ESR swmss or musmou‘ ‘~ METAL IONS IN UNSTABLE OXIDATION STATES Thesis for the Begree of Phg D. MECHRGAN STATE LENWERSITY JGHN ROBERT SHOCK 1 9 7 3 This is to certify that the thesis entitled ESR STUDIES OF TRANSITION METAL IONS IN UNSTABLE OXIDATION STATES presented by John Robert Shock has been accepted towards fulfillment of the requirements for ___EH._D._degree in m , . z J !-'I . Major PJVJ‘" I Date/jams a: I ?75 0-7639 ’ at?! it} A HDAE & SONS ‘ am amum me. LIBRARY amosns Q 931119705!ch ABSTRACT ESR STUDIES OF TRANSITION METAL IONS 'IN'UNSTABLE OXIDATION STATES BY John Robert Shock There are some transition metal ions which form diamagnetic transition metal complexes almost exclusively. In this work, several new paramagnetic species containing these ions in unstable oxidation states have been made either by high-energy irradiation at 77°K or from the melt of alkaline halides containing the diamagnetic transition metal ion. In both cases, the ESR spectra were studied between 77°K and 300°K to determine the structure and to characterize the bonding of the resulting paramagnetic species. The y irradiation of KZNbOFS-HZO at 77°K produced two 93Nb- centered radicals; one of these is shown to be [NbOFSJB- with a d1 configuration and a dxy ground state. The 9, A(93Nb), and A(19F) tensors have been completely analyzed in the single crystal at 77°K. The 9 and metal A tensor for this ion and those found previously for the [VOFSJB- ion by other investigators were used in a John Robert Shock self-consistent charge calculation of molecular orbital coefficients. Also, molecular orbital coefficients were determined from the equatorial fluorine A tensors of these systems. The other Nb-containing ion formed at 77°K is a hole species, thought to be [NbOF5]-. Warming the sample to 190°K resulted in the decay of the INbOF513- ion allowing the study of the spectra of the hole species. The analyses of single crystal and powder Spectra at l90°K suggest that some [NbOFSJ- ions remain at 190°K but that the majority of the ions decay to the NbOF4 ion which rotates freely in the matrix. The y irradiation of K3Co(CN)6 at 77°K produced two 59Co-containing radicals. A complete single crystal ESR study of the g and A(59Co) tensors for one of these species indicates that it has not undergone appreciable reorientation in the lattice. The 9 tensor is consistent with a d7 configuration and a dzz ground state. Super- hyperfine structure from two equivalent nitrogen nuclei and the absence of 13C satellite lines in 13C enriched samples suggest that the axial cyanide ligands have ro- tated to form nitrogen-to-metal bonds. Also, the A(sgco) tensor of this radical, thought to be [Co(CN)4(NC)2]4_, was used to estimate the covalency in molecular orbital containing the odd electron. The other Co-containing radical formed at 77°K is considered to be a Co(II) radical pair but its ESR parameters could not be determined. John Robert Shock Lastly, the Rh(II) ion in several chloro—complexes . 0 - 6 H20 at 77 K pro duced a radical whose g values are consistent with a d7 was studied. The Y irradiation of K3RhCl system with a dzz ground state. This radical, thought to be [RhC1614-, also appears to form in the melt of AgCl containing RhClB. In this matrix, the chlorine super— hyperfine structure from the two axial chlorines was fully analyzed in the single crystal and the results used to estimate covalency in the complex. Also, Y irradiation of K2[RhCls(H20)] at 77°K produced a radical with g values consistent with a d7 configuration and the unpaired elec- tron in the dzz orbital. The g values and the chlorine hyperfine splitting from one chlorine suggest that the radical is [RhC15(H20)]3- or [RhClsl3-. ESR STUDIES OF TRANSITION METAL IONS IN UNSTABLE OXIDATION STATES BY John Robert Shock A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1973 To My Parents ii ACKNOWLEDGMENTS The author wishes to express his sincere apprecia- tion to Professor M. T. Rogers for providing opportunities in research and for affording freedom in the laboratory. The author is also indebted to Dr. S. Subramanian for his encouragement and helpful discussion and to William Waller for the use of his various programs for analyzing ESR data. Final thanks are extended to Michigan State Univer- sity for financial support as a teaching assistant through- out the course of this research and also to the Department of Army and the National Science Foundation for support as a research assistant. iii TABLE OF CONTENTS Page DEDICATION O O O O O O I O O O O O O O O O O O O 0 ii ACKNOWLEDGMENTS. . . . . . . . . . . . . . . . . . iii LIST OF TABLES O I O O O O O O O O O O O O O O O O Vii LIST OF FIGURES o o o o o o o o o o o o o o o o o 0 ix Chapter I 0 INTRODUCTION 0 O O O O O O O O O O O O O I O 1 A. General. . . . . . . . . . . . . . . . . 1 B. y Irradiation of KszOFs-HZO . . . . . . 5 C. y Irradiation of K3Co(CN)6 . . . . . . 6 D. Chlororhodate (II) Complexes . . . . . . 8 E O Other SYBtems O O O O I O O I O O O O O O 9 II 0 THEORY. O I O O O O O O O O O O O O O O O O 10 A. Introduction . . . . . . . . . . . . 10 B. Determination of the Principal g and A Values . . . . . . . . . . . . . 13 C. Signs of Metal Hyperfine Splitting Constants. . . . . . . . . . 17 D. LCAO Molecular Orbital Theory of Transition Metal Complexes. . . . . . . 18 E. Molecular Orbital Theory of g and Metal A Parameters . . . . . . . . 24 F”. Evaluation Of K o o o o o o o o o o o o 2 8 G. Evaluation of Group Overlap Integrals. . 29 H. Determination of Bonding Coefficients from g and Metal A EXpressions . . . . . 37 I. Calculation of Charge on the Central Metal Atom . . . . . . . . . 37 J. Determination of Ligand Hyperfine Values . . . . . . . . . . 38 K. Determination of the Sign of the Principal Ligand A Values. . . . . . . 39 L. Determination of Bonding Coefficients from Ligand Hyperfine Splittings . . . . 41 iv Chapter III. IV. EXPERIMENTAL. O O O O O O I O O O O 0 0 A. ESR Spectrometer Systems . . . . . . B. C. G. H. Y A. B. H be H N |-' o O O 0 l3. K2N1(CN)4°H O and Na2N1(CN)4-3H O IRRADIATION OF K NbOF Sample Preparation . . . . . . . . . l. K2Nb0F5.H20 I O O O O O I O O O K3CO(CN)6 o o o o o o o o o o o o K4Fe(CN)6'3H20. . . . . . . . . Na RI'ICJ- .12H 0. o o o o o o o o o 3 6 2 K3mC16.H20 O O O O O O O O O O O KZIRhC15(H20)]. . . . . . . . Na3RuC16°12H20. . ... . . . . . K2[RuC15(H20)]. . . . . . . . . . K3RuC16-H20 . . . . . . . . . . . (NH4)2[InC15H 2O]. . . . . . . . . KzReFG. . . . . . . . . . . . . . CszGeF6 . . . . . . . . . . . . . wmqmmaww O 2 2 14. Magnus' Green Salt [Pt(NH3)4][PtC1 Crystal Growing. . . . . . . l. Crystals for Irradiation. . 2. DOped Crystals. . . . . . . a. From Solution. . . . . . b. From Melt. . . . . . Identification of Crystallograpi l. Irradiated Crystals . . . . 2. Deped Crystals. . . . . . . y- -Irradiation Method . . . . . . Sample Handling of Irradiated Samples 1. Single Crystals . . . . . . . . . 2. Powders . . . . . . . . Low-Temperature Studies (below 77°K) Conversion Factors . . . . . . . . . 003:0... .000... 2 5.H200 0 Introduction . . . . . . . . Results. . . . . 1. Single Crystal at 77°K. . 2. Powder at 77°K. . . . 3. Variable Temperature Study of Powder Spectra . . . . . . . . 4. Single Crystal at 190°K . . . . . -# Page Chapter C. Discussion . . . . . . . . . . 1. Molecular Orbital Coefficients for [NbOF5]3 and [VOF513 . . . . a. Determined from g and Metal A Tensors. . . . . . Determined from Ligand hyperfine Interaction. . . c. Conclusion . . . . . . 2. Hole Species. . . . . . . 3. Ozonide Ion . . . . . . . b. V. Y IRRADIATION OF K3CO(CN)6. . . . . A. B. C. VI. A. B. C. VII. A. B. REFERENCES APPENDICES OTHER Introduction . . . . . . . . Results. . . . . . . 1. Single Crystal at 77°K. . . 2. Powder and Pellet at 77°K . . 3. Single Crystal and Powder at Room Temperature . . . . 4. Analysis of Spectra of 13c Enriched Samples. . . . . Discussion . . . . . . . . . 1. Low-Temperature Species . 2. Room-Temperature Species. CHLORORHODATE (II) SYSTEMS. . . . . Introduction . . . . . . . Results. . . . . . . . . . 1. Powders at 77°K . . . . 2. Single Crystal at 77°K. Discussion . . . . . 1. y-Irradiated K3RhC16 H20. 2. y- -Irradiated K2[RhC15 (H 20) 3. AgCl: .ha+ O O O O O O O O O O ] SYSTEMS O I O O O C O O O O O Chlororuthenate (III) Complexes. RhC13 in NaF O O I O O O O O O O 2.. [ReF6] in CszGer. . . . . . . Y-Irradiated K4Fe(CN)6 o o o o o y-Irradiated K2Ni(CN)4-H20 and Na2N1(CN)4-3H20. . . . . . . y-Irradiated Magnus' Green Salt. Super- Page 84 84 84 91 95 96 103 104 104 106 106 118 122 122 125 125 132 137 137 139 139 142 146 146 148 150 158 158 166 167 168 171 172 174 182 Table 2.1 2.2 4.3 4.4 4.5 4.6 LIST OF TABLES Classification of atomic orbitals into the irreducible representations of the 04v pOint group. O O O O O I O O O O O 0 Contribution to S from each of the other n' 2' electrons in the atom. . . . Effect of charge on orbital exponent for vanadium . . . . . . . . . . . . . . Orbital exponents for fluorine and for oxygen 0 I O O O O O O O O O O I O O O 0 Bond distances for the [NbOF513- and [VOFSJB- ions. 0 o o o o o o c o o o Diatomic overlap integrals for [VOFsl3-. Orbital character ratios used for the hybrid group symmetry orbitals . . . ESR parameters for [NbOF5]3- . . . . . . Calculated line positions for 93Nb hyperfine components . . . . . . . . . . The ESR parameters for the hole species and the ozonide ion. . . . . . . Parameters used in calculating bonding coefficients . . . . . . . . . . MO coefficients as a function of nuclear charge (considering dominant ligand p overlap only). . . . . . . . . . . . . MO coefficients as a function of nuclear charge (considering overlap with hybrid ligand orbitals). . . . . . . . . vii Page 23 31 31 32 32 34 35 64 72 83 87 89 9O Table 4.7 5.3 5.4 6.1 Page Calculated spin densities in the equatorial fluorine orbitals . . . . . . 94 Direction cosines of Co-Ci bonds in K3Co(CN)6 with respect to orthorhombic crystallographic axes. . . . . . . . . . . . 109 The 9, 59Co hyperfine, and 14N hyperfine values with direction cosines for the low- temperature species in K3Co(CN)6 . . . . . . 116 Comparison of experimental g and A values with calculated values for various orientations C O O O O O O O O O I O O I O O 119 The 9 values and 59Co hyperfine values with direction cosines for the room-temperature species in K3Co(CN)6 . . . . . . . . . . . . 123 First order expressions for g values . . . . 127 ESR parameters for the room-temperature and low-temperature species in different matrices O O O O O O O I O O O O O O 130 The ESR parameters for chlororhodate (II) radicals measured at 77°K. . . . . . . . . . 146 viii LIST OF FIGURES Figure 2.1 4.3 4.6 Coordinate system for the atomic orbitals of the tMOF513- ions. . . . . . The molecular orbital energy level scheme for [VO(H20)5]2+. . . . . . . . . Variation of the resonance positions for the ten hyperfine lines from 93Nb with the magnetic field in the be* plane. . . Variation of the resonance positions for the ten hyperfine lines from 93Nb with the magnetic field in the a*c plane. . . Variation of the resonance positions for the ten hyperfine lines from 93Nb with the magnetic field in the ab plane . . . Second-derivative X—band ESR spectrum of y-irradiated K2NbOF5-HZO at 77°K; the magnetic field is in the be plane, 6° from the c axis. The arrows indicate the ten Nb hyperfine lines from those ions with their F-Nb-O bond parallel to H. . . . . Second-derivative X—band ESR spectrum of y-irradiated KZNbOFS-HZO at 77°K with H//c. The intense 10-line pattern is from the two sets of magnetically equivalent ions with their F-Nb-O axes nearly parallel to H; the weak multiplets between the central six strong lines are from the radicals (about 8%) with their F-Nb-O axes nearly perpendicular to H . . . . . A plot of the "apparent g" values for the [NbOF513- radical with the magnetic field in the a*c plane . . . . . . . . . ix Page 19 22 61 62 63 65 67 68 Figure Page 4.7 Coordinate system for the [NbOFsl3- ion used for the 93Nb hyperfine tensor, the g tensor, and the equatorial 19F hyperfine tensors. . . . . . . . . . . . . . 69 4.8 Enlarged portions of the second- derivative spectra of Yéirradiated KszOFs-Hzo showing the superhyperfine splittings. (A) 6 = 0°. The four equivalent equatorial fluorines give a quintet with intensity ratios 1:4:6:4:1. (B) 6 a 90°, ¢ = 0°. The equatorial fluorines give a seven-line pattern with intensity ratios 1:2:3:4:3:2:1, since Am 3 (1/2)Ay. (C)6 = 90°, ¢ = 45°. The four equivalent fluorines give 1:4:6:4:1 quintet. O O O O O O O O O O O O O O O O O O 73 4.9 The second-derivative X—band spectrum of a single crystal of KZNbOFS-HZO y-irradiated at 77°K,JH//a*. Both sets of radicals are magnetically equivalent with the F-Nb-O bond direction perpendicular to H. The arrows indicate the ten93Nb perpendicular hyper- fine resonance positions . . . . . . . . . . 75 4.10 The x-band first-derivative spectrum of y-irradiated polycrystalline . KZNbOFS'HZO at 77°K. The downward point- ing arrows indicate the perpendicular hyperfine features while the upward point- ing arrows indicate the parallel features. The intense central signal is from other species. . . . . . . . . . . . . . . . 76 040‘- Figure 4.11 Page (A) The Q-band spectrum of poly- crystalline KszOFs-HZO, y irradiated at 77°K and warmed to 200°K. The ten-line pattern is from a rotating niobium- containing hole species. (B) The same but at x-band and 190°K. The spectrum from the hole species overlaps with the spectrum from the ozonide ion and wing lines are seen at higher gain. (C) The same but warmed to 400°K. Only the ozonide ' ion remains and gives a three g-value pattern. . . . . . . . . . . . . . . . . . . 78 The X—band spectrum of y-irradiated KZNbOFs-HZO at l90°K with H//b; within the brackets are the weak wing lines . . . . 80 The relationship of the 1M to the 20r cell as seen on the (010) plane. . . . . . . 108 Variation with magnetic field orientation of the two sets of eight 59Co hyperfine lines in the be plane for y-irradiated K3C°(CN)6 at 77°K. o 0 ago 0 o o o o o o o o 110 Variation with magnetic field orientation of the two sets of eight 59Co hyperfine lines in the ac plane for y-irradiated K3CO(CN)6 at 77°K. o o o o o o o o o o o o o 111 Variation With magnetic field orientation of the sets of eight 59Co hyperfine lines in the ab plane for y-irradiated K3C°(CN)6 at 77°K. o o o o o o o c o o o o o 112 The second derivative spectrum of the low- temperature Species in y-irradiated K3C°(CN)6 With H//00 o o o o o o o o o o o o 113 The second-derivative spectrum of the low- temperature species with the magnetic field in the ac plane 10° from the c axis. The upward and downward arrows designate different sites. . . . . . . . . . . . . . . 114 xi . .E L ,‘ r Figure Page 5.7 Powder spectrum of the low-temperature species with the A3, A , and A¢ features designated by the upward, double-headed, and downward arrows, respectively. Also seen is nitrogen superhyperfine splitting of the A3 component and the Spectrum of another radical at low field . . . . . . . . 120 5.8 ESR spectrum of the low-temperature Species in a y-irradiated pellet of K Co(CN) with the Az, Ag, and Ax features dgsignatgd by upward, doubled-headed, and downward arrows, respectively . . . . . . . . . . . . 121 5.9 Schematic representation of the ligand- field stabilization acquired in going from the low-temperature Species to the room- temperature Species. . . . . . . . . . . . . 128 6.1 (A) The first-derivative X-band powder spectrum at 77°K of y-irradiated K3RhCl ~H20. (B) The first-derivative X-band polycrystalline Spectrum of AgClth2+. At high field the seven-line pattern from the interaction with two equivalent 35Cl nuclei is resolved with increased gain . . . . . . . . . . . . . . . 140 6.2 The first-derivative powder pattern of y-irradiated KZIRhC15-HZO] measured at 77°K. 141 6.3 The x-band spectrum at 77°K of AgCl:Rh2+ with H//a. . . . . . . . . . . . . 144 6.4 The X-band spectrum at 77°K of AgCl:Rh2+ with H in the ab plane 45° from b. . . . . . 145 xii Figure 7.1 7.2 (A) The X-band Spectrum at 9°K of the [InC15(H20)] [RuC15(H20)]2- ion in the (NH4)2 matrix with H at an arbitrary orientation. The upward and downward arrows designate the 101,99 magnetically inequivalent sites. Ru hyperfine lines for two (B) The powder Spectrum of this system at 9°K. The X-band powder Spectrum of K4Fe(CN)6 Y irradiated and measured at 77°K. xiii Page 160 169 CHAPTER I INTRODUCTION A. General The initial use of ESR to study transition metal complexes was by solid state physicists. Their primary concern was to develop the theory and SXperimental techniques from which information about local crystal en- vironment and relative energies of various solid state interactions could be ascertained. This work started with the first observation of ESR by Zavoisky1 in 1944 and is continued presently. Progress has been reviewed by Bleaney and Stevens2 in 1953, Bowers and Owens3 in 4 5 1955, Low in 1960, Pake in 1962, Slichtere in 1963, Low and Offenbacher7 in 1965, Orton8 in 1968, and in the recent classic by Abragam and Bleaney9 in 1970. The experimental methods, including design and construction of spectrometers, are discussed in monographs by Wilms- hurstlo, Poolell, and Algerlz. In an ESR study Of a transition metal complex, one monitors the interaction of unpaired electrons with their environment. In the classical work of Owen and StevenslB, the unpaired electron was found not only ‘ l T, to interact with the central metal atom but also with the ligands, i.e., unpaired spin density was transferred to the ligands resulting in ligand hyperfine splittings. Thus, it appeared that the unpaired electron was not localized just in the metal atomic orbitals but in molecular orbitals which spanned the entire molecule. The application then of molecular orbital theory to ESR by Stevensl4, Owen15 and McGarvey16 generated much in- terest among the transition metal chemists. Since the unpaired electron is normally involved in the bonding of the molecular system, the chemist could use ESR as a sensitive probe to measure bonding changes and test bond- ing theories. Reviews of such studies include those by 18, Kokoszka and Gordonlg, and Fujiwara Another series of reviews by Kuska and RogerSZl-23 are McGarveyl7, Kanig more complete but cover only the first row of the transi— tion metals. Lastly, a recent review by Goodman and Raynor24 gives comprehensive coverage of the d1 to d9 ions for the entire transition metal series. In addition to these, current literature is reviewed in the Annual Reports of the Chemical Societyzs, and in the Annual Re— view of Physical Chemistry“, Analytical Chemistry”, and Spectrosc0pic Preperties of Inorganic and Organo- metallic Compoundszs. The use of ESR to study bonding in transition metal complexes, however, is restricted by the 20 requirement (1) that the system has at least one un- paired electron, (2) resonance occurs over a small range of values so that the signal is not inhomogeneously broadened to the point that it is undetectable, and (3) that the environment be such that the relaxation times are neither too long nor too short. Because of these re- strictions most of the earlier single crystal work in- volved d0ping stable paramagnetic complexes of the first— row transition metals into diamagnetic host lattices. Only stable oxidation states could normally be used Since the host crystals were usually grown from solution and magnetic dilation in a diamagnetic host lattice was necessary to prevent dipolar interactions and exchange coupling which would broaden the signal. First-row tran— sition ions were mostly used Since they have relaxation times in the appr0priate range for the signal to be ob- served at room temperature or 77°K. Also, these ions were of more interest initially since more chemistry and physi- cal characterization of the first-row complexes had been done as well as ESR results could be compared with ex- tended Hfickel calculations for these ions. More recently, studies have been made of some of the second- and third— row transtion metals and of complexes with less common crystal symmetries. There are, however, numerous transition metal ions that form diamagnetic complexes almost exclusively. In order to study the bonding of these ions by ESR, condi- tions must be created whereby a paramagnetic oxidation state can be stabilized. One method of achieving such valence states is to grow crystals from the melts of various halide salts d0ped with a diamagnetic ion. Often in such instances, the melt will oxidize or reduce the transition metal ion to a paramagnetic oxidation state. The resulting crystals therefore have these paramagnetic sites trapped within the lattice and surrounded by halide ions in cubic, octahedral, distorted octahedral, or tetrahedral arrangements. This method is somewhat limited since, for the most part, only metal-halogen bonding can be studied and only a few coordination geometries can be studied. A more versatile method for making transition metal complexes with unstable oxidation states is to irradiate Single crystals of the diamagnetic compounds at low temperatures with a high energy source. Often para- magnetic species will form by capture of an electron, loss of an electron, or by rupture of a bond. In the study of stable oxidation states, one usually knows the oxidation state and the ligand field geometry beforehand. Also, the electron configuration of the ground state and the ordering of low-level excited states is usually known from optical spectroscopy. In the case of unstable oxidation states, on the other hand, the valence state, ligand field geometry, and ground state must be inferred from the ESR parameters. Therefore, Since transition metal complexes in unstable oxidation states were studied in this thesis, the radicals had to be identified before their bonding could be studied. With this as a background, introductions to the individual projects will be given in the order they appear in the thesis. B. lIrradiation of KZNbOF5°H20 There has been considerable interest in the ESR study of the transition-metal oxyanion complexes of the type [MOX5]2‘ where M = Cr, Mo. W and X = F, Cl, Br, I29-45. The g, metal hyperfine, and ligand hyperfine tensors have been used to investigate covalency in these compounds. On the other hand, the series [MOX513- where M = V, Nb, Ta, cannot be studied as easily by ESR since niobium does not form a stable paramagnetic oxypentahalide ion and tantalum does not form an oxypentahalide ion at all. The stable [VOF513- complex has been the subject of previous ESR 46-48 studies , so a study of the analogous [NbOF513- com— plex would be of interest. The y irradiation of KszOF5 2 produce the paramagnetic [NbOFSJB- radical along with -H O at 77°K is shown in this investigation to the hole species identified as probably [NbOFsl- and NbOF4. There are very few accounts of ESR spectra of paramagnetic niobium compounds. Chester49 obtained ESR spectra of Nb4+ in T102, Edwards at al.50 observed Nb hyperfine sturcture in y-irradiated CaMoO4 containing Sm l and Nb, and Rasmussen at al.5 studied [Nb(OMe)C15]2-, all in the solid; Lardon and Gunthard52 3 observed the [NbClGJZ- ion, and Gainullin et a1.5 NbO(acac)2, [NbOC1412-, and [NbOF4]2, all in solution. In the present work the ligand superhyperfine interaction tensor of the [NbOF5]3_ complex has been de- termined and used to evaluate covalency effects for com- parison with those found for the [VOF5]3- complex. A complete calculation of molecular orbital coefficients has also been made using g and metal hyperfine Splitting values for both [VOF5]3_ and [NbOF5]3-. While in most previous calculations the charge on the central metal atom is assumed, an attempt has been made in this work