4.8 95 and 192 GHz EPR Spectra of SiCu5……………………………...73
xi
Figure 4.9 95 GHz EPR spectrum Temperature Dependence…………………...74
Figure 4.10 Experimental and Simulated EPR spectra of SiCu5………………..75
Figure 4.11 Coordination Environment of Apical Copper ion in SiCu5…………76
Figure 5.1 Structure of GeFe6 molecule…………………………………………84
Figure 5.2 GeFe6 core structure………………………………………………….85
Figure 5.3 Packing of GeFe6 molecules in ac plane……………………………..86
3+ Figure 5.4 Exchange Coupling model for (Fe )6 hexamer of GeFe6……………88
3+ Figure 5.5 Exchange Energy levels Spectrum of (Fe )6 cluster of GeFe6………90
Figure 5.6 χm and χmT plots as a function of Temperature for GeFe6……………93
Figure 5.7 Theoretical fit to high temperature χmT data………………………….94
Figure 5.8 Room Temperature EPR spectra of GeFe6 at 92 and 240 GHz……....95
Figure 5.9a Temperature dependence of 92 GHz EPR spectrum of GeFe6……...96
Figure 5.9b Comparison of IEPRT with χmT data…………………………………96
Figure 5.10 One of the Possible Spin Configurations for the Ground state singlet of GeFe6………………………………………………………………….98
Figure 5.11 Relative Energies of the First Six Spin states of GeFe6…………….99
Figure 6.1 SiCo15 Molecular Structure…………………………………………105
2+ Figure 6.2 View of (Co )9 core of SiCo15 along C3 axis………………………106
2+ Figure 6.3 Spin Exchange coupling scheme for (Co )9 core of SiCo15……….108
Figure 6.4 Plot of Spin Exchange Energies (E/Jz) vs J′z/Jz ratio……………….111
Figure 6.5 Temperature Dependence of χmT for SiCo15………………………..113
Figure 6.6 Exchange Energy levels relative to the Ground state of SiCo15…....115
xii Figure 6.7 34 and 95 GHz EPR spectra of SiCo15……………………………..117
Figure 6.8 SiCo15 EPR spectra Temperature Dependence at 93 GHz………….118
Figure A.1 Block Diagram of the High Frequency Set up……………………..124
2+ Figure B.1 Diagram of Exchange Coupling Model for (Cu )5 of SiCu5……...126
3+ Figure C.1 (Fe )6 Hexamer Exchange Coupling Model……………………….131
2+ Figure C.2 Spin Exchange Coupling Model for (Co )9 of SiCo15……………..135
xiii ABSTRACT
This dissertation presents studies by magnetization, dc magnetic susceptibility and EPR spectroscopy on several new spin-frustrated polyoxometalate (POM) lattices of increasing spin sizes and complexities. Measurements have been made over the wide temperature range of 1.8-295 K, frequencies of upto 400 GHz and magnetic fields upto 13 Tesla. The goal was to discover compounds with high spin ground states. The POMs studied are Na9[Na3Cu3(H2O)9(α-AsW9O33)2] (AsCu3), Na11Cs[Cu4(H2O)2(B-α-
GeW9O34)2] (GeCu4), K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2] (SiCu5), Na7Cs4[Fe6
(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6) and Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-
SiW8O31)3}] (SiCo15). Spin-frustrated lattices are of current interest due to their potential to provide large spin ground states for certain topologies. Chapter 2 describes the powder and single crystal EPR and magnetic susceptibility characterization of AsCu3 complex, a prototypical spin-frustrated equilateral triangular system with a thermally accessible 2+ magnetic excited state. Chapter 3 is focused on the (Cu )4 tetramer, GeCu4, a four-spin rhombic core, found in a triplet ground state, theoretically and experimentally. Interestingly, the unpaired electrons are delocalized over only two of the four Cu2+ ions. Chapter 4 details magnetic and EPR characterization of a model five spin-coupled system,
SiCu5, which exhibits a spin doublet ground state. The spin Hamiltonian parameters have been analyzed in terms of simple crystal field – molecular orbital model in order to understand the bonding environment of the Cu2+ ion. Chapter 5 describes magnetic 3+ susceptibility and EPR measurements of the Fe hexamer, GeFe6. GeFe6 is a good example of a highly spin-frustrated system with a 111-fold degenerate diamagnetic ground 2+ state (ST = 0). Finally, Chapter 6 presents the magnetic and EPR studies of a (Co )15 cluster, SiCo15. Data analysis reveals the presence of a doubly degenerate S = ½ ground state, once again a result of the spin-frustration present in the system. In conclusion, while the present experimental and theoretical studies of incorporating transition metals in POMs did not yield compounds with high-spin ground states, they are thought to be significant additions to the emerging field of spin-frustrated magnetic systems.
xiv CHAPTER 1
INTRODUCTION AND OUTLINE
1.1. Introduction
The primary goal of this dissertation was to study systematically several new magnetic polyoxometalates (POMs) with increasing nuclearities and unpaired spin arrangements that could serve as models for understanding molecular magnetism. Our aim was to examine how the quantum behavior might evolve into classical behavior as the spin-size and geometry are changed. On the theoretical side, we developed simple angular-momentum coupling methods and effective spin Hamiltonians. Experimentally we used the modern magnetic characterization techniques of electron paramagnetic resonance (EPR) spectroscopy, magnetic susceptibility and magnetization as a function of frequency, magnetic field and temperature. In this undertaking, we start with the simplest arrangement of a spin triangle, a tri-copper(II) cluster and then go to a tetra- copper(II) containing cluster followed by a copper(II) pentamer, a Fe(III) hexamer and, finally, a cluster of fifteen cobalt(II) ions. The POMs studied here are:
Na9[Na3Cu3(H2O)9(α-AsW9O33)2] [1] (AsCu3),
Na11Cs[Cu4(H2O)2(B-α-GeW9O34)2]·31H2O [2] (GeCu4),
K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2]·18.5H2O [3,4] (SiCu5),
Na7Cs4[Fe6(OH)3(A-α-GeW9O34(OH)3)2]·30H2O [5] (GeFe6)
and Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}]·37H2O [6] (SiCo15). All the compounds studied here were synthesized in Dr. Körtz’s laboratory at the International University of Bremen in Germany, but their structural and magnetic characterization was carried out as a part of this dissertation. Before going into further details about each of these inorganic complexes, we briefly discuss why magnetic clusters of high nuclearities and POMs in particular are worthwhile investigating.
1 Magnetic clusters are molecular aggregates formed by a finite number of exchange-coupled paramagnetic centers. As the size of the clusters grows, they should pass from the regime of small clusters, where quantum mechanical effects are dominant, to that of the bulk magnets that exhibit semi-classical or even classical behavior. This cross-over raises an interesting question of how large the cluster size should be in order for us to observe the coexistence of quantum and classical effects. The problem is therefore not only of theoretical interest, because it gives insights in to the limits of validity of quantum theory [7,8], but is also of experimental interest, since it may provide an answer to the question of what is the lower limit to the miniaturization of the magnets that are used for instance as memory elements [9]. The field of magnetism of clusters is thus a meeting ground for solid-state physics and chemistry. In fact clusters of mesoscopic dimensions have been under active investigation [10-25] and some exciting results have already been reported over the last decade [26-43]. These include, magnetic hysteresis behavior at the single molecule level [26-28], slow magnetization relaxation by quantum tunneling [28-32] and phonon bottleneck effect [33-35], semi-conductive and photoconductive behaviors of single-molecule magnets [36,37], magnetic long-range order induced by quantum relaxation [38], isolation of single chain magnet made of a trinuclear MnIII – FeIII – MnIII cluster [39], use of quantum dots in microelectronic devices [40], quantum computation with quantum dots [41], heterogenous catalysts [42,43] etc. POMs are metal-oxide clusters that possess a remarkable degree of molecular and electronic tunabilities with impacts in disciplines as diverse as electron transfer processes [44]; catalysis [45-47]; antiviral, antitumoral and antibacterial agents in medicine [48]; materials science [49-51] and molecular magnetism [52-55]. Polyoxotungstates occupy a special place in the POM family for the following reasons. First, the ability of lacunary tungstates to act as ligands toward 3d-transition metal ions leads to the encapsulation, by the polyoxometalate framework, of a variety of magnetic clusters with different spin ground states that can exhibit ferromagnetic and/or antiferromagnetic exchange interactions [52]. Second, the bulky nonmagnetic POM framework provides not only an effective magnetic isolation of the cluster but also imposes its geometry [53,54].
2
JAF JAF
OR ?
J AF
Figure 1.1. A “Spin-frustrated” equilateral triangle: Spins at the corners of the triangle are antiferromagnetically exchange-coupled.
Third, as the POM chemistry allows the assembly of stable anion fragments into larger clusters, a chemical control of the magnetic nuclearity is thus possible [55]. Finally, some of the POMs studied here are examples of “magnetically frustrated” lattices. Magnetic frustration arises when a large fraction of magnetic sites in a lattice is subject to competing spin interactions [56-58] and can be observed in closed polygons containing odd and even number of magnetic centers [56,58]. For example, as shown in Figure 1.1, when three spins (S = ½) arranged in an equilateral triangle are antiferromagnetically coupled to each other and then a “frustrated” scenario arises in which two of the three spins must share the same orientation. These properties provided us the initial incentive of undertaking a detailed study of AsCu3, GeCu4, SiCu5, GeFe6 and SiCo15. Structurally, the majority of POMs studied here adapt the so-called α-Keggin structure (Figure 1.2), which involves a tetrahedral arrangement of four corner-sharing
three-fold M3O13 triads. Each MO6 octahedron within the triad shares two edges with the neighboring octahedral, where as a heteroatom occupies the central tetrahedral site [59].
Another commonly observed Keggin structure is the C3v symmetry β-structure which is
obtained by the rotation of one of the M3O13 triads by 60º (C3 axis) [60]. When one or
3
P5+ W 6+ O2- (a)
P5+ W6+ O2-
(b)
Figure 1.2. Polyhedral representation of: (a) α-{PW12O40} Keggin ion. (b) Tri-lacunary 6+ 5+ 2- α-{PW9O34} Keggin ion. Color code is as follows: W blue, P green and O red.
4 more ‘M’ atoms are eliminated along with their terminal oxygens either from α- or β- structure, the so-called ‘lacunary’ (deficient) species viz. {XM11O39} (Cs), {XM9O34}
(C3v) etc. are formed [60] (cf. Figure 1.2(b)). Reaction of a stable, lacunary POM with transition-metal ions usually leads to a product with the heteropolyanion framework unchanged. Depending upon the coordination requirement and the size of a given transition-metal ion, the geometry of the reaction product can therefore often be controlled. Since tri-vacant POMs are the best candidates to obtain compounds with largest number of interacting magnetic cations, we chose to study the POMs formed from these tri-lacunary species. The POMs, discussed in Chapters 2–6, show the remarkable potential of these tri-lacunary species to act as nucleophilic ligands towards a wide variety of transition metal cations resulting in the formation of magnetic clusters with different nuclearities and structures.
1.2. Overview
Even though POMs have been known for almost 200 years [60-62], their structural details and potential applications in various fields of science were only revealed only a few decades ago [63-66]. From the magnetism point of view, incorporation of more and more paramagnetic transition metal cations into these POM frameworks with various heteroatoms is still an enticing challenge to many synthetic chemists [52-55]. At the beginning of this work (late 2000), the study of high nuclearity metal ion clusters and the relevance of POMs in the field of molecular magnetism were two emerging fields and our curiosity to explore these two fields set us out to study the magnetic clusters of various sizes embedded in the POM frameworks. As discussed earlier, the simplest example of a spin-frustrated lattice is a triangular arrangement of antiferromagnetically interacting S = ½ spins. The versatile Cu2+ ion with its 3d 9 configuration seemed to be a natural choice to gain insights about a spin-frustrated lattice. The simplicity of Cu2+ ion arises from the fact that it can be treated as a single positive hole in an otherwise filled 3d10 configuration. We recently reported the structural and magnetic characterization [1] of a polyanion containing three
5 9- copper(II) centers [Na3Cu3(H2O)9(α-AsW9O33)2] (AsCu3). The results of this study will only be briefly cited here because the details have been presented elsewhere [67].
The structure of AsCu3 can be described as a central belt of three copper ions and + three Na ions (see Figure 1.3) sandwiched between two (α-AsW9O33) units giving rise
to D3h molecular symmetry (cf. Figure 1.4). Magnetic susceptibility data analysis indicates the presence of antiferromagnetic interactions (J = –1.36 ± 0.01 cm-1) between
copper ions giving rise to a doubly degenerate spin-frustrated ST = 1/2 ground state,
where ST represents the total spin of the magnetic cluster. Since the weak spin exchange -1 interaction in the AsCu3 system places the excited quartet state (ST = 3/2) at 3J ~ 4.1 cm
(~ 6 K), Zeeman transitions from both spin states (ST = 1/2 and 3/2) are observed in high frequency EPR studies even at 4 K. The observed spin-Hamiltonian parameters for
AsCu3 are: ST = 1/2, g|| = 2.117 ± 0.005, g⊥ = 2.254 ± 0.005; ST = 3/2, g|| = 2.060 ± 0.005, -1 g⊥ = 2.243 ± 0.005, |D| = 0.023 cm . Analysis of temperature dependence of the W-band spectrum not only confirms that the ST = 1/2 nature of the ground state but also provides the sign of the zero-field splitting constant D as positive, indicating that M = ± 1/2 is ST
the lower energy state of ST = 3/2. These studies are summarized in Chapter 2. As a next step in studying high nuclear magnetic clusters, our search for a tetra- nuclear copper cluster embedded in the polyoxoanion framework led us to the sandwich-
type polyoxotungstate, Na11Cs2[Cu4(H2O)2(B-α-GeW9O34)2]Cl ·31H2O (GeCu4) [2]. The structure of GeCu4, discussed in Chapter 3, is shown in Figure 1.5. It can be described as a central unit of a centro-symmetric rhomb-like Cu4O16 tetramer of four edge-sharing
CuO6 octahedra sandwiched between two B-α-GeW9O34 polyhedral caps. For each CuO6
octahedron along the long diagonal of the rhomb, a H2O molecule completes the sixth co-
ordination while CuO6 octahedra along the short diagonal are formed from the polyhedral cap oxygens (cf. Figure 1.6).
6 {Na3Cu3(H2O)9O12}
Cu Na Na
Cu Cu
Na
Na Cu O H2O
Figure 1.3. Ball and stick representation of central {Na3Cu3(H2O)9O12} fragment of AsCu3.
Our magnetic and EPR results show that the metal ions are antiferromagnetically coupled to give a degenerate ground state of spin singlet and triplet for GeCu4. The spin-triplet ground state of GeCu4 is a result of spin-frustration caused by the conflicting antiferromagnetic exchange interactions. Furthermore, the 7-line hyperfine structure observed for GeCu4 indicates that only two out of four Cu(II) ions carry the unpaired electron spin density.
7
Na9[Na3Cu3(H2O)9(α-AsW9O33)2]
Na Cu As H2O WO6
Figure 1.4. Combined ball and stick and polyhedral representation of arseno tungstate + Na9[Na3Cu3 (H2O)9(α-AsW9O33)2] (AsCu3). Nine Na counter ions have been omitted for clarity.
The quest of Kortz et al. for the synthesis of copper-rich polyoxoanions led to the
discovery of a first penta-copper(II) substituted POM K10[Cu5(OH)4(H2O)2(A-α-SiW9
O33)2] (SiCu5) [3]. The successful magnetic characterization of tri- and tetra-nuclear copper clusters encouraged us to study the expected greater complexity of the spin-
frustrated lattice of SiCu5. Figure 1.7 shows the structure of SiCu5 and can be described 10- as consisting of two A-α-[SiW9O34] Keggin moieties that are linked via two adjacent 6+ W-O-W bonds and stabilized by a central {Cu5(OH)4(H2O)2} fragment lead to a
structure with idealized C2v symmetry.
8 Na11Cs2[Cu4(H2O)2(B-α-GeW9O34)2]Cl
CuO6 WO6
GeO4
Figure 1.5. Polyhedral representation of germanotungstate Na11Cs2[Cu4(H2O)2 (B-α- GeW9O34)2]Cl (GeCu4). Counter ions have been omitted for clarity.
The copper(II) ions in the central fragment of SiCu5 are arranged in a rectangular pyramidal arrangement (cf. Figure 1.8) and can be considered as a good model for understanding a frustrated system of 5 coupled spins. Variable-frequency, variable temperature high-field EPR measurements and magnetization data established the ground
state to be an ST = 1/2. -1 -1 The exchange constants were found to be Ja = –51 ± 6 cm , Jb = –104 ± 1 cm , Jc -1 = –55 ± 3 cm , where Ja, Jb are coupling constants along the sides of the rectangular base
and Jc is the coupling constant between the base and apex copper ions. Observation of a four line hyperfine structure in the EPR spectra is evidence of spin localization on only one copper and a simple molecular orbital – crystal field model analysis, performed to understand the nature of bonding environment around the spin carrying copper center,
9 {Cu4O14(H2O)2}
Cu2'
Cu1' Cu1
Cu2
Cu O H2O
Figure 1.6. Ball and stick representation of central {Cu4O14(H2O)2} unit of Na11Cs[Cu4(H2O)2(B-α-GeW9O34)2] (GeCu4) .
indicates a moderate (~30%) contribution from the ligand oxygen orbitals to the ground state. Chapter 4 details these studies. Iron(III) containing clusters have been receiving much attention since the discovery of the single molecule magnet (SMM) [(C6H15N3)6Fe8O2(OH)12]
Br7(H2O)Br·8H2O, commonly known as Fe8 [68]. All of the eight Fe(III) ions in Fe8 are antiferromagnetically exchanged coupled to yield a spin-frustrated ST = 10 ground state.
Zero-field splitting of the M levels in the ST = 10 manifold creates an anisotropy barrier ST to magnetization reversal. For this reason each molecule behaves analogously to a ferromagnetic particle with a net magnetic moment corresponding to ST = 10. SMMs are attractive as potential elements of memory storage at the molecular level [26] because of their characteristic ability to behave as tiny magnets at this level.
10
K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2]
WO6 CuO6
Figure 1.7. Polyhedral representation of K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2] (SiCu5) silicotungstate. Counter, potassium, ions have been omitted for clarity.
Zipse’s efforts to prepare an iodine analog of Fe8 led to the synthesis of
[(C6H15N3)4Fe4O(OH)5]I7·2.5H2O (Fe4), which exhibited SMM-like behavior not in its ground state, but in its excited state [69]. With this information in mind, Kortz et al. attempted to incorporate Fe(III) ions into POM framework [5]. Their synthetic interests resulted in the discovery of a novel Fe(III) containing POM GeFe6, and Chapter 5 discusses its magnetic characterization in detail. 10- The structure of GeFe6 can be described as two lacunary [A-α-GeW9O34]
Keggin moieties linked via a trigonal-prismatic Fe6(OH)9 fragment leading to a structure
with idealized D3h symmetry (see Figure 1.9).
11
{Cu5(OH)4(H2O)2}
Cu3 Cu4
Cu5
Cu1 Cu2
Cu OH H2O
Figure 1.8. Ball and stick representation of the copper connectivity in SiCu5. The Cu5 center is projecting towards the reader. Polyhedral cap oxygen atoms completing the copper ion coordination have been omitted for clarity.
From the point of view of magnetism, this compound can be considered as two spin- frustrated Fe(III) (S = 5/2) triangles connected antiferromagnetically via hydroxo bridges
(cf. Figure 1.10) to give a total spin singlet, ST = 0, ground state. A high-temperature model has been used to extract spin-exchange coupling constant of J = –12 cm-1 from the magnetic susceptibility data. Room temperature EPR spectra at different frequencies
show one broad isotropic Lorentzian peak at giso = 1.992 whose signal intensity drops steadily to zero, without any significant change in the peak-to-peak width, consistent with a diamagnetic ST = 0 ground state.
12
Na7Cs4[Fe6(OH)3(A-α-GeW9O34(OH)3)2]
WO6 GeO4
FeO6
Figure 1.9. Polyhedral representation of mixed-salt germanotungstate Na7Cs4 [Fe6(OH)3(A-α-GeW9O34(OH)3)2](GeFe6). Counter cations have been omitted for clarity.
Cobalt is a magnetically interesting element in the sense that the octahedral Co(II) 7 4 (3d ) ion possesses a considerable orbital moment in the electronic T1 ground state. Most of the Co(II) compounds exhibit spin-3/2 magnetism at 77 K and above [70]. However, the large spin-orbit coupling constant of Co(II) (λ ~ –180 cm-1 for the free-ion) splits the 4 T1 state into a set of three levels with degeneracies 2, 4, and 6 [58,70]. At temperatures below 30 K, only the ground Kramers doublet is significantly populated and even though this is a spin-orbit doublet, almost all the Co(II) compounds known to date are characterized with an effective spin 1/2 ground state. Magnetic susceptibility, EPR and Inelastic Neutron Scattering (INS) results clearly indicate the anisotropic nature of this Kramers doublet [71-74].
13
{Fe (OH) } 6 9
Fe4 Fe3 Fe3 ′
Fe2
Fe1 Fe1′
Fe OH
Figure 1.10. Ball and stick representation of the hexa-iron(III) unit, {Fe6(OH)9} of GeFe6.
The importance of Co(II) ion, as discussed above, along with the ability of the di- 8– lacunary [γ-SiW10O36] to isomerize easily in aqueous-acidic medium upon heating to give oligomeric products with unexpected structures in the presence of first-row transition metal cations prompted Kortz et al. [6] to explore Co(II) interactions with the 8– silicotungstate anion [γ-SiW10O36] . Their explorations lead to the discovery of the first pentadecanuclear Co(II)-substituted tugstosilicate, Na5[Co6(H2O)30{Co9Cl2(OH)3
(H2O)9(β-SiW8O31)3}]·37H2O (SiCo15). This can be described as a satellite-like structure (cf. Figure 1.11), where the core of nine Co(II) ions, encapsulated by three unprecedented – II β-SiW8O31 fragments and two Cl ligands, is surrounded by six antenna-like Co (H2O)5, that are bound to terminal oxo groups. The central unit can be regarded as a set of three
Co(II) triangles connected via two μ3-chloro bridges (see Figure 1.12).
14
Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}]
WO6 SiO4 CoO6
Figure 1.11. Polyhedral representation of silicotungstate, Na5[Co6(H2O)30 {Co9Cl2 (OH)3(H2O)9(β-SiW8O31)3}] (SiCo15), containing fifteen cobalt(II) ions. Five counter Na+ ions have been omitted for clarity.
15
{Co9Cl2O21(OH)3(H2O)9}
Co2'
Co1a'
Co1' Cl1a Co1a'' Cl1 Co1'' Co1a
Co1 Co2 Co2''
Co O Cl
Figure 1.12. Ball and stick representation of central {Co9Cl2O21(OH)3(H2O)9} unit of
SiCo15.
Magnetic susceptibility and EPR studies of SiCo15 are discussed in detail in Chapter 6. The exchange interaction between the six circumferential Co(II) ions and the nine core Co(II) ions is neglected and the low-temperature magnetic susceptibility data
int ra -1 int er -1 has been fitted to a fully anisotropic Ising model ( J z = 17 cm , J z = –13 cm ) to gain insight into the nature of exchange interactions within the core. It is interesting to point out that while most of the Co(II)-POMs reported in the literature exhibit ferromagnetic interactions, the Co(II) nonamer core of SiCo15 exhibits both ferro- and antiferromagnetic interactions, resulting in a spin ST = ½ ground state. At low temperatures a broad asymmetric transition, associated with an anisotropic Kramers
16 doublet, is observed at all frequencies and, as the temperature increases above 70 K, it broadens beyond detection, indicating a magnetic spin ground state. The effective g- values of geff(xx) = 2.63, geff(yy) = 3.89 and geff(zz) = 5.72 are consistent with an effective spin ST = 1/2 Kramers doublet ground state for an octahedrally coordinated Co(II) ion. The magnetic susceptibility and EPR data presented through out the text have been analyzed using the electronic Hamiltonian given in Eq. (1.1).
H = Hexchange + Hspin (1.1) where, Hexchange accounts for the spin-spin exchange interactions and Hspin the quantum mechanical spin interactions. The Heisenberg-Dirac-van Vleck [58,70,75] (HDVV) spin Hamiltonian, given in Eq. (1.2), has been used to describe the spin-spin exchange interactions of all the clusters described in this work.
n H exchange = − 2 ∑ J Siik • Sk (1.2) ik => 1
th th Here, Jik is the exchange integral between the i and k ions, Si and Sk are the spins and n the number of paramagnetic ions of the cluster. We will use the convention Jik < 0 for antiferromagnetic interactions and Jik > 0 for ferromagnetic interactions. This work utilizes the general approach of fitting the temperature dependence of the magnetic susceptibility data in the presence of small external magnetic fields to obtain the sign and magnitude of the spin exchange coupling constant Jik. In the presence of external magnetic fields, the eigenvalues of the Hamiltonian (1.2) will be split into (2ST + 1) levels, where ST is the total spin of the cluster. If we define the z-axis to be the direction of the applied field magnetic field, the splitting effect can be accounted by adding a term gβB M to the eigenvalues of the Hamiltonian (1.2). The complete eigenvalue equation ST can then be given as:
Ei = E(ST) + gβB M (1.3) ST where, g is the Landé splitting factor, β the Bohr magneton, H the z-component of the applied field and M the eigenvalue of the z-component of total spin ST of the cluster. ST
17 The magnetic susceptibility per mole of cluster (χm), as shown in Eq. (1.5), is then obtained by substituting Eq. (1.3) in the van Vleck formula [55,70] (cf. Eq. (1.4)).
2)1( )2( )0( N ∑[(En kT )− 2En ] exp(− En kT ) n χ = )0( (1.4) ∑exp()− En kT n
)0( )1( )2( th Here, N is the Avogadro number; En , En and En are the n level energies respectively, in zero-field, first- and second-order Zeeman coefficients; k the Bolztmann constant and T the temperature in Kelvin.
M 2 e− SE T /)( kT 22 ∑ ∑ ST Ng β ST M S χ = T (1.5) m − SE T /)( kT kT ∑ 2( ST + )1 e ST
Here the summations are over all the allowed values of ST and M . Further ST simplification of Eq. (1.4) leads to the commonly used [58,70,75] HDVV equation (1.6).
S (S + 2)(1 S + )1 e− SE T /)( kT 22 ∑ T T T Ng β S χ = T (1.6) m − SE T /)( kT 3kT ∑ 2( ST + )1 e ST
H spin, written in Eq. (1.7), is the standard EPR spin Hamiltonian [76-78] that describes the Zeeman splitting of spin levels within the system.
⎛ 2 S(S + )1 ⎞ 2 2 n H spin = βB g S – βngnB I + I A S + D⎜ Sz − ⎟ + E(Sx − S y ) + O (1.7) ⎝ 3 ⎠
Here, βn is the nuclear magneton; H is the applied field; g is the electron g-tensor and gn is the nuclear g-factor (usually isotropic); S and I are the electron and nuclear spin operators; A is the hyperfine tensor; D and E are the axial and rhombic zero-field splitting parameters, respectively. While the first and second terms in Eq. (1.6) represent the
Zeeman splitting of MS and MI levels, the third term represents the electron-nuclear hyperfine interaction and On accounts for higher order terms. The various terms in
18 equations (1.2), (1.6) and (1.7) will be adjusted to suit the spin cluster and the corresponding theoretical approach will be described in detail throughout the text.
1.3. Organization
The dissertation is organized as follows. Chapter 2 summarizes our studies on
AsCu3 while Chapter 3 discusses the teranuclear cluster GeCu4. Chapter 4 presents the penta-copper(II) substituted POM SiCu5, with Chapter 5 detailing the GeFe6 cluster. A novel pentadecanuclear Co(II)-POM, SiCo15, will be described in Chapter 6 and the major results and conclusions in Chapter 7. Appendix A contains the instrumental details of the locally developed high frequency EPR spectrometer and Appendix B gives the details of the theoretical model employed for magnetic susceptibility data analysis of
SiCu5. Finally, Appendix C lists the computer codes used to generate the spin state energies of GeFe6 and SiCo15.
19 CHAPTER 2
MAGNETIZATION AND EPR CHARACTERIZATION OF A TRI-COPPER(II) COMPLEX: A MODEL SPIN-FRUSTRATED TRIANGULAR SYSTEM
This chapter presents the synthesis, structure and magnetic characterization of a
tri-copper(II) containing arsenotungstate Na9[Cu3Na3(H2O)9(α-AsW9O33)2]·26H2O
(AsCu3). As a first step in studying spin-frustrated systems of different nuclearities, we
chose AsCu3 because it contains an equilateral triangle of antiferromagnetically 2+ 2+ interacting Cu ions, the simplest possible spin-frustrated lattice. In addition to a (Cu )3 + triangle, the central belt of AsCu3 has three Na ions. The molecular structure of AsCu3 can thus be described as a sandwich-type where the central belt of three Cu2+ and three + Na ions is sandwiched between two {α-AsW9O33} Keggin fragments. The strength of 2+ -1 exchange interaction between any two Cu ions of AsCu3 is shown to be ~ 1.4 cm (~2 K). The weak antiferromagnetic exchange interactions result in a doublet spin ground
state with a low-lying excited triplet state at ~6 K. A typical EPR spectrum of AsCu3 contains three well-resolved peaks which can be assigned to a total spin ST = 3/2, where the central peak of the triplet is overlapped by the singlet peak arising from an ST = 1/2 spin state. As the temperature decreases the intensity of the excited state transitions, relative to the ground state, decreases, indicating that ST = 1/2 spin-state is in fact the ground state. However, we were unable to attain low enough temperatures to depopulate completely the excited spin ST = 3/2 state. The ground and excited spin states are, respectively, characterized by spin Hamiltonian parameters: ST = 1/2, g|| = 2.117 ± 0.005
and g⊥ = 2.254 ± 0.005 and ST = 3/2, g|| = 2.060 ± 0.005, g⊥ = 2.243 ± 0.005, D = 230 ± 5 -1 2+ G (0.023 cm ). It is shown that the unpaired electron on each Cu ion of AsCu3 resides
in a 3 d 22 orbital, consistent with its square-pyramidal coordination environment with − yx axial elongation at each Cu2+ site. This compound should serve as a model for further studies of spin-frustration, as discussed in the conclusions.
