1": ‘w— v'—' . AN ELECTRON SPIN RESONANCE STUDY OF BADIOALS FORMED BY HIGH ENERGY IRBADIATION 0F 1&2?ch AND K2Pt014 THESIS FOR THE DEGREE 0F PH. D. MICHIGAN STATE UNIVERSITY 'I'IIWAS MICHAEL KRIGAS I 977 I NNNLNNNNNNNINN : 4606 This is to certify that the thesis entitled An Electron Spin Resonance Study of Radicals formed by High Energy Irradiation of KZPdCI4 and KthC14 presented by THOMAS MICHAEL KRIGAS has been accepted towards fulfillment of the requirements for Ph.D. degree in Chemistry WWWQZM/a « Major 0-7639 ' '—‘— 1* .—_—_.-.._ .-. 4A . — «- ~ _ .._. .W.WWV— I said 21997. ABSTRACT .AN ELECTRON SPIN RESONANCE STUNY 0F RADICALS FORMED BY HIGH ENERGY IRRADIATION 0F K2PdCl4 and K2Pt014 By Thomas Michael Krigas All known square-planar complexes of Pt (II) and Pd (II) are diamagnetic with d8 electron configurations and therefore cannot be studied by electron spin resonance spectroscopy. In this work serveral new paramagnetic species have been produced by high-energy irradiation of solid diamagnetic compounds to give Pt and Pd containing radicals in which one-electron oxidation or reduction has occurred. The struc— tures of these new species have been obtained from electron spin resonance studies. The X-band electron spin resonance spectra of single crystals of K2PdC14 and KthCl4 that were irradiated by y-rays from a 6000 source or by l-MeV electrons have been studied at temperatures between 77°K and 296°K with the primary purpose of elucidating the structure and bonding in species showing unusual oxidation states of palladium and platinum. Irradiation of K2Pd(II)C14 produces two identifiable paramag- netic radicals: one is shown to be (Pd(I)C14)3- with a 4d9 electron configuration and the unpaired electron in a dx2-y2 orbital; the second radical is believed to be (Pd(III)C15)2— with the unpaired electron in a 4d22 platinum atomic orbital. Thomas Michael Krigas Crystals of K2Pt(II)C14 irradiated at 770K show two groups of electron spin resonance lines: one belongs to a radical that shows hyperfine interaction with two equivalent platinum nuclei; the second arises from a radical showing hyperfine interaction with one platinum and three chlorine nuclei. It is suggested that these species are {(Pt(II)C14)(Pt(III)C14)}3- and (Pt(I)Cl3)2-, respectively, where the metal electron configurations are 5d15 and 5d9. 0n warming to 125°K some of the dimeric radical is converted to a new species whose spectra are consistent with those predicted for (Pt(III)él5)2'. Thus, each identifiable radical contains platinum or palladium in which the original diamagnetic, low spin, (18 configuration of the metal ion M(II) (M=Pt or Pd) has been oxidized or reduced to form para- magnetic species with the metal in the unusual oxidation states M(III) or M(I). Energy level schemes for each radical are proposed based upon the electron spin resonance Spectra. The nature of the metal-chlorine bonds in the new species is discussed and the extent of covalency is estimated by using a simplified molecular orbital picture. AN ELECTRON SPIN RESONANCE STUDY OF RADICALS FORMED BY HIGH ENERGY IRRADIATION OF K2PdCl4 and K2PtCl4 By Thomas Michael Krigas A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1971 To My Wife Mary Susan Krigas ii ACKNOWLEDGMENTS To Professor Max T. Rogers under whose guidance this investi- gation was conducted, I wish to express my appreciation for his continued interest, counsel and assistance. I wish to express my gratitude to Amoco Chemicals Corporation and the United States Army for their financial support of this study. I I want to thank Professor Barnett Rosenberg of the Biophysics Department of Michigan State University for his interest and encourage- ment both scientifically and personally. Of the many colleagues who have helped me in experimental and conceptual problems I want particularly to thank Professor H. A. Kuska of the University of Akron, Professor P. T. Manoharan of the Indian Institute of Technology, Kanpur, India, and Dr. V. A. Nicely of Eastman Kodak. iii TABLE OF CONTENTS INTRODUCTION . HISTORICAL . . . . . . . . ESR Literature Reviews ESR Studies of Platinum and Palladium THEORETICAL . . . Introduction . . . Spin-Orbit Coupling . g Values Angular Variation of the g Value Zeeman Effect . Sign of the g Shift - Sample g-Value Calculation Hyperfine Interactions Introduction The Hyperfine Hamiltonian Isotropic Hyperfine Interaction Analysis of Metal Hyperfine Interactions Covalency from Metal Hyperfine Splittings Angular Variation of the Hyperfine Splitting Sign of the Hyperfine