to arrive at a charge which is self-consistent with the cal- culated molecular orbital coefficients. And finally, a critical examination has been made for the use of second- order theory of the g and metal A tensors to derive molecular orbital coefficients. C. Irradiation of K3Co(CN)6 There has been several studies, including a com- plete single crystal analysis, of the radical formed by the irradiation of K3Co(CN)6 at room temperatureS4-57 but there has not been any detailed single crystal analysis of the radical formed by irradiating this compound at 77°K. Since, for the studies of the room temperature radical, there are considerable discrepancies in the g and A parameters reported in the literature, a review of this work is given and a possible explanation for these discrepancies is offered. It has been generally accepted that this room temperature radical is [Co(II)(CN)5]3-. However, the 13C results in this thesis shed some doubt on this assignment and suggest that the radical might be [Co(II)(CN)4]2-. In the case of the low-temperature radical, the metal g and A tensors with their direction cosines are derived from the analysis of the single crystal spectra. Because of the nitrogen superhyperfine Splitting from two equivalent nitrogens is observed58 and 13C satellite lines are absent in enriched samples, the structure of the radical has been assigned as [Co(II)(CN)4(NC)2]4-. Also a second radical, formed by an ionic migration within the lattice, appears at.77°K and is possibly a Co(II) radical pair. Variable temperature studies Show that the room temperature radical forms directly from the low temperature radical by rupture of Co-NC bonds. The 9 values in con- junction with first-order theory indicate that both the room temperature and low temperature radicals have the unpaired electron in the metal dzz orbital. Covalency in these radicals is characterized using first-order hyper- fine interaction theory. D. Chlororhodate (II) Complexes There hardly has been any d7 rhodium complexes reported in the literature. In the host lattice ZnWO4, lO3Rh Splittings have been observedsg; Dessy et al. have observed a rhodium radical thought to be [(n-C5H5)Rh + (n-C2H2)2] where (n-CSHS) and (n-C ) are n bonded 232 cyclopentadiene and acetylene, respectively, as well as a rhodium radical produced by the one-electron reduction 61 60 . . of [(n-C5H5)Rh 82C2(CF3)2] ; 311119 et a1. and Maki 62 have observed the 103 et a2. Rh coupling in [Rh(MNT)2]2- where MNT = maleonitriledithiolate; and Keller and Wawersik made a study of Rh(n-C5H5)263. Therefore, Since there had been no studies of d7 halorhodate (II) complexes, such an investigation was the objective of this project. The y irradiation of K3RhCl6-HZO at 77°K pro- duced a radical identified from the powder ESR data as [RhC16]4-. Also, K2[Rhc15(H20)], y irradiated at 77°K, produced a radical identified from the powder ESR data as possibly [RhC1513- or [RhCls(H20)]3_. The [RhC1614- ion was also prepared in an AgCl matrix by crystallization from the melt of AgCl containing RhCl For each radical, 3. first-order g theory was used to determine that the odd electron is localized mainly in the d32 orbital. Because the 103Rh doublet splitting was less than the line width for all of the Spectra, first-order metal hyperfine theory could not be used to determine covalency in these complexes. However, since the chlorine superhyperfine tensor for the [RhC1614- ion in the AgCl lattice could be fully analyzed, first-order hyperfine theory was ap- plied to derive an expression for these Splittings which enabled the covalency to be estimated. E. Other Systems This section includes examples for which the ESR spectra were not fully analyzed either as a result of experimental difficulties or inherent shortcomings of the system. The results which are discussed include the first ruthenium hyperfine Splitting observed for a halide complex, the [RuC15(HZO)]2- ion; identification of the [Fe(CN)6]5- radical in K4Fe(CN)6 y-irradiated at 77°K; and identification of a radical thought to be [Ni(CN)4(NC)]2- in K2Ni(CN)4°H O y-irradiated at 77°K. Also, suggestions 2 for future work on these systems, as well as for other systems that were investigated but for which ESR Spectra were not observed are included. CHAPTER II THEORY A. Introduction Since the electron is a spinning charged particle, it has a magnetic moment given by pa = -geBeS(erg/gauss), (2.1) where 88 is the Bohr magneton (0.9273le0-20erg/gauss), S = 1/2‘ is the spin quantum number of the electron, and 9e is the Landé g factor (g value) which is dimen- sionless and has a value of 2.0023 for a free electron. In the absence of a magnetic field, the two Spin state with ms ==il/2 are degenerate but in the presence of a mag- netic field the degeneracy is removed and the difference in energy between the states is given by AE = hv = geBeH' (2.2) where ge and 88 have been defined above, H is the mag- netic field in gauss, h is Planck's constant (6.6252 x10-27 erg-sec) and v is the frequency (Hz) of the energy required for a transition between the two states. There- fore, from this equation it is apparent that if the 10 11 radiation frequency v is fixed; the field at which the transition between states will occur depends upon the g value. The 9 values for transition metal complexes, how- ever, usually deviate from 2.0023 as a result of Spin- orbit coupling mixing orbital angular momentum of excited states into the ground state. The excited states which can mix with the ground state depend on the geometry of the complex and the amount of mixing depends on the spin- orbit coupling constant of the metal atom and the energy difference between the ground state and the admixed ex- cited states. Thus, for transition metal complexes the g values, together with theoretical expressions for this parameter, can provide much information about the com- plex's geometry, ground state, and excited states. In systems where the unpaired electron can inter- act with nuclei which have a magnetic moment, there is another effect which influences the field position of the resonances. This effect is called the hyperfine inter- action and it arises from the fact that in such cases the unpaired electron feels an "apparent field" which is the sum total of the applied field and the field produced by the local nuclei. Since a nucleus with a magnetic moment of spin I has (2I+1) possible orientations relative to the applied field, for a large number of molecules the number of electrons sensing each nuclear vector will be 12 the same. Hence, experimentally one observes (2I+l) lines centered about the position at which resonance would occur if the nuclei were absent. The distance between the hyper— fine lines is called the hyperfine Splitting constant A. Its magnitude is related to the magnitude of the nuclear magnetic moment and to the average distance between the unpaired electron and the nucleus. Obviously, the hyper- fine constant can also give much information about bonding in a complex, and those complexes having both a central metal and ligands with nuclear magnetic moments give the most information. With this as a general background, we will examine the more specific molecular orbital considerations and the g-, metal A—, and ligand A-tensor theories used to calculate bonding coefficients for the series [VOF513- and [NbOF513-. Also, most of the theoretical considera- tions necessary to understand the discussions of the other transition metal ions will be covered. More detailed treatments are available in the reviews and monographs already mentioned. Also, texts by Baird and Bersohn64, 65 66 Assenheim , and Carrington and McLachlan provide elementary introduction to the subject. For additional information regarding the bonding theories for transition 67 68 metal complexes, the monographs by Ballhausen , Figgis , 69 70 71 Watanabe , Cotton , and Ballhausen and Gray are ex- cellent references. 13 B. Determination of the Principal g and A Values In ESR the experimental results are interpreted in terms of a Spin Hamiltonian. For the [MOF5]3_ ions studied here, the spin Hamiltonian for the interaction of the unpaired electron with the central metal nucleus is J—CM = gl IBeHzSz+giBe(HxSx+HySy) + Al IIZSz+A_L(SxIx+Sny) , (2. 3) A where S is the electron Spin operator, I is the nuclear Sp in operator, and the other terms have been defined pre- Vi ously. Schonland's method72 has been used in this thesis to determine the principal values (gl I 'gi'Al I “41.) and di rection cosines for the g and A tensors. This method requires that the single crystal be rotated about three orthogonal axes. It should be noted, however, that this is only a restriction of this particular method; Waller and Rogers have solved the equations for the general case Of rotation about any three axes73. Since the direction cosines obtained from such a, method relate the principal tensor directions to three orthogonal rotation axes, it 13 most informative to choose crystallographic axes for the rotations. Finally, the tensors found l4 experimentally are for the physical quantities 92 and 66 ng2 Since both 92 and gZAZ are second rank tensors, the procedure for determining principal values is the same in both cases and hence only the theoretical development of the 92 tensor and the procedure for its diagonaliza- tion will be discussed here. We begin by rewriting the spin Hamiltonian in terms of the crystal axes as JC = B[Hz’Hz’Hs] 911 912 913 311 921 922 923 52 L931 932 933_ L53_ , (2.4) since the rotation axes are generally not coincident with the principal g axes. The electron spin does not inter- aCt directly with the field H but instead its energy de- Pends on the magnitude and direction of vector 3?. Thus, since there are two spins Ia) and [8) quantized aulong the direction defined by 3?, the separation between these spin states is given by (AE)2 = 62(§-'g')(§-E§) = 5323-32-3 . (2.5) Hence, experimentally the quantity that is measured at a Particular field position is given by - 1 ._ (93) = [2122231 (92)11 (g2)12 (92)13 21W 2 2 2 (9 )21 (9 )22 (9 )23 12 2 2 L(g2)31 (g )32 (g )33 L23- I (2.6) where 9.1, £2, 13 are the direction cosines of E relative to the crystal axes. Before this (g2) tensor can be evaluated, however, its components 0% g (92)”. must be determined. i=1 J=1 The Schonland method provides a straight forward method of determining these tensor components using the ge neral express ion (g2) = a + 8c0826 + ysin26 , (2.7) where 6 is a rotation angle and a, B, and y are parameters Which must be determined. If the maximum and minimum Values of 9 during a rotation are denoted by gt and occur at 6:, respectively, the above parameters can be defined ams 20 = gi+gf 28 = (gi-gf)cosze+ 2y = (gi-gf)sin26+ . (2.8) The (92)ij tensor elements can then be determined from t'J‘lese a, B, and Y parameters or, as was done in this study, from a two—parameter method. In this method the 16 diagonal terms are defined as 2 (g )1] — a2+a3-a1 (2.9) and the off-diagonal terms are given by 2 1 2 (g )12 = i[(A3+a1-a2)(A3-a1+a2)] / , (2.10) where A = 1/2(gi-gf) The other components are generated by a cyclic permutation of the axes 1, 2, 3 throughout the expressions. Having determined the elements of the (92) tensor, it can now be diagonalized by one of several methods. The Jacobian method has been used here to give the diagonal matrix. L (9 )33 J . Since these principal Values are the same as the squares of the principal values of the g tensor, the two tensors naturally have the same Principal axes. Also, because the g values are positive from theory, there is no ambiquity arising from the fact that'experimentallyuwe observe the (g2) tensor. In the caSe of the (9242) tensor, on the other hand, the sign of A can be positive or negative. 17 C. Signs of Metal Hyperfine Splitting7Constants After determining the magnitude of the principal A values, one must choose between the possible combination of signs. In the case of an axially symmetric hyperfine tensor, Al I and A_|_ can either be positive or negative giving four possible sign combinations. Since these hyper— fine tensors can be expressed as All = 1180+“? and A_|_ = Aiso'Ap' one can determine the correct sign combination if the signs of the isotropic splitting A1180, and the anisotropic splitting AP are known. In this thesis the method of F‘ortman74 has been used to determine these signs. Fortman determined the sign predicted for an odd electron in different type of metal orbitals using a model System in which the nucleus and unpaired electron are con- sidered to be point charges and simple magnetic dipoles. The results are summarized here for the case of a positive nuclear moment; opposite signs are predicted for a negative nLimelear magnetic moment. If the electron is in the or- bital along the unique axis of the molecule (by convention tl'le Z axis) ,ethe anisotropic splitting component will be POsitive. On the other hand, if the unpaired electron is in an orbital perpendicular to the axis of symmetry, the anisotropic splitting component AP will be negative. The isOtropic splitting Aieo is normally negative but, if the Valence shell 3 contribution is large, it is possible to 18 have a positive splitting. The latter case is predicted for those ions whose geometry allows the valence shell 3 orbital to mix with the ground state orbital. D. LCAO Molecular Orbital Theory of Transition Metal Complexes As mentioned previously, in the molecular orbital picture of bonding the electrons occupy orbitals which span the entire molecule. Applying this theory to transi- tion metal complexes, expressions for these orbitals are obtained by forming linear combinations of the atomic orbitals in the following manner. The valence shell or- bi tals of the ligands are used as a basis for a represen- tation of the point group of the molecule, and this repre- sentation is decomposed into its component irreducible representations. The ligand orbitals are then combined into linear combinations belonging to these irreducible representations, and the interactions between ligand and metal orbitals of the same symmetry are computed. The eIIergies obtained are then used to determine the metal and ligand group-orbital coefficients which are the true “‘0 lecular orbitals of the complex. Applying this method to the [MOF513- ion, where M = V,Nb, we start by choosing a coordinate system for the atomic orbitals. The coordinate system shown in Figure 2.1, was chosen to be consistent with the one l9 1"igure 2.l--Coordinate system for the atomic orbitals of the [MOF5]3_ ions. which will be used later to analyze the 9, metal A, and the ligand A tensors for these ions. The metal orbital Z axis is along the F-M-O bond direction and X and Y axes are along the F-M-F bond directions. Also, the oxygen and the axial fluorine have this coordinate system but the equatorial ligands have their x axis along the M-F bond, their z axis parallel with the F-M-O bond, and their y axis chosen to form a right—handed coordinate system. Using this axis system, the ligand atomic orbitals are cOmbined into linear combinations having the symmetry 20 of the various irreducible representations of the C4” point group. These linear combinations, along with the metal orbitals having the same transformation properties, are listed in Table 2.1. In order to form molecular orbitals from these atomic orbitals, all the linear combinations of ligand orbitals having the same symmetry are next combined into group symmetry orbitals. For instance, the group sym— metry for the b1 molecular orbital is 1 2 3 4 ¢L - 01(8 -8 +3 -3 ) 1 2 3 4 + 02(px-px+px-px) (2.11) This is then combined with a linear combinations of the metal orbitals which transform under the same representa- tion to form the molecular orbital. When the energy of such molecular orbitals is de- tEermined, two solutions are found. One has less energy th an the noninteracting atomic orbitals and corresponds to a bonding molecular orbital of the form b ‘P = a|¢M> + b|¢L>; the ,other solution has energy greater than the noninteracting atomic orbitals and corresponds to an antibonding molecular orbital of the form W“ '= ol¢M> - d|L> . These molecular orbitals have two Properties which enable the coefficients of both the anti- bonding and bonding molecular orbitals to be determined if only one coefficient is known. First, each molecular 21 orbital is normalized, 72.2. , @blwb> = 1 and secondly, they are orthogonal to one another, 71.9. , (WNW) = 0. Finally, if there are no ligand group symmetry orbitals to combine with a metal orbital of a particular symmetry, the metal orbital experiences no interaction with the ligand orbitals; its energy remains the same and is re- ferred to as a nonbonding orbital. In order to calculate energy level diagrams using these molecular orbitals, certain approximations must be made. Ballhausen and Gray have used the VSIE method of calculating coulomb integrals, and the Wolfsberg- Helmholz approximation for evaluating exchange integrals, to arrive at the molecular orbital energy level scheme shown in Figure 2.2 for [VO(H20)5]2+315. In this cal- culation, n-bonding with the equatorial ligands was neglected and this bonding, in the case of the fluoride complexes is important. However, since this effect does not alter the energy levels very much, the diagram will be helpful in subsequent discussion. The major differ- ence, in the case of the fluoride ions where n bonding is important, is that the b2 orbital containing the odd elec- tron is an antibonding orbital instead of a nonbonding orbital as shown for [VO(H20)5]2+. All of the molecular orbitals shown in the energy level diagram play an important note in the bonding of the complex. In ESR, however, we can only acquire 22 VANADIUM MO. LEVELS OXYGEN ORBITALS ORBITALS Figure 2.2-9The molecular orbital energy level scheme for [VO(H20)5]2+. ‘7. ant-- m s v. {I 23 Table 2.1. Classification of atomic orbitals into the irreducible representations of the C4v point group. Transition Ligand Symmetry Metal Orbitals Orbitals A1 8 35 5 pz 0 P3 3 dZZ 81+82+83+84 1 2 3 4 P3+P3+P3+Pz 1 2 3 4 px+px+px+px 1 2 3 4 A2 ---- py+py+py+py B] d 2 2 81-82+83-34 x -y 1_ 2+ 3_ 4 pz p3 p3 pz 1_ 2+ 3_ 4 pm pm pm pm 1 2 3 4 B d - + - 2 my py py py py o o E (dxz,dyz (px,py) ( ) ( 5 5) anpy anPy (31-33),(32-s4) 1 3 2 4 (pa-pz)(pz-p3) 1 3 2 4 (px-px)(px-px) 1 3 2 4 - ) - ) (2y py (py py 24 information about the ground state and admixed excited states. How this information is acquired is, in part, the topic of the following section. E. Molecular Orbital Theory of g and Metal A Parameters DeArmond at al.34 , extending the basic theory of Abragam and Pryce76, have related the ESR parameters (9", gi, All and AL) of the spin Hamiltonian given by Equation (2.3) to bonding coefficients for the series [MOFSJZ- where M = Cr, Mo, W. The theoretical deve10p- ment of these expressions is included here since they will be used in this study of bonding in the analogous series [MOF513- where M = V, Nb. 1 The general Hamiltonian for the d [MOF513- ions is given as a sum of terms listed in decreasing energy: 2 z 92 Z 32 " _ j 2 k —— 1c “ E g ‘ 2m Vi ‘ rik +i = BZIdxy> - 82|¢xy> , and, under the 04v point group, the I81) = Bllde-y2> — 81' I 4x2_y3>and |E>= 6 Id - e'|¢ excited state xz,yz> xz,yz> 26 wave functions will mix. For convenience, the ground state will be denoted here by |o> and the excited states by In) . The first-order energy than is simply <0|J2"|0> . In calculating this energy, the following assumptions are made: (1) all integrals involving A(r) between transition metal functions and ligands are neglected and (2) all in- tegrals involving r_3 which contain ligand functions are neglected. Since <0|2|0> = 0, this calculation yields following first-order solution A A 2 E = geBe '5 + 82P[ + 2 -%( ) + K26] . (2.13) S ac (C y y In correcting this solution to second order, only the <0I(b)|n> /(En - E0), <0|(b)|n>/ (En - so), and (0| (b) In) 2/(En - E0) does not give terms in the spin Hamiltonian. This procedure yields: (2) A E = Aij Beyisj + (Aéj - suij)sin , (2.14) where Aij e .. 2 n20 (alur) Ziln> /En—EO) A A 3 Aid = - 2 ”£0 (olxmziln) /(En-E0) . A 5 pij e - ieikm 25.210 (alumzm | n) 12 and AE e n e n ' (bz-e) (52—b1) are the energy differences between the ground state and those excited states which will mix, Sb = ' Se = ' and K is the Fermi contact term. The P values can be determined from S Hartree-Fock wave functions for the atoms and the AE values can be determined from optical spectra. The de- termination of S values and K demand more detailed dis- cussion. F. Evaluation of K In the case of d1 complexes, where the unpaired electron is in a dmy orbital, the value of K is considered to be a measure of the polarization of the inner s elec— trons. This parameter can be evaluated by solving the first-order isotrOpic hyperfine expression21 for K as follows: K = ((g)- 3.0023) _ Q} , (2.20) where (A) <9) (All + 2AJ.)/3 (gll + 2g-L)/3 . In order to evaluate K using this expression, it is necessary to know the exPerimental isotropic (g) and (A) 29 values and to assume values for P and 8:. Since K for a transition metal is considered constant for complexes with the same electronic configuration45, the value of K used for [VOF513- is taken to be the same as that found for the solvated VO2+ ion in an aqueous solution of V0804. 2+ For [vo(H20)5]. V2+ was used to evaluate P and since the solvated VO the Hartree-Fock radial function for 2+ ion is considered nearly ionic, a value of 0.97 was as- sumed for 82. Using these parameters, a value of 0.85 was determined for K. Since solution spectra are not available for the NbO2+ species, a different approach was taken to evaluate 77 K for [NbOF5]3_. The first—order expressions for (A) , All' and Al were solved for K and B: as shown below: K = - (A) + ( (2.24) (I) l e - ’ 34 mmo.o Hma.o mma.o hmo.o Hmo.o o.v+ mmo.o mma.o mvH.o oaa.o mmo.o o.m+ mvo.o omH.o hmH.o vNH.o mno.o o.N+ hvo.o hma.o mma.o Hma.o «mo.o o.H+ A mas 3 mm _ mm qNBmumV Amqwmm _ quNRNuMV AWQN _ mmlmafimv Ammm _ mmlmamumv AMQN _ mafimv ESHWMGM> mmumnu .umfimmo>g How mamummucfi mmaum>o UfieouMflo .m.m magma 35 where _ 1 2 3 4 1 2 3 4 ¢x2_y2 ' 01(3 ‘8 *3 ‘3 ) + 02 (Pm-px+px-px) 1 2 3 4 9 = ( - + - ) xy py p2 py py _ o 5 1,2 3,4 xz’yz — d1(px’y) + d2(px’y) + d3(pz -pz ) (2.25) The group overlap orbitals have been calculated both by considering just the dominant ligand p orbital overlap, and also by considering the entire ligand hybrid orbital overlap. In the former case, the c d , and d3 1’ 2 coefficients are taken as zero, giving the following group overlap integrals as expressed in terms of diatomic over- lap integrals: (I) II b g <3d2 2|2p:> x -y 0') II b 2 <3dxy | 2p:> _ 0 Se _ <3dxz,yz|2px,y> (2.26) In.the latter case, the degree of hybridization used was 5&5 that determined in Van Kemenade' extended Hfickel calcu- lations for [CrOF5]2-. Table 2.7. Orbital character ratios used for the hybrid group symmetry orbitals. ratio [CrOFSJZ- 0.65 _2.26 ‘2.26_‘ 36 Using these orbital character ratios, shown in Table 2.7, to determine the ligand hybrid orbital coefficients, the group orbitals were normalized and integrated with their corresponding metal orbitals to give the following eXpres- sions for the overlap integrals: 8 Sb] = 1.088 (361 2 2|2s) x -y 8 + 1.348 <3d 2 2l2px> (2.27) x -y s = 2 3d 2 e . .2 < .1 py> <2 2., __ 0 Se — 0.656 <3dxz’yzl2px’y> a + 0. 436 <3dxz,yz I2px’y> + 0.872 (sdxyl2p:> (2.29) The group overlap integrals for [NbOF5]3- were determined by extrapolation from those for [VOF513- as- suming that the ratio S[VOF5]3_/S[NbOF5]3_ for a given overlap integral such as Se would be the same as found for S[CrOF5]2-/S[MoOF5]2- in the extended Hfickel calcula- tions on Group VIb complexes45. The overlap integrals for [NbOFsl3- and for [VOF5]3- calculated by considering only dominant ligand p overlap are shown in Table 4.5 and those values determined by considering ligand hybrid orbital overlap are shown in Table 4.6. 