20 2.1. Introduction
Detailed studies of the spin-frustrated lattices are of high interest in the field of molecular magnetism [57,58,79-82]. Toulouse was the first one to introduce the concept of spin-frustration [83] and, as he stated, “spin-frustration is a phenomenon where topological constraints prevent neighboring spins from adopting a configuration with every bond energy minimized”. The simplest case is any lattice based on an equilateral triangular arrangement of antiferromagnetically coupled spins. When the strength of the exchange interaction between any two nearest neighbors is equal, it is apparent that only two of the three spin constraints can be satisfied simultaneously. One of the interesting properties of the spin-frustrated compounds is that their unpaired electrons have several degenerate energy states with respect to their spin orientations [57,58]. With the impetus of obtaining detailed experimental data on unpaired spin interactions of spin-frustrated lattices, we set out to find a simple, structurally well-characterized model triangular system. Copper(II) compounds are expected to provide good examples of frustrated lattices not only because they are readily available but also because Cu2+ ion has spin S = ½ configuration and as mentioned above, triangular lattices of S = ½ ions are the simplest examples of frustrated-lattices. The class of AsIII-containing polyoxotungstates has been reported earlier [84-86]. The presence of a lone pair of electrons on the heteroatom does not allow the closed Keggin unit to form, and therefore, many structures could not be easily predicted. However, structures of some arsenotungstate(III) species have been elucidated. The first copper-containing derivative of this type was structurally characterized in 1982 by Robert and coworkers [87]. Single-crystal X-ray analysis of the potassium salt of [Cu3(H2O)2(α- 12- 2+ AsW9O33)2] revealed a sandwich-type structure with a triangle of Cu ions linking 9- two [α-AsW9O33] units. Surprisingly, the three copper ions were not equivalent, because only two of them had a terminal water molecule, resulting in square-pyramidal coordination, whereas the third Cu2+ ion exhibited square-planar coordination. The
authors identified a glide of one AsW9 subunit with respect to the other, which they
21 explained to be a result of lone-pair/ lone-pair repulsion of the two AsIII atoms [87]. The
symmetry of the anion was reduced to Cs. 2+ Recently, when Kortz et al. reacted Na9[α-AsW9O33] with Cu ions in aqueous solution and determined the structure of the resultant sodium salt of the copper- containing arsenotungstate(III), they did not observe any distortion in the polyanion 12- structure [88]. The polyanion [Cu3(H2O)3(α-AsW9O33)2] exhibited D3h symmetry, indicating that all three copper centers were equivalent. Therefore we chose to study the 2+ polyoxotungstate Na9[Na3Cu3(H2O)9(α-AsW9O33)2] (AsCu3) with its (Cu )3 equilateral triangle as a model spin-frustrated system [1].
2.2. Synthesis and Experimental Details
2.2.1. Synthesis. Kortz et al. synthesized [88] the precursor polyanion Na9[α-
AsW9O33]·19.5H2O according to the published procedure [86]. A 12.1 g (6.8 mmol)
sample of CuCl2·2H2O was dissolved in 50 mL of H2O, and then 10.0 g (4.1 mmol) of
Na9[α-AsW9O33]·19.5H2O was added. The solution was refluxed for 1 h and filtered after it cooled (pH6.2). Slow evaporation at room temperature led to large green crystals of
Na9[Cu3Na3(H2O)9(α-AsW9O33)2]·26H2O (AsCu3) suitable for X-ray diffraction.
3 2.2.2. X-ray Crystallography. Crystals of AsCu3 (0.2 × 0.16 × 0.14 mm ) were mounted on a glass fiber for indexing and intensity data collection at 173 K on a Siemens SMART CCD single-crystal diffractometer using MoKα radiation (λ = 0.71073 Å). SHELXS86 and SHELXL93 were used to solve the structure and to locate the atoms, while structural refinement was done using the SADABS program [89]. Crystallographic data for AsCu3 are summarized in Table 2.1.
22 Table 2.1. Crystal Structure Data for Na9[Na3Cu3(H2O)9(α-AsW9O33)2] (AsCu3).
emp formula AsCu1.5H35Na6O50.5W9 α(deg) 90 fw 2806.2 β (deg) 109.4050(10) crystal size (mm3) 0.2 × 0.16 × 0.14 γ (deg) 90 3 space group (No.) P21/m (11) vol (Å ) 4426.3(5) a (Å) 13.4989(9) Z 2 b (Å) 20.7463(14) temp (°C) -100 c (Å) 16.7571(11) wavelength (Å) 0.71073
2.2.3. dc Magnetic Susceptibility Measurements. Magnetic susceptibility (χ)
measurements of AsCu3 were carried out using a Quantum Design MPMS-XL SQUID magnetometer. Polycrystalline powder samples of 75.35 mg mass were used for data collection over the temperature range of 1.8-200 K at 1000 G. The data were then corrected for contributions from the sample holder, sample diamagnetism using Klemm constants [90] and temperature-independent paramagnetism (TIP) using a value of 6×10-5 emu/mol per Cu(II) ion [58].
2.2.4. Powder and Single crystal EPR Meaurements. Polycrystalline powder EPR spectra
of AsCu3 were recorded using a Bruker Elexsys-500 spectrometer at the X-band (ν ~ 9.5 GHz) and Q-band (ν ~ 34 GHz) in the 4–300 K temperature range. The temperature was controlled with an Oxford continuous flow liquid He cryostat and was monitored using Oxford instruments ITC 503. The magnetic field was calibrated using a built in NMR teslameter and the frequency was monitored with a digital frequency counter. W-band (ν ~ 95 GHz) measurements were conducted at the high-field electron magnetic resonance facility at the National High Magnetic Field Laboratory in Tallahassee [91,92] and the instrumental details are given in Appendix A. In all experiments the modulation amplitudes and microwave power were adjusted for optimal signal intensity and
23 resolution and all EPR spectra were simulated using Bruker’s Simfonia and Xsophe programs.
2.3. Molecular Structure
III The tri-copper(II) substituted As -dimer Na9[Cu3Na3(H2O)9(α-AsW9O33)2] 9- + ·26H2O (AsCu3) consists of two [α-AsW9O33] Keggin moieties linked by three Na ions 2+ and three Cu ions resulting in a sandwich-type structure with idealized D3h symmetry + (see Figure 2.1). Each Na is bound to four µ3-oxygen atoms and two terminal water molecules, in cavities separating adjacent copper ions, as shown in Figure 2.2. The octahedral coordination geometry and the bond lengths (Na1–O, 2.456 - 2.4807 Å; Na2– O, 2.339 - 2.494 Å) indicate that the three sodium ions are tightly bound in the central belt. Two of the three copper centers present in the central belt are crystallographically inequivalent, which inevitably results in two different Cu····Cu separations (cf. Figure 2.2). Both types of Cu2+ ions are in square-pyramidal coordination geometries, where the basal plane is formed by polyhedral cap oxygen atoms while the fifth coordination site is occupied by a water molecule. The observed equatorial and axial Cu–O bond lengths and the O–Cu–O bond angles, as listed in Table 2.2, are consistent with a Jahn-Teller distorted Cu2+ ion with axial elongation. Neglecting the minor differences in the equatorial bond lengths around Cu1 and Cu2(2′) ions (cf. Table 2.2), the Cu2+ ion site
symmetry can be assigned as C , which makes the 3 d 22 orbital the spin carrier. 4v − yx
Table 2.2. Axial and equatorial bond lengths (Å) and angles (deg) around Cu atoms in Na9[Na3Cu3(H2O)9 (α-AsW9O33)2] (AsCu3).
Cu1–O Cu2–O O–Cu1–O O–Cu2–O Equatorial 1.912 - 1.918 1.909 - 1.949 89.1 - 90.4 88.9 - 90.5 Axial 2.371 2.390 88.0 - 99.2 88.5 - 100.1
24
Na9[Na3Cu3(H2O)9(α-AsW9O33)2]
Na Cu As H2O WO6
Figure 2.1. Combined polyhedral and ball and stick representation of Na9[Na3Cu3(H2O)9 + (α-AsW9O33)2] (AsCu3). Nine counter Na ions have been omitted for clarity.
25
Central {Na3Cu 3(H2O)9O12} fragment
Cu Na Na 4.696 Å 4.696 Å
Cu 4.689 Å Cu
Na Cu Na O H2O
Figure 2.2. Ball and stick representation of central belt {Na3Cu3(H2O)9O12} of AsCu3. Cu····Cu distances are given in Angstroms (Å) and counter sodium ions have been omitted for clarity. The oxygen atoms shown in red are part of the polyhedral cap.
26 2.4. Magnetic Susceptibility
2.4.1. Theoretical models
1 1
J J J J1 1
J 2’ 2 2’ J2 2
(a) (b)
Figure 2.3. Spin-exchange models for AsCu3: (a) Equilateral triangle (b) Isosceles triangle. Numbering corresponds to Figure 2.2.
The experimental magnetic susceptibility data of AsCu3 has been analyzed in terms of two spin-exchange models viz. equilateral and isosceles triangle. As described in 2+ section 2.3, there are two types of Cu ions per AsCu3 molecule. The equilateral triangle model shown in Figure 2.3(a) neglects the small difference (0.007 Å) in Cu····Cu separation between Cu1 and Cu2(2′) ions, while the isosceles triangle model shown in Figure 2.3(b) considers this difference between Cu1 and Cu2(2′) ions. Given the fact that
Cu1 and Cu2(2′) ions are in very similar oxygen ligand environments (four µ3-oxygen atoms and a terminal water molecule) with similar equatorial and axial bond lengths and bond angles, the approximation of an equilateral triangle is not too unreasonable. For the equilateral spin-exchange scheme shown in Figure 2.3(a), the isotropic Heisenberg exchange Hamiltonian can be written as:
Hexchange = –2J [S1 S2 + S2 S2′ + S1 S2′] (2.1)
th where, J is the exchange coupling constant and Si the spin operator on i ion.
27 Following Kambe vector-coupling method [93], we define S22′ = S2 + S2′ and ST = S22′ +
S1 and rearrange the Eq. (2.1) as in Eq. (2.2) with eigenvalues given in Eq. (2.3).
2 2 2 2 Hexchange = –2J [(ST) – (S1) – (S2) – (S2′) ] (2.2)
E(ST, S1, S2, S2′) = –J [ST (ST + 1) – S1 (S1 + 1) – S2 (S2 + 1) – S2′ (S2′ + 1)] (2.3)
2+ 9 For each Cu ion (3d ), since S1 = S2 = S2′ = ½, Eq. (2.3) transforms into Eq. (2.4), which can then be used to calculate spin-exchange energies corresponding to different 2+ spin states. Table 2.3 lists these energies along with the possible ST values for a (Cu )3 triangle.
E(ST) = –J [ST (ST + 1) – 9/4] (2.4)
The molar magnetic susceptibility (χm) for AsCu3 is then obtained by substituting the energies listed in Table 2.3 into Heisenberg-Dirac-van Vleck Eq. (2.5) [58,70,75] and is given in Eq. (2.6).
S (S + 2)(1 S + )1 e− SE T /)( kT 22 ∑ T T T Ng β S χ = T (2.5) m − SE T /)( kT 3kT ∑ 2( ST + )1 e ST
Ng 2 β2 ⎡1+ 5e 3( J kT ) ⎤ 2.6 χm = ⎢ 3( J kT ) ⎥ ( ) 4kT ⎣⎢ 1+ e ⎦⎥
Here, N is the Avogadro number, g the average g-value, β the electron Bohr magneton, k
the Boltzmann constant and T the temperature in kelvin. An expression for χm as a function of temperature, T, for the isosceles triangle model can be derived in a similar way, where we replace equations (2.1) – (2.3) by equations (2.7) – (2.9), appropriate for an isosceles model.
Hexchange = –2J1 [S1 S2 + S1 S2′] –2J2 [S2 S2′] (2.7)
2 2 2 2 2 2 Hexchange = –2J1 [(ST) – (S22′) – (S1) ] –2J2 [(S22′) – (S2) – (S2′) ] (2.8)
28 Table 2.3. Possible spin states and their energies for equilateral and isosceles triangle models. The energies are calculated, respectively, from Eq. (2.4) and Eq. (2.10).
Spin exchange energies
n S22′ ST Equilateral Isosceles
1 0 1/2 3J/2 3J2/2
2 1 1/2 3J/2 2J1 – J2/2
3 1 3/2 -3J/2 –J1 – J2/2
E(ST, S22′, S1, S2, S2′) = –J1 [ST (ST + 1) – S22′ (S22′ + 1) – S1 (S1 + 1)]
–J2 [S22′ (S22′ +1) – S2 (S2 + 1) – S2′ (S2′ + 1)] (2.9)
E(ST, S22′) = –J1 [ST (ST + 1) – S22′ (S22′ + 1) – 3/4] –J2 [S22′ (S22′ +1) – 3/2] (2.10)
In Eq. (2.9) S22′ can take values from |S2 - S2′| to S2 + S2′ and ST from |S22′ - S1| to S22′ + S1 9 2+ and Eq. (2.10) is obtained from Eq. (2.9) by using S1 = S2 = S2′ = ½ for 3d Cu ion.
Considering that S22′ takes values from |S2 - S2′| to S2 + S2′ and ST from |S22′ - S1| to S22′ +
S1, the possible spin states, (S22′, ST), can be written as: (0, 1/2), (1,1/2) and (1,3/2). Energies corresponding to these spin states, calculated from Eq. (2.10), are also listed in Table 2.3. Finally, as shown in Eq. (2.11), an expression for the molar magnetic susceptibility can be obtained by applying Eq. (2.5) to the energies listed in Table 2.3.
2 2 3( J / kT ) (2( J −J ) kT ) Ng β ⎡1+10e 1 + e 1 2 ⎤ 2.11 χm = ⎢ 3( J / kT ) (2( J −J ) kT ) ⎥ ( ) 4kT ⎣⎢ 1+ 2e 1 + e 1 2 ⎦⎥
It can be seen from Table 2.3 that the spin states (0,1/2) and (1,1/2) are degenerate in the equilateral triangle case, making either Cu2 or Cu2′ a ‘spin-frustrated’ center, whereas they are separated by 2(J2 – J1) in the isosceles case. When the exchange coupling constant J is antiferromagnetic i.e. J < 0, the degenerate spin states (0,1/2) and (1,1/2) are the ground states for the equilateral triangle. Similarly, for the isosceles triangle when J1 and J2 are antiferromagnetic and |J2| > |J1|, (0,1/2) is the ground state,
29
1 1 1
JAF JAF JAF JAF JAF JAF
2′ 2 2′ 2 2′ 2 JAF JAF JAF (a) (b) (c)
(S22′, ST): (0, 1/2) (1,1/2) (1,3/2)
Figure 2.4. Schematic of the spin arrangement corresponding to the spin states, (S22′, ST): (a) (0,1/2) (b) (1, 1/2) and (c) (1, 3/2). Numbering corresponds to Figure 2.2. The double headed arrow shown between (a) and (b) implies the degeneracy of the two states in the equilateral case.
Energy
(1,3/2) (1,3/2)
3J J1 + 2J2
(1,1/2)
–2J1 + 2J2 (0,1/2) (1,1/2) (0,1/2)
Equilateral Isosceles
triangle triangle
2+ Figure 2.5. Spin state spectra of equilateral and isosceles triangle models for (Cu )3 triangle of AsCu3. Spin states are labeled as (S22′, ST). Energies of the excited spin states with respect to the ground states are also shown.
30
Figure 2.6. Plot of χmT vs T for Na9[Cu3Na3(H2O)9(α-AsW9O33)2] (AsCu3) at an external magnetic field, B, of 0.1 Tesla. Solid line represents the theoretical fit to the equilateral triangle model described in section 2.4.1.
where as for |J1| > |J2|, (1,1/2) will be the ground state. A schematic of spin configurations pertaining to the equilateral case is depicted in Figure 2.4. The degeneracy of two ST = 1/2 spin states is represented by a double headed arrow and the copper ion at 2′ site experiences the spin-frustration. The spin state energy levels governed by equations (2.4) (equilateral case) and (2.10) (isosceles case) are schematized in Figure 2.5.
2.4.2. Experimental Data Analysis.
Figure 2.6 shows the observed temperature dependence of χmT for AsCu3. χmT remains nearly constant at ~1.36 emu·K·mol-1 in the temperature region 260 – 70 K and then steadily decreases to ~0.53 emu·K·mol-1 at 1.8 K, which is indicative of the admixture of both ST = 1/2 and 3/2 spin states. A decrease in the χmT with decreasing
31 temperature is indicative of the presence of antiferromagnetic exchange interactions. An estimate of the exchange coupling constant J is obtained by fitting the experimental χmT vs T data to the equilateral triangle model expression given in Eq. (2.6). The agreement between the theoretical curve (solid line in Figure 2.6) and measured data is quite -1 satisfactory. The best least-squares fit is achieved with J = -1.38 ± 0.01 cm , gave = 2.212
± 0.001. This g-value is nearly consistent with the isotropic, giso, value of 2.208 ± 0.001 obtained from EPR measurements (vide infra) within experimental error. In order to consider the crystallographic inequivalence of the two of the three copper ions in AsCu3, we also attempted to fit the χmT vs T data to the isosceles triangle model given in Eq. (2.11). However, due to the similar magnetic environment around all three Cu2+ ions, fits could not be improved by introducing two spin exchange coupling 2+ constants J1 and J2. Hence, we will consider the (Cu )3 triangle of AsCu3 as equilateral
for the rest of the discussions. In AsCu the copper 3 d 22 orbitals, which contain the 3 − yx unpaired electrons, are directed along the Cu–Oeq bonds. Therefore the stabilization of the ST = 1/2 and ST = 3/2 spin states must involve indirect electronic coupling pathways. The available indirect pathway for the magnetic exchange interaction between any Cu2+ ions in AsCu3 is via six bonds involving two tungsten and three oxygen atoms of each 2+ AsW9O33 fragment (see Figure 2.1). Hence, we expect the interaction between the Cu ions to be very weak. This is supported by the small magnitude of the spin exchange coupling constant J ~ -1 cm-1. The negative sign of J indicates the presence of 2+ antiferromagnetic intra-trimer coupling between the three Cu ions of AsCu3. As -1 mentioned earlier, the χmT value at 1.8 K is ~0.53 emu·K·mol and, while we were unable to attain low enough temperature to ascertain the expected χmT value of 0.458 -1 emu·K·mol corresponding to giso = 2.21 for the spin doublet ground state, our conclusion is considered well supported.
32 2.5. EPR Spectroscopy
Additional verification of the disposition of the various spin-spin interactions, and also the zero-field splitting D, was obtained through EPR measurements as discussed
below. EPR spectra of AsCu3 were analyzed using the spin Hamiltonian shown in Eq. (2.12).
Hspin = βB•g•ST + ST •D•ST (2.12)
Here, β is the electron Bohr magneton, B the external applied magnetic field, g the Landé
g-factor, ST the total spin operator and D the zero-field splitting parameter. As mentioned 2+ in section 2.4.2, the (Cu )3 triangle will be treated as equilateral with possible spin states 63,65 ST = 1/2 and ST = 3/2. Hyperfine structure due to Cu nuclei is not resolved in our EPR spectra, most likely because the rate of spin exchange process is higher than the hyperfine splitting and hence will be neglected in our analysis of the experimental EPR data. Also, we do not consider J here because the variable-frequency EPR analysis shows no other effects that could be related to the exchange interaction. Figure 2.7 shows a diagram of the energy levels splitting as a function of the magnetic field (B) applied parallel to the crystal c-axis of AsCu3 and a typical powder EPR spectrum at 34 GHz. The arrows denote the ∆ M = ±1 Zeeman transitions expected from ground state spin-doublet and ST excited spin-quartet states. Specifically, the numbers 1, 2, 3 and 4 correspond to the transitions given in Eq. (2.13):
|ST, M > → |ST, M +1> ST ST 1 = |1/2, -1/2> → |1/2, 1/2> 2 = |3/2, -3/2> → |3/2, -1/2> 3 = |3/2, -1/2> → |3/2, 1/2> 4 = |3/2, 1/2> → |3/2, 3/2> (2.13)
33
(a)
(b)
2+ Figure 2.7. (a) Zeeman energies of (Cu )3 triangle of AsCu3 for B || c-axis. Arrows denote the expected EPR transitions. (b) 4 K Q-band (υ = 33.96 GHz) powder EPR spectrum of AsCu3. Unprimed numbers correspond to figure (a) and the primed numbers represent the perpendicular transitions.
34
Figure 2.8. Comparison of the experimental angular dependence of Na9[Cu3Na3(H2O)9(α-AsW9O33)2] (AsCu3) with the theory for the ST = 3/2 state. The solid lines represent the calculated line positions, and the circles are experimental data from Q-band EPR spectra at 4 K.
Single crystal EPR experiments were also carried out on AsCu3 at 34 GHz for
accurate determination of the magnetic parameters of excited spin quartet, ST = 3/2. The crystal c-axis was aligned 10º with respect to the applied field direction to get maximum separation between the three fine structure peaks. X-ray diffraction studies confirm that
this direction is the molecular trigonal (C3) axis. Figure 2.8 shows the angular variation of
the three Zeeman transitions, expected from a ST = 3/2 state, with respect to the crystal orientation in the applied magnetic field (B) at 4 K. The angular dependence data were successfully reproduced by the method of Abragam and Bleaney [76] (solid line in Figure
2.8) with the parameters: g|| = 2.060 ± 0.005, g⊥ = 2.243 ± 0.005, |D| = 230 ± 5 G. At an angle θ = 55 ± 5º the three resonance lines collapse to single line based on the (3cos2θ - 1) dependence of the zero-field (D) splitting.
35 When the applied frequency is increased to the W-band (~95 GHz), the g-tensor components further separate, providing more resolution (Figure 2.9) and hence more 2+ information about the magnetic parameters of (Cu )3 triangle ground spin-state. The most intense lines (labeled 1 and 1 ) correspond to ∆ M = ±1 Zeeman transitions arising ′ ST from ST = 1/2 ground state. Because of the weak spin-exchange interaction (~6 K), even at 4 K, the Zeeman transitions (labeled 2, 3, 4 and 2′,3′,4′) corresponding to excited ST = 3/2 state are also observed, however with relatively smaller intensities. While the parallel component of the ST = 1/2 Zeeman transition is well resolved, the perpendicular component falls partially under the first perpendicular fine structure line of the quartet state. The simulation of the 4 K, 95 GHz EPR spectrum with the spin Hamiltonian parameters, g|| = 2.117 ± 0.005 and g⊥ = 2.254 ± 0.005, is considered to be quite satisfactory (lower panel of Figure 2.9). The temperature dependence of the W-band spectrum is shown in Figure 2.10. As the temperature is lowered, the parallel peak centered at B = 3.15 T (g|| = 2.117) grows in intensity, thus confirming that the doublet spin state is in fact the ground state. At 4 K the fine structure line intensity shifts into the outermost parallel and perpendicular peaks, indicating a positive sign for the D value, and therefore that M = ±1/2 of ST = 3/2 is the lower energy state. ST Spin-Hamiltonian parameters derived from EPR spectra can be correlated to the Cu2+ ion coordination environment in the following way. First, we note that the observed g-factors (g in Eq. (2.12) are molecular g-factors which can be related to individual Cu2+ ion g-values [1,94,95]. The extracted Cu2+ ion g-values can then be used to understand 2+ the nature of orbital ground state of Cu ions. The geometrical arrangement of CuO5 groups in AsCu3 is such that their (x, y) plane is parallel to the molecular C3 axis while their z-axes are perpendicular to the C3 axis. If we define g(m) as the g-matrix for a CuO5 group and g in Eq (2.12) as the molecular g-matrix and assume each Cu2+ ion has the same g||(m) and g⊥(m) values, the relation between them can be written as [1,94,95]:
g|| = g⊥(m) (2.15a)
g⊥ = [g||(m) + g⊥(m)]/2 (2.15b)
36
Figure 2.9. Experimental (solid line) and simulated (dashed line) W-band (ν = 93.165 GHz) powder EPR spectra of Na9[Cu3Na3(H2O)9(α-AsW9O33)2] (AsCu3) at 4 K. The numbering corresponds to Figure 2.7. The numbers 2,3 and 4 represent parallel peaks, while the numbers 2′, 3′ and 4′ represent perpendicular peaks.
37
Figure 2.10. Temperature dependence of the W-band (ν = 93.165 GHz) EPR spectrum of Na9[Cu3Na3(H2O)9(α-AsW9O33)2] (AsCu3). Numbers correspond to Figure 2.7. Primed numbers represent perpendicular Zeeman transitions and the unprimed ones represent parallel transitions.
Using g|| = 2.060 and g⊥ = 2.243, g||(m) and g⊥(m) values can be, respectively, calculated as 2.426 and 2.060. The g||(m) > g⊥(m) > ge pattern proves that the unpaired electron on 2+ each Cu ion resides in the 3 d 22 orbital [76], in agreement with the crystal structural − yx data.
2.6. Summary
Magnetic susceptibility and EPR measurements (34 and 95 GHz) were used to explore the magnetic properties of a tri-copper(II) substituted arsenotungstate,
Na9[Cu3Na3 (H2O)9(α-AsW9O33)2]·26H2O (AsCu3). The three copper(II) ions in AsCu3
38 form a quasi-equilateral triangle which is sandwiched between two diamagnetic
{AsW9O33} Keggin hosts. Analysis of magnetic susceptibility data in terms of an isosceles triangle model has been attempted, to account for the crystallographic inequivalence of two of the three Cu2+ ions. However, a satisfactory fit was obtained only when the two exchange coupling constants J1 and J2 (cf. Figure 2.3(b)) were set equal. -1 The best-fit values are: gave = 2.212, J1 = J2 = J = -1.38 cm (-1.99 K). While the 2+ negative sign for exchange coupling constant implies that Cu ions in AsCu3 are antiferromagnetically exchange coupled, its small magnitude suggests a weak interaction. 2+ 2+ Since all three Cu ions are magnetically equivalent, the (Cu )3 triangle can be considered as an equilateral triangle and hence an example of a spin-frustrated system. Powder and single crystal Q-band (~34GHz) EPR studies from room temperature down to 4 K show a set of three peaks arising from the excited triplet. The Zeeman transition from the ground state doublet is overlapped by the |3/2, -1/2> → |3/2, 1/2> transition, where the label represents |ST, M > → |ST, M +1>. Magnetic parameters ST ST of the excited spin-triplet state were obtained from the powder and single crystal spectral -1 simulations as: g|| = 2.060 ± 0.005, g⊥ = 2.243 ± 0.005, |D| = 230 ± 5 G (0.023 cm ). Using these molecular g-values, we were also able to extract individual Cu2+ ion g- values, g(m) as: g||(m) = 2.426, g⊥(m) = 2.060. The pattern g||(m) > g⊥(m) > ge shows that
the unpaired electron is in 3 d 22 orbital, consistent with the square-pyramidal geometry − yx of the Cu2+ ion. Even though the major contribution to the 4 K, 95 GHz EPR spectrum is from the ground state spin doublet, we do see excited triplet transitions with relatively small intensities. We attribute this observation to the low energy difference (~6 K) between ground ST = 1/2 spin state and the excited spin ST = 3/2 state. The ground state spin-doublet has been successfully simulated with the spin Hamiltonian parameters: g|| =
2.117 ± 0.005 and g⊥ = 2.254 ± 0.005. In conclusion, our studies show that these polyanions are some of the few examples where one is able to fully characterize by EPR the ground state as well as the excited spin levels [1]. We believe that this study will elicit further theoretical, as well as synthetic, investigations.
39 CHAPTER 3
2+ EPR AND MAGNETISM OF A (Cu )4 SUBSTITUTED GERMANOTUNGSTATE: A TRIPLET GROUND STATE
This chapter describes the structure and magnetic properties of a novel dimeric
germanotungstate Na11Cs2[Cu4(H2O)2(GeW9O34)2]Cl·31H2O (GeCu4). X-ray single- crystal analysis shows that GeCu4 crystallizes in the triclinic system, space group P⎯1(2), with a =12.234 Å, b =12.383 Å, c =15.449 Å, α = 100.04°, β = 97.03°, = 101.15°, and Z 10- = 1. The polyanion consists of two lacunary B-α-[GeW9O34] Keggin moieties linked via a rhomb-like Cu4O16 group leading to a sandwich-type structure. The Cu4O16 rhomb can also be viewed as two triangles sharing an edge and for our study of spin-frustrated triangles, GeCu4 seemed to be a suitable system. Magnetic susceptibility studies yield the -1 -1 exchange parameters J1 = −11 ± 1 cm , and J2 = −82 ± 1 cm , where J1 and J2 are the exchange coupling constants, respectively, along the edge and short diagonal of the rhomb, implying that the ground state is a degenerate diamagnetic ST = 0 and paramagnetic ST = 1 spin states. Detailed EPR studies on GeCu4 at temperatures down to 2 K and variable frequencies (9.5 GHz to 95 GHz) confirm the spin-triplet ground state with spin Hamiltonian parameters: g|| = 2.4303 ± 0.0005 and g⊥ = 2.0567 ± 0.0005 and
|A||| = 4.5 ± 0.5 mT, with D = -12 ± 1 mT. A seven line pattern on each of the fine structure peaks indicates that the two unpaired electrons corresponding to the ground state are delocalized on only two of the copper(II) ions. Correlation of these spin parameters with the molecular structure shows that the copper(II) ions (Cu1 and Cu1′) along the long diagonal of the rhomb, which are related by C2 symmetry axis, carry the spin. Therefore, the single ion and observed molecular Hamiltonian parameters are Cu Cu Cu Cu related as: (g )|| = g|| = 2.4303 and (g )⊥ = g⊥ = 2.0567 and (A )|| = 8.8 mT. (g )|| >
40 Cu (g ) pattern implies that the 3 d 22 orbital is the ground state for the unpaired electron ⊥ − yx
on each Cu2+ ion.
3.1. Introduction
Phosphotungstates and silicotungstates are probably the most intensively studied systems among the family of heteropolyoxotungstates, because they exhibit a large variety of lacunary species that can be usually synthesized in one- or two-step procedures 7- 7- 9- 9- 8- in high yields (e.g. α-PW11O39 , -PW10O36 , A-PW9O34 , B-PW9O34 , α-SiW11O39 , - 8- 10- SiW10O36 , A-SiW9O34 ) [62]. The number of germanium-containing polyoxoanions is very small and most of the published work is based on the Keggin-type 4- germanododecamolybdate, [GeMo12O40] , and the analogous germanotungstate, 4- [GeW12O40] [96,97]. In 1993 Liu et al. reported on the trivanadium-substituted 7- [GeW9V3O40] [98]. The multiple transition-metal-substituted germanotungstates known in the POM literature until recently are the series of trisubstituted, monomeric n- 3+ 2+ germanotungstates, A-α-[M3(H2O)3GeW9O37] (n = 7, M = Cr ; n = 10, M = Mn , Co2+, Ni2+, Cu2+) reported by Qu et al. [99] and a titanium-substituted species A-β- 14- [Ti6O3(GeW9O37)2] [100]. However, the proposed formulas and structures of the transition-metal-substituted species mentioned above remain to be confirmed by X-ray diffraction. Sandwich-type polyoxometalates containing four transition-metal centers based n- V V IV on either Keggin type B-α-[XW9O34] (X = P , As , Si ) [101-110] or Wells-Dawson 12- type B-α-[X2W15O56] fragments [71,111-113], constitute a well-known class of 10- compounds. The first example of this type, [Co4(H2O)2(PW9O34)2] , was reported by Weakley et al. [101], where as Evans et al. were the first to report on a As(V) [102] 10- derivative of the Keggin type, [Zn4(H2O)2(AsW9O34)2] . Kortz et al. reported on the first 12- 2+ 2+ examples of sandwich-type silicotungstates, [M4(H2O)2(SiW9O34)2] (M = Mn , Cu , Zn2+) [109] and recently, Bi et al. extended the As(V) Keggin series by several
41 10- 2+ 2+ 2+ 2+ 2+ 2+ 2+ compounds, [M4(H2O)2(AsW9O34)2] (M = Mn , Co , Ni , Cu , Zn , Cd , Fe ) [110].
The polyoxotungstate Na11Cs2[Cu4(H2O)2(GeW9O34)2]Cl·31H2O (GeCu4) has been synthesized for the first time and its synthesis is based on reaction of the three
components GeO2,Na2WO4, and CuCl2 in an aqueous, acidic medium. The isolated yield for GeCu4 is 71%, which indicates that formation of the (B-α-GeW9O34) fragment in a heated aqueous acidic medium is strongly favored. Most likely, synthesis of this tri- lacunary building block is further facilitated by the presence of transition-metal ions and the formation of the dimeric polyanion GeCu4. This chapter describes the structural and magnetic characterization of this tetra-copper-substituted germanotungstate and has been reported by us recently [2].
3.2. Experimental Details
3.2.1. Synthesis. Na11Cs2[Cu4(H2O)2(GeW9O34)2]Cl·31H2O (GeCu4) was synthesized by
Kortz et al. [2]. 0.334 g (1.96 mmol) of CuCl2·2H2O, 0.0928 g (0.888 mmol) of GeO2
and 2.64 g (8.00 mmol) of Na2WO4·2H2O were dissolved in 40 mL of 0.5 M sodium acetate buffer (pH 4.8) with stirring. This solution was then heated to 90 °C for 1 hr and cooled to room temperature. Single crystals suitable for X-ray crystallography were obtained by layering the above solution with a dilute CsCl solution and evaporating slowly (yield: 1.8 g, 71%).
3.2.2. X-ray Crystallography. Crystals of GeCu4 were mounted on a glass fiber for indexing and intensity data collection at 173 K on a Siemens SMART CCD single-crystal diffractometer using Mo Kα radiation (λ = 0.71073 Å). SHELXS86 and SHELXL93 were used to solve the structure and to locate the atoms, while structural refinement was
done using the SADABS program [89]. Crystallographic data for GeCu4 are summarized in Table 3.1.
42 Table 3.1. Crystal Data and Structure Refinement for Na11Cs2[Cu4(H2O)2(GeW9O34)2]Cl (GeCu4).
emp formula ClCs2Cu4Ge2H66Na11O101W18 α(deg) 100.041(2) fw 5945.5 β (deg) 97.034(2) space group (No.) P⎯1 (2) γ (deg) 101.153(2) a (Å) 12.2338(17) vol (Å3) 2231.3(5) b (Å) 12.3833(17) Z 1 c (Å) 15.449(2) temp (°C) -100 wavelength (Å) 0.710 73
3.2.3. Magnetic and EPR measurements. Magnetization and magnetic susceptibility
measurements of GeCu4 were carried out on powder samples using a Quantum Design MPMS-XL SQUID magnetometer over the temperature range 1.8 – 200 K up to 7 T. Experimental data were corrected for diamagnetism, using Klemm constants [90] and temperature independent paramagnetism (TIP) value of 6×10-5 emu/mol per Cu(II) ion [58].
Polycrystalline powder EPR spectra of GeCu4 were recorded using a Bruker Elexsys-500 spectrometer at X-band (~ 9.5 GHz) in the temperature range 4 – 300 K. Variable temperatures were achieved by using an Oxford temperature controller ITC 503 and magnetic field was calibrated using an NMR gauss meter and a Phase Matrix EIP 548B digital frequency counter. High-frequency EPR experiments were conducted on a custom-built variable frequency EPR spectrometer at the National High Magnetic Field Laboratory in Tallahassee [91,92] and the instrumental details are given in Appendix A. In all experiments the modulation amplitudes and microwave power were adjusted for optimal signal intensity and resolution and all the EPR spectral simulations were obtained with the Bruker XSophe program. Experimental parameters were used with the appropriate spin Hamiltonian (vide infra) to generate the simulated spectrum, until a visually satisfactory comparison was seen.
43 Table 3.2. Selected Bond distances (Å) and Angles (deg) for Na11Cs2[Cu4(H2O)2(B-α-Ge W9O34)2]Cl (GeCu4).
Cuint–O(Ge) 1.973–1.986 Ge···Ge 5.732
Cuint–O(W) 1.931 Cuint···Cuint′ 3.069 * Cuint–O(W,Cu) 2.406–2.427 Cuint···Cuext 3.174, 3.176
Cuext–O(Ge) 2.364 Cuext···Cuext′ 5.559
Cuext–OH2 2.346 Cuext–O(Ge)–Cuint 93.3, 93.7
Cuext–O(W) 1.969–1.974 Cuint–O(Ge)–Cuint′ 101.7
Cuint–O(W,Cu) 1.966–1.988 Cuext–O–Cuint 91.9, 92.1
* Cuint represents the copper ions along short diagonal of the rhomb while, Cuext represents the copper ions along long diagonal of the rhomb.
3.3 Crystal and Molecular Structure
The dimeric germanotungstate Na11Cs2[Cu4(H2O)2(GeW9O34)2]Cl (GeCu4)
crystallizes in the triclinic system with space group P⎯1 (2). GeCu4 consists of two 10- lacunary B-α-[GeW9O34] diamagnetic Keggin moieties linked via a rhomb like centrosymmetric Cu4O16 group leading to a sandwich-type structure with C2h symmetry, as shown in Figure 3.1. The central Cu4O16 group is made of four coplanar CuO6 octahedra sharing edges (see Figure 3.1(a)). This magnetic cluster shares seven oxygen 10- atoms with each tungstogermanate ligand, (GeW9O34) . Two water molecules complete the sixth coordination for copper ions along the long diagonal of rhomb, while polyanion cap oxygen atoms complete the octahedral coordination for copper ions along short
diagonal. Figure 3.2 shows the central {Cu4O14(H2O)2} unit. All four copper ions are in Jahn-Teller axially distorted octahedral environments, with their long axes parallel to each other. This fact will be useful in understanding the magnetic exchange interactions
between copper atoms (vide infra). Selected bond distances and angles of GeCu4 are listed in Table 3.2.
44 Na11Cs2[Cu4(H2O)2(B-α-GeW9O34)2]Cl
CuO6 WO6 GeO 4
(a)
Cu W Ge
O H2O
(b)
Figure 3.1. Molecular structure of Na11Cs2[Cu4(H2O)2(B-α-GeW9O34)2]Cl (GeCu4): (a) Polyhedral representation, (b) Ball and stick representation. Counter ions have been omitted for clarity purpose.
45
Central unit, {Cu4O14(H2O)2}, structure of GeCu4
Cu2'
Cu1' Cu1
Cu2
Cu O H O 2
Figure 3.2. Ball and stick representation of the central Cu4O16 unit, {Cu4O14(H2O)2}, of Na11Cs2[Cu4(H2O)2(B-α-GeW9O34)2]Cl (GeCu4).
3.4. Magnetic studies
3.4.1. Theoretical model
A cartoon of the spin exchange model for GeCu4 is shown in Figure 3.3. For a tetramer, the Heisenberg spin exchange Hamiltonian, can be written as:
H exchange = – 2J1 (S1 S2 + S2 S1′ + S1′ S2′ + S2′ S1) – 2J2 (S2 S2′) (3.1)
where, J1 is the exchange coupling constant along the side of the rhombus, J2 the
coupling constant along the short diagonal of the rhombus and Si the spin operator of the ith metal ion. The interaction between Cu1 and Cu1′ is neglected because of the relatively large distance (~5.6 Å) compared to either rhombus edges (~3.2 Å) or short diagonal (~3.1 Å).
46 2′ J1 J1
1′ J2 1
J 1 J1 2
Figure 3.3. Diagram of the exchange coupling model for GeCu4. Numbering corresponds to Figure 3.2.
By defining S11′ = S1 + S1′, S22′ = S2 + S2′ and ST = S11′ + S22′ and following Kambe’s vector-coupling method [93] Eq. (3.1) can be rearranged as in Eq. (3.2) with eigenvalues given in Eq. (3.3).
2 2 2 2 2 2 H exchange = – 2J1 (ST − S − S ) - 2J2 (S − S − S ) (3.2)
E(S2, S4, ST) = – J1 [ST (ST + 1) – S11′ (S11′ + 1) – S22′ (S22′ + 1)]
– J2 [S22′ (S22′ + 1) – S2 (S2 + 1) – S2′ (S2′ + 1)] (3.3)
2+ 9 Since S1 = S2 = S1′ = S2′ = ½ for Cu (3d ) ions of GeCu4, Eq. (3.3) can be simplified as:
E(ST) = – J1 [ST (ST + 1) – S11′ (S11′ + 1) – S22′ (S22′ + 1)] – J2 [S22′ (S22′ + 1) – 3/2] (3.4)
From the definitions |S1 – S1′| ≤ S11′ ≤ S1 + S1′ and |S2 – S2′| ≤ S22′ ≤ S2 + S2′, we get 0 ≤ S11′
≤ 1 and 0 ≤ S22′ ≤ 1. Finally, calculation of the total spin ST using |S11′ – S22′| ≤ ST ≤ S11′ +
S22′, gives rise to two singlets (ST = 0), three triplets (ST = 1) and one quintet (ST = 2). Energies of these spin states are listed in Table 3.3. By substituting energies given in Table 3.3 into HDVV equation [58,70,75] shown in Eq. (3.5), molar magnetic susceptibility (χm) as a function of temperature (T) can be then be derived as in Eq. (3.6).
47 Table 3.3. Spin state energies of copper tetramer in GeCu4. See text for details.
# S11′ S22′ ST E(ST)
1 0 0 0 –3J2/2
2 0 1 1 –J2/2
3 1 0 1 –3J2/2
4 1 1 0 4J1 – J2/2
5 1 1 1 2J1 – J2/2
6 1 1 2 –2J1 – J2/2
S (S + 2)(1 S + )1 e− SE T /)( kT 22 ∑ T T T Ng β S χ = T (3.5) m − SE T /)( kT 3kT ∑ 2( ST + )1 e ST
⎛ 2Ng 22 ⎞⎛ A ⎞ ⎜ β ⎟ χm = ⎜ ⎟⎜ ⎟ (3.6) ⎝ kT ⎠⎝ B ⎠
2( J / kT ) 2( J +J / kT ) 4( J +J / kT ) where, g is the isotropic g-factor, A = 1+ e 1 + e 1 2 + 5e 1 2 ,
2( J / kT ) 6( J +J / kT ) 2( J +J / kT ) 4( J + J / kT ) B = 3 + 3e 1 + 6e 1 2 + 4e 1 2 + 5e 1 2 and rest of the constants have their usual meaning.
3.4.2. Magnetic susceptibility and magnetization
The temperature dependence of χmT of GeCu4 is depicted in Figure 3.4. χmT decreases exponentially up to 50 K, reaches a saturation value of ~0.94 emu K/mol G between 50 and 10 K, and then decreases until 1.8 K due to intermolecular interactions.
The individual metal ions of the tetrameric Cu4O16 unit interact with each other via Cu– O–Cu bridges (see Figure 3.2).
48
Figure 3.4. Plot of χmT vs T for Na11Cs2[Cu4(H2O)2(GeW9O34)2]Cl (GeCu4) at 0.1 Tesla. Solid line represents a least-squares fit to Eq. (3.6).
As shown in Figure 3.3, these interactions are described by two spin-exchange coupling constants J1 and J2, where J1 represents the interactions along the sides of the rhombus
while J2 represents interactions along the short diagonal of the rhombus.
Experimental χmT data has been fit to Eq. (3.6) using a least-squares method. As can be seen from Figure 3.4, a very satisfying description of the experimental data over the whole temperature range is obtained with the following set of parameters: J1 = –11 ± –1 –1 –1 1 cm , J2 = –82 ± 1 cm , giso = 2.24 ± 0.05 and Weiss constant θ = –0.035 ± 0.005 cm , where T in Eq. (3.5) has been replaced with (T-θ) to account for intermolecular interactions. The magnitudes of the exchange interactions can be understood from the structural features of the tetramer.
49
x 2′ z y
1′ 1
2
Figure 3.5. Geometry of the magnetic moiety Cu4O16, showing the orientation of the
3d 22 orbitals in the cluster. Color code and numbering corresponds to Figure 3.2. − yx
As mentioned earlier in section 3.3, CuO6 octahedra are distorted in such a way that their 2+ long axes are parallel. The axial elongation of the Cu ions results in the 3d 22 orbital − yx
ground state i.e. the unpaired electron on each copper(II) ion occupies the 3d 22 orbital − yx and Figure 3.5 shows the disposition of these orbitals in the tetramer. As can be seen from the figure, the diagonal exchange interaction, J2, is favored with respect to the edge
interaction, J , since the two 3d 22 orbitals are pointing toward the bridging -oxygen 1 − yx μ3 atoms, allowing for a larger overlap integral.
Figure 3.6 shows the energy level diagram of E/|J1| as a function of J2/J1 ratio, where the spin-states are labeled as (S11′, S22′, ST). It can be noticed that, for J2/J1 ≥ 2, the ground state of the cluster is formed by both singlet and triplet spin states. Thus, in view of our experimental J2/J1 ratio (~7.5), the ground state of GeCu4 is a combination of
(0,0,0) and (1,0,1) and the intermediate spin ground state (ST = 1) results from spin- frustration. A diagram of the spin alignment corresponding to the spin ground state is shown in Figure 3.7. The dominant short diagonal interaction forces the spins on Cu1 and Cu1′ to be frustrated.
50
Figure 3.6. Plot of E/|J1| as a function of the ratio J2/J1 for Na11Cs2[Cu4(H2O)2(GeW9 O34)2]Cl (GeCu4). The labels indicate (S11′, S22′, ST) values listed in Table 2. The vertical dashed line indicates the experimental J2/J1 ratio of 7.45.
-1 2′ -1 2′ -11 cm -11 cm-1 -11 cm -11 cm-1
-1 -1 1′ -82 cm 1 1′ -82 cm 1
-1 -1 -1 -1 -11 cm -11 cm -11 cm -11 cm 2 2
(S11′, S22′, ST) = (0, 0, 0) (S11′, S22′, ST) = (1, 0, 1)
Figure 3.7. Schematic of the spin arrangement corresponding to the degenerate ground spin-states (0, 0, 0) (left) and (1, 0, 1) (right) of GeCu4. Labels indicate (S11′, S22′, ST) and the numbering corresponds to figure 3.2.
51
Figure 3.8. Magnetization data for Na11Cs2[Cu4(H2O)2(GeW9O34)2]Cl (GeCu4 ) at 1.8 K. The solid line represents the least-squares fit to Eq. (3.6).
The magnetization M/Nβ as a function of H/T for GeCu4 is shown in Figure 3.8.
It reaches a saturation of (~2 µB) at 6 T. The following argument is used to explain the observed magnetization behavior [71]. The core rhombus like arrangement of metal ions can be viewed as being made up of two triangular units sharing a side. Hence, from a thermodynamic point of view a combined spin triplet and spin singlet ground state is equivalent to that resulting from two independent spin doublets. Accordingly, the magnetization data at 1.8 K have been fit to Eq. (3.7) considering two S = 1/2.
M = NgβSBS(η) (3.7) with
1 1 1 η BS ()η = (/1 S )[()S + 2 coth((S + 2)η)− 2 coth( 2 )] (3.8)
52 Here, BS(η) is the Brillouin function, η = gβH/kT, and the variables and constants have their usual meaning. The agreement between theory and experiment is satisfactory when giso = 2.17, in agreement with the EPR results (vide infra). This result strongly supports the nature of the ground state deduced by the magnetic susceptibility measurements.
3.5. EPR Spectroscopy
Variable frequency (9.5–200 GHz) EPR studies were conducted on a
polycrystalline powder sample of GeCu4 over a temperature range of 4-300 K. The EPR transitions arising from the ground state are expected to be entirely from the triplet, ST =
1, spin state as there is no contribution from the diamagnetic singlet ST = 0 spin state. The
4 K X-band (~9.3 GHz) EPR spectrum of GeCu4, shown in Figure 3.9, is in fact representative of spin ST = 1 ground state. The observed spectral features are the expected fine structure transitions for a powder spectrum of a spin triplet state. The experimental spectra at all frequencies and temperatures were simulated using the spin-Hamiltonian given in Eq. (3.9).
Hspin = βH g S + S D S + S A I (3.9)
Here, D is the zero-field splitting parameter, A the hyperfine coupling constant of 63,65Cu nucleus, I the nuclear spin operator, and rest of the constants and variables has their usual meaning. A representative simulation at 4 K and 9.5 GHz is also shown in Figure 3.9 and it can be seen that it is quite satisfactory. The low field, broader doublet is the parallel
feature with a g-value centered at g|| = 2.4303 ± 0.0005. The more intense, sharper lines originate from molecules oriented perpendicular to the applied magnetic field. The splitting between these two lines yields the zero-field splitting parameter (|D|) and is 12 ±
1 mT. The g-value associated with this doublet is g = 2.0567 ± 0.0005. With the use of the relation giso = (g|| + 2g⊥)/3, a giso value of 2.1811 was obtained from the EPR
experiments [76], which is in good agreement with giso = 2.17 obtained from the magnetization data at 1.8 K. The giso value of 2.24 obtained from the best fit to the χmT measurements, however, is larger by 3%.
53
(a)
(b)
Figure 3.9. (a) The experimental (black trace) and simulated (red trace) X-band EPR spectrum of Na11Cs2[Cu4(H2O)2(GeW9O34)2]Cl (GeCu4) at 4 K. Experimentally deduced parameters are used in the simulation. (b) A close-up of the hyperfine structure of both parallel fine structure transitions in the X-band EPR spectrum of GeCu4 at 4 K.
54 This may be due to the small thermal population of the excited states. The EPR and magnetization parameters were obtained at very low temperature where only the ground state should be populated thermally. A closer look at the parallel transitions reveals hyperfine structure associated with interaction of the unpaired electrons with the 63,65Cu 2+ nuclei. There are four Cu centers per GeCu4 molecule which would give a 13 line (2nI + 1) pattern should both unpaired electrons be delocalized over all copper atoms. This pattern should be observed on each of the fine structure transitions. However, if the two unpaired electrons are delocalized on two Cu2+ centers, the hyperfine coupling will be reduced significantly and the expected hyperfine splitting pattern would be 7 lines. A 7- line hyperfine splitting pattern is in fact observed (see Figure 3.9(b)) with a hyperfine coupling of |A||| = 4.5 ± 0.5 mT. No hyperfine structure is observed for the perpendicular lines as the splitting would be smaller. A lower limit of the electron spin-exchange dynamics has been determined to be 4.36×10-10 Hz based on the low-temperature X-band EPR results. At higher temperatures, the electron motion is faster and the observed dipolar interactions are averaged out as shown in Figure 3.10.
The experimental W-band (~94 GHz) EPR spectrum of GeCu4 is shown in Figure
3.11. The strong signal again represents the perpendicular transitions of the ST = 1 ground spin state. Resolution of the two transitions is not observed as the zero-field splitting |D| ~ 12 mT (observed at ~9.5 GHz) is smaller than the experimental line width (~38.0 mT) observed at ~94 GHz. Analysis of the parallel transitions over the temperature range from 4 to 100 K provides information about the sign of the D value. At 4 K, the low field transition has the most intensity, indicating a negative D value i.e. M = ±1 is the ST ground-state energy level.
As discussed in section 3.4.2, ground state of GeCu4 is made up of spin states
(0,0,0) and (1,0,1), where the labels represent (S11′, S22′, ST). Since the spin carrying Cu1 and Cu1′ are related by C2 symmetry axis, the observed molecular g-values are the single Cu ion g-values, i.e. g1,|| = g101,|| = 2.4303, g1,⊥ = g101,⊥ = 2.0567. Furthermore, (A )|| = Cu 2*(A ) = 8.8 mT. The pattern g > g implies that the 3 d 22 is the ground state for 101 || 1,|| 1,⊥ − yx Cu2+ ion, in agreement with its axially-elongated, octahedral coordination environment.
55
Figure 3.10. Temperature dependence of X-band spectrum of Na11Cs2[Cu4(H2O)2 (GeW9O34)2]Cl (GeCu4).
Figure 3.11. W-band spectrum of Na11Cs2[Cu4(H2O)2 (GeW9O34)2]Cl (GeCu4) at 4 K. Full resolution is not observed because the zero-field splitting is smaller than the experimental line width. Inset shows parallel peak enlarged.
56 3.6. Summary
The synthesis, structural and magnetic characterization of a tetra-copper(II) containing dimeric germanotungstate, Na11Cs2[Cu4(H2O)2(GeW9O34)2]Cl·31H2O
(GeCu4), have been described in detail. GeCu4, with its sandwich-type structure, not 10- only constitutes the first polyoxoanion containing the (B-α-GeW9O34) fragment but also represents the first example of a structurally characterized germanium-containing heteropolytungstate. In GeCu4, the four paramagnetic copper(II) ions are arranged as a rhombic Cu4O16 metal-oxo cluster, where the bridging μ2- and μ3-oxo groups act as super- exchange pathways. The magnetic susceptibility data have been analyzed in terms of two spin-exchange coupling constants J1 (along edge) and J2 (short-diagonal) with the values: -1 -1 J1 = −11 ± 1 cm , and J2 = −82 ± 1 cm , indicating that the copper(II) ions are antiferromagnetically coupled giving rise to a degenerate spin-singlet (ST = 0) and spin- triplet (ST = 1) ground state. X-band (9.5 GHz) EPR studies on GeCu4 over temperatures down to 4 K yield the spin Hamiltonian parameters for the paramagnetic ground state ST
= 1 as: g|| = 2.4303 ± 0.0005 and g⊥ = 2.0567 ± 0.0005 and |A||| = 4.5 ± 0.5 mT, with D = -12 ± 1 mT. Observation of 7-line hyperfine structure is consistent with the localization of two unpaired electrons, making up the ground state spin ST = 1, on the copper (II) ions along the long diagonal of the rhomb. Since these copper(II) ions are symmetry related, Cu the single ion g-values are the observed molecular g-values i.e. (g )|| = g|| = 2.4303 and Cu (g ) = g = 2.0567, in agreement with a 3 d 22 orbital ground state. When the ⊥ ⊥ − yx frequency is increased to 95 GHz, fine structure as well as hyperfine structure becomes unobservable due to the line broadening. Even though tetra-copper(II) containing n− V V IV polyoxotungstates [Cu4(H2O)2(XW9O34)2] (X = P , As , n = 10; X = Si , n = 12), similar to GeCu4, are known in the literature [104,109,110], GeCu4 is the only polyanion with a well-resolved hyperfine structure, suggesting that the spin-dynamics can be fine tuned by changing the heteroatom.
57 CHAPTER 4
MAGNETIC AND EPR PROBING OF THE SPIN GROUND STATE OF A COPPER(II) PENTAMER: A FIVE SPIN FRUSTRATED CLUSTER
This chapter details the synthesis, structural, magnetic and EPR characterization of a novel dimeric, penta-copper(II) substituted tungstosilicate K10[Cu5(OH)4(H2O)2(A-α-
SiW9O33)2] (SiCu5). This study was undertaken because SiCu5 has the potential to be a
model system for a 5-spin electronically coupled, spin-frustrated system. SiCu5 can be 6+ described as a {Cu5(OH)4(H2O)2} fragment embedded between two diamagnetic A-α-
SiW9O33 Keggin moieties. Analysis of the magnetic susceptibility and magnetization data 6+ implies that the copper ions in the pentameric core {Cu5(OH)4(H2O)2} of SiCu5 are -1 strongly antiferromagnetically coupled with coupling constants Ja = –51 ± 6 cm , Jb = – -1 -1 104 ± 1 cm and Jc = –55 ± 3 cm , where Ja, Jb represent in-plane copper-copper
interactions and Jc that of the apical copper with the plane ones. Furthermore, the ground
state is shown to be a frustrated spin ST = 1/2 state. Variable temperature and variable
frequency (upto 190 GHz) EPR measurements confirm the spin doublet (ST = 1/2) ground state which can be described with the spin-Hamiltonian parameters:
gzz = 2.4073 ± 0.0005, gyy = 2.0672 ± 0.0005, gxx = 2.0240 ± 0.0005, Azz = –340 ± 20 MHz (–0.0113 cm-1). The observed four-line hyperfine structure on the z-component of the spectrum indicates that the unpaired electron spin density is mainly localized on the spin-frustrated apical Cu2+ ion. Further analysis of the spin Hamiltonian parameters, obtained from EPR data, in terms of simple molecular-orbital – crystal-field theory shows
that the unpaired electron resides in a 3d 22 type molecular orbital ground state, with x − y ~30% contribution from oxygen ligands.
58 4.1. Introduction
The sandwich-type transition metal substituted polyoxometalates (TMSPs) represent the largest subclass of polyoxometalate (POM) family [114] To date the Weakley-, Hervé-, Krebs- and Knoth-type sandwich polyanions can be distinguished [114]. However, considering that formation of polyanions occurs via self-assembly, the discovery of new TMSPs with fundamentally novel structures continues to be a focus of ongoing research [55,114]. These synthetic efforts are often accompanied by attempts to incorporate a large number of paramagnetic transition metal ions in lacunary polyanion fragments, in order to obtain products with interesting magnetic properties [55]. Kortz’s group efforts to synthesize copper rich polyoxotungstates with unprecedented structures resulted in the discovery of a novel penta-copper(II) containing silicotungstate
K10[Cu5(OH)4(H2O)2(A-a-SiW9O33)2] (SiCu5) [3], whose structural details are described in Section 4.3. As a continuation of our study of different size spin-frustrated transition metal clusters, progression from a tri-nuclear cluster to a tetramer to a pentamer seemed interesting. Furthermore, the unusual square-pyramidal arrangement of five copper(II) ions in SiCu5 attracted our attention. It has potential to act as a promising model to study complex spin behavior, arising from competing magnetic interactions, in isolated clusters. Numerous complexes of Cu2+-containing, sandwich-type POMs have been reported to date. Interestingly, most of these polyanions are dimeric and contain three or four Cu2+ centers [1,2,88,109,110,115]. However, recently Mialane et al. described the tetrameric Cu14-containing tungstosilicate [116] and very recently Kortz et al. reported on 25- the wheel-shaped Cu20 tungstophosphate [Cu20Cl(OH)24(H2O)12(P8W48O184)] , which contains more divalent transition metal ions than any other polyoxometalate reported to date [117]. Even though copper(II) pentamer embedded in POM framework has not been reported until SiCu5, a few examples of penta-copper(II) clusters with organic ligands have been reported in the literature [118-122]. While most of these clusters have a planar arrangement of Cu2+ ions [119-122], clusters with square-pyramidal arrangement of Cu2+ ions are rare [118]. For example, the five copper atoms of the pentanuclear cluster
59 Cu5(OH)2(L)2(NO3)4·2.5H2O (hereafter Cu5) are arranged as a rectangular base pyramid
[118], similar to our SiCu5. The ligand H2L is 3,6-bis((4-methylpiperazino) methyl)pyrocatechol. Although both SiCu5 and Cu5 have a rectangular base pyramidal arrangement of Cu2+ ions, there are quite significant differences in the copper-copper connectivity. In SiCu5, the copper ions are connected via µ2-hydroxo (long edge of the rectangle), µ2-H2O and µ3-hydroxo (short edge of the rectangle) and µ3-hydroxo (apical copper to the base of the pyramid). On the other hand, in Cu5, the copper atoms at the short edges of the rectangle are bridged by a hydroxide while those at the long edges are bridged by the catecholate ligand and the apical copper is bridged to each of the other copper atoms by a catecholate oxygen [118].