37 H. Determination of Bonding Coefficients from 3 and Metal A Expressions For a particular assumed charge on the central metal atom, bonding coefficients were determined in the following manner. First, for a given set of parameters 82, 81 and s, the corresponding 85, Si and 8' coefficients were deter— mined from the normalization condition. These coefficients were then substituted into Equation (2.16-2.19) to deter- mine the theoretical values for Agi', A313 Ail and 41. Next, the total squared relative error between the experi- mental Agll, Agzlf All and {L values and the above theoret- icali values was evaluated by use of the eXpression Error = [(Agil-Ag||)/Agll]2 + [(AqirAqL)/AQL]2 [(Ail-A||)/All]2 + [(Ai-Ai)/A_L12. (2.30) Finally, a best-fit solution was determined by a minimiza— tion program which systematically searched the Space spanned by 81, 82 and 8 until the smallest value of "Error" was found. I. Calculation of Charge on the Central Metal Atom In order to calculate a charge on the central metal atom, the corresponding bonding molecular orbital coefficients were determined from the above antibonding coefficients using the orthogonality relationship 38 = 0 and the normalization relationship = 1. With the bonding and antibonding coefficients so determined, it is now possibly to correct the +4 formal charge on the central metal for valence shell covalency. The formal charge of +4 assumes that the electron density of the bonding molecular orbital is completely on the ligand and the antibonding electron density is completely on the metal. However, using wb = a(¢M) + b(¢L) as a general expression for a bonding molecular orbital, a Mulliken population analysis82 shows that there is Qb = 2(b2+ab3) electron density on the ligands for each filled bonding orbital and, using w* = 0(¢M) - d(¢L) to represent the half-filled antibonding molecular orbital, a Mulliken population analysis shows this orbital contri- butes a charge of Qa = (ca-ads) to the central metal atom. Thus, the calculated charge is given by n Q=4.0-Z l Qbi + Qa , (2.31) l where n is the number of filled bonding molecular orbitals. J. Determination of Ligand Hyperfine Values The interaction of an unpaired electron with ligand nuclei is interpreted in terms of a spin Hamiltonian. For the [NbOF513- ion, this Hamiltonian is given by 39 4 JCL = A s E I + [Ax(Ix1+Ix3) + Ay(Ix2+Ix4)] 3x + [Ay(Iy1+Iy3) +Ax(Iy2+Iy4)]Sy . (2.32) Since the unpaired electron in this case, as in most other n*fi: cases, interacts with several ligand nuclei, the result- 5 ing hyperfine lines are difficult to follow in a rotation, especially when they are superimposed on metal hyperfine if a .‘u «nu- "0 Ax‘w‘.’ Fa‘. lines. Therefore, in this case one cannot use a diagonaliza- tion technique to determine the principal values. However, from theory we know that the principal values of the ligand hyperfine tensor lie along the ligand bonding directions, . 3- 2.3.,for [NbOF5] , along the ligand p0, pfly, and pnz directions. Thus, using the direction cosines determined from the g and metal A diagonalization, and available crystal structure information, the crystal can be oriented in the magnetic field such that the principal value are measured directly. K. Determination of the Sign of the Principal Ligand A Values The ligand hyperfine tensor is composed of an isotrOpic part and an anisotropic part. Since the trace of the anisotropic part sums to zero, in solution only the isotropic part is observed. Thus, from solution Spectra one can usually establish the relative signs of 40 the principal values using the relationship Aiso = 1/3IAx+Ay+Az]' Although in the study of ions in unstable oxidation states solution spectra are not available, re- sults for analogous compounds in stable oxidation states can be used to determine the relative signs. Even if the relative signs are known, one must still determine the correct combination of signs. This is done by analyzing the possible combination of signs for the ligand hyperfine tensor in terms of its various component tensors. The component tensors are given here taking y and z to denote the ligand 0 bond directions and x to denote the 0 bond direction. A A. _ 2A x .280 d Ay = Aisq + -Ad L As Aisoj -Ad .1 L L .4 _ r _ 2A 1 - W + -A0 + 2Afly -A - L O_ __ 773! J ’ 1 -A 02 + _A (2.33) 02 2Anz ‘- .1 Assuming that the ligand nucleus has a positive magnetic moment, the expected relative magnitudes and signs of these components are given for the different bonding cases (noting of course that in each case the component 41 would have opposite sign if the nuclear moment were nega- tive). For the case where the unpaired electron is in a metal d orbital which has a w overlap with the ligand orbitals, the A. and A 880 .afiiso due to direct n delocal- ization will bepositive and large relative to the negative Aiso and A arising from spin-polarization aniso of the 0 orbitals. For the case where the electron is in a metal d orbital which has a o overlap with the ligand orbitals, Aiso and A due to the direct 0 delocaliza- aniso' tion, will be positive and large relative to the negative A and A arising from spin-polarization of the 0 £80 aniso orbitals. In both cases Ad is positive and its magnitude can be calculated from the expression Ad = geBegan/r3 (ergs.). L. Determination of Bonding Coefficients from Ligand Hyperfine Splittings Since ligand hyperfine splittings provide the best demonstration of covalency in transition metal com- plexes, one should be able to relate this parameter to molecular orbital bonding coefficients for these com- pounds. Two approaches to this problem were taken in this thesis work. For th [v05513‘ and (Nbors13‘ series, certain assumptions about spin-polarization (or configura- tion interaction, depending on how one wants to look at this) enabled the anisotropic part of the ligand hyper- fine tensor to be decomposed into axially symmetric tensors. The one tensor with its unique axis along the 42 ligand pTry direction was considered to arise from direct delocalization of the unpaired electron in the metal-dmy orbital into the ligand pTry orbital. Relating a Mulliken population analysis for this molecular orbital to the total experimental spin density transferred to the ligand pfly orbitals, enabled the bonding coefficients to be de- termined. The other method involves using the ground state molecular orbital to determine the expectation value for the dipolar interaction between the unpaired electron and the ligand nuclear magnetic moment. This method involves, for instance in the case of [NbOF513—, the following inte- grals: (OIRLIO> = 8: - 28282 (dxyl}CLl¢xy> + Bég<¢xyIJCLl¢xy>. (2.34) However, when molecular orbital coefficients are actually determined we focus on the interaction with just one ligand, the expression used only involves the diatomic integrals: L 2 Aaniso = 82 _ B282 52 + T as Ad , ignore the second inte— gral since good wave functions were not available, and use PC]. for . It should be noted that the molecular orbital coefficients calculated for [RhC16]4- in this manner are only very approximate, since Van Kemenade45, applying the above method, found that not only did he have to evaluate all the integrals but also calcu— late second-order correction terms to achieve good agree- ment between experiment and theory. CHAPTER III EXPERIMENTAL A. ESR Spectrometer Systems The ESR measurements were carried out with 100 KHz field modulation using a Varian V-4502 X-band spec- trometer, a Varian E-4 spectrometer, and a Varian 4503 Q—band spectrometer. Since the Varian V-4502 X-band spectrometer has provisions for measuring the frequency and field position very accurately, it was used for all quantitative measurements. And because of its Operational stability and facility, the E—4 spectrometer was often used for initial qualitative work. The Q-band spectrometer, with a magnetic field range approximately four times that of the X-band spectrometer, was used to study systems which contained more than one species with different 9 values . A rather complete description of the Varian V-4502 ESR system has been given by Kuska83. A Varian Associates 12-inch electromagnet furnished the magnetic field. The field position was determined using a marginal-oscillator NMR.probe with the oscillator frequency measured by a Monsanto counter-timer in conjunction with an Ameco 44 45 preamp. A calibrated TS-148/UP U.S. navy spectrum analyzer was used to measure the microwave frequencies. Spectra were recorded either on a Moseley 7000A x-y recorder or a Hewlett Packard 7005B x-y recorder. B. Sample Preparation l. KszOFS-HZO.-—This compound was purchased from Organic/Inorganic Chemical Corp., Sun Valley, Calif., and recrystallized from aqueous solution. 2. K3Co(CN)6.—-Cobalt cyanide was precipitated from a boiling solution of cobalt chloride by adding potas- sium cyanide. The cobalt cyanide was then added to a solution of potassium cyanide to obtain K4Co(CN)6. By boiling the solution of potassium hexacyanocobaltate (II), the complex was oxidized to potassium hexacyanocobaltate (III)84. 3. K4Fe(CN)6-3H20.--Baker and Adamson potassium hexacyanoferrate (II) was recrystallized from water. 4. Na3RhC16°12H20.--Sodium hexachlororhodate (III) was obtained by chlorination of a mixture of sodium chloride and rhodium (III) chloride at high temperatures. The sodium hexachlororhodate (III) dodecahydrate was then formed by crystallizing from a solution of this reaction mixture in the presence of excess sodium chloride85. 46 5. K RhCl 'H O.--The potassium hexachlororhodate 3 6 2 (III) monohydrate was made directly by chlorinating a mixture of rhodium (III) chloride and potassium chloride at high temperatures and then crystallizing from a solu- tion of the reaction mixture containing excess potassium chloride. The compound was also made indirectly by first converting the sodium hexachlororhodate (III) dodecahy- drate to hexachlororhodic (III) acid and then adding po- 85 tassium chloride in excess . 6. K2[RhC15(HZOH.-—This compound was made by the recrystallization of potassium hexachlororhodate (III) 86 monohydrate from water . 7. Na3RuCl6-12H20.-—Ruthenium (III) chloride tri— hydrate and sodium chloride were added to a solution of ethanol and concentrated hydrochloric acid. This solution was taken to dryness. The product was crystallized from water87. 8. K2[RuC15(H20)].--Ruthenium (III) chloride tri- hydrate was added to a boiling dilute solution of hydro- chloric acid and ethanol. After boiling for an appro— priate period, potassium chloride was added and the solu— 88 tion taken to dryness . 9. K3RuCl6-H20.-—This compound was made from a solution of potassium aqquentachlororuthenate (III) by cooling in ice water and passing hydrogen chloride gas 87 t1L'lz‘ough until the solution was saturated . 47 10. (NH4)2[InC15(H20)].-—Stoichiometric amounts of indium (III) chloride and ammonium chloride were dissolved in hydrochloric acid. Crystals were recovered by evaporating the solution89. ll. K2ReF6.--There are two methods for preparing this compound in the literaturego’gl. These preparations, however, give products with different physical appearances. The method of Peacock90 was first attempted. Am- monium hexaiodorhenate (IV) was made by evaporating a solu- tion rhenium heptoxide and ammonium hydroxide with excess hydroiodic acid just to drynessgz. The (NH4)2 ReI6 was then fused with potassium hydrogen fluoride at 400°C. White crystals of KzReF6 were recovered by recrystalliza~ tion of the fusion product. The x-ray powder spectrum of this substance indicated that the product was mostly K2ReO4. The method of Weise91 was tried next. Potassium hexabromorhenate (IV) was made by the reduction of potas— sium perrhenate with hypOphosphorus acid in the presence of potassium bromide and hydrobromic acid93. Using a nitrogen atmosphere, the KzReBr6 was then fused with anhydrous potassium hydrogen fluoride at 700°C. Pink crystals were recovered by recrystallization of the fusion product. The x—ray powder spectra of the pink substance indicated that this was pure K2ReF691. 94 La Valle also noted the discrepancies in the literature as to the color of the KzReF6 complex. 48 His infrared analysis indicated that the pink product was the pure compound. 12. CszGeF6.--Germanium dioxide was dissolved in 20% HF solution and a solution of CsCl added. The volume of this mixture was reduced by heating. Cooling in an ice bath yielded clear crystals of CsZGeF695. 13. K2N1(CN)4'H O and Na Ni(CN)4'3H O.--Nickel (II) 2 2 2 cyanide was first made by adding a solution of KCN to an aqueous solution of NiSO4°6H20. Next an apprOpriate amount of the Ni(CN)2 was added to solutions of KCN or NaCN which were heated to obtain crystals of K2Ni(CN)4°H20 or NaZNi(CN)4-3H O, respectively96. 2 l4. Magnus' Green Salt [Pt(NH ][PtC14].-—The 3)4 Magnus' green salt was prepared by mixing solutions of K PtCl in a dilute solution of HCl. 2 4 and Pt(NH3)4Cl 2 C. Crystal Growing l. Crystals for Irradiation.-—Single crystals of K NbOF5°H o, K3Co(CN) K4Fe(CN)6°3H o, K2[Rhc15820)], 2 0 were obtained by slow 6’ O, and NazNi(CN)4-3H 2 2 K2N1(CN)4-H2 2 evaporation of saturated aqueous solutions of the salts; crystals of K3RhCl6-HZO and Na3RhC16-12H20 were made by slow evaporation of saturated solutions of the salts with excess KCl and NaCl, respectively. All crystals obtained 49 by the evaporation technique were made in beakers coated with a thin film of Dow Corning high-vacuum silicone grease to prevent deposition of the salt onto the side of the beaker. Sheets of Parafilm (American Can Company) punched with small holes were stretched across the tOps of the beakers to insure slow evaporation and to prevent dust from settling into the solutions. The solutions were kept in an isolated drawer to eliminate sudden thermal and vibrational disturbances. A diffusion technique was employed to grow crystals of the Magnus' green salt. Saturated solutions of K2PtC14 and Pt(NH3)4Cl2 wer prepared in narrow-necked Erlen- meyer flasks. The flasks were placed in a large beaker which was carefully filled with 0.1M HCl and sealed with a sheet of Parafilm. The [PtCl412- ions and [Pt(NH3)4]2+ ions slowly diffused through the dilute hydrochloric acid medium to form crystals at the lip of the Erlenmeyer flasks. 2. Doped Crystals. a. From Solution.—-Crystals of NaCl doped with [RuC1613- were obtained by evaporating a saturated 3RuC16'12H20. The yellow color of these crystals was a visible in- solution of NaCl containing about 0.1% Na dication that the [RuC16]3- ions entered the NaCl lat- tice homogeneously. Attempts to dOpe the [RuC16]3- ion 3RuC16-H20 in a saturated KCl solution did not appear as successful. into the KCl lattice using 0.1% K 50 The very light color of these crystals could not be con- sidered as positive evidence that the [RuC16l3- ion had entered the lattice. The [RuC15(H20)]2_ ion was doped into the (NH4)21nCls-H20 lattice by evaporating a 1M HCl solution, saturated with (NH [InC15(H20)] and containing 0.1% 4’2 K2[RuC15(H20)]. The [RuC15(H20)]2- ion did not always enter the lattice homogeneously as was evidenced by areas of deeper red coloration. doped with the [ReF6]2- ion were Crystals of Cs GeF 2 6 grown by the slow evaporation of a 20% HF solution saturated with CszGeF6 and containing 0.1% K ReF . The technique used 2 6 to grow the doped crystals was the same as that described above for the crystals prepared for irradiation. b. From the Melt.--These crystals were grown by zone melting. The furnace consisted of a 2cm tube 45cm long wrapped with asbestos tape with a nichrome wire heating element wound about the central portion. The ends of the furnace were made of Transite and the casing of aluminum. Vermiculite insulator was used to fill the area between the tube and the casing. A synchronous clock motor was geared to a spool of nichrome wire to lower the samples through the zone furnace at a rate of 2mm/min. Crystals of AgCl containing various dOpants were made in 6mm quartz tubes with cone tips. Rhodium was doped into this host lattice by placing homogeneous 51 mixtures of AgCl with 1% RhCl3 into the tubes, evacuating, and passing the sealed tubes through the zone furnace set at 500°C. The cylindrical crystals obtained by this method were dark red. Also, mixtures of AgCl with 1% RuCl3 were placed into the cone-tipped tubes, evacuated, and passed through the zone melter to give very dark, nearly black, cylindrical crystals. The NaF samples were prepared in 1/4" i.d. graphite tubes with conical bottoms. The graphite tubes were placed in a larger quartz tube, evaculated, and heated with a hot- air gun to insure dryness of the sample and container. The vapors from the molten NaF attacked the quartz tubing re- sulting in almost complete corrosion and decomposition. Placing about two atmospheres of helium in the tube be- fore sealing alleviated the corrosion problem enough to and RhCl mixtures with 3 3 NaF were used with the furnace set at 1000°C but only in obtain crystals. Both 1% RuCl the case of the RhCl dOpant was a single crystal obtained. 3 D. Identification of Crystallographic Axes 1. Irradiated Crystals.--The morphological descrip- 97 tions in Groth and other sources combined with the use of a pOlarizing microscope permitted optical identification of the crystallographic axes in almost all cases. One exception was the crystals of KZNbOFS'HZO which grew in thin sheets with the 001 plane as the only usable 52 morphological feature. The crystals were cut into rec- tangular slabs by cleaving parallel and perpendicular to the extinction axis in the 001 plane. The a and b axes were distinquished from one another by examining the ESR spectra of the irradiated crystals. 2. Dgped Crystals.--The crystallographic axes of the doped crystals grown from solution could be easily identified from their morphology. On the other hand, by using cone-ended tubes, the cubic crystals grown from the melt could be assumed to have a crystallographic axis (assigned as the c axis) along the length of the crystal. Cylindrical slabs of these crystals were made by cleaving perpendicular to this axis. The other axes could be identified from the ESR spectra by rotating in the 001 plane. E. y-Irradiation Method All samples (powders in vials, or tubes, crystals in vials, or pre-mounted on rods) were submerged in a Dewar of liquid nitrogen. The Dewar was placed in the center of the Michigan State University 60Co y-source and 6 subjected to an effective dose of 1X10 rads/hr for a period of 3 to 4 hours. F. Sample Handling of Irradiated Samples 1. Single Crystals.—-Two methods were used for mounting the single crystals. One method consisted of 53 mounting the irradiated crystals between brass clips glued to the end of a quartz rod. This method involved mounting and aligning the sample under liquid nitrogen using forceps. A detailed description of this method, including figures, has been given by Watson98. The other method con- sisted of gluing crystals to the flattened tip of a wire inserted into the end of a quartz tube. The entire sample holder with attached crystal was irradiated. The glue (Pliobond Cement, Goodyear Tire and Rubber Co.), when irradiated at 77°K gave only a broad line at g = 2.0026 and the second-derivative signal was weak. The "brass clip" and the "glue" methods each have different advantages. Since often the same crystal can be used for more than one rotation, the "brass clip" method is useful for systems where there are a limited number of single crystals available. Also, with this method there is no extraneous ESR signal from irradiated glue. One disadvantage of the method is that unless the crystals are large enough to be clamped firmly between the brass clips, the crystal alignment can change during a rotation due to vibrational disturbances caused by nitrogen gas bubbling from the tip of the ESR Dewar. Another disadvantage of this method is the difficulty in- volved in obtaining an accurate initial alignment of the crystal, since this must be done under liquid nitrogen. 54 The "glue" method, on the other hand, was found to be more advantageous and was used for all the systems ex- cept K3Co(CN)6. This method allows thin crystals (as in the case of KZNbOFs-HZO) to be mounted securely. Also, since the crystals are not mounted under liquid nitrogen, initial alignment can be made more accurately. The only disadvantages are that there is a weak second derivative signal from the glue and once a crystal is mounted it can rarely be removed intact to be used for another orienta— tion. Regardless of which method was used to mount the crystals, for studies at 77°K the crystal holder with the attached irradiated crystal was placed in a specially de- signed Dewar filled with liquid nitrogen. The quartz tip of the Dewar was made to fit inside the Varian V—4531 multipurpose cavity. Attached to the Dewar was a metal pointer which was used with a protractor scale to deter— mine the angle of rotation. The rods were centered in the Dewar with a cylindrical foam insert at the top of the Dewar while the sample was adjusted vertically in the cavity until the signal was maximized. The initial align- ment of the crystal in the Dewar was done visually with refinement using the oscilloscope mode of the ESR spec- trometer. For the variable temperature work, a Varian V-4540 variable temperature accessory was used. The sample rods were held in a goniometer attached to the ESR cavity. 55 2. Powders.--For powder studies at 77°K, the powder samples irradiated in vials were poured into the ESR Dewar filled with liquid nitrogen. After the sample settled into the tip of the Dewar, the vertical position of the Dewar in the cavity was adjusted to give a maximum signal- to-noise ratio. For variable temperature studies, the powders were irradiated in sealed quartz tubes. Since irradiated quartz gives an ESR signal, steps were taken to annihilate this signal from the tube. While keeping the end of the tube containing the sample submerged in liquid nitrogen, the other end was heated with a torch until white hot. The tube was then completely submerged in liquid nitrogen, inverted, and the sample transferred by tapping into the end which had been heated. Finally, the quartz tube was placed into the ESR cavity and the Varian V-4540 assembly used to vary the temperature. G. Low Temperature Studies (below-77°K) There were two methods used to achieve these tem- peratures. One method, which will be referred to as the flow method, consists of transferring helium gas from an externally located thirty-liter Dewar containing liquid helium to the cavity. Inserted into the cavity from below is an evacuated cold finger assembly to which the gaseous helium is transferred. The sample then is placed into 56 the cavity from above by centering it in the cold-finger jacket. The temperature is regulated by controlling the boil-off rate of the helium in the thirty—liter Dewar by adjusting the current going to a heating element located at the bottom of this Dewar. Temperatures in the range of 6°K can be approached with this system. The other system which was used is called the Andonian Variable Temperature Cryogenic System (O-25/7M Series), Waltham, Mass. This consists of a three—liter Dewar with a spectrasil quartz cold finger extending from the bottom. The Dewar is positioned above so that the cold finger reaches into the center of the cavity. The sample, attached to a specially designed rod with a Lukolux tip, is lowered through the Dewar system until it reaches the proper position in the sample zone. Helium gas, which is admitted from the main helium reservoir to the sample zone through a throttle valve, flows around and in intimate contact with the sample and exits to the atmosphere. The throttle valve controls the flow rate of helium gas into the sample zone and consequently the rate of energy removed from it. This system can approach 4.2°K if the throttle valve is left wide-open long enough for liquid helium to reach the system. H. Conversion Factors The following conversion factors and equations were used for the analysis of spectra and are included for con- venient reference: 57 H(gauss) = [2.348682X102][vp(MHz)], (3.1) g = [0.7§:4§:i;:?