The magnetic susceptibility data of Cu5 have been analyzed [118] as a sum of a monomer and two different dimers and it was found that the hydroxide-bridged coppers along the short edge of the rectangle experience strong antiferromagnetic exchange interactions of ca. -80 cm-1 and -145 cm-1 while the apical copper is more weakly coupled to the four others. The authors [118] attributed the weak interaction of apical copper with its four neighbors to the nonplanarity of the system. In other words, the large dihedral angle of ~129º, between the apical copper ion basal plane (that contains the magnetic
3d 22 orbital) and its four neighbor’s basal planes, is responsible for the reduced − yx coupling of apical copper ion. On the contrary, in SiCu5 we expect significant exchange interactions not only between apical copper and its neighbors because of the average dihedral angle of 52º but also between the copper ions along the long edges of the rectangle. In fact, we observe (vide infra) the antiferromagnetic exchange coupling to be in the order of -55 cm-1 and -51 cm-1, respectively.
60 4.2. Synthesis and Experimental Details
4.2.1. Synthesis. Kortz et al. [3] synthesized the trilacunary precursor K10[A-α-SiW9O34]
according to the published procedure [123]. A 0.50 g (0.16 mmol) sample of K10[A-α-
SiW9O34] was added with stirring to a solution of 0.076 g (0.44 mmol) CuCl2·2H2O in 20 mL 0.5 M sodiumacetate buffer (pH 4.8). This solution was heated to 80 ºC for 30 min. and then cooled to room temperature and filtered. Slow evaporation at room temperature resulted after about 1-2 weeks in green crystals of K10[Cu5(OH)4(H2O)2(A-a-
SiW9O33)2]·18.5H2O (SiCu5) that were filtered off and air-dried. Yield: 0.28 g (63%). [3]
4.2.2. X-ray Crystallography. A light-green block of SiCu5 with dimensions 0.20 x 0.20 x 0.16 mm3 was mounted on a glass fiber for indexing and intensity data collection at 173 K with a Bruker D8 SMART APEX CCD single-crystal diffractometer by use of Mo Kα radiation (λ = 0.71073 Å). SHELXL97 was used to solve the structure and to locate the atoms, while structural refinement was done using the SADABS program [89].
Crystallographic data for SiCu5 are summarized in Table 4.1.
Table 4.1. Crystal data for K10[Cu5(OH)4(H2O)2(A-a-SiW9O33)2]·18.5H2O (SiCu5).
emp formula Cu5H45K10O90.5Si2W18 α (°) 100.0840(10) fw 5567.6 β (°) 101.9270(10) crystal size (mm3) 0.20 x 0.20 x 0.16 γ (°) 103.3990(10) space group (No.) P-1 (2) vol (Å3) 4653.2(4) a (Å) 13.4108(7) Z 2 b (Å) 15.5496(8) temp. (°C) -100 c (Å) 24.1156(12) wavelength (Å) 0.71073
61 4.2.3. Magnetic Measurements. dc Magnetic susceptibility measurements were carried on
compacted powder samples of SiCu5 from 1.8-300 K at an external field of 0.1 T with a Quantum Design MPMS SQUID magnetometer. The data were corrected for the diamagnetism estimated from Klemm constants [90] and temperature independent paramagnetism (TIP) using a value of 6×10-5 emu/mol per CuII ion [58]. Magnetic
moment as a function of field has also been measured at 1.8 K on SiCu5 powder samples.
4.2.4. Powder EPR Measurements. Polycrystalline (powder) EPR spectra of SiCu5 were recorded at frequencies ranging from 34 to 190 GHz and in the 4–300 K temperature range. A Bruker Elexsys-500 spectrometer was used for Q-band (ν ~ 34 GHz) measurements, in which the temperature was controlled with an Oxford continuous flow liquid He cryostat and was monitored using Oxford instruments ITC 503. The magnetic field was calibrated using a built in NMR teslameter and the frequency was monitored with a digital frequency counter. The high frequency measurements were conducted at the high-field electron magnetic resonance facility at the National High Magnetic Field Laboratory in Tallahassee [91,92] and the instrumental details are given in Appendix A. In all experiments the modulation amplitudes and microwave power were adjusted for optimal signal intensity and resolution and all experimental spectra were simulated with locally-developed computer programs.
4.3. Molecular Structural Details
The dimeric polytungstate K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2] (SiCu5) consists 10- of two A-α-[SiW9O34] Keggin moieties which are linked via two adjacent W-O-W 6+ bonds and stabilized by a central {Cu5(OH)4(H2O)2} fragment leading to a structure
with idealized C2v symmetry (see Figure 4.1) [3,4]. The structure of SiCu5 can also be 16- visualized as an open Wells-Dawson polyanion [Si2W18O66] (first reported by Hervé and coworkers [124]) which has taken up the cationic copper-oxo cluster 6+ {Cu5(OH)4(H2O)2} .
62 K10[Cu5(OH)4(H2O)2(A-a-SiW9O33)2]
CuO6 WO6
(a)
W Si
Cu O
(b)
Figure 4.1. (a) Polyhedral representation of K10[Cu5(OH)4(H2O)2(A-a-SiW9O33)2] (SiCu5). (b) Ball and stick representation of SiCu5. Counter potassium ions have been omitted for clarity.
63 Central {Cu (OH) (H O) } fragment 5 4 2 2
Cu3 Cu4
O34C
O13C O24C
Cu5
O1CC O25C
Cu O H2O Cu1 Cu2 OC12
Figure 4.2. Ball and stick representation of the core square-pyramidal copper, {Cu5(OH)4(H2O)2}, arrangement of SiCu5. Cu5 is pointing towards the reader. Polyhedral cap oxygen atoms completing the octahedral coordination of Cu2+ ions are omitted for clarity.
Such an arrangement of oxo-bridged transition metal centers has not been reported before in polyoxoanion chemistry and hence the structural details of the unprecedented 6+ {Cu5(OH)4(H2O)2} fragment, as shown in Figure 4.2, are of interest. Further structural analysis indicates that all bridging oxo groups linking adjacent copper atoms in the central penta-copper(II) core are either mono- or diprotonated [125]. Specifically, the oxygen atoms O1CC, OC12, O25C and O34C are monoprotonated (OH) whereas oxygen
atoms O13C and O24C are diprotonated (H2O) (cf. Figure 4.2). Bond lengths and bond angles between the copper ions and the oxygen atoms mentioned above are listed in Table 4.2. The equatorial Cu–O distances range from 1.907 – 2.084(13) Å, where as the axial Cu–O distances are 2.280 – 2.387(13) Å. The octahedral coordination spheres of all
copper(II) centers are Jahn-Teller distorted, with axial elongation. If we approximate C4v as the site-symmetry at each Cu(II) site, then the ground state for the unpaired electron on
each Cu(II) ion is 3 d 22 oribtal. − yx
64 6+ Table 4.2. Bond distances (Å) and angles (º) for the central {Cu5(OH)4(H2O)2} fragment in K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2] (SiCu5).
Cu1 Cu2 Cu3 Cu4 Cu5 Cu–O–Cu O13C 2.280 2.374 85.0(5) OC12 1.945 1.922 128.4(6) O24C 2.302 2.366 83.6(5) O34C 1.952 1.908 129.3(7) O1CC 2.085 2.015 1.959 100.2(5) 122.6(6) 123.1(6) O25C 2.047 2.027 1.983 99.5(5) 122.8(6) 123.1(6)
6+ The Cu–O–Cu angles of the central {Cu5(OH)4(H2O)2} fragment range from 83.6 –
129.3(6)° and the Cu···Cu separations in SiCu5 range from 3.11 – 3.56 Å.
4.4. dc Magnetic susceptibility and Magnetization studies
Field scans have been performed on powder samples of K10[Cu5(OH)4(H2O)2(A- a-SiW9O33)2] (SiCu5) to evaluate the ground state spin. Figure 4.3 shows the experimental data at 1.8 K as M/Nβ vs B/T, where T is the temperature in Kelvin. It is seen that the magnetization reaches a saturation of ~1 Bohr magneton (BM) around 6 T, indicating the presence of one electron per SiCu5 molecule, i.e. spin S = ½ is the ground state, assuming g = 2.0. The data can be satisfactorily modelled over the entire field range using Eq. (4.1) with g = 1.949 ± 0.005.
M = NgβSBS(η) (4.1) with
1 1 1 η BS ()η = (/1 S )[()S + 2 coth((S + 2)η)− 2 coth( 2 )] (4.2)
65
Figure 4.3. Magnetization as a function of field at 1.8 K. Open circles represent the experimental data while the solid line represents the theoretical fit to Eq. (4.1). See text for details.
Here, N is the Avogadro number, g the g-value, β the electron Bohr magneton, BS(η) is the Brillouin function, S the spin, η = gβB/kT, B the external field, k the Boltzmann constant and T the temperature in Kelvin.
Figure 4.4 shows magnetic susceptibility data for SiCu5 as a plot of χmT vs T, where T is the temperature in Kelvin. χmT steadily decreases upon cooling from 1.15 emu K/mol at 300 K to 0.44 emu K/mol at 80 K and slowly saturates to 0.39 emu K/mol as the temperature further decreases to 1.8 K. Decrease in the magnetic moment as temperature decreases indicates the presence of antiferromagnetic exchange interactions. Comparison of the low-temperature saturation value (0.39 emu K/mol) to the calculated value of 0.41 emu K/mol for S = 1/2 and g = 2.1, implies that, in fact ST = 1/2 is the ground state.
66
Figure 4.4. Plot of χmT vs T for K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2] (SiCu5) at B = 0.1 Tesla.
To gain further knowledge about the ground and excited spin states and the strength of exchange coupling constants, experimental magnetic susceptibility data has been analysed in terms of Heisenberg exchange interactions. Following the numbering scheme in Figure 4.5, the isotropic spin-exchange Hamiltonian for SiCu5 can be given as:
H exchange = –2 [J12 S1 S2 + J24 S2 S4 + J34 S3 S4 + J13 S1 S3 + J15 S1 S5 +
J25 S2 S5 + J45 S4 S5 + J35 S3 S5] (4.3)
Considering the C2v symmetry of the pentamer, the above Hamiltonian can be re-written as:
H exchange = – 2Ja [S1 S2 + S3 S4] – 2Jb [S1 S3 + S2 S4]
– 2Jc [S1 S5 + S2 S5 + S4 S5 + S3 S5] (4.4)
67
Ja 3 4
Jc Jc 5 Jb Jb Jc Jc
1 2 Ja 6+ Figure 4.5. Spin-exchange coupling in {Cu5(OH)4(H2O)2} core of SiCu5, where numbering corresponds to Figure 4.2. Cu5 is projecting towards the reader and the double headed arrow on it represents the spin-frustration experienced by the unpaired electron spin on it.
where J12 = J34 = Ja, J13 = J24 = Jb and J15 = J25 = J35 = J45 = Jc. The Hamiltonian in Eq.
(4.4) gives rise to ten spin states corresponding to the total spin operator ST = S1 + S2 + S3
+ S4 + S5 viz. five doublets (ST = 1/2), four quartets (ST = 3/2) and one sextet (ST = 5/2). The eigenvalues associated with the Hamiltonian in Eq. (4.4), obtained by solving the 32 × 32 matrix (see Appendix B for details), are listed in Table 4.3. The molar magnetic susceptibility expression shown in Eq. (4.6) was then obtained by substituting the energies given in Table 4.3 in the Heisenberg-Dirac-van Vleck equation given in Eq. (4.5) [58,70,75].
S (S + 2)(1 S + )1 e− SE T /)( kT 22 ∑ T T T Ng β S χ = T (4.5) m − SE T /)( kT 3kT ∑ 2( ST + )1 e ST
68 Table 4.3. Eigenvalues associated with the spin exchange Hamiltonian for central copper pentamer {Cu5(OH)4(H2O)2}. See text for details.
# ST E(ST) # ST E(ST)
1 5/2 –Ja – Jb – 2Jc 6 1/2 2 2 Ja + Jb – 2 J a − J Jba + Jb
2 3/2 Ja – Jb – Jc 7 1/2 2 2 Ja + Jb + 2 J a − JJ ba + Jb
3 3/2 –Ja + Jb – Jc 8 1/2 Ja –Jb +2Jc
4 3/2 Ja + Jb – Jc 9 1/2 –Ja +Jb + 2Jc
5 3/2 –Ja – Jb + 3Jc 10 1/2 Ja + Jb + 2Jc
⎛ Ng 22 ⎞⎛ A ⎞ ⎜ β ⎟ χm = ⎜ ⎟⎜ ⎟ (4.6) ⎝ 4kT ⎠⎝ B ⎠
Here N is the Avogadro Number, g the Landé g-factor, β the electron Bohr magneton, k the Boltzmann constant, T the temperature in Kelvin, A = 35e(2x + 2y + 5z) + 10e(2y + 4z) +
2 2 2 2 10e(2x + 4z) + 10e(4z) + 10e(2x + 2y) + e(3z+2 x −xy+ y ) + e(3z−2 x −xy+ y ) + e(2y + z) + e(2x + z) +
2 2 e(z) and B = 3e(2x + 2y + 5z) + 2e(2y + 4z) + 2 e(2x + 4z) + 2 e(4z) + 2 e(2x + 2y) + e(3z+2 x −xy+ y ) +
(3z−2 x2 −xy+ y 2 ) (2y + z) (2x + z) (z) e + e + e + e , with x = Ja / kT, y = Jb / kT and z = Jc / kT. The experimental data were fitted to Eq (4.6) with g, Ja/k, Jb/k and Jc/k as fit parameters. As - shown in Figure 4.4, the least-squares fit is quite satisfactory and yields: Ja = –51 ± 6 cm 1 -1 -1 , Jb = –104 ± 1 cm , Jc = –55 ± 3 cm and g = 2.035 ± 0.002. The spin state spectrum along with the energies relative to the ground state is shown in Figure 4.6. The doublet -1 ground state is well separated from the first excited state (ST = ½) by ~70 cm (~101 K), which is consistent with our EPR results (vide infra).
69
Figure 4.6. Relative spin-exchange energies of SiCu . The color code is: S = 1/2 5 T (black), S = 3/2 (red) and S = 5/2 (blue). T T
The observed J values can be correlated with the molecular structure by considering the available super-exchange pathways between the Cu2+ ions. The magnetic
orbitals 3 d 22 on Cu1(3) and Cu2(4) interact via µ –hydroxo bridges (cf. OC12 and − yx 2 O34C oxygens in Figure 4.7), where the symmetry related Cu2+ ions are written in parentheses. As expected [126,127], the Cu1(3)–OC12(34C)–Cu2(4) bridging angle of -1 ~129º results in antiferromagnetic exchange coupling constant (Ja = –51 ± 6 cm ).
Similarly, the 3 d 22 orbitals on Cu1(2,3,4) also interact with 3 d 22 orbital of apical − yx − yx
Cu5 via µ3–hydroxo bridges with an angle of ~123º, thus giving rise to antiferromagnetic -1 exchange interactions (Jc = –55 ± 3 cm ). On the other hand, Cu1(2) and Cu3(4) interact
via both a µ2–OH2 and a µ3–OH, with bridging angles of about 84º and 100º, respectively, and therefore either ferromagnetic or antiferromagnetic interaction can be the dominant one [126,127].
70 Cu5 x y z
Cu H2O
O OH
x x
z y y z Cu(1,3) Cu(2,4)
2+ Figure 4.7. Relative orientation of equatorial and axial bonds of Cu ions in SiCu5. Choice of (x,y) is arbitrary, where as z axis is taken as the axial Cu–O bond.
Careful observation of coordination geometry around Cu1, Cu2, Cu3 and Cu4 from
Figure 4.7 reveals that the µ3–OH forms the equatorial bond, while µ2–OH2 is the
elongated axial bond for both Cu1(2) and Cu3(4). Since 3 d 22 is the orbital with the − yx
unpaired electron, super-exchange between Cu1(2) and Cu3(4) occurs mainly via the µ3–
OH pathway, making the antiferromagnetic interaction the dominate one (Jb = –104 ± 1 cm-1). The magnetic exchange parameters obtained in the present study are consistent with other penta-nuclear Cu2+ complexes reported in literature [118-122]. The spin arrangement on copper(II) ions is also shown in Figure 4.5, where Cu1, Cu2, Cu3, Cu4 are in the plane of paper and Cu5 is projecting out of the plane. The dominant antiferromagnetic exchange interactions in the plane align the spins anti-parallel, thus making Cu5 a spin-frustrated center.
71 4.5. High Frequency EPR studies
Q-band (34 GHz) as well as 95 and 190 GHz EPR measurements were carried out to complement our magnetic susceptibility measurements. Figure 4.8 shows 95 and 190 2+ GHz powder spectra of SiCu5 at 5 K and they are typical Cu spectra, with a four line hyperfine structure (Azz) on the low-field Zeeman peak (gzz). We assign it to the spin- 2+ frustrated apical Cu ion. Axx and Ayy were not resolved, implying that their magnitude is at least 1/3 of the observed linewidths. The minute high-field peaks marked as ‘∗’ are from impurities. As the temperature increases, the hyperfine structure broadens out and disappears at about 45 K, and finally the overall spectrum also broadens and becomes unobservable above 60 K (see Figure 4.9). Neither the g-values nor Azz exhibited any temperature dependence in the range investigated, implying that observed spectrum originates from a ground state, here ST = ½ as discussed above. Figure 4.10 shows a representative simulation at 95 GHz and 5 K, obtained using a Gaussian line shape with line-widths: ∆Bxx = 23 ± 2 mT, ∆Byy = 13 ± 2 mT and ∆Bzz = 7 ± 0.5 mT. The agreement between the observed and the simulated spectra is considered to be satisfactory. The fact that the spectra at all frequencies were reproduced satisfactorily with the Hamiltonian parameters: gzz = 2.4073 ± 0.0005, gyy = 2.0672 ± 0.0005, gxx = 2.0240 ± 0.0005, |Azz| = -1 340 ± 20 MHz (0.0113 cm ) implies that the ground state ST = 1/2 is well isolated, in agreement with the magnetic susceptibility data. We assigned a negative sign for Azz -1 based on the literature [128,129] i.e. Azz = –340 ± 20 MHz (–0.0113 cm ), as expected from the 3d → inner s electron-spin-polarization mechanism. The observed g-anisotropy is not surprising if we consider the elongated rhombic-octahedral stereochemistry around
Cu5 of SiCu5 (see Figure 4.11). The g- and A-values observed for our copper pentamer are consistent with the literature values reported [76,78,126-130] for a single octahedral oxygen co-ordinated Cu2+ ion with rhombic distortion and confirm that the unpaired electron resides in a
3d 22 orbital. − yx
72
(a)
(b)
Figure 4.8. Polycrystalline powder EPR spectra of K10[Cu5(OH)4(H2O)2(A-α-Si W9O33)2] (SiCu5) at 5 K and (a) 94.902 GHz (b) 191.162 GHz. The peak marked as ‘∗’ is from an impurity. See text for details.
73
Figure 4.9. Temperature dependence of powder EPR spectra of K10[Cu5(OH)4 (H2O)2(A- α-SiW9O33)2] (SiCu5) at 94.902 GHz.
As the Cu–O bonds are not purely ionic, we discuss below the relation between the spin Hamiltonian parameters and the nature of the chemical bonding around the apical Cu2+ ion (Cu5 center) in terms of a simple molecular-orbital – crystal-field model. Considering that the apical Cu2+ ion is in an all-oxygen ligand environment, the small 2+ differences in Cu5―Oeq bond lengths will be ignored and the site-symmetry of Cu will be taken as C4v. Unfortunately, our lack of resolution regarding the measurement of Axx 2+ and Ayy and the approximation of C4v site-symmetry for the apical Cu ion renders the following discussion to be only qualitative, but nevertheless instructive. Furthermore, we 2+ shall use the expressions [78,128-135] reported for a D Cu ion with 3d 22 ground 4h x − y state. This assumption is justified because Hathaway and Billing have shown [130] that the expressions for the g-values are the same for equivalent point groups, provided the
74
Figure 4.10. Experimental and simulated powder EPR spectra of K10[Cu5(OH)4 (H2O)2(A-α-SiW9O33)2] (SiCu5) at 94.902 GHz and 5 K. Simulation used a Gaussian line shape with line-widths: ∆Bxx = 23 ± 2 mT, ∆Byy = 13 ± 2 mT and ∆Bzz = 7 ± 0.5 mT.
ground state is identical. In other words, g-value expressions for D4, D4h, C4v and D2d symmetries will be the same, if the ground state of a metal ion is identical in all of the point-groups. Based on group theory, allowance for covalent bonding is made by combining the proper linear combination of ligand orbitals with the copper d-orbitals to give the wave functions of the form [78,128-136]:
75 2.339 Å
2.038 Å 2.044 Å
1.959 Å 1.983 Å 2.333 Å z Cu O OH x y
Figure 4.11. Co-ordination environment of Cu5 in K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2] (SiCu5). The bond lengths are given in Angstroms to show the approximate rhombic distortion present at the Cu centre. The choice of x- and y- axes is arbitrary and z-axis is projecting out of the plane of paper.
2 2 2/12 (x − y ) = d 22 + 1( − ) (oxygen) B1 α x − y α B1 2 2 2/12 3( z − r ) = βd 22 + 1( − β ) (oxygen) A1 3 −rz A1 (xy) = d + 1( − ) 2/12 (oxygen) B2 xy B2 (xz,yz) = δd + 1( − δ ) 2/12 (oxygen) E yzxz, E (4.7) When these wavefunctions are applied to the Hamiltonian of Abragam and Pryce [76,137] (cf. Eq. (4.8)), the magnetic parameters obtained [78,128-136] are given in Eq. (4.9).
Hspin = g||βBzSz + g⊥β(BxSx + BySy) + A||SzIz + A⊥(SxIx + SyIy) (4.8)
76 2 2 g|| = 2.0023 – 8λα γ / ∆Exy [4.9(a)]
2 2 g⊥ = 2.0023 – 2λα δ / ∆Exz,yz [4.9(b)]
2 A|| = P [–κ – (4/7)α + (g|| – 2.0023) + (g⊥ – 2.0023)] [4.9(c)]
2 A⊥ = P [–κ + (2/7)α + (11/14) (g⊥ – 2.0023)] [4.9(d)]
In the expressions 4.9(a) – 4.9(d), λ is the spin-orbit coupling constant for free ion, ∆Exy = -3 E – E 22 , ∆E = E – E 22 , P = 2.0023g (r ) and κ is the isotropic xy − yx xz,yz xz,yz − yx nβeβn av hyperfine (contact) term arising from the polarization of inner s electrons by the unpaired spin in the d-orbital.
The values for ∆Exy and ∆Exz,yz were determined by running the optical absorption 4 -1 of SiCu5 in aqueous solution. The spectrum consists of a broad peak around 1.2×10 cm and based on the literature, [130,138] taken as ∆Exy. The intense charge transfer 4 -1 transitions set in at ~2.5×10 cm with no hint of any shoulder. We therefore take ∆Exz,yz ≥ 2.5×104 cm-1. Based on λ = –828 cm-1 (free-ion value for Cu2+), P = 0.036 cm-1 (free- 2+ ion value for Cu ), κ = 0.33, g|| = gzz = 2.4073, g⊥ = (gxx + gyy) / 2 = 2.0456, A|| = Azz = –0.0113 cm-1 in the equations 4.6(a) – 4.6(c), the following values can be deduced for the bonding parameters α, γ, δ: α2 = 0.71, γ2 = 1.0, δ2 ≥ 0.92
These values are in reasonable agreement with other similar tetragonal Cu2+ complexes reported in the literature [78,128-136]. A value of 0.71 for α2 indicates a moderate (~ 30%) contribution from the oxygen orbitals.
4.6. Summary
A new penta-copper(II) containing silicotungstate K10[Cu5(OH)4(H2O)2 (A-a-
SiW9O33)2] (SiCu5), has been successfully characterized by magnetic and high field EPR 10- techniques in the solid state. SiCu5 can be considered as two A-α-[SiW9O34] Keggin
77 moieties linked via two adjacent W–O–W bonds and stabilized by a central 6+ {Cu5(OH)4(H2O)2} fragment leading to a structure with idealized C2v symmetry. The Cu(II) ions in the central fragment are arranged at the vertices of a rectangular based
pyramid and are connected via (µ2, µ3)-hydroxo and µ2-water groups. Analysis of the magnetic susceptibility data in the realm of isotropic Heisenberg
exchange interactions, reveal that the antiferromagnetic spin-state ST = ½ is the ground -1 -1 state. Using the exchange coupling constants Ja = –51 ± 6 cm , Jb = –104 ± 1 cm and Jc -1 = –55 ± 3 cm , where Ja, Jb represent in-plane copper-copper interactions and Jc represents apical copper interaction with in-plane ones, it can be calculated that the
ground state doublet is separated from the first excited spin ST = 1/2 doublet state by ~70 cm-1 (~101 K). Variable temperature (5–300 K) and variable frequency (9.5–190 GHz) EPR
spectra of polycrystalline powder samples of SiCu5 are representative of a spin doublet 6+ (ST = 1/2) ground state for the copper(II) pentamer, {Cu5(OH)4(H2O)2} . Observation of four line hyperfine structure on the z-component of the spectrum establishes that the unpaired electron is mainly localized on one Cu2+ ion and together with magnetic susceptibility results we assign the apical Cu2+ ion to be the carrier of unpaired electron spin density, thus making it the spin-frustrated center. EPR spectra were satisfactorily
simulated with the spin-Hamiltonian parameters gzz = 2.4073 ± 0.0005, gyy = 2.0672 ± -1 0.0005, gxx = 2.0240 ± 0.0005, Azz = –340 ± 20 MHz (–0.0113 cm ). The g-values are 2+ consistent with a 3d 22 type molecular orbital ground state, as expected for a Cu ion − yx in an elongated rhombic-octahedral co-ordination environment of oxygen atoms. A
qualitative analysis of the g- and Azz values in terms of molecular-orbital – crystal-field theory yields α2 = 0.71, where α is the molecular orbital coefficient of the ground state,
indicating a moderate (~ 30%) contribution from the oxygen orbitals. SiCu5, with its unprecedented structure, serves as a model for a complex spin-frustrated system with five metal centers.
78 CHAPTER 5
MAGNETIZATION AND EPR STUDIES OF AN IRON(III) HEXAMER: DIAMAGNETIC GROUND STATE WITH LOW LYING EXCITED STATES
This chapter details the structural and magnetic studies of an iron(III)-substituted tungstogermanate Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6). Our interest in 3+ GeFe6 arose from the fact that it has a highly attractive magnetic (Fe )6 core which could lead to high spin ground states, possibly even S = 15. Single-crystal X-ray analysis
showed that GeFe6 crystallizes in the monoclinic system, space group C2/m, with a =
36.981(4) Å, b = 16.5759(15) Å, c = 16.0678(15) Å, β = 95.311(3)°, and Z = 4. GeFe6 3+ consists of two (A-α-GeW9O34) Keggin moieties linked via six Fe ions, leading to a double-sandwich structure. The equivalent iron centers represent a trigonal prismatic 3+ (Fe )6 fragment, resulting in D3h symmetry for GeFe6. Magnetic susceptibility (χm) -1 measurements indicate a diamagnetic (ST = 0) ground state, with an average J ~ −12 cm and g = 2.00. EPR studies confirm that the ground state is indeed diamagnetic, since the EPR signal intensity steadily decreases without any line broadening as the temperature is lowered and becomes unobservable below ~50 K. The signal is a single broad peak at all frequencies (90−370 GHz), ascribed to the thermally accessible excited states. Its giso is 3+ 1.99251, as expected for a high-spin Fe -containing species, and supports the χm data analysis. Thus while our initial expectation of a very high-spin ground state were not realized, we discovered a system of two frustrated triangular clusters, with a diamagnetic ground state but thermally accessible excited states. Such systems are of current interest for studying quantum spin dynamics and spin entanglement. A preliminary report of this work has recently appeared [5].