(MHz)l (3.2) A(ergs) = 11(gauss)[9.274096X10"21 x g], (3.3) A(cm-l) = A(gauss) [4.668599X10-5 X g], (3.4) A(MHz) = A(gauss) [1.399611 x g]. (3.5) where H is the magnetic field position, up is the proton oscillator frequency, g is the electronic 9 factor, H0 is the field position at the center of the spectrum, 08 is the klystron frequency, and A is the measured hyper— fine splitting. CHAPTER IV Y IRRADIATION OF KszOFS-HZO A. Introduction At 77°K the ESR lines from a 93Nb containing radical are observed for y-irradiatedpolycrystalline KZNbOFs-HZO. The perpendicular features of the spectrum exhibit fluorine superhyperfine splittings and the parallel features spread over a 3000 gauss region. The 9, A(93Nb), and A(19F) tensors for this radical obtained from a complete analysis of the single-crystal ESR spectra, show that it is [NbOF513- with a d1 configuration and a dry ground state. At 77°K strong lines in the g = 2.0023 region, arising from other radicals produced during irradiation, are also observed. The structure of these radicals could not be studied at 77°K since their spectra are obscured by the overlapping spectrum from the [NbOF513— species. However, better spectra of these radicals were obtained by warming the y—irradiated K2NbOF5-HZO powder sample from 77°K. On warming to 190°K, the signal from the [NbOF5]3‘ radical slowly decays until it is completely gone; a sharp signal at 2.0014, presumably from trapped electrons, gradually increases in intensity to a maximum; a three 58 59 g-value pattern, shown to arise from the ozonide radical, also increases somewhat in intensity over this temperature range; and, lastly, a ten-line pattern, overlapping with the lines from the trapped electron and the ozonide radical, becomes better resolved. The ten-line pattern has been identified as a hole species, either [NbOF5]- or possibly NbOF4, with its unpaired electron density localized on the 93Nb oxygen atom. This assignment is based on the small hyperfine splitting values for this radical and the g values being greater than the free—spin value. On warming the sample further, the line from the trapped electron decreases in intensity until it disappears at 220°K, the signal from the hole species decreases in intensity until it disappears at 250°K, and the ozonide radical very slowly decays but is still stable even at 550°K. B. Results 1. Single Crystal at 77°K.-—A detailed crystal structure for KZNbOFS-HZO has not been reported but 97 show the unit cell to be monoclinic crystallographic data with B = 103°46'. The crystals grow as thin, transparent plates with the 001 faces clearly developed; making the 0* axes easily identifiable. The a and b axes were found using a polarizing microsc0pe in conjunction with ESR spectra of the y-irradiated samples. 60 Isofrequency plots of the 93Nb hyperfine lines for rotations about the three orthogonal a, b, and 0* axes in— dicate that the unit cell of KszOFS-HZO contains two magnetically distinct sites (Figures 4.1—4.3). Using Scholand's method72, principal values and direction cosines for the metal hyperfine tensors of these sites have been determined (Table 4.1). The direction cosines indicate that the two sites lie in the be plane, tilted relative to one another. Although the angle between them can be determined by taking the dot product of the appropriate direction cosine vectors, a more precise determination was made from a rotation about the a* axis. Since the "apparent g" tensor does not vary appreci- ably and, as will be shown, does not appear to correspond to the true 9 tensor, the variation of A2 instead of A292 was plotted for the rotation about the a* axis. The A2 93 plot for the Nb hyperfine splittings did not, however, exhibit well defined maxima, making it necessary to use a least-squares curve fitting program to determine the pre- cise angle at which the maxima occur. By curve fitting the 93Nb hyperfine splitting data to the expression, 2 2 2 A A g = a + B c0326 + ysin26 , (4.1) III values for a, b and Y were found for each site. These parameters were then used in the expression defining the nz Eoum mmcfla mcwmuwmhn cop .mcmam son 0:» ca pamwm owuwcmmfi man aue3 on» How mcoeuemom mocmc0mmu 0:» mo c0e00flum>lna.v onsmem mm .or 61 .8. AA .I\\...u ‘ Tlllli .87 Doom -I\\e_ -I\£ 62 0.2 mm scum mmcHH mcflmummxc sou may e0 02 .mcmam use on» ca waowm owgmcmme on» sues now mc0fluwmom monocommu may no sowumwum>lum.v «Haven 1 L L n 1% I§u 63 s2me scum mmcwa mcflmummws sou mnu How .mcmam as may cw pamwm oeumcmma on» cufi3 Cl oo. 09 “II—- “ — w ._ 1 " Ooon _ _ '- d L mcowuwmom MOGMGOmmH can no cowumeum>nlm.q madman I\\O I\\b +issnv 64 Table 4.1.--ESR parametersa for [NbOF513—. Tensor Components Direction Cosinesb gll 3,1.870 91.: 1.914 0.976 0.000 —0.217 —0.018 20.996 -0.082 0.217 20.084 0.973 A (93Nb) = 159.8 J. All(93Nb) = 302.1 19 _ A( F)eq - 19.84 39.85 19 A( F)eq 19 A( F)eq 8.73 aThe parameters are corrected for higher-order effects and the hyperfine Splittings are in cm’1 X 104 units. bRelative to the a, b, 0* crystallographic axes of K2NbOF5°H20. angle at which the A2 maximum occurs, emax = [tsn'1(v/8)/21 , (4.2) to determine the angle between the sites. The results show that the sites are tilted 6° on either side of the c axis giving an angle of 12° between them (Figure 4.4). While most of the [NbOF5]3- complexes are oriented with the Nb—O bond 6° from the c axis, some of the com- plexes are oriented with the oxygen at any of the four equatorial vertices of the original octehedral unit. 65 .m on Hoaaouom coon OIQZIm Hfionu nufl3 mace omonu Scum mosfia ocwmuomhn nz sou ozu oumuaocw msonno one .mflxm o ocu scum om sonoam oe.ocu cw me caoflm oHuocmmE onu «some as cmm.mmonz~z omumeemuueu> mo ssuuowmm mmm esmnux 0>eum>enmeuecoommuus.e masses 66 In Figure 4.5 evidence of this distribution is shown in the spectrum taken with the magnetic field along the c axis. The spectrum shows both the strong absorption from the radicals oriented in the preferred direction, that are nearly parallel to the magnetic field, and the weak ab— sorption from those radicals that have the orthogonal orientations. The estimated ratio for the number of radicals that have their Nb-O bond in the preferred orien- tation to those radicals having the perpendicular orenta- tions is 13:1. Efforts to diagonalize the g tensor using Schon- land's method72 93 failed. Higher-order effects due to the large Nb hyperfine tensor cause the "apparent g" values determined from the center of the spectra to deviate con- siderably from the true 9 values. The deviation from true g tensor behavior is evident in the plot of "apparent g" values for the b rotation (Figure 4.6), which exhibits two maxima 60° on either side of a minimum. The 9 and A(93Nb) tensors have therefore been determined by the method outlined below assuming that they are coaxial, as has been found for the other halooxymetallates. To facilitate the analysis of the metal hyperfine and ligand hyperfine interactions, an apprOpriate coordinate system for the [NbOF5]3- complex is defined (Figure 4.7). The metal hyperfine interaction is considered to originate at the niobium nucleus, so its Z axis is chosen along the 67 .m on Hoasoeocom )Hom waumoc moxm ounzIm neon» sues Awm usonov manuapou on» scum ouo nosed vacuum xwm Houucoo one coo3uon muoamfluase xoo3 on» «m on Hoaaouom wauooc moxo ounzlm neon» cuea mcoe ucoflo>wsvo >HHm0HuommoE mo upon 03» onu Eoum we :Houuom ocqaloa oncoucfl one .o\\& suw3 Mann no 0mm. monz M wouowoonuwlr mo Eduuoomm Mmm oconux o>Huo>wnoolucooom1Im.v oHsmHm I - .Ooon. 68 * H//a* H/lc H/CI 2.00 1 1 L 1.954 9 1.90- 1.85- 1.80 . . . 0: 90° 180° 0 Figure 4.6--A plot of the "apparent g" values for the [NbOF5]3“ radical with the magnetic field in the a*c plane. Figure 4.7--C83rdinate system for the [NbOF ]3— ion used for the Nb hyperfine tensor, the g t nsor, and the equatorial 19F hyperfine tensors. 70‘ O-Nb-F bond with the X and Y axes along the F-Nb—F bond directions in the equatorial plane. The origin of the fluorine superhyperfine interaction tensor is the fluorine atom; hence each equatorial fluorine atom is assigned a coordinate system with the z axis parallel to the O-Nb—F bond, the x axis along the equatorial Nb-F—bond, and the y axis chosen to form a right-handed coordinate system. If the nuclear quadrupole and nuclear Zeeman terms are neglected, the electronic Zeeman and metal hyperfine tensors obey the angular relationships 9 = (ggcosg8+gisin280082¢+g§sin2Beingo)1/2 (4.3) and 2 2 2 2 2 . 2 2 gA = (Azgzcos 6+AXgX32n 6008 ¢ +A§g§singesin2¢)1/2 , (4.4) where the spherical polar angles 8 and 0 relate the ex- ternal magnetic field vector H to the Z and X axes, re— apectively. Thus, the spectrum obtained at 6 = 0° cor- responds to 92, A and the spectrum obtained at 0 90° Z and ¢ = 0° corresponds to 9X, A Since [NbOF5]3— is X' axially symmetric, Equations (4.3, 4.4) may be simplified by letting AZ = All, gz = gll, 9X = gY = 913 and AX = AY _ Al. 71 Since the 93Nb hyperfine Splitting values are quite large, it was decided to adjust the ESR parameters initially to second order. A least-squares fitting program was used to minimize the error for the magnetic field positions of the various mI transitions as determined from the equations (see Appendix A): 2 hv = gllBH(mI)+AllmI+ §%5[I(I+1)-m§] (for63= 0°) (4.5) and (AI (2.111(2) 2 h\) = giBH(mI)+A mI + 4}” [I(I+1)—mI] (for 0 = 90°), (4.6) where (g = Ho/hv), H(mI) is the resonance field corre- sponding to the nuclear quantum number m , v is the klystron I frequency, and All and AL are the average parallel and per— pendicular hyperfine splittings. The gll, gi, All, and AL values, corrected to second order by the above method, were then corrected for higher—order effects using the program MAGNSPEC 399. This program determines the spin Hamiltonian energy matrix, finds the diagonal values, and, finally, calculates the field positions of the various mI transitions. The final adjusted parameters were selected as those giving the best fit between the calculated and experimental mI resonance positions (see Table 4.2). Table 4.2.--Ca1culated line positions for 9 components. 3Nb hyperfine I MAGNSPEC 3 Experiment MAGNSPEC 3 Experiment Perpendicular Lines Parallel Lines 9/2 2595 Gauss 2595 1957 1956 7/2 2680 2680 2265 2262 5/2 2794 2793 2582 2583 3/2 2933 2932 2908 2911 1/2 3095 3094 3245 3249 -1/2 3279 3278 3591 3594 -3/2 3484 3482 3947 3953 -5/2 3709 3710 4313 4319 -7/2 3953 3954 4688 4690 -9/2 4215 4215 5073 5072 In order to analyze the fluorine hyperfine Split- ting tensor, it is necessary to orient the crystal so that the magnetic field vector makes the appropriate angles with the [NbOF5]3_ complex. With the applied field parallel to the O-Nb-F bond (i.e., 6 = 0°), the niobium parallel hyperfine lines are split into quintets of equal spacing with intensity ratios 1:4:6:4:1 (Figures 4.4 and 4.8(A)). These quintets arise from the four equivalent equatorial fluorines and their separation is designated as 43(19F)eq. At the e = 90°, ¢ = 0° orientation the applied field is 73 A A 16.76 B 50.26 C H 70.86 Figure 4.8--En1arged portions of the second-derivative spectra of y-irradiated K2NbOF5-H20 showing the superhyperfine split- tings. (A) 0 = 0°. The four equivalent equatorial fluorines give a quintet with intensity ratios 1:4:6:4:1. (B) 0 = 90°, 0 = 0°. The equatorial fluorines give a seven-line pattern With intensity ratios l:2:3:4:3:2:l, since A” ; 41/2)Ay- (c) 9 = 90°,wsvo maaooauoc name one mamoapon mo muom zoom .«o\\m .Mohh no douowuouuwlr Omm.mmonz~x mo Houmauo oamcwm 8 mo Esuuuomm econlx o>wum>wnoplvcooom onsllm.v onsmflm 76 .mofloomm uonuo Eoum an Hocmem Houucoo oncoucw one .monnumom HoHHonm on» ouoowocfi m3ouuo mcwucflom chasm: on» oHHns monsuoom onwmuomhn “masoflccomuom on» ouooflonw mzouuo mcHunwom ouozc30© ona .xohn no Cam.mmonz~x ocHHHmummuomHom wouoaomnuwlr mo Eduuoomm o>wuo>wuovlumuam ononlx onanloa.¢ ousmam n n n n n 4 n n n 1. .n....>.: 77 The 9 and A(93Nb) values obtained from the powder spectrum facilitated the single-crystal analysis since it was then possible to know with certainty when the applied field was along the parallel or perpendicular directions. The powder spectrum also supplemented the 93 single crystal spectra in providing the Nb hyperfine line positions used to correct for higher-order effects. 3. Variable Temperature Study of Powder Spectra.-- The first-derivative Q-band spectrum of polycrystalline K2Nb0F5°H2 is shown in Figure 4.11(A). The ten-line pattern from a 93Nb-containing radical partially overlaps at high 0, y-irradiated at 77°K and warmed to 200°K, field with the group of lines from the ozonide ion. On the other hand, in the x—band powder spectrum at 190°K (Figure 4.ll(B)) the ten-line pattern is shown to completely overlap with the set of lines from ozonide. Also, on either side of the ten-line pattern, weak multiplets are seen at higher gain. To verify that the underlying structure in these spectra is from the ozonide ion, the samples were warmed until the signal from the 93Nb-containing species disappeared. The underlying structure still remains at higher temperatures and gives the three g-value spectrum of the ozonide ion shown in Figure 4.ll(C). 78 100 (3 J 1006' B (: ’hflmjh’~jfl 100(3 Figure 4.ll--(A) The Q-band spectrum of polycrystalline KZNbOFS-HZO, y irradiated at 77°K and warmed to 200°K. The ten-line pattern is from a rotating niobium-containing hole Species. (B) The same but at X-band and 190°K. The Spectrum from the hole species overlaps with the spectrum from the ozonide ion and wing lines are seen at higher gain. (C) The same but warmed to 400°K. Only the ozonide ion remains and gives a three g-value pattern. 79 4. Single Crystal at l90°K.--Sing1e crystals of K2NbOF5°H20 y irradiated at 77°K were rotated at 190°K about their a, b, and 0* axes. The weak pattern in the wings of the spectra was difficult to resolve and could not be followed in the b and 0* rotations and only with marginal success in the a rotation. In this rotation, the greatest splitting of the outer set of lines occurs with the magnetic field along the b axis (see Figure 4.12). At this orientation, a considerable portion of the outer multiplets extends beyond the strong central ten-line pattern. It appears that these outer sets of multiplets arise from the weak interaction of an unpaired electron with a 93Nb nucleus and a 19 F nucleus, giving two sets of ten lines. AS the magnetic field is rotated away from the b axis toward the 0* axis, the weak outer multiplets move into the strong central ten-line pattern until the two patterns completely overlap. It is not possible therefore to determine the minimum of the fluorine split— ting. Throughout this rotation, the 1ine-widths and resolution of the central ten-line pattern varied con- siderably but the outermost lines of the pattern did not move appreciably. This was also found for the b and 0* rotations, indicating that central ten—line pattern arises from the isotrOpic part of a 93Nb hyperfine tensor. The picture that emerges from this analysis is that the isotropic ten-line pattern arises from a rotating 80 15 Figure 4.12--The X-band spectrum of y-irradiated K2NbOF5-H20 at 190°K with H//b; within the brackets are the weak wing lines. 81 niobium containing species. Since the niobium hyperfine splitting is small, the unpaired electron is considered to be localized mainly on the oxygen atom. The possible radicals that are consistent with these results are a rotating [NbOFsl— ion or a rotating NbOF4 ion. Similarly, because of the small 93Nb and 19 F hyperfine splittings of the weak outer multiplets, these also appear to arise from a radical with the unpaired electron localized mainly on the oxygen atom. However, the radicals in this instance are stationary as evidenced by the anisotrOpic fluorine interaction seen in the a rotation. The only radical that is consistent with these results is the [NbOFSI- species. Also, assuming that this radical doesn't reorient within the site and therefore has the same orientation as the [NbOF5]3_ ion, the maximum fluorine splitting found along the b axis should correspond to the fluorine tensor com— ponent perpendicular to the F-Nb-O bond (i.e., 0 = 90°, 0 = 45°). There are two possible eXplanations for the spec- trum at 190°K. First, the [NbOF5]- species is formed through the ejection of an electron upon Y irradiation at 77°K and, on warming, slowly decays to the NbOF4 Species through the rupture of the weak axial Nb-F bond. At 190°K, then, most of the [NbOFsl- ions have decayed to the NbOF4 species. The NbOF4 species, being somewhat con- tracted in Size and without charge, would be expected to 82 have a lower barrier to rotation than the [NbOF5]_ species and rotates freely at 190°K. The other possibility is that, again, the [NbOF5]_ species forms upon y irradiation at 77°K but, as the sample is warmed, thermal energy alters the trapping site enough to allow rotation. However, in this case it is necessary that the isotropic part of the (*“' axial fluorine hyperfine tensor be negligible, since other- wise the rotating species would give an isotropic pattern with more than ten lines. The anisotropic pattern would : be from those [NbOFsl- species which, as a result of thermal distribution, do not have enough energy to break the barrier to rotation. The fact that cooling back to 77°K does not seem to alter the distribution of the rotating and stationary species, seems to support the first explanation since the NbOF would not be expected 4 to change back to [NbOF5]‘ on cooling. However, the second explanation could still hold if the [NbOFsl‘ re‘ mained in the high-temperature site on recooling; such changes in radical environment on warming are often not reversible on cooling. In Table 4.3 are shown the A and g values for the isotrOpic 93Nb hyperfine value, and the 9 value for the anisotropic pattern with H parallel to b (all measured at 190°K); the g values for the ozonide ion measured at 400°K are also shown. 83 Table 4.3.-—The ESR parameters for the hole species and the ozonide ion. NbOF (190°K) 4 = 2.02213 93 Ai80( Nb) = -21.3 G [NbOFSI— (190°K) g = 2.0252 H//b A(93Nb) = —15.7 G 19 A( F) = 267 G [Nbo412‘ (195°K) (ref. 50] gll = 2.0208 All = -27.9 G gi_ = 2.0250 Ai' = 27.0 G Ozonide y-KszOF5°H20 (400K) y-KClO3 (77°K) (ref. 1001 g = 2.0014 2.0025 00.2: g = 2.0388 2.0174 82 g = 1.9579 2.0013 22 84 C. Discussion 1. Molecular Orbital Coefficients for [NbOF]3- and [v00513‘. a. Determined from g and Metal A Tensors.—~Using 75 have described an LCAO-MO method, Ballhausen and Gray the electronic sturcture of the vanadyl ion (VOZ+) in the penta-aquo complex. They suggest that the most important feature of these ions is the presence of considerable oxygen-to-metal n bonding. The investigation of the elec- tronic structures of VO('acac).2 and [VO(NCS)5]3- by Fan101 indicates that the inclusion of both out-of—plane and in- plane 0 bonding, as well as o bonding to the equatorial ligands, is also important in describing their electronic structures. Quite similar to the electronic structures of these ions are those for the stable [VOF5]3_ ion, and for the [NbOF5]3- ion formed by irradiation. In an at— tempt to further elucidate the bonding in these ions, MO coefficients have been determined using the second- order expressions for the spin Hamiltonian parameters. The [MOF5]3- ion [M = V,Nb] has C symmetry with 40 the unpaired electron in a 232 ground state. To derive spin Hamiltonian parameters, perturbation theory is applied using the perturbation Hamiltonian expression for the unpaired electron. The basis set chosen for the perturbation treatment consists of the ground 82 state 85 along with the lowest excited BI and E states arising from the promotion of the unpaired electron into the b1 and e molecular orbitals. The LCAO-MO wave functions for these orbitals are '84) I31) I4 > where the ligand orbitals 9 are group orbitals of appro— II 82 l dry) - 82 I ¢ccy>’ led 2 2>- Bi|¢ 2 2): x y x sld (4.7) xz’dyz>- €'|¢xz’¢yz>’ priate symmetry. Using second-order perturbation theory as described in the theoretical section, and the baSic g and A tensor theory as developed by Abragam and Pryce76, DeArmond, et 01.34 derived the expressions for the eXperi- mental Spin Hamiltonian parameters Shown in Equations (2.16-2.19). Values for the group overlap integrals Sb]: sz and Se, as well as for P and 1M, all depend on the assumed charge on the transition metal ion; hence the calculated bonding coefficients are also sensitive to the assumed charge. In most previous work on pentahalooxymetallate systems a charge of +2 less than the formal charge on the transition metal ion was assumed in the calculation of bonding coefficients. In this work an attempt to arrive at a self-consistent charge was made by varying the assumed charge and, for each value so assumed, computing 86 a charge by obtaining the MO coefficients and carrying out a Mulliken population analysis. Using the B], 82, and e coefficients obtained from the normalization rela— tionships, in conjunction with an iterative best—fit solution to Equations (2.16-2.19), the Mulliken population analysis was determined for the bonding b2, b? b orbitals, and the anti—bonding b2 orbital (see program and 0 listed in Appendix B). Unfortunately, Since this calcula- tion does not account for population in the a] bonding orbitals, total consistency between the assumed and calculated charge could not be checked. Van Kemenade45 did a Similar variable-charge calculation on the series [MOX5]2_ where M = V, Mo, W and X = Cl, Br, F. From his extended Hfickel calculations, he found a charge contribu- tion of +0.5 to the population of the a] orbitals. It has been assumed that such a contribution should also hold here and therefore have selected as the "self- consistent" charge that assumed charge which led to a calculated charge 0.5 greater. The independent parameters needed to calculate the bonding coefficients of [VOF5]3- and [NbOF5]3- are listed in Table 4.4 and the charge dependent parameters are shown in Tables 4.5 and 4.6 for charges +1 to +4. The A and g values for [VOF513— were measured by Manoharan and Rogers48 for (NI-I4)3VOF5 4)3A1F6. Since V and Nb have positive nuclear moments, the vanadium doped into (NH 87 Table 4.4.--Parameters used in calculating bonding coef- ficients. Parameter [VOF5]3_ [NbOF513— g 1.937 1.870 gll 1.977 1.914 A (cm-l) -0.01790 -0.0302 A (cm-l) -0.00641 —0.0160 1F(cm‘1) 270 270 K 0.85 1.34 AE(bZ-+e)(cm‘l) 14,100 15,000 02(02 + b1)(cm_l) 18,200 17,800 and niobium hyperfine parameters have been taken as negative. The spin—orbit coupling parameters AM for vanadium and niobium were taken from the tables of Griffithloz and AL from McClure103. The electronic energies for the transi- tions b2 + b1 and b2 + e in the [VOFSJB- complex have been assigned48. These energies for [NbOF5]3- were estimated by comparing the [VOF5]3_ values to those for [CrOFslz‘ and [MoOFSJZ- 104 The P values were calculated from the Hartree-Fock atomic orbital functions for the free ionslos'los. The calculation of the Fermi contact term and the overlap integrals involve more detailed considera— ations, so their evaluation is included in Chapter II as separate sections. 