79
5.1. Introduction
Over the past several decades the interest in polynuclear iron(III) compounds with oxygen-based ligation has increased significantly, due to their relevance in two fields, bioinorganic chemistry [139-144] and molecular magnetism [26,27,145]. Iron-oxo centers are found in several metalloproteins [139]. For example, hemerythrin [140,141], methane monoxygenase [140,142] and ribonucleotide reductase [143] are some of the enzymes with di-iron active metallosites, whereas the protein ferritin, responsible for iron storage, detoxification and recycling, can store up to 4500 ferric ions in an iron/oxide/hydroxide core [144]. Since the discovery of single molecule magnets (SMMs) [26,27,145], clusters with large spin ground states have become a strong focus of the research in molecular magnetism. SMMs are molecules that display slow magnetization relaxation rates and which, below a certain temperature, known as the blocking temperature TB, can function as single-domain magnetic particles of nanoscale dimensions [26,27,28,30,145-147]. One of the two conditions for a compound to behave as a SMM is that the cluster should possess a large ground state spin value, second being large and negative zero-field splitting parameter, D [26,27,28,30,145-147]. From this perspective, multi-nuclear iron-oxo clusters made of high spin iron(III) ions (3d 5, S = 5/2) are of interest because, with high enough nuclearity and appropriate topology they can sometimes possess large spin ground states [15,148-151]. Although the interactions 3+ between Fe(III) ions in these (Fe )x clusters are normally antiferromagnetic, spin frustration in certain topologies can result in large spin ground states [15,148-151]. One
such topology is a planar arrangement of two triangular {Fe3(μ3-O)} units joined together at two of their apices by hydroxo- or alkoxo or carboxylato-bridges [15,148-151]. Even though large spin ground state is one of the main conditions to exhibit SMM behavior,
Zipse et al. recently reported on an Fe(III) tetramer (diamagnetic ground spin ST = 0 state)
that exhibits SMM behavior in the excited triplet spin state (ST = 1) [69]. This information in combination with the fact that polyoxometalates (POMs) have the potential to accommodate large cluster sizes of interesting topologies, gave us the impetus to find an iron-substituted POM.
80
Even though some structures of Fe(III)-containing POMs have been reported in the literature [152-162], almost all of them are based on tungsto-phosphate [150-159],– silicate [160,161], and –arsenate [162] fragments and contain at most four Fe(III) ions [157-159,162]. Very recently, Kortz et al. described the synthesis, characterization, and
magnetic properties of the Weakley-type sandwich polyanions [M4(H2O)2(B-α- 12- II II II II GeW9O34)2] (M = Mn , Cu , Zn , Cd ) [2]. Following their core synthetic interests to synthesize POMs with electrocatalytic, and magnetic properties, they studied the 10- interaction of Fe(III) ions with the tri-lacunary [A-α-GeW9O34] precursor [163]. Their explorations lead to the discovery of a new iron-substituted germanotungstate
Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6). A few years ago Müller et al. reported on the synthesis and magnetic properties of a six-iron-substituted polyoxomolybdate with an apparent trigonal prismatic arrangement of the iron centers. However, in this case the trigonal prism is composed of two distant,
eclipsed Fe3 triangles on opposite sides of the polyoxoanion [164]. GeFe6, on the other hand, has six Fe3+ ions at the corners of a trigonal prism and is thus considered to be an interesting new compound worthy of detailed magnetic studies.
5.2. Synthesis and Experimental Details
5.2.1. Synthesis. The germanotungstate, Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2]·30H2O
(GeFe6), was synthesized in Kortz’s laboratory as follows. A 43.5 g (13.5 mmol) sample of K6Na2[GeW11O39]·13H2O [165] was dissolved in 400 mL of water with stirring. Then
22.5 g (162.8 mmol) of K2CO3 was added in small portions to this solution. The white solid product formed after stirring for about 50 min (pH = 9.5), was collected on a sintered glass frit, washed with saturated KCl solution (20 mL) and air-dried. A 0.15 g
(0.56 mmol) sample of FeCl3·6H2O was dissolved in 20 mL of 0.5 M sodium acetate buffer (pH 4.8), and then 0.52 g (0.17 mmol) of K8Na2[A-α-GeW9O34]·25H2O was added with gentle stirring. The solution was heated to 50 °C for about 1 h and filtered after it had cooled to room temperature. Then 0.5 mL of 1.0 M CsCl solution was added to the
81
red filtrate. Slow evaporation at room temperature led to 0.31 g (yield 58%) of a yellow crystalline product after about 1 week. [5]
5.2.2. X-ray Crystallography. A yellow, block-shaped crystal with dimensions 0.13 × 0.08 × 0.06 mm3 was mounted on a glass fiber for indexing and intensity data collection at 200 K on a Bruker D8 SMART APEX CCD single-crystal diffractometer by use of Mo Kα radiation (λ = 0.710 73 Å). SHELXL97 was used to solve the structure and to locate the atoms, while structural refinement was done using SADABS program [89]. Crystallographic data are summarized in Table 5.1.
Table 5.1. Crystal Structure Data for Cs4Na7[Fe6(OH)3(A-α-GeW9 O34(OH)3)2] (GeFe6).
emp formula Cs4Fe6Ge2H69Na7O107W18 α (°) 90 fw 6263.9 β (°) 95.311(3) crystal size (mm3) 0.13 × 0.08 × 0.06 γ (°) 90 3 space group (No.) C2/m (12) vol (Å ) 9807.1(16) a (Å) 36.981(4) Z 4 b (Å) 16.5759(15) temp. (°C) -73 c (Å) 16.0678(15) wavelength (Å) 0.710 73
5.2.3. dc Magnetic Susceptibility Measurements. Magnetic susceptibility measurements
were carried out on compacted powder samples of GeFe6 using a Quantum Design MPMS SQUID magnetometer in the temperature range of 1.8-300 K with an applied dc field of 0.1 Tesla. The data were corrected for molecular diamagnetism using Klemm constants [90].
82
5.2.4. EPR Measurements. Polycrystalline powder EPR spectra of GeFe6 were recorded at frequencies ranging from 90 to 370 GHz and temperatures 4 – 295 K at the high-field electron magnetic resonance facility at the National High Magnetic Field Laboratory in
Tallahassee [91,92]. The instrumental details of these custom-built EPR spectrometers are given in Appendix A. In all experiments the modulation amplitudes and microwave power were adjusted for optimal signal intensity and resolution and the Bruker XSophe EPR simulation program was used with the appropriate spin Hamiltonian to generate simulated EPR spectra.
5. 3. Molecular Structure
The novel dimeric tungstogermanate Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2]
(GeFe6) crystallizes in the monoclinic system, space group C2/m, with a = 36.981(4) Å, b
= 16.5759(15) Å, c = 16.0678(15) Å, β = 95.311(3)°, and Z = 4. GeFe6 consists of two 10- lacunary [A-α-GeW9O34] Keggin moieties linked via a trigonal-prismatic {Fe6(OH)9} fragment, leading to a structure with idealized D3h symmetry (see Figures 5.1 and 5.2).
Alternatively, the structure of GeFe6 can be described as a Keggin dimer, formed by 4- fusion of two hypothetical [Fe3(OH2)3(A-α-GeW9O34(OH)3)] monomers. The six FeO6 5 octahedra (3d , high spin) in GeFe6 are corner-sharing (cf. Figure 5.1a), which leads to a central, trigonal prismatic Fe6(OH)9 fragment (cf. Figure 5.2). Detailed structural analysis confirms that all oxo groups linking two iron(III) atoms are monoprotonated [125]. It can
be seen from Table 5.2 that the Fe3+ ions are fairly regularly coordinated octahedrally (Fe–O, 1.949-2.172(13) Å), and the Fe–O–Fe bond angles can be subdivided in inter- Keggin connectivities (131.8-134.3°) and intra-Keggin connectivities (139.5-142.3°). In the solid-state assembly of GeFe6 neighboring polyanions are oriented parallel to each other, resulting in layers in the ac plane that are offset to each other (see Figure 5.3).
However, separations of the closest magnetic Fe6 fragments are relatively large (>7.5 Å) so that intermolecular interactions are negligible.
83
Na7Cs4[Fe6(OH)3(A-α-GeW9O34(OH)3)2]
WO6 GeO4
FeO 6
(a)
W Ge Fe O
(b)
Figure 5.1. (a) Polyhedral representation of Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6). (b) Ball and stick representation of GeFe6. The cesium and sodium counter ions are omitted for clarity.
84
{Fe6(OH)9}
Fe4 Fe3 O34F Fe3′ O3Fe O34F′
O24F
O13F O13F′
O12F O12F′ O1Fe Fe2 Fe1 Fe1′
Fe OH
Figure 5.2. Ball and stick representation of the central {Fe6(OH)9} fragment in Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2]( GeFe6).
Table 5.2. Bond distances (Å) and Angles (deg) for the central {Fe6(OH)9} fragment in Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6).
Fe1 Fe2 Fe3 Fe4 Fe1′ Fe3′ Fe–O–Fe O1Fe 1.963(7) 1.963(7) 142.3(11) O12F 2.005(12) 2.000(12) 139.5(7) O13F 1.949(12) 1.956(12) 131.8(6) O3Fe 2.022(6) 2.022(6) 140.8(9) O24F 1.939(18) 1.953(17) 134.3(9) O34F 1.978(13) 1.974(13) 141.2(7)
85
WO6 GeO4
FeO6 FeO6
Figure 5.3. Packing arrangement of Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6) molecules along the crystallographic b-axis. Polyanions with green FeO6 octahedra are located in ac plane closer to the viewer than the polyanions with yellow FeO6 octahedra.
86
5.4. Magnetochemistry
5.4.1. Theoretical model
Table 5.3 lists the Fe···Fe distances in the {Fe6(OH)9} fragment of GeFe6 and Figure 5.4 schematizes the spin exchange model. In this model, we neglect the small differences in the Fe···Fe distances within each triangular unit and set the exchange
coupling constant as J1 for both the triangles. The exchange interaction between the
triangles is represented by the coupling constant J2. We also neglected the interactions between Fe(III) ions that are ~5 Å apart. The Heisenberg spin exchange Hamiltonian corresponding to the model depicted in Figure 5.3 can then be written as:
H exchange = –2J1 [S1 S2 + S1′ S2 + S1 S1′ + S3 S4 + S3′ S4 + S3 S3′]
– 2J2 [S1 S3 + S2 S4 + S1′ S3′] (5.1)
th where, Si is the spin operator on the i ion and J1 and J2 are defined earlier. Following Kambe vector-coupling method [93], we define:
S12 = S1 + S2, S121′ = S12 + S1′, S34 = S3 + S4, S343′ = S34 + S3′ and ST = S121′ + S343′ (5.2)
Using the relations in Eq. (5.2), we can rearrange the Eq. (5.1) as in Eq. (5.3).
2 2 2 2 2 2 2 2 H exchange = –J1 [(S121′) + (S343′) – (S1) – (S2) – (S1′) – (S3) – (S4) – (S3′) ]
2 2 2 – J2 [(ST) – (S121′) – (S343′) ] (5.3)
The eigenvalues of Eq. (5.3) can be written as:
E (ST, S121′, S343′, S1, S2, S3, S4, S5, S6) = –J1 [S121′ (S121′ + 1) + S343′ (S343′ + 1) – S1 (S1 + 1)
– S2 (S2 + 1) – S3 (S3 + 1) – S4(S4 + 1) – S5 (S5 + 1) – S6 (S6 + 1)]
– J2 [ST (ST + 1) – S121′ (S121′ + 1) – S343′ (S343′ + 1)] (5.4)
where, the intermediate spins S12, S121′, S34, S343′ and the total spin ST can take the values:
S12 = |S1 – S2| to S1 + S2 ; S121′ = |S12 – S1′| to S12 + S1′ ; S34 = |S3 – S4| to S3 + S4,
S343′ = |S34 – S3′| to S34 + S3′ and ST = |S121′ – S343′| to S121′ + S343′ (5.5)
87
Table 5.3. Fe···Fe distances in the central {Fe6(OH)9} fragment of Cs4Na7[Fe6(OH)3(A- α-GeW9O34(OH)3)2] (GeFe6).
Fe1 Fe2 Fe1′ Fe3 Fe4 Fe1 Fe2 3.710 Fe1′ 3.668 3.710 Fe3 3.573 5.167 5.151 Fe4 5.126 3.588 5.126 3.685 Fe3′ 5.151 5.167 3.573 3.755 3.685
J1
Fe4
Fe3 Fe3′
J2
Fe2 Fe1 Fe1 ′
J1
Figure 5.4. Schematic of the spin exchange model for central {Fe6(OH)9} unit Cs4Na7 [Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6). J1 is the intra-trimer exchange coupling constant and J2 the inter-trimer constant.
88
3+ 5 Eq.(5.4) can be re-written as Eq. (5.6) by noticing that for Fe (3d ) ion, S1 = S2 = S1′ =
S3 = S4 = S3′ = 5/2.
E (ST, S121′, S343′) = –J1 [S121′ (S121′ + 1) + S343′ (S343′ + 1) – 105/2]
– J2 [ST (ST + 1) – S121′ (S121′ + 1) – S343′ (S343′ + 1)] (5.6)
The above described spin formalism results in 4332 different spin states ranging from ST
= 0–15, corresponding to various combinations of S121′ and S343′, which in turn depend on
S12 and S34, respectively. Table 5.4 lists the total number of spin states corresponding to different values of ST and figure 5.5 shows a plot of E/|J2| as a function of J1/|J2| for all the 4332 spin states. It can be seen that the spin exchange levels span a continuum in the range plotted. The program code used to generate the 4332 spin state energies is given in Appendix C.
5.4.2. Magnetic Susceptibility data analysis
The solid-state magnetic behavior of GeFe6 has been investigated at 0.1 Tesla in the temperature range of 1.8 - 300 K. Figure 5.6 shows the temperature dependence of the magnetic susceptibility (χm) as a plot of χm vs T (Figure 5.5(a)) and χmT vs T (Figure -1 -1 5.5(b)). χm slowly increases from ~0.031 emu·mol at 300 K to ~0.041 emu·mol at 80 K, then exponentially to a maximum of ~0.16 emu·mol-1 at 3.8 K, and followed by a decrease to ~0.14 emu·mol-1 at 1.8 K. The decrease after 3.8 K is ascribed to
intermolecular interactions. χmT decreases steadily from ~9.3 emu·K/mol at 300 K to ~1.14 emu·K/mol at 10 K and falls down exponentially to ~0.25 emu·K/mol at 1.8 K.
Comparison of the 300 K χmT value (~9.3 emu·K/mol) to that of 26.2 emu·K/mol for a cluster of six non-interacting Fe3+ (S = 5/2) ions with g = 2.00 clearly points to the presence of strong antiferromagnetic spin exchange interactions between the Fe3+centers
and a spin ST = 0 ground state. Since the rigorous approach involves the diagonalization of the 46656 × 46656 matrix, we attempted to analyze the magnetic susceptibility data
89
Table 5.4. Spin state degeneracies (n) corresponding to different values of ST of the Fe(III) hexamer of GeFe6. The Heisenberg spin exchange energies (E(ST)) calculated for the J1 = J2 case are also given. See text for details.
ST n E(ST) ST n E(ST) ST n E(ST) ST n E(ST) 15 1 –187.5J 11 70 –79.5J 7 405 –3.5J 3 575 40.5J 14 5 –157.5J 10 126 –57.5J 6 505 10.5J 2 475 46.5J 13 15 –129.5J 9 204 –37.5J 5 581 22.5J 1 315 50.5J 12 35 –103.5J 8 300 –19.5J 4 609 32.5J 0 111 52.5J
3+ Figure 5.5. Spin exchange energy levels spectrum of the (Fe )6 cluster shown as a plot of E/|J2| vs J1/|J2|.
90
using a simple spin exchange model where intra- and inter-trimer spin exchange
constants were set equal, i.e., J1 = J2 = J. This approximation can be justified by taking a closer look at the type of available super-exchange pathways, Fe–O bond distances and Fe–O–Fe bond angles in GeFe6 (cf. Table 5.2). First, both intra- and inter-trimer exchange interactions occur via the μ- hydroxo bridges connecting the iron(III) ions. Secondly, the average intra- vs inter-trimer
Fe–O distances (~1.99 Å vs ~1.95 Å) demand |J2| ≥ |J1|, whereas the average intra-vs inter-trimer Fe–O–Fe bond angles (~141° vs ~133°) demand |J2| ≤ |J1| [2,18]. Since, the difference in either Fe–O bond distances (~0.04 Å) or Fe–O–Fe bond angles (~8°) is not large enough for one interaction to dominate the other, it is not too unreasonable to assume that they have approximately equal magnitudes. Furthermore, the Fe–O–Fe bond angles suggest that both the intra-and inter-trimer spin exchange interactions are antiferromagnetic in nature [140,151]. The assumption J1 = J2 = J transforms Eq. (5.6) into Eq. (5.7). The resultant energies are listed in Table 5.4.
5.7 E(ST) = –J [ST (ST + 1) – 52.5] ( )
Substitution of the energies and their degeneracies listed in Table 5.4 into the Heisenberg-Dirac-van Vleck equation [58,70,75], shown in Eq. (5.8), results in Eq. (5.9).
S (S + 2)(1 S + )1 e− SE T /)( kT 22 ∑ T T T Ng β S χ = T (5.8) m − SE T /)( kT 3kT ∑ 2( ST + )1 e ST
⎛10Ng 2 β2 ⎞⎛ A ⎞ = ⎜ ⎟ (5.9) χm ⎜ ⎟⎜ ⎟ ⎝ kT ⎠⎝ B ⎠
Here N is the Avogadro number, g the average g-factor, β the electron Bohr magneton, k the Boltzmann constant, T the temperature in Kelvin, A = 63 e(2J/kT) + 475 e(6J/kT) + 1610 e(12J/kT) + 3654 e(20J/kT) + 6391 e(30J/kT) + 9191 e(42J/kT) + 11340 e(56J/kT) + 12240 e(72J/kT) + 11628 e(90J/kT) + 9702 e(110J/kT) + 7084 e(132J/kT) + 4550 e(156J/kT) + 2457 e(182J/kT) + 1015 e(210J/kT) + 248 e(240J/kT) and B = 111 + 945 e(2J/kT) + 2375 e(6J/kT) + 4025 e(12J/kT) + 5481
91 e(20J/kT) + 6391 e(30J/kT) + 6565 e(42J/kT) + 6075 e(56J/kT) + 5100 e(72J/kT) + 3876 e(90J/kT) + 2646 e(110J/kT) + 1610 e(132J/kT) + 875 e(156J/kT) + 405 e(182J/kT) + 145 e(210J/kT) + 31 e(240J/kT). Since the ground state is diamagnetic, we were particularly interested in the high-temperature region and, as can be seen in Figure 5.7, our model fits fairly well all of the high- temperature (80-300 K) experimental χmT data. The best least-squares fit, shown as the solid line in Figure 5.7, yields J = –11.5 ± 0.2 cm -1 with fixed g = 2.0. These results confirm the presence of an ST = 0 ground state and an excited spin triplet (ST = 1) ~ 24 -1 3+ cm above the spin singlet ground state and are in agreement with other (Fe )6 containing compounds reported in the literature [151,166-173].
5.5. EPR Spectroscopic Studies
Variable frequency EPR measurements have been conducted on polycrystalline powder samples of GeFe6 in an effort to better understand the spin environment. One broad (∆B ~ 0.25 Tesla) Lorentzian isotropic EPR transition at g = 1.99251 was observed at all frequencies between 90 and 370 GHz and room temperature (see Figure 5.8). This is expected for a high-spin Fe3+ (3d 5) center [76]. Figure 5.9(a) shows the temperature dependence of the observed resonance peak at ~92 GHz. It can be seen that as the temperature is lowered, the EPR signal intensity drops steadily to zero, without any significant change in the peak-to-peak width, indicating that the ground state is diamagnetic, in agreement with the susceptibility analysis. The observed high temperature signal results from low-lying paramagnetic excited spin states. Figure 5.9(b) shows a plot of χmT and (IEPRT) as a function of temperature (T), assuming that the EPR intensity (IEPR) is proportional to the molar susceptibility (χm). Though the calculated EPR intensities are approximate because of the saturation effects and lack of good line width control on the high-frequency instrument, there is a reasonable agreement between the EPR intensity and susceptibility data.
92
(a)
(b)
Figure 5.6. (a) χm as a function of temperature T for Cs4Na7[Fe6(OH)3(A-α-GeW9O34 (OH)3)2] (GeFe6). (b) χmT vs T for GeFe6. Inset in (a) shows an enlarged portion of low temperature magnetic susceptibility (χm).
93
Figure 5.7. A plot of χmT vs T for Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6) in the temperature range 80-300 K. Solid line represents the theoretical fit. See text for details.
94
Figure 5.8. Room temperature EPR spectra of Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6) at 92.338 GHz (black trace) and 240 GHz (red trace). The observed resonances have Lorentzian lineshape with line width ∆B ~ 2500 G.
95
(a)
(b)
Figure 5.9. (a) Temperature dependence of EPR spectrum of Cs4Na7[Fe6(OH)3(A-α- GeW9O34(OH)3)2] (GeFe6) at W-band (ν = 92.338 GHz). (b) Plot of IEPRT (black circles) and χmT (red circles) as a function of temperature (T).
96
5.6. Summary
Structure and magnetic properties of a double-sandwich, hexairon(III) containing germanotungstate Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6) are described in 10- detail. GeFe6 consists of two tri-lacunary [A-α-GeW9O34] Keggin moieties linked via a iron(III) hexamer, {Fe6(OH)9}. The central {Fe6(OH)9} fragment has trigonal-prismatic arrangement of six Fe(III) ions connected via μ2-hydroxo bridges. Magnetic studies of
GeFe6 indicate the presence of a diamagnetic ground state (ST = 0). Analysis of the high- temperature magnetic susceptibility data in terms of a simple spin exchange model with
J1 (intra-trimer spin exchange constant) equals J2 (inter-trimer spin exchange constant), -1 yields J1 = J2 = J ≈ –12 cm with g = 2.0. Figure 5.10 shows one of 111 possible spin alignments corresponding to a singlet spin, ST = 0, state and Figure 5.11 shows the first -1 six energy levels relative to the ground state singlet for J1 = J2 = J ≈ –12 cm case. A single broad Lorentzian peak, centered at 1.99251, is observed at room temperature for all measured frequencies (90 – 370 GHz) and is ascribed to a paramagnetic excited spin state. The room temperature signal broadens out as temperature decreases and finally becomes unobservable at 4 K, confirming the diamagnetic spin ST = 0 ground state. Furthermore, our EPR intensity agrees fairly well with the molar susceptibility data. This material might be interesting because of the current interest in antiferromagnetic rings and their relevance to quantum spin dynamics.
97
Fe2
J J
Fe1 Fe1 J J Fe4 J J
J J
Fe3 Fe3 J
Figure 5.10. One out of 111 possible spin configurations for the ground singlet spin state (ST = 0) of Cs4Na7[Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6). J is the exchange coupling constant and the numbering corresponds to Figure 5.2.
98
Figure 5.11. Relative energies of the first six spin states of Cs4Na7[Fe6(OH)3(A-α-GeW9O34
(OH)3)2] (GeFe6). The ST values along with their degeneracies (n) are also shown. See text for further details.
99
CHAPTER 6
2+ MAGNETIC AND HIGH-FIELD EPR STUDIES OF A (Co )15 CLUSTER: A TRIANGLE OF TRIANGLES COUPLED SPIN SYSTEM
This chapter summarizes our structural, magnetic and EPR studies of a new 15-
cobalt(II)-substituted polyoxotungstate Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8
O31)3}] (SiCo15). This 15-spin core system was investigated with the view of obtaining a high-spin ground state single molecule magnet. Single-crystal X-ray analysis shows that
SiCo15 crystallizes in the hexagonal system, space group P63/m, with a = 19.8754(17) Å, b = 19.8754(17) Å, c = 22.344(4) Å, α = β = 90°, γ = 120° and Z = 2. Nine out of fifteen 2+ Co ions of SiCo15 are encapsulated by three (β-SiW8O31) fragments, while the rest of the Co2+ ions are present on the periphery of the molecule. In other words the central core 2+ {Co9Cl2(OH)3(H2O)9O21} is surrounded by six [Co(H2O)5] groups resulting in a
satellite-like structure. From the magnetism standpoint, SiCo15 is interesting because the core of nine Co2+ ions can be viewed as a triangle of triangles of 3d7 spins. The Co2+ ions with in each triangle interact via the oxo- and hydroxo-bridges and the interactions are expected to be ferromagnetic because of the orthogonality of the magnetic orbitals (Co−O−Co: 94 - 101º). On the other hand, the Co−Cl−Co angles of ~120º should make the inter-trimer interactions antiferromagnetic. Indeed, magnetic susceptibility results over 1.8-300 K show the presence of both antiferro- and ferromagnetic coupling within 2+ the (Co )9 core. An Ising model has been employed to describe the exchange-coupling 2+ between the Co ions of the core. The susceptibility analysis yields gavg = 4.16 ± 0.05, -1 intra-trimer exchange constant Jz = 16.0 ± 2 cm , and inter-trimer exchange constant J′z -1 = −11 ± 1 cm . A theoretical model indicated a doubly degenerate spin doublet (ST =
1/2) ground state separated from a four-fold degenerate spin quartet (ST = 3/2) excited state by ~34 ± 1 cm-1 (~50 K). Variable frequency (34 – 400 GHz) and variable temperature (4 – 300 K) EPR studies confirm the spin doublet ground state with effective
100
g-values, geff(xx) = 2.63 ± 0.01, geff(yy) = 3.89 ± 0.01, and geff(zz) = 5.72 ± 0.01. The
isotropic effective g-value (geff(iso) = 4.08) is in agreement with the average g-value of 4.12 obtained from magnetic susceptibility. The effective g-values reveal the presence of
an anisotropic Kramer’s doublet ground state (effective spin Seff = ½) for an octahedral Co2+ ion. Thus the initial goal of a high-spin ground state was not realized, nevertheless the compound is a good model of three coupled triangular spin systems. This study was recently reported [6].
6.1. Introduction
2+ This study reports on a (Co )15 complex. It was undertaken because cobalt is a magnetically interesting element in the sense that the octahedral Co2+ (3d 7) ion possesses 4 2+ a considerable orbital moment in the electronic T1 ground state. Most of the Co compounds exhibit spin S = 3/2 magnetism at 77 K and above [70]. However, the large spin-orbit coupling constant of Co2+ (λ ~ –180 cm-1 for the free-ion) in conjunction with 4 local distortion of the octahedral sites can split the T1 state up to six anisotropic Kramers doublets [58,70]. At temperatures below 30 K, only the ground Kramers doublet is significantly populated and even though this is a spin-orbit doublet, most of the time 2+ octahedral Co ion is characterized with an effective spin Seff = ½ ground state. Since most of the Co2+-containing polynuclear compounds are known to exhibit ferromagnetic spin exchange interactions [71-73,174-176], the idea of incorporating a large number of Co2+ ions into a cluster seemed promising. Once again, the potential of polyoxometalate (POM) frameworks to encapsulate multinuclear magnetic clusters attracted us to search for a Co2+-substituted POM containing a large number of Co2+ ions. A common synthetic strategy for the preparation of transition metal substituted polyoxotungstates involves the reaction of a transition metal ion with a lacunary POM. The tungsten-oxygen framework is usually preserved in the product, if a stable lacunary 10- 12- 10- POM is used (e.g., α-PW11O39 , P2W15O56 , A-SiW9O34 ) [62]. Kortz’s group has 8- shown that this is not the case for the divacant decatungstosilicate, [ -SiW10O36] , which 8- was first reported by Hervé and co-workers [177]. Reaction of [ -SiW10O36] with a
101
12- variety of first-row transition metals has led to dimeric [{β-SiNi2W10O36(OH)2(H2O)}2] 12- 2+ 2+ 2+ 2+ [178]; [M4(H2O)2(B-α-GeW9O34)2] (M = Mn , Cu , Zn , Cd ) [109], trimeric [(β2- 15- 24- SiW11 MnO38(OH)3] [179], and tetrameric [{β-Ti2SiW10O39}4] [180] products, and in
all cases the γ-tungsten-oxo framework was not preserved. So, it can be concluded that 8- the di-lacunary precursor [γ-SiW10O36] isomerizes easily in an aqueous, acidic medium upon heating and in the presence of first-row transition metal ions, it can result in oligomeric products with unexpected structures. Therefore, Kortz et al. decided to 2+ 8- 2+ investigate the system Co /[γ-SiW10O36] in some detail [6]. The reaction of Co ions 8- with [γ-SiW10O36] in the ratio 12:1 in a 1M NaCl medium (pH adjusted to 5.4) resulted
in the novel, trimeric Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}] (SiCo15). The
interesting features of SiCo15 are as follows: (1) SiCo15 contains more cobalt metal centers than any other cobalt-containing polyoxotungstate known to date [174]. (2) It represents only the second example of a structurally characterized cobalt-substituted tungstosilicate [123]. (3) To our knowledge the Keggin fragment (β-SiW8O31) has not been observed before in polyoxoanion chemistry. (4) It represents the first discrete POM with a paramagnetic core and shell (vide infra), and can also be viewed as a hybrid 2+ polyoxoanion/coordination complex. (5) Finally, SiCo15 has a core of nine Co ions arranged in a triangle of triangles and since our goal was to study different size spin- frustrated clusters, pursuit of SiCo15 was an enticing challenge to undertake.
The nona-cobalt core of SiCo15 is most closely related to Weakley’s trimeric 16- tungstophosphate [Co9(OH)3(H2O)6(HPO4)2(PW9O34)3] [181] (PCo9). The three
Keggin tungsten-oxo fragments in PCo9 are of the (B-α-PW9O34) type. Also, the 2- nonacobalt cluster is capped by a HPO4 ligand above and below. The magnetic properties of PCo9 have been investigated by Coronado and co-workers [174]. It is 8- noteworthy to point that SiCo15 was synthesized starting from [γ-SiW10O36] and therefore the mechanism of formation of SiCo15 must involve metal insertion, rotational
isomerization ( -Keggin → β-Keggin), and loss of tungsten (SiW10 → SiW8). It is not
clear if SiCo15 is formed from three monomeric Keggin fragments in one condensation step or by gradual growth involving a dimeric intermediate. Furthermore, it is not clear at
102
2+ which point in the formation of SiCo15 the antenna-like, outer Co ions come into play.
A preliminary account of our studies on SiCo15 was reported recently [6].
6.2. Synthesis and Experimental Details
6.2.1. Synthesis. The di-lacunary precursor K8[ -SiW10O36] was synthesized according to the published procedure [182] by Kortz’s group. Typically, a 1.00 g (0.36 mmol) sample of K8[ -SiW10O36] is added with stirring to a solution of 1.14 g (4.75 mmol) of
CoCl2·6H2O in 20 mL of 1 M NaCl. After complete dissolution (~5 min), the pH was adjusted to 5.5 by addition of 0.1 M NaOH. This solution was heated to 50 °C for 30 min and then cooled to room temperature and filtered. Slow evaporation at room temperature resulted in a purple/red crystalline product (yield: 0.66 g (65%)) of
Na5[Co6(H2O)30{Co9Cl2(OH)3 (H2O)9(β-SiW8O31)3}]·37H2O (SiCo15) after 2-3 days that was filtered off and air-dried. [6]
6.2.2. X-ray Crystallography. A red block of SiCo15 with dimensions 0.15 × 0.05 × 0.03 mm3 was mounted on a glass fiber for indexing and intensity data collection at 200 K on a Bruker D8 SMART APEX CCD single-crystal diffractometer using Mo Kα radiation (λ = 0.71073 Å). Direct methods were used to solve the structure and SHELXS-97, SHELXL- 97 were used to locate all the atoms. Further structural refinement was performed using the SADABS program [89]. Crystallographic data are summarized in Table 1.
6.2.3. dc Magnetic susceptibility and EPR Measurements. dc magnetic susceptibility
measurements on powder samples of SiCo15 were carried out using a Quantum Design MPMS-XL SQUID magnetometer over the temperature range 1.8-300 K at an external applied field of 100 G. Data were corrected for diamagnetism (–3.0×10-3 emu/mol) using Klemm constants [90] and TIP (1.5×10-4 emu/mol per CoII ion) reported by Casañ-Pastor et al. [71,72].
103
Table 6.1. Crystal Structure Data for Na5[Co6(H2O)30{Co9Cl2(OH)3 (H2O)9 (β- SiW8O31)3}] (SiCo15).
emp formula Cl2Co15H155Na5O172Si3W24 α (º) 90 fw 8475.2 β (º) 90 crystal size (mm3) 0.15 × 0.05 × 0.03 (º) 120 3 space group (No.) P63/m (176) vol (Å ) 7643.9(16) a (Å) 19.8754(17) Z 2 b (Å) 19.8754(17) temp (ºC) -73 c (Å) 22.344(4) wavelength (Å) 0.71073
Polycrystalline (powder) EPR spectra of SiCo15 were recorded using a Bruker Elexsys-500 spectrometer at Q-band (ν ~ 34 GHz) in the 4–300 K temperature range. The temperature was controlled with an Oxford continuous flow liquid He cryostat and was monitored using Oxford instruments ITC 503. The magnetic field was calibrated using a built in NMR teslameter and the frequency was monitored with a digital frequency counter. High frequency (ν ~ 95 - 400 GHz) measurements were conducted at the high- field electron magnetic resonance facility at the National High Magnetic Field Laboratory in Tallahassee [91,92] and the instrumental details are given in Appendix A. In all experiments the modulation amplitudes and microwave power were adjusted for optimal signal intensity and resolution.
6.3. Structural Details
The polyoxotungstate Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}]
·37H2O (SiCo15) crystallizes in the hexagonal system, space group P63/m, with a = b = 19.8754 Å, c = 22.344(4) Å, α = β = 90º, = 120º and Z = 2. The core of polyanion 2+ SiCo15 is composed of nine Co ions that are encapsulated by three unprecedented (β- - SiW8O31) fragments and two Cl ligands (see Figure 6.1(a)).
104
Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}]
W Si Co O
Cl (a)
WO6 SiO4
CoO6
(b)
Figure 6.1. (a) Ball and stick representation (C3 axis view) of Na5[Co6(H2O)30 {Co9Cl2(OH)3 (H2O)9(β-SiW8O31)3}] (SiCo15). (b) Side view polyhedral representation of + SiCo15. The counter Na ions are omitted for clarity.
105
Central {Co9Cl2(OH)3(H2O)9O21} fragment
Co2'
Co1a' Co1' Cl1a Co1a'' Cl1 Co1''
Co1a Co1 Co2 Co2''
Co Cl
O OH OH2
Figure 6.2. Ball and stick representation (view along C3 axis) of the core {Co9Cl2(OH)3 (H2O)9O21} of Na5[Co6(H2O)30{Co9Cl2(OH)3 (H2O)9(β-SiW8O31)3}] (SiCo15).
17- This central assembly {Co9Cl2(OH)3 (H2O)9(β -SiW8O31)3} is surrounded by six 2+ antenna-like Co (H2O)5 groups, which are bound to terminal oxo groups (Co3-O2T 2.07(1) Å, W2-O2T 1.75(1) Å). Three of these antennas are each above and below
SiCo15, so that its structure could be described as satellite-like (cf. Figure 6.1(b)), with C3 molecular symmetry. The average bond lengths and angles around the Co2+ ions are 2+ given in Table 6.2 and it can be seen that all fifteen Co ions of SiCo15 are in fairly regular octahedral environments. We believe that the six “outer” CoII ions play an important stabilizing role by reducing the charge of the core of SiCo15 by 12 units from -17 to -5.
106
2+ Table 6.2. Bond lengths (Å) and angles (º) around Co ions of Na5[Co6(H2O)30{Co9Cl2 2+ (OH)3(H2O)9(β-SiW8O31)3}] (SiCo15). Co1(1a), Co2 are core Co ions whereas Co3 is the peripheral Co2+ ion. See text for details.
Co1(1a)–O O–Co1(1a)–O Co2–O O–Co2–O Co3–O O–Co3–O 2.034 – 81.72 – 96.50 2.026 – 80.96 – 2.042 – 87.02 – 2.148 2.152 95.57 2.179 92.97
Table 6.3. Intra- and inter-trimer Co····Co distances (Å) of Na5[Co6(H2O)30{Co9Cl2 (OH)3(H2O)9(β-SiW8O31)3}] (SiCo15).
Intra-trimer Inter-trimer Co1····Co1a 3.038 Co1····Co1′(1 ) 4.246 Co1(1a)····Co2 3.141 Co1a····Co1a′(1a ) 4.246
Structural calculations indicate that all terminal ligands associated with CoII ions are
water molecules (nine associated with the Co9 core and thirty with the outer Co-antenna)
[125]. Furthermore, the three μ3-oxo within the Co9 core of SiCo15 are hydroxo groups.
Figure 6.2 shows structure of the nona-cobalt(II) core, {Co9Cl2(OH)3(H2O)9O21}, 2+ of SiCo15 and it can be seen that there are only two crystallographically different Co ions in the core viz. Co1 and Co2. The arrangement of nine Co2+ ions in the core can be viewed as a triangle of triangles connected at the two apices (Co1 and Co1a) by μ3-chloro bridges. The Co2+ ions with in each triangle (Co1, Co1a and Co2) are connected by three 2+ μ3-oxo groups of the polyhedral cap and a μ3-hydroxo group. In other words, the Co
ions of each triangle are bi-bridged via a μ3-hydroxo and μ3-oxo groups. Table 6.3 lists the intra- and inter-triangle Co····Co distances.
107
6.4. Magnetic Studies
6.4.1. Theoretical model
3 J 1 2
J2 1
J3 J3 5 8 9 J2 J2 4 7 J1 J1 J3 6 Co O Cl
2+ Figure 6.3. Schematic of spin-exchange coupling for the (Co )9 core of Na5[Co6 (H2O)30 {Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}] (SiCo15). The numbering 1 through 9 corresponds to 1, 1a, 2, 1′, 1a′, 2′, 1 , 1a and 2 in Figure 6.2. The color code is as follows. Intra-trimer exchange constants are J1, J2 and the inter-trimer constant is J3. Limited oxygens are shown for clarity.
108
4 2+ The T1 high-spin ground state of an octahedral Co ion splits into six anisotropic Kramers doublets via spin-orbit coupling and local distortion of the octahedral sites [58,70]. So, the splitting pattern of the lowest lying spin states of the cluster is expected to result from the interaction of lowest anisotropic Kramers doublets of the Co2+ ions.
Even though this model restricts our analysis of SiCo15 magnetic susceptibility data to the low temperature (T < 30 K) range, where only the lowest lying Kramer’s doublet with
effective spin Seff = 1/2 is populated, it is adequate to obtain useful information on the exchange interactions. Following the spin-exchange scheme shown in Figure 6.3, the 2+ anisotropic Hamiltonian for the core (Co )9 can be written as:
Hexchange = –2J1z [S1zS3z + S2zS3z + S4zS6z + S5zS6z + S7zS9z + S8zS9z]
– 2J2z [S1zS2z + S4zS5z + S7zS8z]
– 2J3z [S1zS4z + S1zS7z + S2zS5z + S2zS8z + S4zS7z + S5zS8z] (6.1)
where, J1z, J2z are intra-trimer exchange coupling constants, J3z the inter-trimer exchange
constant, Siz the z-component of the spin operator associated with the effective spin Seff = 1/2 of the ith ion. Following Kambe vector coupling method [93], Eq. (6.1) can be rearranged as in Eq. (6.2).
2 2 2 2 2 2 2 2 2 Hexchange = –2J1z [(S123) + (S456) + (S789) – (S12) – (S45) – (S78) – (S3) – (S6) – (S9) ]
2 2 2 2 2 2 2 2 2 – 2J2z [(S12) + (S45) + (S78) – (S1) – (S2) – (S4) – (S5) – (S7) – (S8) ]
2 2 2 2 – 2J3z [(ST) – (S123) – (S456) – (S789) ] (6.2)
The subscript ‘z’ is dropped for convenience and the intermediate, total spins are defined as:
S12 = S1 + S2 ; S123 = S12 + S3 ; S45 = S4 + S5 ; S456 = S45 + S6 ;
S78 = S7 + S8 ; S789 = S78 + S9 ; SA = S123 + S456 ; ST = SA + S789 (6.3)
109
Table 6.4. Spin state degeneracies (n) corresponding to various values of total spin ST for 2+ the (Co )9 core of Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}] (SiCo15). 2+ Degeneracies are calculated using an effective spin Seff = 1/2 for Co ion. See text for further details.
# ST n 1 9/2 1 2 7/2 8 3 5/2 27 4 3/2 48 5 1/2 42
The eigenvalues corresponding to Eq. (6.2) are:
E(ST, S123, S456, S789, S12, S45, S78, S1, S2, S3, S4, S5, S6, S7, S8, S9) =
–J1z [S123(S123+1) + S456(S456+1) + S789(S789+1) – S12(S12+1) – S45(S45+1)
– S78(S78+1) – S3(S3+1) – S6(S6+1) – S9(S9+1)] – J2z [S12(S12+1) + S45(S45+1) + S78(S78+1)
– S1(S1+1) – S2(S2+1) – S4(S4+1) – S5(S5+1) – S7(S7+1) – S8(S8+1)] – J3z [ST (ST+1) –
S123(S123+1) – S456(S456+1) – S789(S789+1)] (6.4)
2+ Considering that Co ion has an effective spin Seff = 1/2, Eq. (6.4) rewritten as:
E(ST, S123, S456, S789, S12, S45, S78) = –J1z [S123(S123+1) + S456(S456+1) + S789(S789+1) –
S12(S12+1) – S45(S45+1) – S78(S78+1) – 9/4] – J2z [S12(S12+1) + S45(S45+1) + S78(S78+1) –
9/2] – J3z [ST (ST+1) – S123(S123+1) – S456(S456+1) – S789(S789+1)] (6.4)
Here, spin Sij takes values from |Si – Sj| to Si + Sj. The above described spin formalism results in 126 spin states given in Table 6.4. Energies corresponding to these states are given in Appendix C along with the program code used for their generation.
110
2+ Figure 6.4. A plot of spin exchange energy levels (E/Jz) of (Co )9 core of SiCo15. as a function of J′z/Jz ratio. Dotted line represents the experimental J′z/Jz ratio of ~ 0.7. The total spin values (ST) are shown on the left. See text for further details.
2+ Table 6.5. Spin exchange energy levels and their degeneracies (n) of the (Co )9 core of Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}] (SiCo15) corresponding to different intermediate spins S123, S456 and S789. See text for further details.
# ST n E(ST,S123,S456,S789) # ST n E(ST,S123,S456,S789)
1 9/2 1 –4.5Jz – 13.5J′z 8 3/2 24 1.5Jz + 1.5J′z
2 7/2 6 –1.5Jz – 7.5J′z 9 3/2 12 –1.5Jz + 4.5J′z
3 7/2 2 –4.5Jz – 4.5J′z 10 3/2 4 –4.5Jz + 7.5J′z
4 5/2 12 1.5Jz – 3.5J′z 11 1/2 16 4.5Jz + 1.5J′z
5 5/2 12 –1.5Jz – 0.5J′z 12 1/2 12 1.5Jz + 4.5J′z
6 5/2 3 –4.5Jz + 2.5J′z 13 1/2 12 –1.5Jz + 7.5J′z
7 3/2 8 4.5Jz – 1.5J′z 14 1/2 2 –4.5Jz + 10.5J′z
111
Neglecting the small difference between Co1–Co1a (3.037 Å) and Co1(1a)–Co2 2+ distances (3.141 Å), each (Co )3 triangle of the SiCo15 core is considered as equilateral
(J1z = J2z). This approximation further simplifies the Eq. (6.4) into Eq. (6.5), where J1z, J2z
and J3z of Eq. (6.4) are replaced, respectively by Jz and J′z. The spin exchange energies
calculated from Eq. (6.5) are listed in Table 6.5 and plotted in Figure 6.4 as E/Jz vs J′z/Jz.
E(ST, S123, S456, S789, S12, S45, S78) = –Jz [S123(S123+1) + S456(S456+1) + S789(S789+1)
– S12(S12+1) – S45(S45+1) – S78(S78+1) – 27/4]
– J′z [ST (ST +1) – S123(S123+1) – S456(S456+1) – S789(S789+1)] (6.5)
6.4.2. dc Magnetic Susceptibility data analysis
Figure 6.5(a) displays the results of the magnetic measurements on SiCo15. The
effective moment χmT decreases continuously with decreasing temperature, showing the presence of antiferromagnetic exchange interactions. When we compare the experimental
300 K χmT value of ~43 emu K/mol (~ 18.5 µB) to that of the spin-only value of 28.13 2+ emu K/mol (15 µB) for 15 non-interacting Co ions (S = 3/2) with g = 2.0, we can see that there is an appreciable spin-orbit coupling, which is expected for octahedrally coordinated Co2+ ions [58,70]. As described earlier, six out of fifteen Co2+ ions are present on the periphery of the molecule, far from each other (~ 7.7 Å) and also far (~ 6.6 2+ 2+ Å) from the core of nine Co ions. Thus the entire system of fifteen Co ions of SiCo15 can therefore be considered essentially as two independent subsystems. In our analysis, we neglected both of these spin exchange interactions and considered the contribution of II the six peripheral Co ions to the total magnetic moment as additive.
The experimental χmT data were fit (see Figure 6.5(b)) to the parallel magnetic susceptibility expression given in Eq (6.6):
2 2 (χmT)para = (χmT)core,para + 6Ng β Seff(Seff+1)/3k (6.6)
112
(a)
(b)
Figure 6.5. (a) Temperature dependence of χmT for Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9 (β-SiW8O31)3}] (SiCo15). (b) Theoretical fit to the experimental data in the temperature range 1.8-30 K.
113
where N is the Avogadro number, g the Landé g-factor, β the electron Bohr magneton, k 2+ the Boltzmann constant and Seff the effective spin of the Co ion. In Eq. (6.6) , the first term corresponds to the nine central Co2+ ions whereas the second term represents the 2+ contribution from the six peripheral Co ions with effective spin Seff = 1/2. Using the Heisenberg-Dirac-van Vleck equation, shown in Eq. (6.7) [58,70,75] and the energies listed in Table 6.5, the expression for (χmT)core,para can be derived as:
S (S + 2)(1 S + )1 e− SE T /)( kT 22 ∑ T T T Ng β S χ = T (6.7) m − SE T /)( kT 3kT ∑ 2( ST + )1 e ST
⎛ Ng β 22 ⎞⎛ A ⎞ T ⎜ ⎟ (6.8) ()χm core,para = ⎜ ⎟⎜ ⎟ ⎝ 4k ⎠⎝ B ⎠ where N, g, β, and k have their usual meaning and A = 165 +504 e(3x +6y) +168 e(9y) + 420 e(6x +10y) + 420 e(3x +13y) + 210 e(16y) + 80 e(9x +12y) + 240 e(6x +15y) + 120 e(3x +18y) + 40 e(21y) + 16 e(9x +15y) + 12 e(6x +18y) + 12 e(3x +21y) + 2 e(24y), B = 5 + 24 e(3x +6y) + 8 e(9y) + 36 e(6x + 10y) + 36 e(3x + 13y) + 9 e(16y) + 16 e(9x +12y) +48 e(6x +15y) +24 e(3x +18y) + 8 e(21y) +16 e(9x +15y) + (6x +18y) (3x +21y) (24y) 12 e + 12 e + 2 e with x = Jz/kT and y = J′z/ kT. The best-fit values are Jz -1 -1 = 16.0 ± 1.5 cm , J′z = –11 ± 1 cm , and g = 4.16 ± 0.05. This average g-value is about the same as those reported for other high spin octahedral Co2+ ions [76]. We note that while the fit is not as satisfactory as it could be, the analysis clearly showed that the intra- trimer interactions are ferromagnetic while the inter-trimer interactions are antiferromagnetic. The poor agreement between the theory and the experimental data in the low temperature range could be either due to neglecting the perpendicular components (Jx, Jy, J′x and J′y) of intra- and inter-trimer exchange interactions (Ising 2+ model approximation) or the treatment of individual (Co )3 triangle as an equilateral (vide supra). The spin exchange parameters are in good agreement with the values reported in the literature for other Co2+-substituted polyoxotungstates [71-73,174-176].
114
Figure 6.6. Spin level energies relative to the ground state. The S values along with T their degeneracies (n) are color coded as shown. The ground state is a doubly degenerate 1/2 and separated from the four-fold degenerate first excited state (ST = 3/2) -1 by ~34 ± 1 cm .
It can be seen from Figure 6.4 that for experimental J′z/Jz ~ -0.7, the ground state is a spin -1 doublet (ST = 1/2) with an excited quartet (ST = 3/2) lying above at ~34 ± 1 cm (~50 K). The results are summarized in Figure 6.6.
The signs and relative magnitudes of the exchange parameters Jz, J′z correlate reasonably well with the structural features of SiCo15. The intra-trimer Co–O–Co angles are in the range 94–101° favoring orthogonality of the magnetic orbitals. Therefore, ferromagnetic spin exchange interactions are expected. On the other hand, the Co–Cl–Co angles (~120°) are significantly larger, suggesting the presence of antiferromagnetic interactions between trimers. Also, the average Co–Co intra-trimer distances (3.1 Å) are much shorter than the inter-trimer distances (4.3 Å). As a result, we expect the magnitude of intra-trimer exchange interactions to be stronger than that of inter-trimer exchange.
115
6.5. High Frequency EPR Studies
The magnetization data were complemented by powder EPR measurements over a
wide frequency and temperature range. Figure 6.7 shows the 4 K EPR spectrum of SiCo15 at 34 and 93 GHz. There is a broad, asymmetric transition at low field, associated with an anisotropic Kramer’s doublet [76]. The small peak at g ≈ 2, marked as “A” in Figure 6.7, is due to an impurity most likely a result of air oxidation but is not of interest here because of its small concentration. The effective g-values associated with the Kramer’s doublet are geff(xx) = 2.63 ± 0.01, geff(yy) = 3.89 ± 0.01, and geff(zz) = 5.72 ± 0.01, as 2+ expected for Co systems [58,76]. This effective ST = 1/2 ground state with geff(iso) = 4.08 is in agreement with the average g-value of 4.16 obtained from the magnetic susceptibility analysis. For SiCo15 we observed no other transitions, even though we employed very high frequencies up to 400 GHz, and so we tentatively concluded that the zero-field splitting parameter (D) is much larger than 400 GHz (~14 cm-1). This interpretation is consistent with literature data on related Co2+-substituted polyoxoanions [71-73,174-176] and supports our treatment of 3d 7 Co2+ ion (S = 3/2) as having an effective spin Seff = ½. As the temperature is increased, the EPR signal intensity decreases and becomes undetectable above 70 K (see Figure 6.8), most likely due to line broadening from fast spin-lattice relaxation processes.
6.6. Summary
The trimeric polyoxotungstate Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8 2+ O31)3}] (SiCo15) has a core of nine Co ions encapsulated by three unprecedented (β-
SiW8O31) fragments and two chloride ligands. This assembly is surrounded by six 2+ antenna-like [Co(H2O)5] groups resulting in the satellite-like structure of SiCo15. SiCo15 POM represents only the second example of a structurally characterized cobalt- substituted tungstosilicate.
116
(a)
(b)
Figure 6.7. EPR spectra of Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9 (β-SiW8O31)3}] (SiCo15) at 4 K and (a) Q-band (34 GHz) and (b) W-band (~94 GHz). Unassigned resonance peak “A” is ascribed to an impurity. See text for details.
117
Figure 6.8. Temperature dependence of Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9 (β-Si W8O31)3}] (SiCo15) at 93 GHz. “A” corresponds to an impurity peak shown in Figure 6.7.
Molar magnetic susceptibility (χm) data of SiCo15 has been analyzed in terms of simple anisotropic Ising model, where the susceptibility contribution from the antenna- 2+ like [Co(H2O)5] groups is treated as Curie-type addition to the total susceptibility 2 2 (χm)total i.e. (χm)total = (χm)core + 6Ng β /3kT. Our analysis reveals the presence of both -1 ferromagnetic intra-trimer (Jz = 16 ± 1.5 cm ) and antiferromagnetic inter-trimer (J′z) 2+ interactions for the (Co )9 core of SiCo15. Figure 6.6 (vide supra) shows the spin level energies relative to the ground state. The ground state spin doublet (ST = 1/2) and the -1 excited quartet (ST = 3/2) are separated by ~33 cm (~47 K). Variable frequency (34 –
400 GHz) and variable temperature (4 – 300 K) EPR studies confirm the spin ST = 1/2 ground state that can be described with the g-values: geff(xx) = 2.63 ± 0.01, geff(yy) = 3.89
± 0.01, and geff(zz) = 5.72 ± 0.01. These g-values are consistent with literature reported 2+ 7 values [58,76] for an high-spin octahedral Co ion (3d ) with an effective spin Seff = ½.
118
Even though our results of SiCo15 are only semi-quantitative, because of either the 2+ fully anisotropic Ising approximation or the equilateral (Co )3 triangle approximation, they nevertheless provide a basic understanding of the core exchange interaction. Detailed theoretical and other experimental techniques like Inelastic Neutron Scattering (INS), could provide quantitative information about the exchange parameters. Further- more, it can be envisioned that substituting the six external cobalt ions by other paramagnetic as well as diamagnetic ions, would result in isostructural polyanions with different magnetic properties. Specifically, it is a model of a coupled triangles-of- triangles spin system.
119
CHAPTER 7
CONCLUSIONS AND CRITIQUE
This dissertation has focused on examining the magnetic properties of several new spin-frustrated polyoxometalates (POMs) of various magnetic cluster sizes and geometries. Our interest in this class of inorganic compounds arose from the fact that they can act as ligands toward 3d-transition metal ions encapsulating a variety of magnetic clusters with interesting spin topologies that can exhibit ferromagnetic and/or antiferromagnetic exchange interactions. We have mainly characterized five compounds using dc magnetic susceptibility and high frequency (95 – 400 GHz) electron
paramagnetic resonance spectroscopy techniques. These include Na9[Na3Cu3(H2O)9(α-
AsW9O33)2] [1] (AsCu3), Na11Cs[Cu4(H2O)2(B-α-GeW9O34)2] [2] (GeCu4),
K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2] [3,4] (SiCu5), Na7Cs4[Fe6(OH)3(A-α-
GeW9O34(OH)3)2] [5] (GeFe6) and Na5[Co6(H2O)30{Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}]
[6] (SiCo15). The sizes and geometries of the magnetic clusters described in this work
are: an equilateral triangle (AsCu3), a rhomb-like tetramer (GeCu4), a pentamer with
rectangular-pyramidal shape (SiCu5), a trigonal-prism of six ions (GeFe6) and a triangle
of triangles capped by six antenna-like ions (SiCo15). These studies were undertaken with the following questions in mind: (i) What is the effect of the spin-frustration phenomenon on the nature of the spin ground states as the cluster geometry changes? (ii) How quantum behavior can cross over to classical behavior as the cluster size and geometries are changed? (iii) Do these clusters have the potential to be single molecule magnets? 2+ The triangular (Cu )3 system, AsCu3, described in Chapter 2 was shown to be a model example of a three-spin-frustrated lattice, with a thermally accessible magnetic
excited state. Our experimental data and theoretical modeling indicate that AsCu3 has a doubly degenerate spin-doublet ground state with a low-lying triplet excited state at ~ 4 cm-1 (~6 K). Our studies provide a comprehensive set of information on the nature of the
120 2+ exchange interactions, ground and excited spin states of (Cu )3 triangle. In a true sense 2+ the (Cu )3 triangle is isosceles and even though our attempts to analyze the magnetic susceptibility data in terms of an isosceles triangle model were not successful, the two ST = 1/2 ground states are quasi-degenerate. However, we were unable to reach low enough temperatures to distinguish these two spin ground states and therefore further investigations in the very low temperature range (T < 1.8 K) should shed light on these spin-frustrated ground states. In fact, pulsed magnetization measurements are currently underway on AsCu3 and the preliminary results look interesting [183]. Anti-symmetric exchange interaction (e.g. Dzyaloshinski-Moriya (DM) interaction) induced tunneling was observed in the magnetization measurements at 0.4 K. Chapter 3 details the magnetic and EPR studies of a tetra-copper(II) containing
POM GeCu4. The rhomb-like structure in combination with antiferromagnetic exchange interactions results in a degenerate spin singlet (ST = 0) and a spin-frustrated triplet spin 2+ (ST = 1) ground state for the (Cu )4 tetramer. The observed seven line hyperfine structure in EPR measurements is indicative of the electron delocalization over two Cu2+ ions and we assigned the Cu2+ ions along the long diagonal of the rhomb to be the spin carriers. 2+ The structural and magnetic characterization details of a new (Cu )5 pentamer
(SiCu5) are reported in Chapter 4. The copper ions in the pentameric core 6+ {Cu5(OH)4(H2O)2O} of SiCu5 assume an uncommon rectangular pyramidal shape. The Cu2+ ions are strongly antiferromagnetically coupled, giving rise to a spin-frustrated ground ST = 1/2 spin ground state and hence SiCu5 can be considered as a prototypical 5- spin electronically coupled spin-frustrated system. High field EPR measurements implies that the ground state unpaired electron is mainly localized on the apical Cu2+ ion and further analysis of the spin Hamiltonian parameters in terms of a simple molecular
orbital-crystal field theory shows that the unpaired electron resides in a 3 d 22 type − yx molecular orbital ground state, with ~30% contribution from oxygen ligands.
GeCu4 and SiCu5 could be investigated for the presence of antisymmetric exchange interactions at high fields and low temperatures.
121 3+ The Fe -substituted GeFe6, presented in Chapter 5, has an interesting 3+ arrangement of two corner-connected (Fe )3 triangles. The antiferromagnetic exchange interactions between Fe3+ ions of the hexamer give rise to a diamagnetic ground state 3+ with many low-lying excited states. Also, the (Fe )6 fragment is so-frustrated that the ground state singlet is 111-fold degenerate, and hence can be considered as an illustrative example to study the manifestation of spin-frustration in large exchange coupled systems.
The excited magnetic states in GeFe6 are accessible by field and therefore it should be possible to study spin-level crossings. Level crossings between the ground and excited states are expected to give interesting phenomena such as quantum tunneling of the Neel vector [184,185], level repulsion [186] etc. 2+ 2+ Nine Co ions of the SiCo15 cluster form a triangle of (Co )3 triangles, while the 2+ remaining six Co are present on the periphery of the molecule, thus giving SiCo15 its 2+ novel satellite-like structure. The magnetic behavior of (Co )15 cluster has been
satisfactorily explained in terms of an anisotropic Ising model with effective spin Seff
=1/2. Ferro- and antiferromagnetic exchange interactions present in SiCo15 indicate the presence of a doubly degenerate spin doublet ground state separated from a four-fold degenerate spin-quartet excited state by ~34 cm-1 (~49 K). We believe that our results should provide a basis for further theoretical and experimental investigations such as inelastic neutron scattering (INS) or very high frequency EPR (~ Terahertz). INS has proved to be a valuable tool for obtaining information on magnetic anisotropy present in the system. [175,176] Overall, the present work describes five new magnetic clusters with triangular spin arrangements in various geometrical configurations. We believe that these compounds will serve as good models for future, more in-depth studies of the spin- frustration phenomenon.