88 Bonding coefficients for [VOFSJ3‘ and [NbOFSJ3- have been determined for assumed charges +1 to +4 on the transition metal ion and for the "self—consistent" charge. The calculations have been carried out both assuming only dominant ligand p overlap (Table 4.5), and also assuming overlap with hybrid ligand orbitals (Table 4.6). In each case the "self—consistent" charge is con- sidered to provide the most reliable coefficients and is indicated by the superscript R. The 82 coefficients in- dicate that there is a greater delocalization of the un- paired electron in the case of [VOF5]3-. These results do not agree with the conclusions from ligand spin densities, as will be shown in the following section. 45 Van Kemenadefis variable-charge calculations for the series [MOF5]2—, [M=Cr, Mo, W], gave similar results in that his molecular orbital coefficients indicate a greater delocalization for [CrOFSJZ- than for [MoOF5]2-, whereas the ligand spin densities indicate the reverse trend. Our calculation shows as was found in Van Kemenade's study, that as the assumed charge is increased the 82 coefficient decreases. In such studies the relative ordering of the spin delocalization indicated by the 82 coefficient is therefore extremely sensitive to the charge assumed on the central metal atom, and this charge is a very difficult parameter to fix with any certainty. Also, the coefficients calculated for a particular charge 89 H . 80 oHo 2‘ mo opens n .m umwuomuomSm kn wouoOHoce mosao> encoumwmnootmaoms onu on 00 po>oHHon one omuono Eouo Hopoa Honucoo onu mo mosao> oanofiaou pmoE onao mm.m Ho.H vmm.o mmm.o Ned. va. mom. mmm boa mmm.m+ mm.m oo.H mmm.o mmm.o mNH. «NH. mmm. omh mad oo.v+ Hm.m Ho.H mvm.o mmm.o ova. Ava. com. Ohm 05H oo.m+ mH.m Ho.H Ho.H Hmm.o mmH. mmH. Hmm. 0mm med oo.m+ va.m Ho.H NH.H om.H mmH. hma. Nam. ome OHH oo.H+ amnmmonzi mn.m Ho.a vom.o mo.H mmH. mma. new. man va mom.m+ mh.m Ho.H omm.o mo.H HNH. NNH. omm. mvm NBA oo.v+ mh.m Ho.H mam.o mo.H mma. mma. Hmm. mom omH oo.m+ mm.m Ho.H oo.H mo.H omH. mmH. mum. hwa mNH oo.N+ mm.m Ho.H Ho.H vo.H hma. va. «mm. mma moa oo.H+ (mnmmo>n Ase m N Ase omuonu o mm mm mm no nm Ex EU omuono .oaoo n a) poESmma o.awano moHHo>o a psomfla unoSHEOG msenopemsoov omuono mooaossmfiucoeuocsm 0 mo oucoflowmmooo 02):.m.e oanoa 90 H . ISO OHM :4. MO mu.HCD n .m umeeomuomSm an oouooeoce oozeo> sucoumemcoolmeoms onu on on ©o>oeeon ouo omuono Eouo eouoe eouucoo on» no moSeo> oenoeeou umoa onao em.m mo.e «mm. was. wee. see. emm. mmm ewe mmm.~+ sm.m eo.e 0mm. oo.e «me. see. mam. ome nee oo.e+ mm.m eo.e eve. omm. use. ese. mum. oem one oo.m+ om.m mo.e eo.e oee. mme. mme. mmm. omm wee oo.~+ mm.m mo.e me.e so.e mom. ewe. sum. ems oee oo.e+ Imemmonza se.m eo.e hoe. mo.e eme. eme. mom. men ome mm~.m+ mm.m eo.e mmm. so.e pee. wee. mam. msm Nee oo.s+ me.m eo.e ems. mo.e wee. mme. mem. mom ome oo.m+ em.m mo.e eo.e s~.e ewe. mme. men. use mme oo.~+ mm.m No.e eo.e no.e mee. see. mom. one woe oo.e+ ammem0>_ wwsto 0 mm em so New eem 24 so mewmwo .oeoo n en ooESmod 8.xmesuesso mesmee sesame sues moeeo>o mceuooeocoov omeono Hooeosc mo coeuonom o no mucowowmmooo .O.ZII.m.v oanoa 91 are found to be sensitive to the particular overlap inte- grals and K values used. It may be noted that the g values of NbO2+ com— plexes follow trends previously found for complexes con- taining MOn+ [M = V,Cr,Mo], where it was found43 that g||gi for [CrOF5]2- and for [MoOC15]2-. This reverse trend in the chloro complexes has been attributed43 to the large spin-orbit coupling value of the chlorine ligand, which is shown in Equation (2.16) to influence 9" through the -AL 85 8} term. As for the NbO2+ complexes, both NbO(acac)2 and [NbOFS]3_ have g||qi b. Determined from Ligand Superhyperfine Interac— tion.--The most significant evidence of covalency in the [NbOFSJ3- complex is the presence of ligand superhyper- fine interaction resulting from the transfer of unpaired electron spin to the ligands. The absolute magnitude of the ligand superhyperfine principal tensor components were determined from the single-crystal analysis. Since the [NbOF5]3_ complex is unstable in solution, the isotropic ligand superhyperfine value cannot be determined experi- mentally. However, the isotropic superhyperfine value can be determined by averaging the principal superhyperfine tensor components. But first the signs of the principal components must be determined. 92 The experimental ligand A(19F)eq values (in cm-1 X 10-4) are shown in Table 4.1. For all pentahalooxy— metallates where the ligand isotropic superhyperfine Splitting can be determined from the solution spectra, it has been found that can only be equal to(Ax+Ay+AZ)/3 if and Ay have the opposite Sign to Ax and Az' The absolute value is then determined by assuming that the dipolar part of Ay is positive, since the dominant con- tribution to the dipolar part comes from the ligand 2py . orbital. The signs of experimental ligand superhyper- fine tensor components have been assigned by this method and the tensor then decomposed into an isotropic component plus a dipolar tensor of zero trace: 1 ' ‘ 7 W ’ T -19.84 3.76 -23.6 Ay = 39.85 3.76 36.1 (4.8) L A -8.73 3.76 ~12.5 Z J L _ L- .. ‘- .1 Experimental IsotrOpic Dipolar The dipolar tensor is not axially symmetric, as it would be if the unpaired density on fluorine were only in the Zpy orbital; hence there must be some unpaired electron density also in the fluorine 2pm or 2pz orbital. The latter is probably negligible, since extended Hfickel cal- culations Show that out-of-plane n bonding with the equatorial fluorines is quite sma1145. Therefore, we decompose the dipolar tensor further into two axially symmetric tensors with principal axes along x and y, 93 4 -1 and maximum principal components Apr = —7.4 x 10- cm , A = +32.4 x 10'4cm'1: PH -23.6 -7.4 -16.2 36.1 = 3.7 + 32.4 (4.9) _1205 3.7 _1602 o The experimental 19F superhyperfine interaction tensor for the equatorial fluorines of [VOF5]3_ has been analyzed in the same manner48, and the spin densities in the equa- torial fluorine 28, 2pm, 2py and 2pz orbitals for [VOF513- and [NbOF5]3- are shown in Table 4.7. These have been calculated using the appropriate values107 for the iso- tropic contact term per 28 electron, (A0)8 = (8/3)ngeBeganlw(0)I2, where 0(0) is the value of the fluorine 28 wave function at the nucleus, and for the dipolar interaction per 2p electron. (A0)p = (4/5)geBegan, where is the average for the 2p wavefunction. The strength of the in-plane n bonding between the dry orbital of vanadium (or niobium) and the ligand group orbital with b2 symmetry can be related to the Spin densities in the ligand py orbitals through a Mulliken population analysis82 2 , . . . [(85) - BZBZszl, which gives the total Spin density in the b2 group symmetry orbital. Since the b2 group orbital is the sum of the four equatorial py ligand orbitals, the Mulliken population analysis should give four times the spin density in the ligand 2py 94 Table 4.7.-—Ca1culated spin densities in the equatorial fluorine orbitals.a:b . f% 3.. 30% 3_b Orbital [NbOF5] [VOF5] 28 0.025 0.027 2px 0.77 0.342 Zpy 3.34 2.92 2pz 0.0 0.0 aValues of 0(0) 2 and for these calculations were taken from Ref. 107. 2p bSpin densities for [VOF5]3- are from Ref. 48. orbital. By assuming an overlap value for sz, the Mulliken population analysis and the normalization condition give two equations in two unknowns. Using the Sb2 values which were determined as most reliable in the metal hyperfine splitting calculations, this system of equations was then solved for 82 and 85. Using sz = 0.135 for [VOF5]3-, 82 = 0.969 and.Q§= 0.413 were found, while using sz = 0.144 for (Nb08513‘ led to the values 82 = 0.963 and B; = 0.441. These bonding coefficients, as well as the Zpy spin densities, clearly indicate that the ordering of covalency for these complexes is [NbOF5]3- > [VOF5]3-. The spin density in the fluorine 2py orbitals has been explained as arising directly from the delocalization of the unpaired electron in the b2 molecular orbital. 95 It is necessary to invoke a less direct mechanism to ex- plain the spin density in the fluorine 2px and 28 orbitals. One possible explanation is configuration interaction, where an electron in the filled b? bonding orbital is pro- moted to an empty b1 antibonding orbital. This configura- tion is chosen since the 2px and 28 orbitals of the 19F equatorial ligands transform under the b1 representation. Another possible eXplanation is that spin polarization108 of the ligand 28 and 2px orbitals by the 2py spin density is important. c. Conclusion.--We find the metal hyperfine split— tings and g values for [VOF5]3_ and [NbOF513- tend to be unreliable because of the sensitivity of the calculated coefficients to the charge on the central metal atom, a quantity which is difficult to evaluate with any certainty. The spin densities calculated from the ligand superhyper- fine splittings appear to give a truer picture of the trends in covalency in these complexes, although precise data of this type are more difficult to obtain eXperi- mentally. Attempts to relate the ligand spin densities to bonding coefficients, however, also involve assumptions as to the charge on the central metal atom as well as to the degree of spin polarization or configuration inter- action occurring in the complex. Thus, since ESR does 96 not provide enough information to determine the charge dis- tribution within the complex, or to predict quantitatively the extent of spin polarization or configuration inter- action, it cannot be used alone as a tool to determine accurate bonding coefficients. However, if the charge distribution were to be measured by some other experimental means, the ESR parameters in conjunction with these data could possibly give accurate bonding coefficients. In spite of these Shortcomings, the ESR parameters provide about the best means for evaluating the results of MO theory since, if the assumed bonding picture is accurate, the calculated bonding parameters for a particular com- plex should reproduce the eXperimental ESR data. 2. The Hole Species.--The molecular orbital energy level scheme has been calculated for [MoOC15]2_ neglecting 109 and for [MoOF5]2- including 0 bonding45. n bonding Both schemes show the highest filled M0 to be the 8b or- bitals. By anology the highest filled orbitals in [NbOF5]2— are also the 8b orbitals. If upon y irradiation KZNbOFs-HZO an electron is removed from the [NbOFSJZ- ion, the resulting paramagnetic species, namely [NbOF5]_, would have an unpaired electron in the doubly degenerate 8b orbitals, giving a 2E ground state. 97 The doubly degenerate 0b orbitals are composed of the niobium d orbitals and 0” , the apprOpriate xz,yz Iz,yz hybrid ligand group symmetry orbitals. The 0x2 yz orbitals J consist of the oxygen pxfl/orbitals, the axial fluorine px,y orbitals, and the equatorial fluorine pi’Z-pg’4 orbitals, but they mostly have oxygen px,y character. The MO coefficients for the 8b orbitals found from the self-consistent charge calculation of the ESR parameters for [NbOFSJB- give a metal orbital coefficient of 0.0708 and a group symmetry orbital coefficient of 0.9851. Thus, for [NbOF5]-, the unpaired electron in the 0b orbital would spend most of its time on the oxygen atom, with some spin—density on the axial fluorine and even less on the equatorial fluorines and the niobium atom. Similarly, the NbOF4 ion which also possibly forms, would have the unpaired electron in the 8b orbital, but in this case, there is no axial fluorine involved in the ¢xz,yz orbital. Hence, the molecular orbital schemes for both ions are consistent with a radical having most of the spin density on the oxygen atom. With the niobium-containing Species narrowed to [NbOF5]7 and possibly NbOF certain predictions can be 93 4: made regarding the observed Nb isotropic hyperfine splittings. Since the unpaired electron is localized mainly on the 2pn orbitals of oxygen for both cases, the AiBO value would arise primarily from Spin-polarization of the 0 electron in the Nb-O bonds making the Sign of 98 the coupling negative. This polarization mechanism re- sults in unpaired spin-density in the 58 orbital and hence, an approximate 1.4% Spin-density is determined for this orbital using the experimental Ai80(Nb) value along with the A:BO(Nb) value of 1550 gauss calculated for an elec- tron in a 58 orbitalllo. Another possible mechanism con- tributing to the Aiso value is the spin-polarization of the inner filled 8 levels by unpaired electron density in the niobium dxz’yz orbitals. Using the ab molecular or- bital coefficients shown above and the apprOpriate overlap integrals, a Mulliken population analysis predicts an un- paired spin-density of about 1.65% in the niobium 4dxz,yz orbitals. Judging then from the isotropic niobium hyper- fine value of -235 gauss for [NbOF5]3_ where the unpaired electron is localized mainly in the dry orbital, the con- tribution from the inner filled 8 orbitals to Aiso should be small, about -3.9 gauss. Using similar reasoning, predictions can be made about the anisotrOpic part of the 93 Nb hyperfine coupling. However, before this can be discussed, it is necessary to examine the electronic structure of these radicals more closely. The prediction that the unpaired electron should be in the 0b molecular orbital came from calculations which assumed C40 symmetry in these ions. With an un- paired electron in the doubly degenerate eb orbitals, however, the symmetry of the ion would lower to remove 99 this orbital degeneracy. This distortion would be small and could arise inherently from the Jahn-Teller effect or from a lowering of the site symmetry by the neighbor— ing ions. The equilibrium position of the distortion would give the lowest total lattice and electronic energies. Depending on the kind of influences involved, the unpaired electron could either be in a bonding 0x2 molecular orbital for some of the ions in the crystal, and in an wyz orbital for the remaining ions, or in one of these types of molecular orbitals throughout the {EH-2:" crystal. Unfortunately, since the anisotropic coupling could only be followed in the 0 axis rotation, it is not possible to determine which of these two cases occurs. However, at H//b the two sites are equivalent and the field lies along the 0 = 90°, 0 = 45° direction relative to the molecular axes, so the two cases would give iden- tical results at this orientation. Hence, to expedite the discussion of the different sources of anisotropic coupling, the unpaired electron will be assumed to be in the bonding wxz orbital. With this assumption then, the unpaired electron will Spend most of its time in the px orbital of the oxygen, giving rise to point-dipolar interaction with the Nb nucleus. Such an interaction for a Nb-O bond length of 1.7 A would give a dipolar tensor 8 x of (2.8 -l.4 -l.4) gauss with the maximum value directed along the Nb-O bond. Also, polarization of the c electrons 100 in the Nb-O bond would result in a tensor with its unique axis along the same direction. Using the 1.4% spin density attributed to this mechanism in the discussion of the isotropic coupling, and an anisotropic coupling of -85 gauss calculated for an electron in a Nb 4d Orbitalllo: the tensor resulting from polarization of the 0 bond is estimated as (~152 056 056) gauss. Lastly, the Mulliken population analysis Shown above for the 8b orbital indi- cated a small spin-density in the dxz,yz orbitals and this would give rise to a dipolar tensor. Assuming this Spin density to be the same for the bonding wxz orbital and using again the anisotrOpic value for an electron in a Nb 4d orbital,the estimated tensor for this interaction is (057 057 -1.4) gauss. The conclusion drawn from these estimated dipolar tensors is that the anisotropic coupling Should be small and have at least one negative component. Although tensor quantities calculated above for the Nb isotropic and anisotropic hyperfine coupling are only estimates, they are helpful in determining whether the isotrOpic ten-line pattern arises from a rotating NbOF or [NbOFsl- ion. In the above analysis, the isotropic 4 coupling was shown to be negative, and the anisotropic coupling tensor was shown to be small and with at least one tensor component negative, this depending on the exact mag- nitude of the contributing dipolar tensors. Therefore, if the isotrOpic pattern arises from a rotating [NbOFSJP 1:.. 101 ion, either the All or Al value for this ion should be greater than the Aiso value for the rotating Speéies. How— ever, rotation about the a axes shows that the All and Al value for [NbOFs]- are both less than the AiSO value for the rotating species. Thus, the isotrOpic ten-line pat— tern appears to arise from the rotating NbOF4 species. The hyperfine splitting for the equatorial fluorine in [NbOF5]- found with H//b is 267 gauss. The magnetic field at this orientation lies along the 0 = 90°, 0 = 45° direction relative to the molecular axes. Thus, since the bonding 0x3 orbital includes the fluorine pm orbital, the fluorine Splitting at this orientation can be eXpressed 2 211/2 as l/2[Ax(19Fa ) + 1/2 Ax(19 . This formulation X Fax) assumes that there is no other contribution to the split- ting and gives 477 gauss for Ax. Using 1084 gauss for an electron in a fluorine 2p orbital107 and the Ax value found by the above manner, the axial fluorine px orbital is estimated to have a 44.0% spin-density. This spin- density is larger than expected, since only about 20% spin- density is estimated for this atom by extrapolating from the atomic orbital coefficients calculated for 0x3 in [MoOFSJZ- 45. This discrepancy is most likely a result of spin polarization of the Nb-Fax 0 bond and possibly other orbitals which overlap with Fax' namely the wyz orbital. Because of the incomplete experimental informa- tion for this axial fluorine tensor, it is difficult to .- Inca-5.. - fl . F‘W‘I". 102 know with certainty which effect, if any, dominates the tensor. It should be noted that because of the large isotropic splitting (Aiso = 17,200 gauss) for an elec- tron in the 28 orbital of fluorine107 , only a very small spin polarization of the Nb-Fax 0 bond is necessary to result in noticeable isotropic coupling. Spin polariza— ( tion in this bond by an unpaired electron in a bonding w orbital is expected, especially since there is 0:3 evidence that this bond is polarized in other penta- halooxymetallates even where the unpaired electron is in an antibonding We, orbital43. Thus, according to this - q 1.1-. 11 analysis, there most likely is an A (F) component for £80 the axial fluorine tensor and hence, the pattern arising from a rotating [NbOFSJ- ion would consist of more than ten lines. The conclusion therefore drawn from this analy- 93 sis agrees with that from the Nb hyperfine analysis, 2.0" the rotating species is NbOF and the stationary 4 species is [NbOF5]_. The g values are also consistent with the electronic structures proposed above for the [NbOFSJ- and NbOF4 ions. AS noted previously, there should be an electron deficiency in the ab orbitals for these ions. However, the ions Should undergo a distortion to remove the degeneracy of these orbitals. Thus, the orbital containing the unpaired electron (0x2 for discussion purposes), would be expected to mix through Spin-orbit coupling with the nearly 103 degenerate filled wyz orbital. Since the admixed wyz orbital is filled, there should be a positive 9 shift from the free-spin value for these ions, as has been found. Because the 0x3 orbital has mostly oxygen 2pn character, the 9 value should be similar in magnitude to those found for other oxyniobium complexes having an electron de- ficiency localized in the oxygen 2pn orbitals. This is found to be the case for just such an ion, [NbO412-, as shown by the reported 9 values in Table 4.3. 3. Ozonide Ion.--The ozonide ion has 020 symmetry and 19 valence electrons. This according to the energy 71 level scheme determined by Ballhausen and Gray , would place the unpaired electron in a b2 molecular orbital. Under the 0 symmetry group, the resulting 282 ground 2v state will mix through spin-orbit coupling with various amounts of the 2A 2A , and 28 excited states along the 1' 2 1 different molecular axes. Thus, since there is no hyper- fine coupling, the ESR spectrum of 03- should give a three g-value pattern, as has been found here. The 9 values Shown in Table 4.3 vary more from 2.0023 than do the g values reported for ozonide in y irradiated KC103100, also shown in this table. This discrepancy arises from the different host lattices and temperatures used in the two measurements. CHAPTER V Y IRRADIATION OF K3CO(CN)6 A. Introduction Single crystals and powders of K3Co(CN)6, y irradiated and investigated with ESR at 77°K, give sets of lines belonging to two radicals. The most intense set of lines belongs to a 59 Co containing radical which exhibits l4N superhyperfine splittings from two equivalent nitrogens. A complete ESR study of the single crystal and of the powder have been made for this radical. The g, A(59Co), and A(14N) values have been used to identify the radical as a d7 system in a weak, tetragonally- elongated field; the most probable structures are (Co(ii)cu)614‘ or [06(11)(0N)4(N0)214‘. Since this radical is only stable at low temperatures, it will be referred to as the low-temperature species. The other set of lines has considerably less intensity and, in the powder, shows a rather complex pattern centered at g = 2.2760. When the powder sample is pressed into a pellet and irradiated, the low-field radical did not form. The high 9 value for this pattern coupled with the fact that it does not form in the irradiated pellet, suggests that 104 105 it may be a cobalt (II) radical pair. Since radical pairing involves some migration in the lattice, perhaps in the case of the pellet the crystal is broken into such small crystallites that they approach unit cell size, in- hibiting the migration necessary for the radical to form. In-any event, since the signal from this radical is weak and overlaps with the spectrum of the low-temperature species, it is not possible to follow the lines in the single crystal and thus obtain the g and A tensors neces- sary to further elucidate its structure. There is one additional feature in the spectra at 77°K. This is a peak around g = 2.0023, which seems more prominent in the case of the pellet, and has been identified as arising from an F center produced on Y irradiation. When the Y irradiated powder samples are warmed from 77°K, the intensity of the low-temperature species signal decreases until it is gone at 133°K. At this tem- perature the low field pattern centered at g = 2.2760 still remains and a triplet centered about the F center line has emerged. The triplet splitting is about 71.4 gauss and seems to be a result of an interaction of a neighboring nitrogen with the F center. At 193°K, the lines from the low-field pattern disappear; the intensity of the triplet has increased; its splitting has been re- 59 duced to 60.8 gauss; and the lines from another Co- containing radical have become more evident. At 253°K, 106 the resolution of the spectrum from the new 59Co-containing radical improves and the triplet signal disappears, leaving the pattern from the F center at this field position. On- warming to room temperature, only the $9 Co-containing radical remains along with the signal from the F center. Cooling back to 77°K did not reverse this process but did improve the resolution of the 59 Co-containing radical. Since this radical also forms upon irradiation at room temperature and is stable at this temperature, it will be referred to as the room—temperature species. The 9 values and A(59Co) values found in the powder for this radical have been used to identify it as a d7 system in a fairly strong tetragonally-elongated field with the structure of [Co(II)(CN)5]3- or possibly [Co(II)(CN)4]2—. Also, crystals made with 15.5% K13CN were Y ir- radiated and the spectra of the low-temperature and room-‘ temperature species studied. B. Results 1. Single Crystal at 77°K.