122 APPENDIX A
INSTRUMENTAL DETAILS OF THE HIGH FREQUENCY EPR SET UP
High frequency measurements (95 – 400 GHz) were conducted in the Electron Magnetic Resonance Division of the National High Magnetic Field Laboratory on a custom–built spectrometer. The temperature was controlled with an Oxford continuous flow liquid He cryostat. The Zeeman field was applied using an Oxford Instruments Teslatron superconducting magnet sweepable between 0 and 17 T and a 92 – 97 (AB Millimeter #ESA1-95-5) gun diode provides tunable microwave energy for EPR experiments. The source is phase locked and the frequency is monitored with an EIP578B (EIP Microwave Inc.) frequency counter. Very high frequencies are achieved by fitting the microwave source with the appropriate harmonic filter (Radiometer Physics GmbH). Figure A.1 shows a block diagram of the high frequency setup. Continuous wave radiation passes through a corrugated horn which causes the propagating TE01 wave to be transformed into a linearly polarized HE11 mode. This mode has low losses through an oversized circular corrugated waveguide which has a diameter of ~2 cm for 100 - 300 GHz. The 2m probe is constructed with two corrugated waveguides in parallel with a modulation coil at the bottom of one tube. The sample is placed within the tube here. As radiation passes through the sample, it is reflected by two 45º mirrors through the second waveguide to an InSb hot-electron Bolometer detector QFI/3BI (QMC Instruments Ltd.). The bolometer has a wide useful detection frequency range of 50 – 1200 GHz, making it ideal for multi-frequency experiments. These systems have been described earlier [91,92].
123
Figure A.1. Block diagram of the High Frequency EPR Spectrometer at the National High Magnetic Field Laboratory. The microwave power is detected with the bolometer and “M” indicates mirrors.
124 APPENDIX B
BASIS FUNCTIONS, HEISENBERG EXCHANGE MATRIX AND ITS 2+ EIGENVALUES FOR THE (Cu )5 PENTAMER OF SiCu5
B. 1. Basis Functions.
The spin wave functions for the pentamer K10[Cu5(OH)4(H2O)2(A-α-
SiW9O33)2]·18.5H2O (SiCu5) are derived from the basis set |Ms1, Ms2, Ms3, Ms4, Ms5>, th 2+ where Msi is the microstate corresponding to the i ion. As each Cu has Si = 1/2, Msi can take +1/2, –1/2 and from here onwards represented, respectively, as ‘+’, ‘–’. Since
5
the MsT values corresponding to the total spin ST is MsT = ∑Msi , we have MsT = ±5/2, i=1
±3/2, ±1/2. The possible linear combinations of Msi would give the complete set of eigenfunctions Øi, as shown in Table B.1.
B. 2. Exchange matrix (32 × 32) and Eigenvalues.
Following the spin-exchange schematic shown in Figure B.1, the isotropic spin- exchange Hamiltonian can be given as:
H exchange = – 2Ja [S1•S2 + S3•S4] – 2Jb [S1•S3 + S2•S4]
– 2Jc [S1•S5 + S2•S5 + S4•S5 + S3•S5] (B.1) where, Ja, Jb, Jc represent the exchange coupling constants and Si the spin operator on the ith ion. Equation (B.2) can be obtained by expanding the Hamiltonian given in Eq. (B. 1) in terms of (x,y,z) components.
125 Table B. 1. The complete set of eigenfunctions, Øi, corresponding to the possible linear combinations of Msi.
MsT = 5/2 MsT = –5/2 |+, +, +, +, +> = Ø1 |–, –, –, –, –> = Ø32 MsT = 3/2 MsT = –3/2 |–, +, +, +, +> = Ø2 |+, –, –, –, –> = Ø27 |+, –, +, +, +> = Ø3 |–, +, –, –, –> = Ø28 |+, +, –, +, +> = Ø4 |–, –, +, –, –> = Ø29 |+, +, +, –, +> = Ø5 |–, –, –, +, –> = Ø30 |+, +, +, +, –> = Ø6 |–, –, –, –, +> = Ø31 MsT = 1/2 MsT = –1/2 |–, –, +, +, +> = Ø7 |+, +, –, –, –> = Ø17 |–, +, –, +, +> = Ø8 |+, –, +, –, –> = Ø18 |–, +, +, –, +> = Ø9 |+, –, –, +, –> = Ø19 |–, +, +, +, –> = Ø10 |+, –, –, –, +> = Ø20 |+, –, –, +, +> = Ø11 |–, +, +, –, –> = Ø21 |+, –, +, –, +> = Ø12 |–, +, –, +, –> = Ø22 |+, –, +, +, –> = Ø13 |–, +, –, –, +> = Ø23 |+, +, –, –, +> = Ø14 |–, –, +, +, –> = Ø24 |+, +, –, +, –> = Ø15 |–, –, +, –, +> = Ø25 |+, +, +, –, –> = Ø16 |–, –, –, +, +> = Ø26
Ja 3 4
Jc Jc
Jb 5 Jb
Jc Jc
1 2 Ja Figure B.1. Cartoon of spin-exchange coupling scheme adapted for the Cu2+ pentamer of K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2] (SiCu5), described in Chapter 4. Numbers correspond to the copper centres.
126 H exchange = –2Ja [(S1x S2x + S1y S2y + S1z S2z) + (S3x S4x + S3y S4y + S3z S4z)]
–2Jb [(S1x S3x + S1y S3y + S1z S3z) + (S2x S4x + S2y S4y + S2z S4z)]
–2Jc [(S1x S5x + S1y S5y + S1z S5z) + (S2x S5x + S2y S5y + S2z S5z) +
(S3x S5x + S3y S5y + S3z S5z) + (S4x S5x + S4y S5y + S4z S5z)] (B.2)
+ – + – From the relations Sx = (S + S ) ⁄ 2 and Sy = (S − S ) ⁄ 2i, the Hamiltonian in Eq (B.2) can be re-written as:
+ – – + + – – + H exchange = –2Ja [(S1z S2z) + (S1 S2 + S1 S2 ) + (S3z S4z) + (S3 S4 + S3 S4 )]
+ – – + + – – + –2Jb [(S1z S3z) + (S1 S3 + S1 S3 ) + (S2z S4z) + (S2 S4 + S2 S4 )]
+ – – + + – – + –2Jc [(S1z S5z) + (S1 S5 + S1 S5 ) + (S2z S5z) + (S2 S5 + S2 S5 )
+ – – + + – – + + (S3z S5z) + (S3 S5 + S3 S5 ) + (S4z S5z) + (S4 S5 + S4 S5 )] (B.3)
The exchange matrix corresponding to the Hamiltonian in Eq (B.3) with the matrix elements < Øi | Ĥexch | Øj >, can then be constructed as:
127
Ø1
Ø1 α Ø2 Ø3 Ø4 Ø5 Ø6
Ø2 −c −a −b 0 −c
Ø3 −a −c 0 −b −c
Ø4 −b 0 −c −a −c
Ø5 0 −b −a −c −c
Ø6 −c −c −c −c β Ø7 Ø8 Ø9 Ø10 Ø11 Ø12 Ø13 Ø14 Ø15 Ø16
Ø7 δ 0 −b −c −b 0 −c 0 0 0
Ø8 0 ε −a −c −a 0 0 0 −c 0
Ø9 −b −a γ −c 0 −a 0 −b 0 −c
Ø10 −c −c −c c 0 0 −a 0 −b 0
Ø11 −b −a 0 0 γ −a −c −b −c 0
Ø12 0 0 −a 0 −a ε −c 0 0 −c
Ø13 −c 0 0 −a −c −c c 0 0 −b
Ø14 0 0 −b 0 −b 0 0 δ −c −c
Ø15 0 −c 0 −b −c 0 0 −c c −a
Ø16 0 0 −c 0 0 −c −b −c −a c
128 Ø17 Ø18 Ø19 Ø20 Ø21 Ø22 Ø23 Ø24 Ø25 Ø26
Ø17 δ 0 −b −c −b 0 −c 0 0 0
Ø18 0 ε −a −c −a 0 0 0 −c 0
Ø19 −b −a γ −c 0 −a 0 −b 0 −c
Ø20 −c −c −c c 0 0 −a 0 −b 0
Ø21 −b −a 0 0 γ −a −c −b −c 0
Ø22 0 0 −a 0 −a ε −c 0 0 −c
Ø23 −c 0 0 −a −c −c c 0 0 −b
Ø24 0 0 −b 0 −b 0 0 δ −c −c
Ø25 0 −c 0 −b −c 0 0 −c c −a
Ø26 0 0 −c 0 0 −c −b −c −a c Ø27 Ø28 Ø29 Ø30 Ø31
Ø27 −c −a −b 0 −c
Ø28 −a −c 0 −b −c
Ø29 −b 0 −c −a −c
Ø30 0 −b −a −c −c
Ø31 −c −c −c −c β Ø32
Ø32 α
where α = −Ja −Jb −2Jc; β = 2Jc −Ja −Jb; δ = −Ja + Jb; ε = Ja −Jb; γ = Ja + Jb ; a = Ja; b = Jb; c = Jc. The eigenvalues of the above given exchange matrix are listed in Table B.2.
129 Table B.2. Eigenvalues associated with the spin exchange Hamiltonian for K10[Cu5(OH)4(H2O)2(A-α-SiW9O33)2] (SiCu5).
# ST E(ST) # ST E(ST)
1 5/2 –Ja – Jb – 2Jc 6 1/2 2 2 Ja + Jb – 2 J a − J Jba + Jb
2 3/2 Ja – Jb – Jc 7 1/2 2 2 Ja + Jb + 2 J a − JJ ba + Jb
3 3/2 –Ja + Jb – Jc 8 1/2 Ja –Jb +2Jc
4 3/2 Ja + Jb – Jc 9 1/2 –Ja +Jb + 2Jc
5 3/2 –Ja – Jb + 3Jc 10 1/2 Ja + Jb + 2Jc
130 APPENDIX C
COMPUTER CODES TO CALCULATE THE SPIN EXCHANGE ENERGIES 3+ 2+ OF (Fe )6 AND (Co )9 CLUSTERS
3+ C.1. (Fe )6 hexamer
C.1.1 Review of Spin-exchange model
3+ Figure C.1 shows a cartoon of the spin-exchange model for the (Fe )6 hexamer,
Cs4Na7 [Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6), described in Chapter 5.
J1
Fe4
Fe3 Fe3 ′
J2
Fe2
Fe1 Fe1′
J1
Figure C.1. Schematic of the Heisenberg spin exchange model for central {Fe6(OH)9} unit Cs4Na7 [Fe6(OH)3(A-α-GeW9O34(OH)3)2] (GeFe6). J1 is the intra-trimer exchange coupling constant and J2 the inter-trimer constant.
131 The Heisenberg spin exchange Hamiltonian corresponding to the model shown in Figure C.1.1 can be written as:
H exchange = –2J1 [S1 S2 + S1′ S2 + S1 S1′ + S3 S4 + S3′ S4 + S3 S3′]
– 2J2 [S1 S3 + S2 S4 + S1′ S3′] (C.1)
th where, Si is the spin operator on the i ion and J1 and J2 are defined earlier. Following Kambe vector-coupling method [93], we can rearrange the Eq. (C.1.1) as Eq. (C.1.2).
2 2 2 2 2 2 2 2 H exchange = –J1 [(S121′) + (S343′) – (S1) – (S2) – (S1′) – (S3) – (S4) – (S3′) ]
2 2 2 – J2 [(ST) – (S121′) – (S343′) ] (C.2)
Here, S12 = S1 + S2, S121′ = S12 + S1′, S34 = S3 + S4, S343′ = S34 + S3′ and ST = S121′ + S343′ are the spin operators. Considering that for Fe3+ (3d 5) ion spin S = 5/2, the eigenvalues of Eq. (C.1.2) can be given as:
E (ST, S121′, S343′, S1, S2, S3, S4, S5, S6) = –J1 [S121′ (S121′ + 1) + S343′ (S343′ + 1) – S1 (S1 + 1)
– S2 (S2 + 1) – S3 (S3 + 1) – S4(S4 + 1) – S5 (S5 + 1) – S6 (S6 + 1)]
– J2 [ST (ST + 1) – S121′ (S121′ + 1) – S343′ (S343′ + 1)] (C.3)
where, the intermediate spins S12, S121′, S34, S343′ and the total spin ST can take the values:
S12 = |S1 – S2| to S1 + S2 ; S121′ = |S12 – S1′| to S12 + S1′ ; S34 = |S3 – S4| to S3 + S4,
S343′ = |S34 – S3′| to S34 + S3′ and ST = |S121′ – S343′| to S121′ + S343′ (C.4)
The above described spin formalism results in 4332 different spin states ranging from ST
= 0–15, corresponding to various combinations of S121′ and S343′, which in turn depend on
S12 and S34, respectively. The math software Mathematica [187] is used to write a general code to calculate Heisenberg exchange energies corresponding to Eq. (C.3). Although, the code given in 3+ section C.1.2 is shown for the (Fe )6 hexamer of GeFe6, in principle it can be used for any spin combinations with trigonal-prism topology.
132 3+ C.1.2. Program code for the (Fe )6 hexamer of GeFe6
np = 4 S1 = S2 = S3 = S4 = S5 = S6 = 5/2 stmp = OpenWrite["Fe6_heisenberg.dat", FormatType -> OutputForm] Write[stmp, "Heisenberg spin exchange energies for a dimer of triangular arrangement \ of spin 5/2 Fe(3+) ions"] Write[stmp,"S12", " ", "S123", " ", "S45", " ", "S456", " ","ST", " ", "Energy"] Do[S12 = 0 + ooo; Do[S123 = 0 + nnn; Do[S45 = 0 + mmm; Do[S456 = 0 + lll; Do[ST = 0 + kkk; Energy = -(J1*(S123*(S123+1)+ S456*(S456+1)- S1*(S1+1)- S2*(S2+1)- S3*(S3+1)- S4*(S4+1)- S5*(S5+1)-S6*(S6+1))) - (J2*(ST*(ST+1)- S123*(S123+1) - S456*(S456+1))); Write["Fe6_heisenberg.dat", SetPrecision[S12,2], " ", SetPrecision[S123,2], " ", SetPrecision[S45,2], " ", SetPrecision[S456,2], " ", SetPrecision[ST,3], " ", SetPrecision[Energy, np]]; Clear[ST], {kkk, Abs[S123 - S456], S123 + S456}]; Clear[S456], {lll, Abs[S45-S6], S45+S6}]; Clear[S45], {mmm, Abs[S4-S5], S4+S5}]; Clear[S123], {nnn, Abs[S12-S3], S12+S3}]; Clear[S12], {ooo, Abs[S1-S2], S1+S2}] Close[stmp]
Brief description of the code is as follows. ‘np’ in the first line defines the number of decimal places; spin values (S) are fed in the second line; third line creates the output file; the ‘Do’ loops perform the calculations and write the results to the output file created
133 in the third line. Table C.1. shows a representative example of the output created for spin
ST = 0.
Table C.1. A sample output file format created by the aforementioned code.
Output file name: Fe6_heisenberg.dat
Heisenberg spin exchange energies for a dimer of triangular arrangement of spin 5/2 Fe(3+) ions.
S12 S123 S45 S456 ST Energy 0 2.5 0 2.5 0 35J1 + 17.5J2 0 2.5 0 2.5 1 35J1 + 15.5J2 0 2.5 0 2.5 2 35J1 + 11.5J2 0 2.5 0 2.5 3 35J1 + 5.5J2 0 2.5 0 2.5 4 35J1 - 2.5J2 0 2.5 0 2.5 5 35J1 - 12.5J2 0 2.5 1 1.5 1 40J1 + 10.5J2 0 2.5 1 1.5 2 40J1 + 6.5J2 0 2.5 1 1.5 3 40J1 + 0.5J2 0 2.5 1 1.5 4 40J1 - 7.5J2 0 2.5 1 2.5 0 35J1 + 17.5J2 0 2.5 1 2.5 1 35J1 + 15.5J2 0 2.5 1 2.5 2 35J1 + 11.5J2 0 2.5 1 2.5 3 35J1 + 5.5J2 0 2.5 1 2.5 4 35J1 - 2.5J2 0 2.5 1 2.5 5 35J1 - 12.5J2
134 2+ C.2. (Co )9 nonamer
C.2.1 Review of the spin-exchange model
3 J 1 2
J2 1
J3 J3 5 8 9 J2 J2 4 7 J1 J1 J3 6 Co O Cl
2+ Figure C.2. Schematic of spin-exchange coupling for the (Co )9 core of Na5[Co6 (H2O)30 {Co9Cl2(OH)3(H2O)9(β-SiW8O31)3}] (SiCo15). The color code is as follows. Intra-trimer exchange constants are J1, J2 and the inter-trimer constant is J3. Limited oxygens are shown for clarity.
The appropriate anisotropic exchange Hamiltonian, described in Chapter 6 for the core 2+ (Co )9 of SiCo15 can be written as:
Hexchange = –2J1z [S1zS3z + S2zS3z + S4zS6z + S5zS6z + S7zS9z + S8zS9z]
– 2J2z [S1zS2z + S4zS5z + S7zS8z]
– 2J3z [S1zS4z + S1zS7z + S2zS5z + S2zS8z + S4zS7z + S5zS8z] (C.4)
135 where, J1z, J2z are intra-trimer exchange coupling constants, J3z the inter-trimer exchange constant, Siz the z-component of the spin operator associated with the effective spin Seff = 1/2 of the ith ion. The numbering, 1 through 9, of the atoms in Eq. (C.4) respectively correspond to the cobalt ions in Figure C.2. Once again, using Kambe vector coupling method [93], Eq. (C.4) can be rearranged as in Eq. (C.5).
2 2 2 2 2 2 2 2 2 Hexchange = –2J1z [(S123) + (S456) + (S789) – (S12) – (S45) – (S78) – (S3) – (S6) – (S9) ]
2 2 2 2 2 2 2 2 2 – 2J2z [(S12) + (S45) + (S78) – (S1) – (S2) – (S4) – (S5) – (S7) – (S8) ]
2 2 2 2 – 2J3z [(ST) – (S123) – (S456) – (S789) ] (C.5)
The eigenvalues corresponding to Eq. (C.5) are:
E(ST, S123, S456, S789, S12, S45, S78, S1, S2, S3, S4, S5, S6, S7, S8, S9) =
–J1z [S123(S123+1) + S456(S456+1) + S789(S789+1) – S12(S12+1) – S45(S45+1)
– S78(S78+1) – S3(S3+1) – S6(S6+1) – S9(S9+1)] – J2z [S12(S12+1) + S45(S45+1) + S78(S78+1)
– S1(S1+1) – S2(S2+1) – S4(S4+1) – S5(S5+1) – S7(S7+1) – S8(S8+1)] – J3z [ST (ST+1) –
S123(S123+1) – S456(S456+1) – S789(S789+1)] (C.5) where, spins of the form Sij and Sijk are the intermediate spins that can take values, respectively from |Si – Sj| to Si + Sj and |Sij – Sk| to Sij + Sk and ST is the total spin of the nonamer. There are 126 spin states corresponding to various combinations of spins Sij and 2+ Sijk. Once again, the code given in section C.2.2 even though is shown for Co ion with
effective spin Seff = ½, it can be used for any spins making up the triangle of triangle shape. The code generated spin energy levels are listed in Table C.2.
136 2+ C.2.2. Computer code for the (Co )9 cluster of SiCo15
np = 2 S1 = S2 = S3 = S4 = S5 = S6 = S7 = S8 = S9 = 1/2 stmp = OpenWrite["Co9_ising.dat", FormatType -> OutputForm] Write[stmp, "Ising spin exchange energies for a triangle of triangles arrangement \ of effective spin 1/2 Co(2+) ions"] Write[stmp,"S12", " ", "S123", " ", "S45", " ", "S456", " ", "S78", " ", "S789", " ", "SA", " ", "ST", " ", "Energy"] Do[S12 = 0 + rrr; Do[S123 = 0 + qqq; Do[S45 = 0 + ppp; Do[S456 = 0 + ooo; Do[S78 = 0 + nnn; Do[S789 = 0 + mmm; Do[SA = 0 + lll; Do[ST = 0 + kkk; Energy = -(J1*(S123*(S123+1)+ S456*(S456+1)+ S789*(S789+1)- S12*(S12+1)- S45*(S45+1)- S78*(S78+1)- S3*(S3+1)- S6*(S6+1)- S9*(S9+1))) - (J2*(S12*(S12 + 1)+ S45*(S45+1)+ S78*(S78+1)- S1*(S1+1)- S2*(S2+1)- S4*(S4+1)- S5*(S5+1)- S7*(S7+1)- S8*(S8+1))) - (J3*(ST*(ST+1)- S123*(S123+1) - S456*(S456+1)- S789*(S789+1))); Write["Co9_ising.dat", SetPrecision[S12,np], " ", SetPrecision[S123,np], " ", SetPrecision[S45,np], " ", SetPrecision[S456,np], " ", SetPrecision[S78,np], " ", SetPrecision[S789,np], " ", SetPrecision[SA,np], " ", SetPrecision[ST,np], " ", SetPrecision[Energy, np]]; Clear[ST], {kkk, Abs[SA - S789], SA + S789}]; Clear[SA], {lll, Abs[S123-S456], S123+S456}]; Clear[S789], {mmm, Abs[S78-S9], S78+S9}];
137 Clear[S78], {nnn, Abs[S7-S8], S7+S8}]; Clear[S456], {ooo, Abs[S45-S6], S45+S6}]; Clear[S45], {ppp, Abs[S4-S5], S4+S5}]; Clear[S123], {qqq, Abs[S12-S3], S12+S3}]; Clear[S12], {rrr, Abs[S1-S2], S1+S2}] Close[stmp]
Table C.2. A sample list of spin energy levels generated by the code.
S12 S123 S45 S456 S78 S789 SA ST Energy 0 0.5 0 0.5 0 0.5 0 0.5 4.5 J2 + 1.5 J3 0 0.5 0 0.5 0 0.5 1 0.5 4.5 J2 + 1.5 J3 0 0.5 0 0.5 0 0.5 1 1.5 4.5 J2 - 1.5 J3 0 0.5 0 0.5 1 0.5 0 0.5 2 J1 + 2.5 J2 + 1.5 J3 0 0.5 0 0.5 1 0.5 1 0.5 2 J1 + 2.5 J2 + 1.5 J3 0 0.5 0 0.5 1 0.5 1 1.5 2 J1 + 2.5 J2 - 1.5 J3 0 0.5 0 0.5 1 1.5 0 1.5 -J1 + 2.5 J2 + 1.5 J3 0 0.5 0 0.5 1 1.5 1 0.5 -J1 + 2.5 J2 + 4.5 J3 0 0.5 0 0.5 1 1.5 1 1.5 -J1 + 2.5 J2 + 1.5 J3 0 0.5 0 0.5 1 1.5 1 2.5 -J1 + 2.5 J2 - 3.5 J3
138 BIBILOGRAPHY
1. Kortz, U.; Nellutla, S.; Stowe, A. C.; Dalal, N. S.; van Tol, J.; Bassil, B. S. Inorg. Chem. 2004, 43, 144.
2. Kortz, U.; Nellutla, S.; Stowe, A. C.; Dalal, N. S.; Rauwald, U.; Danquah, W.; Ravot, D. Inorg. Chem. 2004, 43, 2308.
3. Bi, L.-H.; Kortz, U. Inorg. Chem. 2004, 43, 7961.
4. Nellutla, S.; van Tol, J.; Dalal, N. S.; Bi, L.-H.; Kortz, U.; Keita, B.; Nadjo, L.; Khitrov, G. A.; Marshall, A. G. Inorg. Chem. 2005, 44, 9795.
5. Bi, L.-H.; Kortz, U.; Nellutla, S.; Stowe, A. C.; van Tol, J.; Dalal, N. S.; Keita, B.; Nadjo, L. Inorg. Chem. 2005, 44, 896.
6. Bassil, B. S.; Nellutla, S.; Kortz, U.; Stowe, A. C.; van Tol, J.; Dalal, N. S.; Keita, B.; Nadjo, L. Inorg. Chem. 2005, 44, 2659.
7. Legget, A. J. Phys. Rev. B 1984, 30, 1208.
8. Stamp, P. C.; Chudnovsky, E. M.; Barbara, B. Int. J. Mod. Phys. 1992, 6, 1355.
9. Awschalom, D. D.; DiVincenzo, D. P.; Smyth, J. F. Science 1992, 258, 414.
10. Hasset, K. L.; Stecher, L. C.; Hendrickson, D. N. Inorg. Chem. 1980, 19, 416.
11. Caneschi, A.; Gatteschi, D.; Sessoli, R.; Barra, A. L.; Brunel, L. C.; Guillot, M. J. Am. Chem. Soc. 1988, 110, 2795.
12. Schmid, G. Chem. Rev. 1992, 92, 1709.
13. Barra, A. L.; Gatteschi, D.; Pardi, L.; Mueller, A.; Doering, J. J. Am. Chem. Soc. 1992, 114, 8509.
14. Castro, S. L.; Sun, Z.; Grant, C. M.; Bollinger, J. C.; Hendrickson, D. N.; Christou, G. J. Am. Chem. Soc. 1998, 120, 2365.
15. Barra, A. L.; Caneschi, A.; Cornia, A.; Fabrizi de Biani, F.; Gatteschi, D.; Sangregorio, C.; Sessoli, R.; Sorace, L. J. Am. Chem. Soc. 1999, 121, 5302.
16. Coronado, E.; Feliz, M.; Forment-Aliaga, A.; Gomez-Garcia, C. J.; Llusar, R.; Romero, F. M. Inorg. Chem. 2001, 40, 6084.
139
17. Ochsenbein, S. T.; Murrie, M.; Rusanov, E.; Stoeckli-Evans, H.; Sekine, C.; Güdel, H. U. Inorg. Chem. 2002, 41, 5133.
18. Karasawa, S.; Zhou, G.; Morikawa, H.; Koga, N. J. Am. Chem. Soc. 2003, 125, 13676.
19. Ishikawa, N.; Sugita, M.; Ishikawa, T.; Koshihara, S.-y.; Kaizu, Y.; J. Am. Chem. Soc. 2003, 125, 8694.
20. Forment-Aliaga, A.; Coronado, E.; Feliz, M.; Gaita-Arino, A.; Llusar, R.; Romero, F. M. Inorg. Chem. 2003, 42, 8019.
21. Ishikawa, N.; Sugita, M.; Ishikawa, T.; Koshihara, S.-y.; Kaizu, Y.; J. Phys. Chem. B. 2004, 108, 11265.
22. Soler, M.; Wernsdorfer, W.; Folting, K.; Pink, M.; Christou, G. J. Am. Chem. Soc. 2004, 126, 2156.
23. Murugesu, M.; Raftery, J.; Wernsdorfer, W.; Christou, G.; Brechin, E. K. Inorg. Chem. 2004, 43, 4203.
24. Palii, A. V.; Ostrovsky, S. M.; Klokishner, S. I.; Tsukerblat, B. S.; Berlinguette, C. P.; Dunbar, K. R.; Galan-Mascaros, J. R. J. Am. Chem. Soc. 2004, 126, 16860.
25. Murugesu, M.; Habrych, M.; Wernsdorfer, W.; Abboud, K. A.; Christou, G. J. Am. Chem. Soc. 2004, 126, 4766.
26. Christou, G.; Gatteschi, D.; Hendrickson, D.; Sessoli, R. MRS Bulletin 2000, 25, 66-71 and references therein.
27. Gatteschi, D.; Sessoli, R. Angew. Int. Ed. Engl. 2003, 42, 268.
28. Chudnovsky, E. M.; Tejada, J. Macroscopic Quantum Tunneling of the Magnetic Moment (Cambridge University: Cambridge, 1998).
29. Friedman, J. R.; Sarachik, M. P.; Tejada, J.; Ziolo, R. Phys. Rev. Lett. 1996, 76, 3830.
30. Thomas, L.; Lionit, F.; Gatteschi, D.; Sessoli, R.; Barbara, B. Nature 1996, 383, 145.
31. Eppley, H. J.; Tsai, H.-L.; de Vries, N.; Folting, K.; Christou, G.; Hendrickson, D. N. J. Am. Chem. Soc. 1995, 117, 301.
140
32. Bellessa, G.; Vernier, N.; Barbara, B.; Gatteschi, D. Phys. Rev. Lett. 1999, 83, 416.
33. Chiorescu, I.; Wernsdorfer, W.; Müller, A.; Miyashita, S.; Barbara, B. Phys. Rev. B 2003, 67, 020402.
34. Chiorescu, I.; Wernsdorfer, W.; Müller, A.; Böge, H.; Barbara, B. J. Magn. Magn. Mat. 2000, 211, 103.
35. Chiorescu, I.; Wernsdorfer, W.; Barbara, B.; Müller, A.; Böge, H. J. Appl. Phys. 2000, 87, 5496.
36. North, J. M.; Zipse, D.; Dalal, N. S.; Choi, E. S.; Jobiliong, E.; Brooks, J. S.; Eaton, D. L. Phys. Rev. B 2003, 67, 174407.
37. Zipse, D.; Dalal, N. S.; Vasic, R.; Brooks, J. S.; Kögerler, P. Phys. Rev. B 2005, 71, 064417-1.
38. Evangelisti, M.; Luis, F.; Mettes, F. L.; Aliaga, N.; Aromí, G.; Alonso, J. J.; Christou, G.; de Jongh, L. J. Phys. Rev. Lett. 2004, 93, 117202.