--Single crystals of K3Co(CN)6 about 4XZXZ mm in dimension were selected for y irradiation. Using the morphological data reported by Groth97, the orthorhombic crystallographic axes a, b, and 0 could be identified. The 100 face was clearly de- velOped, enabling easy identification of the 0 axis. Upon rotation of the crystal about the 0 axis under the 107 polarizing microscope, extinction occurred along the b and 0 axes. The 0 axis could be distinquished from the b axis by identifying the edge formed by the interSSCtion of the x and x' planes. There is much confusion in the literature over the unit cell dimensions for K3Co(CN)6111_114. This con— fusion has been resolved in an investigation by Kohn and Towneslls, where they showed that K3Co(CN)6 exhibits polytypism (i.e., the existence of different well-defined stacking periodicities). They found four different struc- tural types or polytypes, all having the same morphology. These are described by polytypic nomenclature as 1M (one- layer monoclinic), 20r (two-layer orthorhombic), 3M (three- layer monoclinic), and 7M (seven-layer monoclinic). The 1M polytype and the 20r polytype are the most common structures; their stacking relationships are Shown in Figure 5.1. The 1M unit cell contains two molecules with cell dimensions a = 7.1 3, b = 10.4 A, 0 = 8.4 A and 8 = 107°20'. Within the unit cell the two nonequivalent octahedral sites transform into each other by reflection in the ac plane. Each of the two cyanide octahedral have a twofold symmetry axis directed along the 0 axis, while the fourfold symmetry axis perpendicular to the twofold axis makes an angle of about 27° with the b axis. From 116 the neutron diffraction data of Curry and Runciman , the direction cosines relating the Co-Cl, Co-C2, and 108 (010) H c a a STACKING \ \ DIRECTI07 / MONOCLINIC ORTHORHOMBIC 1 M 2 OR Figure 5.l--The relationship of the 1M to the 20r cell as seen on the (010) plane. 109 Co-C3 bonds of one site to the orthorhombic crystallo— graphic axes have been determined and are shown in Table 5.1. Table 5.1.--Direction cosines of Co-Ci bonds in K3Co(CN)6 with respect to orthorhombic crystallographic axes. Bonds 0 b 0 Co—Cl 0.421 —0.906 :0.044 Co-C2 0.678 +0.237 $0.696 Co-C3 0.642 +0.325 $0.694 Single crystals, Y irradiated at 77°K, were ro- tated at this temperature about the orthorhombic a, b, and 0 axes and spectra recorded every 10°. As shown in the plots of the variation of 59 Co hyperfine lines with magnetic field orientation (Figures 5.2-5.4, the spectra consist of overlapping sets of eight lines except when the external field is parallel to one of the crystal axes. In this case, the two sets coalesce into a single set of eight lines. Each 59 Co hyperfine line is further split into multiplets. The multiplet in some orientations con- sists of a five-line pattern with intensity ratios l:2:3:2:l but in other orientations become six—line patterns with in- tensity ratios 1:3:5:5:3:l and in a few orientations seven line patterns were found (Figures 5.5 and 5.6). 110 .Mohn um mnzovoomm oouoeooeuel> How ocoem on on» Se mocee ocemeoman 00mm uano mo muom 039 on» no coepounoeuo oeoem oeuocmoe nue3 coeuowuo>llm.m ouzmem .o. .I\\n_ 9 C3 C} I . o 2:1 l 1 cm. :3 111 am .Mohh no mAZUVOUmM nouoeoouuel> How ocoem so on» cw mocee onemeommn ou unmeo mo muom 039 on» no coeuounoeuo oeoem oeuocmoe nue3 coauoeuo>|lm.m ousmem .o co .2: : A... ........ 02: ........ ......... .. I\\U ..T_\\U 112 00. .Mohh um mnzovoomm oouoeoouuwl> Mom onoem as one Se mosee ocemeomhn unmwo no muoo one mo noeuouzoeno oeoem oeuonmoe nue3 noeuoeuo>llv.m oezmem coo .. .2: mm . -I\\n -I\U 113 .s\\s sues elzuvoomx emuseessse 1» Ge moeoomm ousuouomfiouISOH on» no Esuuoomm o>euo>euoolpsooom onBIIm.m ouzmem ”- .L mu eves. 114 .mouem ucoeommeo ouonmeoov ozouuo unoScsop new veo3mz onB .mexo 0 on» Eoem ooe oaoem so onu Ge peoem oeuocmoa on» nnes moeoomm ousuoeomfioulzoe on» no Edeuuomm o>epo>enopupcooom onauum.m ouzmeh «I1- db 0 00.. 115 The quintet Splitting has the appropriate intensity ratios to be attributed to an electron interacting equally with two 14N nuclei. The six- and seven-line multiplets could be explained by a Slight 9 shift for nearly equivalent Sites, probably due to a small error in alignment or a re- sult of having a mixture of polytypes within the crystalll7. Using Schonland's method72 the 92 and the g2A2 tensors were diagonalized with the principal values and direction cosines shown in Table 5.2. The A tensor is orthorhombic with its principal values nearly along the bond directions of the octehedral site, and the g tensor, which is nearly axially symmetric, has its unique component parallel to one of the principal A components. With the perpendicular g tensor components nearly equal, the error in their direction cosines could be large. Thus, the direction cosine values associated with perpendicular 9 components do not necessarily rule out the possibility that the A and g tensors are coaxial. These results imply that the radical formed by Y irradiation has not undergone appreciable reorientation in the lattice but 'the original octahedral unit has undergone appreciable distortion. The eXperimental isofrequency plots, showing two sets of eight lines in all orientations except along the Crystallographic axes, indicate that the crystals con— tains four magnetically distinct sites. This interpretation 116 Table 5.2.--The g, 59Co hyperfine, and 14N hyperfine values with direction cosines for the low-temperature species in K3Co(CN)6. Powder analysis gm = 2.0913 Ax = -70.07 G = 2.0904 A = -60.60 0y y G 03 = 2.0080 A2 = 68.08 G 14N = 3.85 G Single crysta1”g% diagonalization a b 0 gm = 2.0927 0.560 —0.768 0.309 gy = 2.0913 0.453 0.597 0.662 92 = 2.0115 0.694 0.231 -0.682 . ‘ 2 2 Single crystal g A diagonization a b 0 Ax = -70.05 G 0.438 -0.898 -0.043 Ay = -60.35 G 0.638 0.278 0.718 A = 68.17 G 0.632 0.342 —0.695 is consistent with the orthorhombic polytype which contains four molecules per unit cell. Within the orthorhombic polytype are two monoclinic unit cells, each related to the other by a reflection in the b0 plane and each con— taining two sites. The Sites within each monoclinic unit are related by a reflection in the 00 plane. The outcome of these geometric considerations is that each site is 117 related to any of the others by changing one column of direction cosines. This assumed geometric relationship for the four distinct sites, along with the experimental g values, A values, and direction cosines, were checked by computing the angular variation of the spectra. The appropriate 14 spin Hamiltonian for this system, excluding the N super- hyperfine interaction, is Jc = 8(gxxHxSx + gyyHySy+gzszSz) +A IS+A IS+A IS xx x x yy y y 22 z z 2 . 2 _ l , 2 + 0 [12 31(I+1)]+Q'(Ix-Iy ) - gan(HxIx+Hny+HzIz) . (5.1) For systems described by this type of Spin Hamiltonian, Tseng and Kikuchi118 , using second-order perturbation theory have derived the equations for determining the resonance positions as a function of external field orientation. These equations, in conjunction with a plot routine, were employed to calculate isofrequency plots for the three rotations. The Q' and Q" values were taken as zero and, since the g and A tensors are considered to be coaxial, the values found in the powder spectrum were used. With the A tensor clearly non-axial, the direction cosines found for the A diagonization were used for both 118 the g and A tensors of one site. The direction cosines for each of the other three sites were obtained by changing the signs of one column of values. The computed isofrequency plots very nearly duplicated the experimental plots, with some measure of the fit indicated by the A and g values shown in Table 5.3 for various orientations of the mag— netic field. 2. Powder and Pellet at 77°K.--The powder and pellet spectra are shown in Figures 5.7 and 5.8, respec— tively. Although these samples were irradiated at 77°K for the same period of time, in the case of the pellet only one radical appears to form whereas the powder Spectrum shows two radicals. The pattern from this second radical extends at X-band frequencies from 2830 gauss up into the lower portion of the spectrum from the low-temperature species to about 2980 gauss with the pat- tern centered at g = 2.2760. Since this low-field pat- tern, presumably from a radical pair, doesn't appear in the case of the pellet, analysis of the spectrum from the low-temperature species is considerably facilitated. The powder spectrum, however, had the advantage of better resolution of the nitrogen superhyperfine splittings and thus aided the identification of the parallel features in the spectrum from the low-temperature species. 119 o ee.ee 0 mm... o «e... o -.ee s\\s u N~.ee o mm.em o -.ee 8 om.me s\\s u em.me o om.mm o em.mm o em.mm s\\s SSE e me... e em... 8 mm.ee o me.em o sm.mo o mm.mm . s RUE o em.ee o eo.oe o so.mm o es.me o om.ee o om.em s memo.m eomo.m uemo.~ oeso.~ s\\e smeo.m omeo.~ emse.~ mmmo.m e\\e seme.~ memo.m eeme.m mmme.m s\\e 29E omeo.m mess." mmeo.m emeo.m eoeo.~ omso.m . e .865 eeeo.m emeo.~ oeeo.m eeeo.m mome.~ meeo.~ e pousmaoo eoucoEeeomxm oouzmeoo eouaofieuomxm nouzmaoo eoucoaeeomxm coeuoucoeeo nexo o uzono coeuouom mexo n uzono coeuouom nexo e usono :oeuouom .mnoeuousoeuo ozoeeo> How moSeo> wouoesoeoo nuez mozeo> s can m eoucofieeomxo mo somehomEOU|l.m.m oenoa 120 .oeoem Boe um emoeooe uonuoco mo Edeuoomm one one economsoo mm on» NO oneuueemm ocemuommneomSm comouuec me zoom owed .heo>euoommoe .mzmenmnoemzczoo one ooooonloensoo peo3mz onu >n oouocmemop moezuoow as one s . w one nue3 moeoomm oesuoeomaouISOe on» no Eseuoomm Hopsomlun. m onsmem 11 0 com 121 .meo>ewoommoe .msoeuo membnsoo use .popoonlpoanzoo .oeo3ms an oouocmemov moezuoom 8w ego . q «we on» nue3 AZUVOUmm mo uoeeom wouoeooueelr m CH moeoomm oesuoquEoulsoe on» no Ezeuoomo mmmnlm.m onsmem -1- db 0 com 122 3. Single Crystal and Powder at Room Temperature.-- In the single crystal the room temperature species gave two sets of eight lines which coalesced into one set when the field was along the crystallographic axes. A complete Single-crystal analysis was not done, since Lin, McDowell, and Ward54 had already completed this work. Spectra were, however, recorded along the crystallographic axes. The 9 and A values found at these orientations, in conjunc- tion with principal g and A values found in the powder, were used to check direction cosines for this species (see Table 5.4) against those of McDowell, et 01.54 4. Analysis of Spectra of 13C Enriched Samples-— At this point in the analysis there are two possible radicals which could eXplain the spectra of the low- temperature species and two different radicals which could explain the results for the room-temperature species. For the low-temperature species the g values indicate that the radical is a d7 system with the unpaired electron in the 6132 orbital. The large nitrogen splitting along the gll direction of the radical indicates that considerable spin density has reached the nitrogen atoms of the two cyanide groups overlapping with this orbital. This could be either a result of spin-polarization through the C-N bond by spin density on the carbon atoms or a result of direct overlap of nitrogen orbitals with the d32 metal orbital in 123 Table 5.4.--The g values and 59Co hyperfine values with direction cosines for the room-temperature species in K3Co(CN)6. Powder analysis 9" = 2.0037 gi = 2.1545 A = 89.70 G A = 26.62 G J I 1 a Single crystal 0 b 0 gll = 2.010 0.65 0.27 0.71 21 = 2.170 i wrt above 2.167 All = 83.5 G 0.62 0.29 0.73 41. = 26.9 G l_wrt above 25.2 G aThese values were obtained by McDowell et 02.54 for x-irradiated K3Co(CN)6. the event that the cyanide groups turn around. The two possibilities for this radical therefore are [Co(II)(CN)6]4- or [Co(II)(CN)4(NC)2]4-. The g values indicate that the room-temperature radical is also a d7 system with the unpaired electron in a dz? orbital but with a greater tetragonal distortion. Also, there is no nitrogen superhyperfine structure with this radical. Two possible radicals consistent with these results are [Co(II)(CN)5]3- or [Co(II)(CN)4]2-. By using Y-irradiated crystals of K3Co(CN)6 made with 15.5% K13CN, 124 one should be able to distinguish between these possi- bilities. In the case of the low-temperature species, 13C nuclei should be evident satellite Splittings from the for the [Co(II)(CN)6]4_ radical. Since the d32 orbital in this instance directly overlaps with the carbons of two cyanide groups, the probability that the unpaired electron interacts with one 13C nucleus is 28.75% and that it in- teracts with two is 2.25%. The dzz orbital is of the correct symmetry to overlap with the carbon 8 and p0 orbitals, so the 13C splitting should be appreciable (i.e., much greater than the line width). To attempt to observe the 13C satellite lines, a Y-damaged crystal made with 15.5% K13CN was oriented at 77°K with the mag— netic field in the 00 plane 40° from the 0 axis. At this orientation one set of Sites is nearly parallel to the gll direction of the radical. If the radical is 13C satellite lines 59 [Co(II)(CN)6]4—, there should be equally spaced on either Side of the Co lines with a peak height about 21% of the 59 Co peak heights. Inspec- tion of the high field lines at this orientation did not reveal such lines. The conclusion then is that the low- temperature radical must be [Co(II)(CN)4(NC)2]4-. In the case of the room—temperature species, 13C satellite splittings should be evident for the [C0(II)(CN)5]3_ radical since here the dZZ’orbital 125 overlaps with one cyanide group. The hyperfine splitting l3C nuclei should be appreciable, since again from the the dz? orbital is of the correct symmetry to overlap with the carbon 8 and p0 orbitals. For the [Co(II)(CN)4]2- radical, however, 13C satellite lines are not expected because the d22 orbital doesn't overlap with a cyanide 13C satellites, Spectra group. To attempt to observe the were recorded with the magnetic field along the crystallo- graphic 0 axis using enriched crystals Y irradiated at 77°K and warmed to room temperature. At this orientation all the sites become equivalent and the field is nearly along the gll direction of the radicals. There was no evidence of the 13C satellite lines at this orientation. Since the [Co(II)(CN)5]3- radical would have peak heights only 9% of the 59Co peak heights, the room-tempearture Species has been tentatively identified as [Co(II)CN4]2_ 13 until work with higher C concentration is completed. C. Discussion l. Low-Temperature Species.--The Y irradiation of K3Co(CN)6, a diamagnetic d6 low—Spin system, could result in the formation of paramagnetic radicals in several ways. The most probable mechanisms involve either the loss of an electron, the capture of an electron, or the rupture of metal-carbon bonds. Depending on which mechanism dominates, the resulting radical could either be a d5 or d7 low spin system. 126 One of the first steps in identifying the low- temperature species is to establish which orbital the un- paired electron is in. This can be done by comparing the eXperimental g values with their theoretical expressions. The first-order expressions for gll and gi determined for d5 and d7 systems54 in all the most probable crystal field distortions are Shown in Table 5.5 The only expression which describes the eXperimental g values adequately is that for a d7 system in a crystal field with a weak tetragonal elongation (i.e., with the electron in a dz2 orbital). The presence of 14N superhyperfine splitting from two equivalent nitrogen nuclei also suggests that the electron is in a dzz type orbital. These splittings could arise either from the d32 orbital leaking enough spin density unto the carbon atom of the axial cyanide groups to result in appreciable spin polarization of the nitrogen Sp 0 bonds, or result from direct overlap of the dzz orbital with two nitrogens, in the event that the axial l3C satellite cyanide groups turn around. The absence of lines in 13C enriched samples serves to support the latter possibility. A theoretical explanation for this phe- nomenon would be that after capturing an electron, the [Co(II)(CN)6]4- complex is unstable so the axial cyanides rotate to provide the necessary crystal field stabiliza- tion as shown in Figure 5.9. 127 Table 5.5.--First order expressions for g values.* Orbital Containing Configuration Odd Electron 91] 31 d7, weak d 2 2 211+31/A1)1 elongation 2 07, strong dx 2[l-(41/A2)] 211+(1/A3)] elongation y 7 d , weak d 2 2 2[1+(4A/A2)] 2[1+(A/A4)] flattening x —y d7, strong dxz 3 very large flattening ,y 05, weak dx 2(1-(41/4211 211+(1/A3)1 elongation y d5, weak dxz 3 very large flattening ,y where A = IE — E | A = IE - E | 1 32 xz,yz 2 x -y2 xy A = IE - E | A = IE - E l 3 my xz,yz 4 2 2 xz,yz *These expressions have been determined assuming a positive A. With the structure of the low-temperature Species established using first-order molecular orbital expressions for the 57 values, the discussion turns to the physical significance of the A tensor of the radical. The A3 com- ponent, that component coincident with gll, is predicted to be positive by applying the method of Fortman74. The other two components were taken as negative, since this was the combination of signs that gives the maximum spin density on the central metal atom. A measure of the 128 .mmwowdm musumnmmfimuIEoou may on mmfiommm musumummfimuu3oa may Eoum mcflom cw omuflswom coflumNHHflnmum pawwmnocmmwa on» no cofiumucmmmummu owumsmnomnum.m musmam Hm xo: 0... OZ=>E<>> ZO_._.<_O NNUIIII‘IIIII / «wt '4' V...” u no \\\\..\\\ a luxpullll ASZOX 00H madcap lull $3530; rgzoii mo $32038; 129 covalency was obtained by using the first—order expres— 77 sions for All and Al as derived by McGarvey for low-spin d7 systems: All = -K + $0.222 - 37-(gi-2.00232P (5.2) - £2 , .11»; Al — -K~- 7a P-+ 14(gi—2.0023)P. (5.3) Using P = 0.0254cm-l'77, the free-ion value for Co(II), the values of a2 = 0.71 and K = 36.04 10"4cm—l were found. The amount of delocalization indicated by the a2 value is consistent with the type of 0 bond found with a d32 orbital. The small value for K is due to con- tribution from the 4s orbital to the contact term, this arising from the fact that the d32 orbital is permitted to hybridize with the 4s orbital under the D4h or 040 point groups. The 59Co dipolar tensor for the low-temperature species is orthorhombic, revealing that the structure of the radical is somewhat distorted from axial symmetry. This distortion in y-irradiated K3Co(CN)6 might be con- nected with the fact that it apparently experiences con- siderably different distortions in different host lattices and under different irradiation conditions (see Table 5.6). The effect of different lattices on the hyperfine values of the low-temperature species, shows this radical to be quite sensitive to the charge distribution of the 130 .ousumummEmu Boon mom mocmum .B.m can mnsumummfimu 30H How mccsum .B.qm mm ms.o H.0H m.mmu v.5m sma.m oooo.~ m Hoamnums as -mH AzoVAHHVoo_ mmaommm.a.m imvo.mmu imvoma.m mm ma.o m.oa ixvo.m~- m.mm ixvmma.~ oeoo.~ “mums can HoomHm mamamnum as um“ AzoViHHvooH mmaumam.a.m mad mh.o o.ma o.m~- o.mm -mfl.m oaoo.~ mizovooaqmmo .omunwtm mmflommm.9.m A»V~.m~- issued.” 0 m em ~5.o m.oa ixva.m~' m.mm ixvoaa.~ ooao.~ Azovoo m.smuufl|x mmflommm.a.m A>V5.5~- “momma.~ m m mm ms.o m.HH ixvm.mm- m.mm Axvmma.~ oeoo.~ Azosoo m.smuufluo mmaommm.e.m hm v5.0 o.~H 0.5"- 0.0m omma.~ omoo.~ wizovoomx.cmuuflu> mmflommm.a.m xuoz mags mn.o ~.~H m.mmu s.mm omma.m amoo.~ sizovoomx.cmuuau> mmnommm.a.m s Hos as mHH Ha.o m.mH- «.0m- m.on mooa.m nsoo.~ :mH Azoooo..cmuuaum mmflommm.a.q mm mm.o h.mm- 0.05- o.sm mmo.m omoo.~ wizosoomx.smuufl-m mmaommm.a.q imvm.omu Awesomo.~ m m xuoz mace an.o m.o~u AxVH.osu H.mm Axvmamo.~ omoo.~ Azovoo x.omuuau> mmaommm.a.q oocmnmmmm mo A30me vaqw on__w .Hw __m xfiuumz mamoflpmm .mmowuumfi accumuwao ca mofloomm ounumummfimulsoa was muonsummfimuleoou map How mumumfimumm mmMI|.m.m manna. 131 nearest-neighbor ions and possibly the next—nearest- neighbor ions. The considerable sensitivity of the ESR parameters for the [Co(II)(CN)4(NC)2]4- radical to its ionic environment is most likely a result of having the negative end of the two axial cyanides directed outward. The discrepancies between Danon's58 hyperfine splitting values for electron irradiated K3Co(CN)6 and the values found in this investigation for y-irradiated K3Co(CN)6 are more difficult to explain and most likely are related to the irradiation reaction mechanism. The fact that the [Co(II)(CN)4(NC)2]4— radical is formed by capturing an electron, coupled with the fact that F centers form during irradiation, strongly suggest that the reaction mechanism involves the formation of holes in the lattice. If the hole is close to the radical, its orientation relative to the radical would influence its structure. For instance, if the hole is stabilized close to the radical and to one side of the gll direction, distortion from axial symmetry would occur. On the other hand, if the hole is stabilized along the gll direction or several ionic radii away, the hole would not distort the radical from axial symmetry. Whether or not the hole stabilizes close enough to the radical to distort the structure could be dependent on the type irradiation used, the temperature of the sample during irradiation, and even possibly the amount of irradiation. §4~ If 132 One other possible influence which could explain the discrepancies between Danon's values and those found here is that we may be dealing with different polytypes. The effect of polytypism on the ESR parameters of sub- stitutionally doped Cr3+ in the K 117 3Co(CN)6 lattice has been noted by Townes, et a1. They found that the sphere of influence for the Cr3+ sites extended beyond its nearest-neighbor ions resulting in slightly different g values for the 1M and 20r polytypes. Although the dif- ferences were small for the Cr3+ case, they should be greater for irradiated KBCo(CN)6 since here there is the effect of the positive hole. Also, the -NC- ligands should be more sensitive to the influence of the positive hole than the -CN- ligands, since the negative charge is largely on the carbon. 2. Room-Temperature §pecies.--The g values for this radical can be used to establish which orbital the unpaired electron is in. As shown in Table 5.5, only a d7 system with the unpaired electron in a dZZ type or— bital could explain the eXperimental g values. One would expect the radical formed at room tem— perature to be considerably more stable than the radical formed at liquid nitrogen temperature. The [Exz,yz’E22] values calculated from the first—order eXpression for 2i (Table 5.5) support this view. Using the spin-orbit 133 coupling value of 533cm_1 found for the Co(II) free ion66, -E32] give 36,000cmm1 for the low- temperature species and 20,500cm-l for the room-temperature calcutions of [E (xz,yz) species. However, since the spin-orbit coupling value in complexes is usually 20%—30% smaller than the free-ion 15 value , these [E -E32] quantities are probably too xz,yz large. Perhaps a better expression of the increase in stabilization acquired in going from the low-temperature species to the room-temperature species is the 43% change in energy of the dag orbital, this quantity being inde- pendent of the spin-orbit coupling value. The considerable change in stability in going from the low-temperature to the room-temperature species indicates that the Co(II) ion must experience quite different ligand fields in the two radicals. Since the absence of any nitrogen superhyperfine splitting for the room—temperature species suggests that metal-nitrogen bonds are not present, the possible radicals which would provide greater ligand—field stabilization for the room- temperature species are [Co(II)(CN)5]3- or [Co(II)(CN)4]2-. Gray, et al. have studied this radical, and the [Co(II)(CN)5]3_ radical formed in ethylene glycol solution, with both Optical and ESR spectrophotometry and concluded that the [Co(II)(CN)5]3_ structure is correct56. However, the absence of 13C satellite lines in 15% 13C enriched samples tends to contradict this conclusion. 