39. Ferbinteanu, M.; Miyasaka, H.; Wernsdorfer, W.; Nakata, K.; Sugiura, K.-i.; Yamashita, M.; Coulon, C.; Clerac, R. J. Am. Chem. Soc. 2005, 127, 3090.
40. Schön, G.; Simon, U. Colloid and polymer science 1995, 273, 101.
41. Loss, D.; Divincenzo, D. P. Phys. Rev. A, 1998, 57, 120.
42. Chusuei, C. C.; Lai, X.; Luo, K.; Goodman, D. W. Topics in Catalysis, 2000, 14, 71-83.
43. Santra, A. K.; Goodman, D. W. J. Phys. Cond. Matter 2002, 14, R31.
44. Weinstock, I. A. Chem. Rev. 1998, 98, 113.
45. Kozhenvnikov, I. V. Chem. Rev. 1998, 98, 171.
46. Mizuno, N.; Misono, M. Chem. Rev. 1998, 98, 199.
47. Sadakane, M.; Steckhan, E. Chem. Rev. 1998, 98, 219.
48. Schinazi, R. F. Chem. Rev. 1998, 98, 327.
49. Coronado, E.; Gómez-García, C. J. Chem. Rev. 1998, 98, 273.
141
50. Yamase, T. Chem. Rev. 1998, 98, 307.
51. Yamase, T.; Pope, M. T. Eds. Polyoxometalate Chemistry for Nano-Composite Design (Kluwer, Dordecht, 2002).
52. McCuster, J. K.; Schmitt, E. A.; Hendrickson, D. N. Magnetic Molecular Materials, NATO ASI Series, Kluwer, 1991, E198, 297.
53. Müller, A.; Peters, F.; Pope, M. T.; Gatteschi, D. Chem. Rev. 1998, 98, 239.
54. Clemente-Juan, J. M.; Coronado, E. Coord. Chem. Rev. 1999, 193-195, 361.
55. Borrás-Almenar, J. J.; Coronado, E.; Müller, A.; Pope, M. T. Eds. Polyoxometalate Molecular Science (Kluwer, Dordecht, 2004).
56. Delfs, C. D.; Gatteschi, D.; Pardi, L. Comm. Inorg. Chem. 1993, 15, 27.
57. Kahn, O. Chem. Phys. Lett. 1997, 265, 109.
58. Kahn, O. Molecular Magnetism (VCH, New York, 1993).
59. Keggin, J. F. Nature 1933, 131, 908.
60. Pope, M. T.; Müller, A. Angew. Chem. Int. Ed. Engl. 1991, 30, 34.
61. Berzelius, J. Poggendorff’s Ann. Phys. 1826, 6, 369.
62. Pope, M. T. Heteropoly and Isopoly Oxometalates (Springer-Verlag: Berlin, 1983).
63. Pope, M. T.; Müller, A. Eds. Polyoxometalates: From Platonic Solids to Anti Retroviral Activity (Kluwer: Dordecht, 1994).
64. Klemperer, W. G.; Wall, C. G. Chem. Rev. 1998, 98, 297.
65. Katsoulis, D. E. Chem. Rev. 1998, 98, 359.
66. Pope, M. T.; Müller, A. Eds. Polyoxometalate Chemitry: From Topology via Self-Assembly to Applications (Kluwer: Dordecht, 2001).
67. Stowe, A.C. Characterization of High Spin Molecular Magnets (Dissertation, Florida State University, 2004).
142
68. Weighardt, K.; Pohl, K.; Jibril, I.; and Huttner, G. Angew. Chem. Int. Ed. Engl. 1984, 23, 77-78.
69. Zipse, D.; Abboud, K. A.; Dalal, N. S. J. Appl. Phys. 2003, 93, 7806.
70. Carlin, R. Molecular Magnetochemistry (Springer-Verlag: Berlin, 1986).
71. Gómez-García, C. J.; Coronado, E.; Borrás-Almenar, J. J. Inorg. Chem. 1992, 31, 1667.
72. Casan-Pastor, N.; Bas-Serra, J.; Coronado, E.; Pourroy, G.; Baker, L. C. W. J. Am. Chem. Soc. 1992, 114, 10380.
73. Andres, H.; Clemente-Juan, J. M.; Aebersold, M.; Güdel, H.-U.; Coronado, E.; Büttner, H.; Kearly, G.; Melero, J.; Burriel, R. J. Am. Chem. Soc. 1999, 121, 10028.
74. Basler, R.; Borrás-Almenar, J. J.; Gaita, A.; Janssen, S. Inorg. Chem. 2001, 40, 1943.
75. Sinn, E. Coord. Chem. Rev. 1970, 5, 313.
76. Abragam, A.; Bleaney, B. Electron Paramagnetic Resonance of Transition Ions (Dover, New York, 1970).
77. Weil, J. A.; Bolton, J. R.; Wertz, J. E. Electron Paramagnetic Resonance: Elementary Theory and Practical Applications (John Wiley & Sons, New York, 1994).
78. Pilbrow, J. R. Transition Ion Electron Paramagnetic Resonance (Clarendon Press, Oxford, 1990).
79. Hendrickson, D. N. In Research Frontiers in Magnetochemistry, Charles, J. O’Connor, Ed. (World Scientific: New Jersey, 1993, pg 87).
80. Terasaki, I.; Sasago, Y.; Uchinokura, K. Phys. Rev. B 1997, 56, 12685.
81. Ray, R.; Ghoshray, A.; Ghoshray, K.; Nakamura, S. Phys. Rev. B 1999, 59, 9454.
82. Greedan, J. E. J. Mater. Chem. 2001, 11, 37.
83. Toulouse, G. Commun. Phys. 1977, 2, 115.
84. Gibbs, W. J. Am. Chem. Soc. 1885, 7, 317.
143
85. Rosenheim, A.; Wolff, A. Z. Anorg. Allg. Chem. 1930, 64, 193.
86. Tourné, C.; Revel, A.; Tourné, G.; Vendrell, M. C. R. Acad. Sci., Ser. C 1973, 277, 643.
87. Robert, F.; Leyrie, M.; Hervé, G. Acta. Crystallogr. 1982, B38, 358.
88. Kortz, U.; Al-Kassem, N. K.; Savelieff, M. G.; Al Kadi, N. A.; Sadanke, M. Inorg. Chem. 2001, 40, 4742.
89. Sheldrick, G. M. SADABS; Siemens Analytical X-ray Instrument Division: Madison, WI, 1995.
90. Vulfson, S. G. Molecular Magnetochemistry (Gordon and Breach Science: Newark, NJ, 1998, pg 241).
91. Cage, B.; Hassam, A. K.; Pardi, L.; Krzystek, J.; Brunel, L.-C.; Dalal, N. S. J. Magn. Reson. 1997, 124, 495.
92. Hassan, A. K.; Pardi, L. A.; Krzystek, J.; Sienkiewicz, A.; Goy, P.; Rohrer, M.; Brunel, L.-C. J. Magn. Reson. 2000, 142, 300.
93. Kambe, K. J. Phys. Soc. Jpn. 1950, 5, 48.
94. Siedle, A. R.; Padula, F.; Baranowski, J.; Goldstein, C.; DeAngelo, M.; Kokoszka, G. F.; Azevedo, L.; Venturini, E. L. J. Am. Chem. Soc. 1983, 105, 7447.
95. Cho, Y. H.; So, H. Bull. Korean Chem. Soc. 1995, 16, 243.
96. Katano, H.; Osakai, T.; Himeno, S.; Saito, A. Electrochim. Acta 1995, 40, 2935.
97. Dorokhova, E. N.; Kazanskii, L. P.; Prokhorova, G. V. Zh. Neorg. Khim. 1985, 30, 2795.
98. Liu, J. F.; Zhao, B. L.; Rong, C. Y.; Pope, M. T. Acta Chim. Sin. 1993, 51, 368.
99. Qu, L. Y.; Sun, Y. J.; Chen, Y. G.; Yu, M.; Peng, J. Synth. React. Inorg. Met.- Org. Chem. 1994, 24, 1339.
100. Meng, L.; Liu, J. F. Chin. Chem. Lett. 1995, 6, 265.
144
101. Weakley, T. J. R.; Evans, H. T. jun.; Showell, J. S.; Tourné, G. F.; Tourné, C. M. J. Chem. Soc., Chem. Commun. 1973, 139.
102. Evans, H. T.; Tourné, C. M.; Tourné, G. F.; Weakley, T. J. R. J. Chem. Soc., Dalton Trans. 1986, 2699.
103. Finke, R. G.; Droege, M.; Hutchinson, J. R.; Gansow, O. J. Am. Chem. Soc. 1981, 103, 1587.
104. Gómez-García, C. J.; Casan-Pastor, N.; Coronado, E.; Baker, L. C. W.; Pourroy, G. J. Appl. Phys. 1990, 67, 5995.
105. Gómez-García, C. J.; Coronado, E.; Gómez-Romero, P.; Casan-Pastor, N. Inorg. Chem. 1993, 32, 3378.
106. Zhang, X.-Y.; Jameson, G. B.; O’Connor, C. J.; Pope, M. T. Polyhedron 1996, 15, 917.
107. Zhang, X.; Chen, Q.; Duncan, D. C.; Lachicotte, R. J.; Hill, C. L. Inorg. Chem. 1997, 36, 4381.
108. Clemente-Juan, J. M.; Coronado, E.; Galán-Mascarós, J. R.; Gómez-García,C. J. Inorg. Chem. 1999, 38, 55.
109. Kortz, U.; Isber, S.; Dickman, M. H.; Ravot, D. Inorg. Chem. 2000, 39, 2915.
110. Bi, L.-H.; Huang, R.-D.; Peng, J.; Wang, E.-B.; Wang, Y.-H.; Hu, C.-W. J. Chem. Soc., Dalton Trans. 2001, 121.
111. Finke, R. G.; Droege, M. W. Inorg. Chem. 1983, 22, 1006.
112. Gómez-García, C. J.; Borrás-Almenar, J. J.; Coronado, E.; Ouahab, L. Inorg. Chem. 1994, 33, 4016.
113. Bi, L.-H.; Wang, E.-B.; Peng, J.; Huang, R.-D.; Xu, L.; Hu, C.-W. Inorg. Chem. 2000, 39, 671.
114. Pope, M. T. Comp. Coord. Chem. II 2003, 4, 635.
115. Weakley, T. J. R.; Finke, R. G. Inorg. Chem. 1990, 29, 1235.
116. Mialane, P.; Dolbecq, A.; Marrot, J.; Rivière, E.; Sécheresse, F. Angew. Chem., Int. Ed. Engl. 2003, 42, 3523.
145
117. Mal, S. S.; Kortz, U. Angew. Chem. Int. Ed. 2005, 44, 3777.
118. Gojon, E.; Gaillard, J.; Latour, J. -M.; Laugier, J. Inorg. Chem. 1987, 26, 2046.
119. Shanmugan, M.; Muthuvijayan, L.; Tiwary, S. K.; Chakravarthy, A. R. Inorg. Chem. 1995, 34, 5091.
120. Doyle, A. A.; Parsons, S.; Solan, G. A.; Winpenny, R. E. P. J. Chem. Soc., Dalton Trans. 1997, 2131.
121. Song, Y.; Liu, J-C.; Liu, Y-J.; Zhu, D-R.; Zhuang, J-Z.; You, X-Z. Inorg. Chim. Acta. 2000, 305, 135.
122. Papaefstathiou, G. S.; Raptopoulou, C. P.; Tsohos, A. T.; Bakalbassis, E. G.; Perlepes, S. P. Inorg. Chem. 2000, 39, 4658.
123. Laronze, N.; Marrot, J.; Hervé, G. Inorg. Chem. 2003, 42, 5857.
124. Laronze, N.; Marrot, J.; Hervé, G. Chem. Commun. 2003, 2360.
125. Brown, I. D.; Altermatt, D. Acta Crystallogr. 1985, B41, 244.
126. Crawford, V. H.; Richardson, H. W.; Wasson, J. R.; Hodgson, D. J.; Hatfield, W. E. Inorg. Chem. 1976, 15, 2107.
127. Buvaylo, E. A.; Kokozay, V. N.; Vassilyeva, O. Y.; Skelton, B. W.; Jezierska, J.; Brunel, L-C.; Ozarowski, A. Inorg. Chem. 2005, 44, 206.
128. Maki, A. H.; McGarvey, B. R. J. Chem. Phys. 1958, 29, 31 & 35.
129. McGarvey, B. R. J. Phys. Chem. 1967, 71, 51.
130. Hathaway, B. J.; Billing, D. E. Coord. Chem. Rev. 1970, 5, 143.
131. Stevens, K. W. H. Proc. Roy. Soc. (London) 1953, A219, 542.
132. Owen, J. Proc. Roy. Soc. (London) 1955, A227, 183.
133. Owen, J. Discussions Faraday Soc. 1955, 19, 127.
134. Kivelson, D.; Neiman, R. J. Chem. Phys. 1961, 35, 149.
135. Gersmann, H. R.; Swalen, J. D. J. Chem. Phys. 1962, 36, 3221.
146
136. Dalal, N. S.; Millar, J. M; Jagadeesh, M. S.; Seehra, M. S. J. Chem. Phys. 1981, 74, 1916.
137. Abragam, A.; Pryce, H. M. L. Proc. Roy. Soc. (London) 1951, A205, 135 & 1951, A206, 164.
138. Billing, D. E.; Hathaway, B. J. J. Chem. Soc. (A) 1968, 1516.
139. Lippard, S. J. Angew. Chem. Int. Ed. Engl. 1988, 27, 344.
140. Kurtz, D. M. Jr. Chem. Rev. 1990, 90, 585.
141. Wilkins, P. C.; Wilkins, R. G. Coord. Chem. Rev. 1987, 79, 195.
142. Ericson, A.; Hedman, B.; Hodgson, K. O.; Green, J.; Dalton, H.; Bentsen, J. G.; Beer, R. H.; Lippard, S. J. J. Am. Chem. Soc. 1988, 110, 2330.
143. Lammers, M.; Follmann, H. Struct. Bonding (Berlin) 1983, 54, 27.
144. Theil, E. C. Annu. Rev. Biochem. 1987, 57, 289 and references therein.
145. Caneschi, A.; Gatteschi, A.; Sangregorio, C.; Sessoli, R. Sorace, L.; Cornia, A.; Novak, M. A.; Paulsen, C.; Wernsdorfer, W. J. Magn. Magn. Mat. 1999, 200, 182.
146. Barra, A. L.; Debrunner, P.; Gatteschi, D.; Schultz, Ch. E.; Sessoli, R. Europhys . Lett. 1996, 35, 133.
147. Sangregorio, C.; Ohm, T.; Paulsen, C.; Sessoli, R.; Gatteschi, D. Phy. Rev. Lett. 1997, 78, 4645.
148. McCusker, J. K.; Christmas, C. A.; Hagen, P. M.; Chadha, R. K.; Harvey, D. F.; Hendrickson, D. N. J. Am. Chem. Soc. 1991, 113, 6114.
149. Delfs, C.; Gatteschi, D.; Pardi, L.; Sessoli, R.; Weighardt, K.; Hanke, D. Inorg. Chem. 1993, 32, 3099.
150. 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. J. Am. Chem. Soc. 1993, 115, 12483.
151. Cañada-Vilalta, C.; O’Brien, T. A.; Brechin, E. K.; Pink, M.; Davidson, E. R.; Christou, G. Inorg. Chem. 2004, 43, 5505 and references therein.
147
152. Mbomekalle, I. M.; Keita, B.; Nadjo, L.; Neiwert, W. A.; Zhang, L.; Hardcastle, K. I.; Hill, C. L.; Anderson, T. M. Eur. J. Inorg. Chem. 2003, 3924.
153. Anderson, T. M.; Zhang, X.; Hardcastle, K. I.; Hill, C. L. Inorg. Chem. 2002, 41, 2477.
154. Zhang, X.; Duncan, D. C.; Chen, Q.; Hill, C. L. Inorg. Synth. 2002, 33, 52.
155. Limanski, E. M.; Piepenbrink, M.; Droste, E.; Burgemeister, K.; Krebs, B. J. Cluster Sci. 2002, 13, 369.
156. Anderson, T. M.; Hardcastle, K. I.; Okun, N.; Hill, C. L. Inorg. Chem. 2001, 40, 6418.
157. Zhang, X.; Chen, Q.; Duncan, D. C.; Lachicotte, R. J.; Hill, C. L. Inorg. Chem. 1997, 36, 4381.
158. Zhang, X.; Chen, Q.; Duncan, D. C.; Campana, C. F.; Hill, C. L. Inorg. Chem. 1997, 36, 4208.
159. Li, M.-X.; Jin, S.-L.; Liu, H.-Z.; Xie, G.-Y.; Chen, M.-Q.; Xu, Z.; You, X.-Z. Polyhedron 1998, 17, 3721.
160. Nozaki, C.; Kiyoto, I.; Minai, Y.; Misono, M.; Mizuno, N. Inorg. Chem. 1999, 38, 5724.
161. Tézé, A.; Vaissermann, J. C. R. Acad. Sci., Ser. IIc: Chim. 2000, 3, 101.
162. Kortz, U.; Savelieff, M. G.; Bassil, B. S.; Keita, B.; Nadjo, L. Inorg. Chem. 2002, 41, 783.
163. Hervé, G.; Tézé, A. Inorg. Chem. 1977, 16, 2115.
164. Müller, A.; Plass, W.; Krickemeyer, E.; Sessoli, R.; Gatteschi, D.; Meyer, J.; Bögge, H.; Kröckel, M.; Trautwein, A. X. Inorg. Chim. Acta 1998, 271, 9.
165. Haraguchi, N.; Okaue, Y.; Isobe, T.; Matsuda, Y. Inorg. Chem. 1994, 33, 1015.
166. Micklitz, W.; Lippard, S. J. Inorg. Chem. 1988, 27, 3067.
167. Micklitz, W.; Bott, S. G.; Bentsen, J. G.; Lippard, S. J. J. Am. Chem. Soc. 1989, 111, 372.
148
168. Brechin, E. K.; Knapp, M. J.; Huffman, J. C.; Hendrickson, D. N.; Christou, G. Inorg. Chim. Acta 2000, 297, 389.
169. Seddon, E. J.; Huffman, J. C.; Christou, G. J. Chem. Soc., Dalton Trans. 2000, 4446.
170. Murugesu, M.; Abboud, K. A.; Christou, G. J. Chem. Soc., Dalton Trans. 2003, 4552.
171. Caneschi, A.; Cornia, A.; Lippard, S. J. Angew. Chem., Int. Ed. Engl. 1995, 34, 467.
172. Caneschi, A.; Cornia, A.; Fabretti, A. C.; Foner, S.; Gatteschi, D.; Grandi, R.; Schenetti, L. Chem. Eur. J. 1996, 2, 1379.
173. Abbati, G. L.; Cornia, A.; Fabretti, A. C.; Malavasi, W.; Schenetti, L.; Caneschi, A.; Gatteschi, D. Inorg. Chem. 1997, 36, 6443.
174. Galán-Mascaró s, J. R.; Gómez-García, C. J.; Borrás-Almenar, J. J.; Coronado, E. Adv. Mater. 1994, 6, 221.
175. Andres, H.; Clemente-Juan, J. M.; Basler, R.; Aebersold, M.; Güdel, H. U.; Borrás-Almenar, J. J.; Gaita, A.; Coronado, E.; Büttner, H.; Janssen, S. Inorg. Chem. 2001, 40, 1943.
176. Clemente-Juan, J. M.; Coronado, E.; Gaita-Ariño, A.; Giménez-Saiz, C.; Güdel, H. U.; Sieber, A.; Bircher, R.; Mutka, H. Inorg. Chem. 2005, 44, 3389.
177. Canny, J.; Tézé, A.; Thouvenot, R.; Hervé, G. Inorg. Chem. 1986, 25, 2114.
178. Kortz, U.; Jeannin, Y. P.; Téze´, A.; Hervé, G.; Isber, S. Inorg. Chem. 1999, 38, 3670.
179. Kortz, U.; Matta, S. Inorg. Chem. 2001, 40, 815.
180. Hussain, F.; Bassil, B. S.; Bi, L.-H.; Reicke, M.; Kortz, U. Angew. Chem., Int. Ed. Engl. 2004, 43, 3485.
181. Weakley, T. J. R. J. Chem. Soc. Chem. Commun. 1984, 1406.
182. Tézé, A.; Hervé, A., G. Inorg. Syntheses 1990, 27, 88.
149
183. Choi, K.-Y.; Matsuda,Y. H.; Nojiri. H.; Ramsey, C.; Stowe, A. C.; Kortz, U.; Dalal, N. S. South East Section American Physical Society meeting, 2005.
184. Meier, F.; Loss, D. Phys. Rev. Lett. 2001, 86, 5373.
185. Honecker, A.; Meier, F.; Loss, D.; Normand, B. Eur. Phys. J. 2002, B27, 487.
186. Affronte, M.; Cornia, A.; Lascialfari, A.; Borsa, F.; Gatteschi, D.; Hinderer, J.; Horvatic, M.; Jansen, A. G. M.; Julien, M.-H. Phys. Rev. Lett. 2002, 88, 167201.
187. Mathematica version 4.0, Wolfram Research Inc.
150
BIOGRAPHICAL SKETCH
EDUCATION
Ph.D.: Physical Chemistry; Florida State University, Department of Chemistry and Biochemistry, January 9, 2006 Research Advisor: Prof. Naresh S. Dalal Dissertation Title: Magnetic and High-Field EPR Studies of New Spin-frustrated Lattices
M.S.: Physical Chemistry; Indian Institute of Technology-Bombay, India, August 2000 Research Advisor: Prof. Parasuraman Selvam Thesis Title: Synthesis, Characterization and Catalytic Properties of Solid Super Acids
B.S.: Mathematics, Physics and Chemistry, Osmania University, India, April 1998
PRESENTATIONS
1. S. Nellutla, N. S. Dalal, Theoretical and Experimental Studies of some new Spin- frustrated Polyoxometalate Systems, Physical Chemistry Seminar Series, Florida State University, November 21, 2005.
2. S. Nellutla, J. van Tol, N. S. Dalal, U. Kortz, A Cu5 Complex as a Model 5 -Spin Frustrated System Studied by High-Field EPR and Magnetization, Physical Phenomena at High Magnetic Fields-V, Tallahassee, FL, August 5-9, 2005.
3. S. Nellutla, J. van Tol, N. S. Dalal, U. Kortz, A Cu20 Inorganic Compound for Studies of Complex Spin Frustrated Systems: Variable Frequency EPR, Magnetization and Theoretical Investigations, Physical Phenomena at High Magnetic Fields-V, Tallahassee, FL, August 5-9, 2005.
4. I. Geru, S. Nellutla, A. C. Stowe, N. S. Dalal, V. M. Mereacre, D. N. Produis, S. G. Shova, C. I. Turta, J. van Tol, Magnetic Characterization of a Heteronuclear Cluster [Fe4Ca2(μ3-O)2(CHCl2COO)12(THF)6], Modern Development of Magnetic Resonance, Kazan, August 15-20, 2004.
151 5. I. Geru, S. Nellutla, A. C. Stowe, N. S. Dalal, V. M. Mereacre, D. N. Produis, S. G. Shova, C. I. Turta, J. van Tol, Magnetic and High Field EPR Investigation of a Heterotrinuclear Cluster [Fe2CuO(CCl3COO)6(THF)3], Modern Development of Magnetic Resonance, Kazan, August 15-20, 2004.
6. C. Stowe, S. Nellutla, N. S. Dalal, U. Kortz, Detailed Analysis of the Hetero Atom Effect on the Magnetic properties of Sandwich-Type Polyoxoanions, 80th Florida Annual Meeting and Exposition of the American Chemical Society, Orlando, FL, May 6-8, 2004.
7. S. Nellutla, A. C. Stowe, N. S. Dalal, I. I. Geru, High Field EPR and th Magnetization studies of [Fe2CuO(CCl3COO)6(THF)3], 80 Florida Annual Meeting and Exposition of the American Chemical Society, Orlando, FL, May6- 8, 2004.
8. S. Nellutla, A. C. Stowe, J. van Tol, N. S. Dalal, U. Kortz, Sandwich-type Germanotungstates: Structure and Magnetic Properties of the Dimeric -12 2+ 2+ th Polyoxoanions [M4(H2O)2(GeW9O34)2] (M = Mn , Cu ), 55 Southeastern Regional Meeting of the American Chemical Society, Atlanta, GA, November 16- 19, 2003.
9. C. Stowe, S. Nellutla, J. van Tol, N. S. Dalal, U. Kortz, Trends in the Magnetic properties of the Tricopper Polyoxotungstates Na12[Cu3(H2O)3(α-XW9O33)2] (X = As, Sb, Se, Te): Effect of Heteroatom, Florida Inorganic Chemistry and Materials Symposium, Gainesville, FL, October 25th, 2003.
10. S. Nellutla, A. C. Stowe, J. van Tol, N. S. Dalal, U. Kortz, Trends in the Magnetic properties of the Tricopper Polyoxotungstates Na12[Cu3(H2O)3(α- rd XW9O33)2] (X = As, Sb, Se, Te): Effect of Heteroatom, 33 Southeastern Magnetic Resonance Conference and Symposium, Tallahassee, FL, October 17-19, 2003.
11. S. Nellutla and N. S. Dalal, EPR and Magnetization studies of Spin-frustrated CuII complexes, Physical Chemistry Seminar Series, Florida State University, April 21, 2003.
12. S. Nellutla, A. C. Stowe, N. S. Dalal, U. Kortz, X-ray crystallography, magnetization and EPR studies of a new CuII tetramer, American Chemical Society National Meeting, New Orleans, LA, March 25, 2003.
13. S. Nellutla, A. C. Stowe, N. S. Dalal, U. Kortz, X-ray crystallography, magnetization and EPR studies of Na12[Cu3(H2O)3(α-AsW9O33)2], American Chemical Society National Meeting, New Orleans, LA, March 25, 2003.
152 14. C. Stowe, S. Nellutla, N. S. Dalal, L-C. Brunel, J. van Tol, U. Kortz, High Field EPR of a copper Trimer Encapsulated between Sandwich-like Arsenotungstates, International Electron Magnetic Resonance Workshop, Tallahassee, FL, December 13-14, 2002.
15. S. Nellutla, C. Ramsey, J. M. North, Teaching Labs Effectively, New Graduate Student Orientation, Florida State University, 2002.
16. S. Nellutla, C. Ramsey, J. M. North, Teaching Labs Effectively, New Graduate Student Orientation, Florida State University, 2001.
PUBLICATIONS
1. Li-Hua. Bi, U. Kortz, M. H. Dickman, S. Nellutla, N. S. Dalal, B. Keita, L. Nadjo, M. Prinz, and M. Neumann, Polyoxoanion with Octahedral Germanium(IV) Hetero Atom: Synthesis, Structure, Magnetism, EPR, Electrochemistry and XPS Studies on the Mixed-Valence 14-Vanadogermanate V IV 8- [GeV 12V 2O40] , J. Cluster Sci. 2006, In press.
2. S. Nellutla, J. van Tol, N. S. Dalal, B. Keita, L. Nadjo, Li-Hua Bi, and U. Kortz, Structure, Magnetism, EPR and Electrochemistry of the Penta-Copper(II) 10- Substituted Tungstosilicate [Cu5(OH)4(H2O)2(A-a-SiW9O33)2] , Inorg. Chem. 2005, 44, 9795.
3. Li-Hua. Bi, U. Kortz, S. Nellutla, A. C. Stowe, J. van Tol, N. S. Dalal, B. Keita, L. Nadjo, Structure, Electrochemistry and Magnetism of the First Iron(III)- -11 Substituted Keggin Dimer, [Fe6(OH)3(A-α-GeW9O34(OH)3)2] , Inorg. Chem. 2005, 44, 896.
4. B. S. Bassil, S. Nellutla, U. Kortz, A. C. Stowe, J. van Tol, N. S. Dalal, B. Keita, L. Nadjo, The Satellite-Shaped Co-15 Polyoxotungstate, [Co6(H2O)30{Co Cl2 -5 (OH)3(H2O)9(β-SiW8O31)3}] , Inorg. Chem. 2005, 44, 2659.
5. C. Stowe, S. Nellutla, N. S. Dalal and U. Kortz, Trends in the Magnetic -n Properties of the Tricopper Polyoxotungstate [Cu3(H2O)3(α-XW9O33)2] (n = 12, X = AsIII, SbIII; n = 10, X = SeIV, TeIV): Effect of the Heteroatom, Eur. J. Inorg. Chem. 2004, 3792.
6. U. Kortz, S. Nellutla, N. S. Dalal, U. Rauwald, W. Danquah, D. Ravot, Sandwich-type Germanotungstates: Structure and Magnetic Properties of the -12 2+ 2+ 2+ 2+ Dimeric Polyoxoanions [M4(H2O)2(GeW9O34)2] (M = Mn , Cu , Zn , Cd ), Inorg. Chem. 2004, 43, 2308.
153
7. U. Kortz, S. Nellutla, N. S. Dalal, J. vanTol, B. S. Bassil, Structure and Magnetism of the Tetra-Copper(II)-Substituted Heteropolyanion -8 [Cu4K2(H2O)8(α-AsW9O33)2] , Inorg. Chem. 2004, 43, 144.
8. Sakthivel, N. Saritha and P.Selvam, Vapour phase tertiary butylation of phenol over sulfated zirconia catalyst, Cat. Lett. 2001, 72, 225.
154