134 The room—temperature species can be made either by Y irradiation of K3Co(CN)6 at room temperature or by decay of the low-temperature species upon warming. The decay mechanism appears to involve the loss of one or both of the axial cyanides. As the system is warmed up appar- ently the vibrational energy becomes too great for the weak isocyanide bonds resulting in their eventual rupture. I The fact that the direction cosines for the 9" components of both radicals are nearly the same also supports the supposition that both radicals occupy the same sites in the lattice with changes occurring along the axial bonds. The 59 Co hyperfine splitting tensor can be used to shed additional light on the structure of the room- temperature radical. However, before any physical signifi— cance can be attached to the tensor, signs must be as- cribed to its principal components. The Az component has been taken as positive using the analysis of Fortman74. The Ax and Ay components have been taken as negative since, when the parallel and perpendicular components are of opposite sign, the spin localized on the metal is maximum; also, the trace of the components then gives an 59 56 A. ( Co) near that found in the solution spectra . $80 Using these signs the experimental tensor was decomposed into a dipolar part and an isotropic part, and these used in the first—order expressions for All and AL given by Equations (5.2) and (5.3) to calculate the value “2‘: Qr73y 135 This value indicates a fair degree of delocalization of the spin out of the d32 orbital, resulting from either hybridization with the cobalt 4s orbital, spin density transferred to the ligand, or both. It should be noted that only the [Co(II)(CN)5]3- radical offers the possi- bility of spin density transferring to the axial ligand. its In Table 5.6 are listed the other reported ESR parameters for this radical. There is general agreement in the All value except for the single crystal work of 54 Lin, McDowell, and Ward , but there is very little con- L_. sistency in the AL values. These discrepancies could be .‘ related to differences in analysis of the powder spectrum, since all the values were derived from powder spectra ex- cept those of McDowell, et a1. When a computer calculated spectrum is fitted to the perpendicular portion of the powder spectrum, it has been shown that Ax and Ay have different values and that angular abnormalities give splittings which are too large for the low—field linesss. Depending therefore on how the perpendicular features of the spectrum are interpreted, different numberical values of Al are obtained. Since both the single-crystal study and the computer fit of the powder spectrum of the room- temperature species in irradiated K3Co(CN)6 show that the A tensor as being orthorhombic, this radical is considered to be distorted from axial symmetry. Such distortions are expected for the room-temperature species since depending 136 on its structure either one lobe or both lobes of the dz? orbital is not bonded, making this radical very sensitive to its lattice environment. Again, either the effect of the neighboring ions or the hole produced by irradiation could provide the distorting influence. CHAPTER VI CHLORORHODATE (II) SYSTEMS A. Introduction Single crystals of K3RhCl6-H20 were y irradiated at 77°K. ESR spectra of the crystals at this temperature showed chlorine superhyperfine structure but since the crystals were small, the signal was too weak to follow as the crystals were rotated in the magnetic field at X-band. The polycrystalline X-band spectrum of this sample at 77°K showed two g values, the rhodium hyperfine splitting to be within the line width, and poorly resolved chlorine structure superimposed on the high-field line. The radi- cal formed appears to be the [RhC16]4- ion with its un- paired electron in the d22 orbital interacting with the two axial chlorines. Since the chlorine hyperfine structure could not be successfuly studied in the K3RhCl -H 0 matrix, attempts 6 2 were made to make the radical in other host lattices. Single crystals of Na3RhC16°12H20 were made, but proved unsatisfactory since the crystals crumble upon radiation. Attempts to make the [RhCl614- ion by y irradiating single crystals of KCl and NaCl doped with [RhC1613- also failed. 137 138 Finally, another approach was taken. Since molten AgCl is a good oxidizing and reducing medium, a 1% mixture of RhCl3 in AgCl was passed through a zone melting furnace. The resulting crystals gave ESR parameters at 77°K which were consistent with a [RhClGJ4- ion having its unpaired electron in the dzz orbital and interacting equally with the two axial chlorine nuclei. A complete analysis of the g and chlorine hyperfine tensors was done in the single crystal. Also, the polycrystalline sample gave a spectrum at 77°K very similar to that found for y-irradiated poly- crystalline K3RhCl6°HZO. The assignment of the electron configuration of the hexachlororhodate radical as d7 instead of d9 is based mostly on physical reasoning, since both, depending on the distortion, could give an unpaired electron in the dzz orbital and to first order, the g theory is the same. With this in mind, additional information was sought by irradiating K2[RhCls(H20)] where the distortion can be determined. Again the crystals were small and the signal too weak to follow throughout a rotation. Assuming the polycrystalline spectrum is from one species, the radical appears to have three 9 values, with a four—line pattern superimposed on the high-field line. This Spectrum is consistent with [RhC15(H20)]3- or possibly [RhCls]3- formed by addition of an electron and tends to support the d7 assignment for the hexachororhodate ion. 139 B. Results 1. Powders at 77°K.--Shown in Figures 6.1(A) and 6.1(B) are first-derivative X-band powder spectra of y- irradiated K3RhC16-H20 and of AgCl doPed with Rh2+ measured at 77°K. The 9 values are nearly the same for , both both systems and because of the small nuclear magnetic moment of rhodium and its nuclear spin of l/2, the rhodium hyperfine coupling is within the line width. The chlorine superhyperfine splitting, superimposed on the gII line, is not very well resolved in either case, but at higher gain all seven lines from two equivalent chlorines can be seen in the case of the AgCl lattice. The differences here could arise from two phenomena which are both dependent on the host lattice. First, the line width should differ for the two lattices since they would have different spin- lattice relaxation times. Secondly, the degree of random— ness in the orientation of the radicals should vary be- cause of the different particle size of the powders and their different powdering characteristics. Shown in Figure 6.2 is the first—derivative powder pattern of y-irradiated K2[RhC15(H20)] measured at X-band at 77°K. Because of the three g-value pattern (i-e-a 3i and gL' are nearly equal and greater than‘free spin and gll is less than free spin), it is evident that the radical, as- sumed to be [Rhc15(H20)]3’ or [RhClslif is slightly 140 A 9||=2~°°7 =.6O 9124 91: 2.430 g": 2'002 Figure 6.1--(A) The first-derivative X-band powder spectrum at 77°K of y-irradiated K3RhC15-H20. (B) The first- derivative X-band polycrystalline spectrum of AgClth2+. At high field the seven-line pattern from the interaction with two equivalent 35Cl nuclei is resolved with increased gain. 141 “Omm. m .xonh um nmusmmme HUQmHNx omumwpmuufllr mo cumuumm Henson m>aum>wnmvlumuflm mcauum.m musmflm 20.7.5 alumnus Elana 142 distorted from its 0 symmetry. Superimposed on the gll 4v line is a four-line pattern having splittings which are consistent with an electron in a d32 orbital interacting with the axial chlorine nucleus. 2. Single Crystal at 77°K.--In cubic crystals with the NaCl structure, M2+ ions entering the.lattice substi- tutionally are expected to trap a charge-compensating cat— ion vacancylzo. This vacancy can distort the cubic (0h) crystalline field differently, depending on its orientation relative to the M2+ ion. If the direction of the line joining the M2+ ion and the trapped vacancy is parallel to one of the crystallographic axes, the crystalline field will experience a tetragonal distortion. Since cation vacancies along the three crystallographic axes are sym- metrically equivalent, this type of distortion will re- sult in three sites for the M2+-vacancy pairs, each with its unique axis directed along one of the crystallographic axes. On the other hand, if the direction of the M2+- vacancy pair is parallel to 110, the crystal field will have orthorhombic symmetry. In this case, symmetry argu- ments show that six sites are expected. As shown below, the ESR results for Rh2+ doped into the AgCl lattice are consistent with the first case, where the cation vacancies are stabilized along the axes. Upon rotating the crystal about the c axis, three sets 143 of seven lines are seen, each belonging to a magnetically distinct site with its unique axis directed along one of the crystallographic axes. Thus, with H//a as shown in Figure 6.3, the sites along the b and c axes are perpen- dicular to the field and the site along a is parallel to the field. As the crystal is rotated about 0 toward the b axis, the site along c remains perpendicular to the field while the signals from the sites along the a and b axes move toward each other, becoming equivalent at 45° (see Figure 6.4). Since the components of the seven-line multiplet have intensity ratios l:2:3:4:3:2:l and the largest splitting occurs along the gll direction, it must arise from an unpaired electron in the dzZ orbital inter— acting with the two equivalent axial chlorine nuclei. Thus, the spin—Hamiltonian used to interpret the spectra is: JC = 9 S + (3 § +2 ) gIIBZZgJ-Bxxyy 6 35 A “n Cl)Sz E I2 .4 + II( 5 6 A A 6 A 2 I"+s 2 I3) (6.1) 35 A + A ( Cl)(S _|_ x 5 a: y 7’1 72 where I5 and I6 are used to designate the spin on the two axial chlorine nuclei and the rhodium hyperfine terms have been omitted since its splitting was within the line width. In Table 6.1 are listed all the ESR parameters 144 .s\\m that + N nmuaomm mo xohh um Eduuommm ocmnlx mcsulm.m mnsmflm animus 0 com 145 .b Eoum one mesam as on» as m nuH3 +~cmuaum¢ mo Mosh um Eduuowmm vcmnlx mnBIIv.m mucmflm omw.mn .0 com 146 obtained from analysis of the single-crystal and powder spectra. Table 6.l.--The ESR parameters for chlororhodate (II) radicals measured at 77°K. . 35 35 Complex 9|] 2L ?i All( CL)ax €i< Cl)ax Rh2+ in AgCl (Powder) 2.002 2.430 y-K3RhC16 H20 (Powder) 2.007 2.460 y-KZIRhC15(H20)] (Powder) 1.992 '2.481 2.355 33.12 G Rh2+ in AgCl (single crystal) 2.012 2.419 27.27 G 11.94 G C. Discussion 3RhClG-H20.--The d6 complex in K3RhC16-H20 is diamagnetic with completely filled tZg bitals. A paramagnetic radical can form from this ion 1. y—Irradiated K or- upon y irradiation by (1) loss of an electron, (2) capture of an electron, or (3) rupture of a bond. Using the g values predicted by the first—order expressions shown in Table 5.5 and other physical arguments, it is feasible to show that only one of the possible radicals which could result from these mechanisms is consistent with all the experimental data. 147 The first possibility, the loss of an electron, would result in a d5 ion with a 2T29 ground state. Be- cause this state is triply degenerate, the ion would undergo distortion to remove the degeneracy. By comparing the ex- perimental g values then with those predicted for a low- spin d5 system under different distortions, the first pos- sibility can be eliminated. Also, because the t orbitals 29 are not very sensitive to distortions, they give three or- bital states which are close in energy. Since these states are connected by spin-orbit coupling, the relaxation times are short for such systems and thus resonance is usually observed only at temperatures much lower than 77°K. In the second case, the addition of an electron would result in a species with an unpaired electron in the doubly degenerate eg orbitals. Again the ion would undergo distortion to remove the degeneracy but, since these or- bitals are sensitive to distortions, the resulting dif- ferences in orbital energy is enough for resonance to be observed at 77°K. Depending on the distortion, the elec- tron could either be in a dzz or de-yZ orbital. Using the spin-orbit coupling value of 1235cmfll found for Rh2+,121 cm-1,122 and the approximate AE 2 value of 20,000 a -xz,yz , the predicted g values are relatively close to the experimental values. Also, with the unpaired elec- tron in the dZZ orbital, there should be some interaction with the axial chlorine nuclei. This appeared to be the case in the single crystal. 148 For the last possible method of producing radicals, the only reasonable reaction would be the loss of a chlorine atom giving [RhC1513-. This ion would have the unpaired electron in the d32 orbital as was found experimentally but the single axial chlorine would give only a four-line pat- tern which wasn't found experimentally. Thus, the picture that emerges from this analysis is that the irradiation of K3RhC16-H20 produces a [RhCl6J4- ion by capturing an electron and this ion undergoes a dis- tortion so that the unpaired electron is in the d32 orbital. The [RhClGJZ- ion formed by the ejection of an electron may also be present but, because of its preditably fast spin-lattice relaxation time, resonance isn't observed at 77°K. 2. y-Irradiated K2[RhC15(HZOn.--A similar approach can be used to analyze the paramagnetic radicals produced in y-irradiated K2[RhC15(H20)]. The [RhC15(H20)]2_ ion is a d6 system wherein the axial H O ligand removes the de- 2 generacy of the t orbitals. Although the H O ligand 2g 2 should give a greater crystal field splitting than chlorine according to the spectrochemical series, it is not uncom- mon that this ordering changes for nearly adjacent members of this series. Thus, without optical spectra for this compound, one cannot know with certainty whether the H20 ligand acts to tetragonally elongate or compress the crystal field. Therefore, if an electron is removed from 149 the radical, the resulting [RhC15(H20)]- ion could have the unpaired electron either in the dxy orbital or the doubly degenerate dxz’yz orbitals. However, the theoretical g values show that neither of these possibilities could give the experimental values and, as seen in the case of the isoelectronic [RuClS(H20)]2- ion in Chapter VII, the relaxa- tion time would probably be too fast for resonance to be observed at 77°K. If, on the other hand, an electron is captured by the complex, the [RhC15(HZO)]3- species is formed. Since the experimental g values are only consistent with those predicted for the odd electron in the dzz orbital, either the H O ligand gives rise to tetragonally elongated crystal 2 field or the H O ligand is lost to form the [RhC15]3— 2 species. In either case the axial symmetry of the ion must be lowered to account for the three 9 values. Such a distortion would not be surprising for these two radicals, since the unpaired electron in the d22 orbital would over- lap with the H O ligand in one case or have an unbonded 2 lobe in the other case and therefore would be sensitive to external influences. These could arise either from the arrangement of the nearest neighbor ions or the hole pro— duced by irradiation. Also, it should be noted that the chlorine splitting is consistent with that expected from the unpaired electron in the dzz orbital. The four-line pattern, superimposed on the gll line, would arise from 150 the electron interacting with the single axial chlorine and the splitting, being greater than that found for the [RhC16]3— ion, is consistent with the larger Rh-Clax over- lap expected for these ions. Lastly, the radicals produced by the rupture of a bond are not consistent with the experimental results. The most likely bond breakage would result in the loss of the H20 ligand but this would not yield a paramagnetic radical. The other likely bond rupture would result in the loss of the axial chlorine but no chlorine hyperfine structure would be found in this case. In summary, the analysis of the ESR parameters shows that the [RhC15(H20)]3- or the [RhC1513- radical, formed by the capture of an electron, are the only species consistent with the experimental data. The [RhC15(H20)]- species may also form but, due to fast relation times, its resonance would not be observed at 77°K. 3. AgCl:Rh2+.--For rhodium doped into AgCl, it is apparent from the analysis of the single crystal ESR spec- tra that the ion enteres the lattice substitutionally and, hence, is surrounded by a octahedron of chloride ions. The g values and seven-line hyperfine pattern arising from this radical indicate that the unpaired electron is in the dz2 orbital interacting with the two axial chlorine nuclei. 2+ Thus, the radical could result from Rh , a d7 system, with 151 a tetragonal elongation or Rh°, a.d9 system, with a tetra— gonal compression. It should be noted that Wilkens, et al. have made a study of the temperature dependence of the g values for this syStemIZB. They attributed their results to the Rh° ion experiencing a dynamic Jahn-Teller distor— tion and apparently failed to realize that their results could also have been explained by the Rh2+ ion undergoing ( a dynamic Jahn-Teller effect with the Opposite distortions. : Hence, before investigating the bonding in this radical, f arguments will be presented for the Rh2+ assignment. 1 In the melt, the Rh3+ ion would first be reduced 2+ to Rh This ion, according to the analysis above for Y-irradiated K3RhC16-H20 and K2[RhCls(H20)], should be stable in an octehedral field of chloride ions. Also, there is a history of other metal (II) ions being sta- bilized in the AgCl lattice124_127, (including the 2+ analogous d7 Co ion) by charge compensation involving cation vacancies. If now the Rh2+ ion were to be further reduced to Rh°, some additional overall stabilization of the system should occur. However, there appears to be no decrease in lattice energy resulting from such a reduc— tion, since charge compensation would also be needed for the Rh° ion. Also, the [Rh°C1616- complex should be less stable than the Rh2+ complex, since it involves two more electrons in antibonding molecular orbitals. Hence, it 2+ is difficult to see why the Rh ion would be further reduced to the Rh° ion. 152 Thus, assuming the ion to be Rh2+ with a tegra- gonally elongated field, the unpaired electron would be in an antibonding |Eg,d22>’orbital. This symmetry assign- ment for the orbital, however, assumes that the ion would essentially have 0h symmetry, since the distortion is probably small as evidenced by the fact that it is dynamic at higher temperatures. The lEg,dzz> molecular orbital is composed mostly of the dz2 orbital but has some ligand orbital character. The form of the orbital is |Eg,dz2> = alsdzz) — awn/2K?) (205+206-01-02-03-c4)] , (6.2) where o = n|3pz>i + (1'"2)1/2|38>i and i = l - 4 designate the equatorial ligand orbitals while i = 5,6 designate the axial orbitals. It is not possible to derive coef- ficients for this orbital using the metal A—tensor theory, since the rhodium hyperfine splittings are within the line width and could not be evaluated. However, it is possible to estimate the degree of covalency in this orbital using the ligand hyperfine splittings. The principal values for the chlorine superhyper- fine splitting tensor are (in units of 1 X lO—4cm—l) P ‘ F. '- A +25.61 Z A = +13.48 x Ay +13.48 . (6.3) L. d - .- 153 Although there are eight possible sign combinations for the principal elements, only the choice with all signs positive is consistent with the assumptions that (l) the spin transferred to the pz orbital is positive (2) the spin-polarization of the pnx and pTTy orbitals would be small, and (3) the isotropic chlorine hyperfine inter- action should be large and positive, since the chlorine 33 orbitals are directly‘involved in the bonding. The principal elements of the chlorine hyperfine interaction tensor can be expressed in terms of the iso- tropic contribution AS, the direct dipolar interaction Ad between the electron in the d22 orbital of Rh and the chlorine nucleus, the dipolar interaction Ap between the electron in the 3pz orbital of chlorine and the chlorine nucleus, and the dipolar interaction A , Any between the nx polarized electron density in the chlorine pr and py or- bital and the chlorine nucleus. As a result of the rela- tionship between the direction cosines of the three chlorine p dipolar terms, only two independent values (AP-Anx) and (Any-Aux) can be determined, such that P - fl A2 0 0 F]. 0 O 0 A 0 = A 0 1 0 x S O 0 A 0 0 1 L. y; .. — 154 2 0 0 + Ad+Ap-AflO-l O __0 0 -1 -l 0 0 + fly - Anx O -l 0 O 0 2_J. (6.4) The Ad = 0.26 x 10"4cm-l term has been calculated from _ _ 3 o . 0 Ad — ggnBBnr uSlng the Rh-Clax distance of 2.150 A, which was estimated from the Ag-Cl interatomic distance 80 The three observed principal components lead to As = 17.52 x 10-4cm'l, _ -4 -l _ —l (Ap - Anx) - 3.78 X 10 cm , and (Any - Aflx) — 0.0cm . and wa are equal, as eXpected for an by allowing for the smaller Rh ionic radius Thus the values Any 0h ion with the unpaired electron in the IEg,d32> anti- bonding orbital. Also, for this type of orbital, the A and ATry values are expected to be negative and small fix relative to the Ap term24. Hence, they will be considered to be approximately zero, giving Ap = 3.78 X 10-4cm-l. With this quantity and A3, one can obtain information about the lEg,d22 > antibonding orbital. In order to correlate these eXperimental quantities to bonding parameters, it is necessary to develOp theoreti- cal expressions for A8 and AP. This can be done using the spin—Hamiltonian expression determined for the hyperfine splitting arising from electron density in the axial 155 chlorine o orbitals. The Hamiltonian will have axial symmetry about the z axis and can be expressed as J% = A § 3 +A (§ 3 +§ f ) . 6.5 L H l " Focusing attention then on the hyperfine splitting result- ing from one of the axial chlorine orbitals, the expecta- tion value of the Hamiltonian leads to the approximate expression III! (cg/3) <66|be|66). (6.6) Several terms have been dropped in this approximation, resulting in the following errors: (1) a relative large error arises from omitting the (dzzlfCLlo6> term which could not be evaluated since good 5d22 wave-functions were not available for Rh2+, (2) a small error has been intro- duced by omitting the .2 terms since the large interatomic distances involved here make the r’3 dependent quantities quite small, and (3) the omission of the term results in essentially no error in the calculation since it corresponds to Ad and there— fore has been accounted for in the experimental Ap value. Evaluation of the above approximate expression for leads to i 2 . . A8 = (a /3)(1-n )As' (6 7) and A = P . 35 = 2 _ -4 where A8( Cl) (8n/3)gegn88nlw38(0) | _ 1570 x 10 cm 156 2 2 (a'/3)(n )A; , (6.8) -1 o 35 _ -3 _ —4 —l and Ap( C1) - (2/5)gegn88n (r >3p — 46.75 X 10 cm have been determined from the I038(0)I2 and molecular orbital. This type of orbital has 58 character and explains the isotropic rhodium Splitting. In [RhC1614—, however, the complex has only a Slight distortion from the 0h point symmetry group and thus the odd electron is essentially in an IEg,d22> orbital. An orbital with this symmetry, on the other hand, has no 53 character and therefore gives small rhodium splittings that are within the line-width. CHAPTER VII OTHER SYSTEMS Included in this chapter are systems whose ESR Spectra were not fully analyzed--either as a result of experimental difficulties or inherent Shortcomings in the system. For each system discussed, there will be given the objectives for the investigation, the results, and an evaluation of the system with regard to future study. Suggestions for future work are given where the system appeared promising. A. Chlororuthenate (III)Complexes One of the main objectives in this investigation was to find the ruthenium hyperfine splittings, Since none had been reported before in halometallate complexes. In fact, the only ruthenium hyperfine structure observed thus far has been for Ru3+ in Co(NH3)6C13128’3, in A12 3 and in the YGa and YAl garnet 1atticesl3o. 129 The [RuC15(H20)]2- ion in the (NH [InCls(H20)] 4)2 lattice proved to be the most promising Ru3+ system in— vestigated here. AS the sample was cooled, using the helium flow system, resonance was first observed at about 20°K and at 12°K the resolution of the signal became 158 I 159 sufficient for an ESR study. However, the single crystal rotations could not be completed successfully Since the crystal holder would freeze into one position as a result of the cold helium vapors mixing with the atmoSpheric humidity. Thus the results of the single crystal study, although quite informative, are only for unknown arbitrary orientations aS is Shown in Figure 7.1(A). The spectrum Shows two six-line patterns, each superimposed on a Strong central line and having about 7% of its intensity. This type of pattern is characteristic of species occupying two inequivalent sites in each of which the odd electron interacts with the ruthenium nucleus. Since ruthenium 99 has two isotopes each of spin 5/2, Ru with a 12.81% 101Ru with a 16.98% natural abundance: natural abundance and and both isotopes give practically the same Splitting, they appear experimentally as a Six—line pattern arising from a 29.79% occurring isotope. Thus the Six hyperfine lines should have, as found experimentally, an intensity of about 7% of the central line. There were two types of doped (NH4)2[InC15(H20)] crystals investigated by ESR. Some had areas of intense red color while others appeared more homogeneously light red throughout. Only in the latter case could the ruthenium hyperfine Splitting be resolved. Apparently in the former case the [RuC15(H20)]2- ions are so close to one another that the hyperfine lines have been so 160 201) (3 l I 17 Figure 7.l--(A) The X-band Spectrum at 9°K of the [RuC15(H20)]2‘ ion in the (NH4)2[InC15(HZO)] matrix with H at an arbitrary orientation. The upward and downward arrows designate the 101'99Ru hyperfine lines for two magnetically inequivalent sites. (B) The pow— der spectrum of this sytem at 9°K. 161 broadened as to not be observable. It was found in these crystals that, for the most part, there appeared to be two magnetically distinct Sites, but in some orientations there appeared to be four magnetically distinct Sites with two sets of Sites being nearly equivalent. It should be of interest then to see if these results can be re— lated to the crystal structure of the host lattice. ‘ {A The crystal structure shows (NH4)2[InC15(H20)] to ‘ be orthorhombic with four molecules per unit celll3l. The H20 molecules in each unit cell are not distributed ran— domly among the Six corners of the [InC15(HZO)]2-octehedra '“ but occupy a particular corner in the symmetry plane. Also, every [InC15(H20)]2- ion is related to another ion in the cell by a C screw axis and the only symmetry in— 2 dividual Sites have is the mirror plane. Thus, if the [RuC15(H20)]2- ion were to enter the lattice with its Cl—Ru-H 0 bond along the Cl-In-H 0 direction, and to assume 2 2 the geometry of the site, there should be only two mag— netically distinct Sites and each site should give rise to a three g-value ESR pattern. But, since four magnetically distinct Sites appear in some orientations, the [RuC15(H20)]2" ion apparently does not have exactly the same orientation in the lattice as the [InC15(H20)]2- ions. Further in- formation about the Site symmetry of the ion in the lat— tice can only be obtained by examining the g values. 162 Because no complete analysis of the single- crystal spectra was made, the powder spectrum must be relied on for this information. The powder spectrum shown in Figure 7.1(B) for a 2500 gauss sweep shows only two 9 values and Sweeping the field further did not re- veal a third g value. This result would indicate that the [RuC15(H20)]2- ion has retained its molecular 64v symmetry I (noting that the ion actually has C symmetry if the 2v hydrogen atoms of the water molecule are included but ; these are not considered Significant for the covalent bonding in the complex). Any lowering of the 64v symmetry Should produce a three g-value pattern. On the basis of the powder pattern, the values gll = 3.013 and.gi = 2.216 have been assigned. It is difficult to understand these 9 values, however, using first-order g theory for a low- Spin d5 system having 04v symmetry. In order to derive first—order g expressions for the [RuC15(H20)]2- ion, one must have some idea of the ordering of molecular orbital energy levels. In such an ion, the axial H 0 molecule removes the degeneracy of 2 the t orbitals. However, not having optical Spectra 29 for this compound, or analogous compounds, one cannot know with certainty whether the b3 orbital would be of higher energy relative to the e* orbitals, or if the Opposite situation occurs. Considering then the first possibility, the b5 orbital would contain the unpaired 163 electron giving rise to the following first—order g—value expressions: gll 2.0023 - 8l/(AEb, b,) (7.1) 1‘ 2 3i = 2.0023 + 2A/(AEb§_e,) . (7.2) From these eXpreSSionS, one would expect 9" to be less than and qi to be greater than the free—spin value. Obviously, if the unpaired electron is in the b3 molecular orbital, the first-order expression for 9" does not adequately describe the Situation. Focusing then on the gll value of 3.0134, there apparently must be greater mix- ing of the filled b1 orbital with the b; orbital than of the b; orbital with the empty b; orbital. For this situa- tion one Should add the term +81/(AEb§;b1) to the 9" expression as was done by Kon and SharpleSS37 to explain the gll value for [CrOC15]2-. For gll of [RuClS(H20)]2-, however, it is difficult to see how this term could make a large enough contribution to account for the eXperimental value. For the other possible distortion, where the b3 orbital is lower in energy than the 2* orbitals, the odd electron would be in the doubly-degenerate 2* orbitals. The molecule Should, in this case, undergo a Jahn-Teller distortion to remove the degeneracy. This would result in a lowering Of symmetry for the ion and should give 164 rise to three 9 values. Therefore, neither possibility seems to adequately explain the eXperimental g values, suggesting that a third g value having a value much less than 2.0023 might be found at very high field. As indicated by the above discussion, the limited analysis of this system has raised some interesting ques- tions. Further analysis Of the system must include a com- ( plete Single-crystal study. Since the [RuClS(H20)]2- ion tends to enter the lattice in clusters, very low amounts Of the dOpant (0.l%-0.01%) should be used in making the crystals. To circumvent the problem involving single- crystal rotation with the helium flow system, perhaps passing warm helium gas across the cavity Opening would help. If this problem cannot be alleviated, the work could probably be done with the Andonian Dewar. Also investigated was the [RuC16]3- ion doped into KCl and NaCl. These systems, however, did not give a signal even at 10°K. Because the complex is d5 and doped into highly symmetric cubic lattices, Jahn—Teller distor- tions are necessary to remove the orbital degeneracy. Since this type of distortion results only in small Shifts in energy, the three orbitals will be close in energy and connected by Spin-orbit coupling. Under these conditions, the ESR Signal is only obtainable at low tem- peratures where the Spin-lattice relaxation time is longer. Thus, it is not surprising that the Signal was not Observed 165 even at 10°K. With regard to future work, it might be necessary to go to 4.2°K to see the signal; only the Andonian Dewar system can approach this temperature. The last ruthenium-containing system to be studied was the complex in Single crystals grown from the melt of AgCl containing RuC13. This system was an attempt to make the ruthenium analogue of the d7 Rh2+ ion doped into the AgCl lattice. Since the d7 system for ruthenium is Ru+, this ion would not need charge compensation to enter the AgCl lattice. Thus it was felt, since the Rh2+ ion Shows that a d7 system can be stabilized in the AgCl matrix, that Ru3+ might be reduced in the AgCl melt to the Ru+ ion. The single crystals produced were a very dark burgandy color, indicating that a reaction occurred in the melt. However, the ESR spectra were not consistent with a paramagnetic ruthenium ion even at 13°K. But the crystal did give a signal which was observable even at 77°K. The Spectrum consists of two portions, (1) a low-field pattern which is more intense and extends from about 2500 gauss to 3000 gauss and (2) a high-field pattern which has broad lines that start at 3300 gauss and end at about 4050 gauss. When the field was along any of the crystal axes the low- field pattern consisted of two sets of doublets with the low-field doublet having about one half the peak height Of the doublet at higher field. This pattern is con— sistent with a A92+ ion with the odd electron in the dngyz 166 orbital. The ESR parameters measured for this radical at 77°K are: 9" = 2.527 All = -68.46 G = 2.292 A = -105.60 G 91 l The high-field pattern has not been identified but it does not appear to contain the Six-line hyperfine structure expected for a ruthenium radical. Since the primary con- cern here was to make a ruthenium-containing radical, a further study was not made. However, there are very few Ag2+ ions reported which have the Odd electron in a de-yz orbital and hence this radical might merit future study. B. RhCl3 in NaF This system was studied in an effort to Obtain 2+, 7:.e., [R11F614- in NaF. 2+ the fluorine analogue of AgCl:Rh Since Chan and Shields were successful in doping the V ion into crystals Of Li? and NaF grown from the melt, using mixtures of the alkaline fluoride and VC13132, the same result might be expected with RhCl3. However, the Rh2+ ion apparently did not enter the lattice since there was no observable Signal even at 10°K. The problem here might be a result Of the Na+ ion having tOO small a radius to be replaced by the larger Rh2+ ion. Since this system would be Of considerable interest, further work would 167 seem in order. Crystals of KF are deliquescent and present problems in sample handling, but RbF and CsF do not have this problem and, with their larger cationic radii, would be reasonable crystals to try. 2.. C. [ReF6] in CSZGeFG Most Of the ESR studies of the Re4+ ion have been done on the [ReC16]2_ ion in the K2PtCl6 lattice133-135. These investigations were done at 4.2K° and did not Show any ligand hyperfine structure--probably as a result of the -.m—:L‘ _... a“ J meat-u . ' h large line widths (25 gauss) and small ligand hyperfine Splittings. Only small ligand hyperfine Splittings would be expected for such a system Since the three unpaired electrons in the tgg orbitals, bonding only with ligand 1r orbitals, cannot interact directly with the ligand a bonding orbitals. The [Rerlz- system was made, then, as a fluorine analoque to the [ReClGJZ- system. Also, because of the much greater magnetic moment of fluorine, ligand hyperfine structure should probably be observable and hence the n- bonding in this ion could be studied. Unfortunately, crystals of CSZGeF6 doped with [ReFGJZ- Showed no ESR signal even when cooled to 9°K. Since the [ReFelz- ion has such a light pink color, one could not be certain if the ion had entered the CS GeF lattice. Therefore, a 1% 2 6 aqueous solution of the [ReF612‘ complex was made and 168 examined at temperatures down to 9°K. This also did not give a Signal. Since the [ReC16]2- study was done at 4.2°K, future work on the [ReFGJZ- ion must also probably be done at this temperature. D. y-Irradiated K4Fe(CN)6 I'_ _‘- AS Shown previously, the d6 K3CO(CN)6 complex, when Y irradiated at 77°K, gave a d7 system in which the Odd electron interacted with two equivalent nitrogens. Hence the K4Fe(CN)6 complex, also a d6 system, could possibly form a similar radical under these conditions. The powder Spectrum for y-irradiated K4Fe(CN)6 is shown in Figure 7.2. The low-field portion of the spectrum consists of three lines, while at higher field there is another line. Gradual warming of the samples showed that the outer two lines of the low field pattern slowly lost their intensity until only the central line Of this pattern, along with the line at higher field, remained at 210°K. Warming further, this remaining signal continued to lose intensity until it was gone at 250°K. Thus, the central line of the low-field pattern and the line at higher field seem to arise from the same radical. The observed 9 values for this radical, gll = 2.0017 and qi.= 2.0998, are consistent with a d7 system having the Odd electron in the d32 or- 7 bital. Therefore, it appears that the d [Fe(CN)6]5_ ion 169 oqumme paw omumaomuua r m . . Azovmmwx mo Esuuommm Hm .Mehw um IIN h Ouflmwh a Soda; mega «a mmv AUAVF 170 forms but, contrary to the d7 hexacyanocobaltate (II) ion, there is no interaction with the two axial nitrogens. Root and Symons have Y irradiated [Fe(CN)6]4- doped into KC1136. In this case they found a radical with very similar 9 values, gll = 1.999 and 91 = 2.095, but which Showed a triplet splitting from the odd electron interacting with one nitrogen nucleus. The 9 values for their radical are again consistent with a d7 system having the unpaired electron in the d22 orbital but in this case one Of the axial CNP groups apparently rotates to give a metal—nitrogen bond. One possible explanation for this is that in hte KCl lattice there is expected to be a cation vacancy along the axial NC-Fe-CN bond direction and perhaps reorientation Of the nearest CN- group would better sta- bilize this vacancy. Also, by increasing the period of irradiation they found wing lines appearing on either Side of the low-field pattern. These lines, which they attribute to a different Species or possibly a radical pair, are probably the same wing lines found in the low-field portion of the Spectrum for y-irradiated K4Fe(CN)6. Finally, Root and Symons report that they did not Obtain any radicals when pure K4Fe(CN)6 was irradiated. Although they don't mention the temperature of irradiation eXplicitly, it ap— pears to be room temperature; this and their Short radia- tion period probably explain the discrepancies between their results and ours. 171 NO single-crystal ESR studies of y-irradiated K4Fe(CN)6 were done since the system did not provide an analogue to the [Co(CN)4(NC)2]4— radical and, without en- riching the sample with 13C or 57Fe, very little could be learned about the bonding in the ion. However, if future work were to include 57Fe or 13C enrichment, this could be an interesting system to study. E. y-Irradiated K2Ni(CN)4-H20 and Na2N1(CN)4°3H20 Krigas initiated ESR studies of a series Of E_- 137 irradiated cyanides, K2M(CN)4-nH 0, where M = Pt, Pd, Ni . 2 This is an interesting series Of complexes since crystal structure investigations Show that the square planar tetracyanometallate ions are stacked one upon another along the fourfold axis of the ion. In his work, Krigas found that crystals Of K2Pt(CN)4-3H20 crumbled upon irradiation and gave unusable Spectra. In the present work, an effort was made to extend the previous studies by examining the ESR spectra of ir- radiated K2Pd(CN)4-H O and K Ni(CN)4-H 2 2 2 these compounds also tended to crumble upon irradiation so O. Crystals of they were covered with Pliobond Glue. This procedure alleviated the problem somewhat but the palladium compound gave unusable spectra as had been found for the platinum compound. The nickel compound, on the other hand, gave strong lines which, at Xkband, extended from 2800 gauss to 172 3300 gauss. With H//c there seem to be two main pertions to the spectrum, a triplet at low field and a very complex pattern at higher field. The triplet appears to originate from the interaction of an unpaired electron with a nitrogen( nucleus; because of this and a g value greater than the free—spin value, the pattern could arise from the d7 [Ni(CN)4(NC)]2_ radical. Rotating the crystal about the a axis Showed that lines move between the two portions Of the Spectra but because there were SO many lines in the high-field portion, it was impossible to follow the lines completely. Irradiation of the Na Ni(CN)4-3H O compound 2 2 also gave strong lines and, in this case, the patterns were less complex and the crystals did not crumble. The Pt and Pd anologueS gave unusable spectra and the Ni systems alone were of limited interest Since no 61Ni hyperfine Splitting was observable, so no further work was done on this series. If, however, these com- 13 61Ni in the case Of the pounds were enriched with C (and nickel complexes) the radicals formed could probably be identified and their bonding characterized. F. Y-Irragiated Magnus' Green Salt PtCl 2 4 found that a (Pt2) radical formedl37. The (PtCl Upon Y irradiation of K at 77°K, Krigas 3... 4) 2 structure was assigned to this radical and it was sug- gested that the formation of dimer Species resulted from rm: m ._. ._.._ 173 the Short Pt-Pt (4.133) distance between the square planar units within the lattice. Applying this hypothesis then, there Should be a considerable likelihood that a (PtZ) radical would form in irradiated Magnus' green salt, [Pt(NH3)4][PtCl4], where the Pt-Pt distance is only 3.253138. Because Magnus' green salt is very Slightly soluble, it is virtually im- possible tO obtain sizable crystals by evaporation tech- niques. The diffusion technique used appears to be the best method available for growing crystals of this material but it yielded crystals only large enough for Q—band study. Irradiation of the powder gave a weak Signal which pro- vided no evidence for dimer Species and which appeared to decay rapidly upon warming. 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An estimate of the quadrupole coupling constant can be determined by including it as an adj us table parameter . SUBROUTINE SECORD SUBROUTINE SECORD¢XA9ERPOR) DIMENSION XA(4)9 XB(4) DIMENSION HPARA(10)9HPERP(10)9SMALLM(10) COMMON/SCALE/XBEG(S)9STDEV(5) DATA HPARA/l957.3l9 2264.569 2581.799 2908.189 3245.089359l.23o DATA HPEPp/2594.469 2679.639 2792.789 2932.049 3094.309 3278.329 T3482.24.3709.789 3954.319 4214.59/ ' DATA SMALLM/40593OS’ZOS’1OS,.S’-.S’-l.5.-2.S,-3OS'-405/ DO 3 1:199 3 XB(I)=XBEG(I)*XA(I)*STDEV(I) H=6.62619OE-27 V=9.258255+9 BIGI=4.SSBOHR=9.274096E-21 0:0 - GPARA=XR(1) $ A=XH(2) 5 B=XB(3) 5 GPERP=XB(4) ERRUR=0.0 DO 10 I=l910 10 ERROR=ERROP*(H“V-((GPARA*ROHR*HDARA(I))+(A*SMALLM(I))0(8992/(Z.09H 19V))*(BIGI*(RIGI*1.0)-SMALLM(I)**2)))**2 DO 11 J=l910 JJ=J ll ERROR=ERROP+(H*V-((GPFPP*BOHR”HPERP(J))+(B*SMALLH(JJ))*((A**Z*B”*2 2)/(4.0*H*V))“(BIGI*(BIGI*I.0)-SMALLM(JJ)**2)*((((Q**Z)*SMALLM(JJ)) 3/(2.0*B))*(2.0*BIGI°(RIGI+1.0)-(2.0*SMALLM(JJ)**2)-l.0))))§*2 PRINT 9999 ERROR9 X39.Q 999 FORMAT(//2X9*THE NEH PARAMETERS*/l0X.*ERROR=*GIS.99/5X9*GPARA=9F10 4.793X9’APARA=*E12.593X9*APERP=’EIZ.SI9l0X96PERP=*F10.795X'Q'*E12.5 ) RETURN END 182 APPENDIX-B The following is a listing of the subroutine used to determine the molecular orbital coefficients and the charge of the central metal ion for [VOF513‘ and [NbOF513'. This sub— routine was used with a minimization program which adjusted the: coefficients (81’ 82, and e) to give the best agreement between the experimental ESR parameters (All, AL, gll’ and 9i) and those determined from the second order molecular orbital expres- sions of DeArmond, et al. for these parameters. Included before the listing is an eXplanation of the input and output data. INPUT GPARA = gll EAPARA = All cm’l _ _ -l , GPERP — gi. EAPERP Al cm i -1 :' CAPPA - K DELTEl - AE(b2+b1) cml fi 881 = Sb] DELTEZ = AE(b2+e) cm $32 = Sb SIGMAM = AM cm'1 2 SE = s SIGMAL = A cm'1 8 L P = P cm"l OUTPUT b b .. I = I BlP — 81 BlPB 81 _ b b _. | = l BZP — 82 B2PB 82 E: e: EB= Eb EP = 8' EPB = E'b Q = charge on the central metal ion. 183 184 SUBROUTINE MOCOEFF SUBROUT INE MCCOEFF (AX 9 ANSI DIMENSION XA(3)9 XRI3) COMMON/TIMEITIMELIM9TREG9TEND9ANOW9IMPoIPP9IVP9IXP COMMON/DATA/DELTEI9DELTEZ9GPARA9GPERP9EAPARAIEAPERP9SIGMAH9 6§IGMAL9CAPPA9P9SBI95329SE COMMON/XREG/XREGISI/5CALE/SCALE(S) COMMON/GROOT/ IFORBQ XX DATA INDEX/0f - AA=OOO S 88:000 $ CcéOOO DO 3 I=l93 3 XB(I)=XREG(I)+XAII)9SCALE(I) 200 S 202 9999 BI=XB(1) $ 82=XR(2) S E=XR(3) BIP=QROOT(1.o.-2.oonlossl.Bloaz-l.0) IF(IFORBOEOOI) AA=XX BZP=QROOT¢1.0o-2.0*BZ#SBE.BZ§*2-l.0) IF(IFOPR.EQ.I) BB=xx ' Ep=QROOT(l009-200”E*SE9E§*2-100) IF(IFORB.EO.1) CC=XX TDGPARA=-2.0*(2.0”SIGMAM*BZ*BI-SIGMAL“82P*BIP)“(2.0”82”Bl-2.0*BlG 182P*SR2-2.0*82*BIP“SBI-BIP#82P)/DELTEI TDGPERP= -(2.0*SIGMAM#82*E)“(82*E-BZ”EP*SE2E*BZP*SBZTIDELTEZ TAPARA=-P*(CAPPA‘PBZ‘WZO(4.0”82**2/7.0)+2.0023-GPARA0(3.0“(2.0023 l-GPERP)/7.0)*6.0*SIGNAM*B2*E*(BZ*EP*SE+E*82P'SHZI/(7.0*DELTE2)+;!.0 2°(2.0*5IGMAM*82*Bl-SIGMAL*BZP*BIP)*(2.0532*BIP*SRI*2.0*BI*BZP*SF§20 3R]P*B?P)/DFLTEI) TAPERD=-D*(CAPPA*RZ*‘?-(2.0*829*2/7.0)0(ll.0*(2.0023-GPERP)/l4.(3)9 lll.0“(SIGMAM982*E)*(BZ’EP‘SE’E'RZP‘SBZ)/(7.0*DELTE2)) FDGPARA=GPARA-Z.0023 EDGDERP=GPFRP-2.0023 ANS=((TDGPARA-EDGPARA)IEDGPARA)**2+((TDGPERP-EDGPERP)lEDGPERP)1h§29 II(TbPAPA-EAPARA)/EAPARA)*’2*I(TAPERP-EAPERP)/EAPERP)**Z INDEX=INDEXOI BN0W35ECOND(AZZZ) IF(IVD.EQ.1)PRINT 2009INDEX9BNOW FORMAT(* VALU52008 INDEX9RNOW = *9I593X9F8.3) IF(IFORB.EO.I) GO TO 100 IF(IVP.ED.1)PRINT 702 FORMAT(//T259*..........ALLOHED REGION.........’) IFIIVP.EQ.I)PRINT 99999AN59XR9BIP9BEP9EP9ANOW FORMAT (l/2X9*THE NEH PARAMETERS‘VI0X9*ERROR=*GI5.99/SX9*Bl=*F10,1 l95X9'BZI'F10.795K9'E80F10.79ISX999193'F10.795X9082P'9F10.795X3 Z'EP!’F10.79T1209*ANOH C 'F6.3) n»;. 185 CALL COEFF (BI9BIP9SBIOBIBOBIPB) CALL COEFF (32932095329 BZBQBZPB’ CALL COEFF ( E9EP9SE9EB9EPB’ 0132.0“(BIB**2*BIB*BIPB*SBII 02:2909(329*92’323982989592) 0134.0“(EB’*Z*EB”EPB*$EI Q4=sz*92-RZ*BZP*SRZ 0:4.0-QI‘QB'Q3*Q4 IFIIVP.EQ.I)PRINT 2039Q9QI9Q29Q39049BIB9BZB9EB9BIPB9BZPB9EPB 203 FORMAT (IISX9*0=*FI0.795X9“Ql=*Fl0.795X9’02=*F10.795X9*033*FlJlo79 100 201 99 VSX.*04=*F10.79/SX9GBIB=”F10.795X9¢BZB=GFIO.795X9'EB!‘F10.79/SX9 Z98198=9F10.795X9*B2PB=*F10.79SX9*EPBS*F10.7) ‘INOEX=0 RETURN DD=AA9BB¢CC ANS=ANSO10000000.0“DD+100000.0*DD**2 IF(IVD.E0.1)PRINT 201 ' FORMAT ‘IITZS9.00000 oooooFORBIDDEN REGIONOOOOOOOOOO.’ IF(IVP.EO.1)PRINT 99999ANS9XB9BIP982P9EP9ANOU RETURN END FUNCTION QROOT (A989C) COMMON/QROOT/ IFORB9 XX IFORB=0 YY=(B**2-4.0*A*C) IF(YY.LT.0.0) IFORB=1 XX=ABS(YY) QROOT=(-8¢SQRT(XX))/(2.0*A) RETURN END SUBROUTINE COEFF (A.B9S9C9D) XX=(B*S-A)/(A*S-B) YY=ABS(1.0/(1.002.0*S*XX*XX**2)I C=SQRT(YY) D=C*XX RETURN END Typod and Printed in the USA- _ Profession! Thesis Preparation Cliff and Paula Haughoy 194 Manlowood Drivo Eu! Lonnhfl. M'cmfian 48823 Telephone (517) 337.1 527 ll‘ul.“ ‘