Splitting Ligand Hyperfine Interaction Sample Calculation iv Page 11 16 18 20 24 25 30 3O 31 34 38 41 43 49 49 53 EXPERIMENTAL . . . . . . . . . . . ESR System , Sample Preparation Crystal Structure of K2(Pd,Pt)Cla. Irradiation Methods Sample Handling . . . . . . . . Error Analysis . . . . . . . . RESULTS . . . . . . . . . . . . . . K2PtC14 . . . . . . . . . . . Introduction (Ptz) Radical . . . . . . . . UV-Photobleach Experiment . (PtCl) Radical (PtCl3)n' Radical . K2PdCl4 and (NH4)2PdCl4 . Introduction . RadiCal I . Radical II . . . . . . . . . (N(C2H5)4)2Pt28r6 . . . . . . . . K2Pt(CN)4.3H20, (Pt(NH3)4)C12 and K(Pt(NH3)Cl3)~H20 K2PtBr4, K2PdBr4 and K2Pt016 . DISCUSSION . . . . . . . . . K2PtC14 . . . . . . . . (Ptz) Radical . . . . . . . . g Values . Pt Hyperfine Interaction Linewidths . . . . . . Page 59 59 6O 6O 61 63 64 67 67 67 69 72 76 77 79 79 79 86 89 90 9O 93 93 93 93 98 101 Page Structure . . . . . . . . . . . . . . . . . . . . . . . 102 (PtCl) Radical . . . . . . . . . . . . . . . . . . . . . . 103 g and A(195Pt) Values . . . . . . . . . . . . . . . . . 103 Chlorine Hyperfine Interaction . . . . . . . . . . . . .106 (Ptc13)“' Radical . . . . . . . . . . . . . . . . . . . . . 108 Reaction Scheme . . . . . . . . . . . . . . . . . . . . . . 109 Kde014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Radical I . . . . . . . . . . . . . . . . . . . . . . . . 110 g Values . . . . . . . . . . . . . . . . . . . . . . . 110 Pd Hyperfine Interaction . . . . . . . . . . . . . . . 110 Chlorine Hyperfine Interaction . . . . . . . . . . . . 111 Radical II . . . . . . . . . . . . . . . . . . . . . . . . 115 Reaction Scheme . . . . . . . . . . . . . . . . . . . . . 116 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 BIBLIOGRAPHY O O O O O O O O I O O O O O O O O O O O O O O O O O O 121 vi Table 10. 11. 12. LIST OF TABLES g Values calculated from crystal—field theory . . . . . . Hyperfine interactions (A) calculated by the theory of Abragam and Pryce O O O O O O O O O O O O O O O O O O O 0 Comparison of calculated and experimental parameters for (N1F6)4- O I O O O O O O O O O O O O O O O O O I O O O Representations and ESR intensities for the (PtC14)23- ion . ESR spectral parameters of radicals in irradiated crystals 0f K2PtCl4 o o o e o o o o o o o o o o o o o o o o o o o 0 Principal values of the spin-Hamiltonian tensors of radicals in y-irradiated K2PdC14 and (NH4)2Pd014 . . . . . Calculated g Values for (Ptz) . . . . . . . . . . . . Hyperfine interaction parameters for platinum species by spin-unrestricted Hartree-Fock calculations . - . . . . . Hyperfine fields at the nucleus (Hn = -K/Zgngn) in various platinum species . . . . . . . . . . . . . . . . . Axial ligand spin densities . . . . . . . . . . . . . . . Isotropic hyperfine fields and covalency parameters for palladium complexes . . . . . . . . . . . . . . . . . Ligand spin densities in some o-bonded d9 square-planar complexes 0 O O O O O O O O O O I O O O I O O O O O O O 0 vii Page 29 40 52 73 74 84 95 100 100 107 112 115 Figure 10. 11. LIST OF FIGURES Possible ordering of the five d orbitals in an octahedral field with an axially elongated tetragonal distortion increasing from A to C . . . . . . . . . - . Axis system for metal (X,Y,Z) and ligand (x,y,z) atoms in (PdCIA) 3- O O O O O O O O O I O I O O O O O O O O O O O - Crystal structure of K2PdC14 and KthC14 . . . . . . - . The first-derivative X-band ESR spectrum of irradiated single crystals of K2PtC14 at 770K with Hlla - . . - . . - The first-derivative X-band ESR spectra of (PtC15)2-: (a) With HI lc, (b) With HI la 0 C O C O O C O O O O O O O O The first-derivative X-band spectra of (PtCl4)23- in irradiated single crystals of KthC14: (a) with Hllc, (b) with Hip. The feature marked X in (a) is centered at g = 2.000 and is from an unidentified species - - - - ° A plot of (1/I—1/Io) versus time for the photobleaching decay of (PtCl4)23‘ indicates that the decay is second order in (PtCl4)23' concentration - . - . . . - - - - The X-band spectra of (PtC13)2-: (a) first-derivative, Hllc, (b) second—derivative, Hl(110), (c) second-deriv- ative, HI la a o o o o o o o o o o e e o o o o o o o o o o o The first-derivative X-band ESR spectrum of irradiated K2PdC14at 77°KwithHHc . . . . . . . . . . . . . . The X-band ESR spectra of irradiated single crystals of KdeCl4 showing the lines from the (PdC14)3" radical ion: (top) second-derivative spectrum with H c, (center) first- derivative spectrum with Hlla, (bottom) second-derivative spectrumwithuium)................... A plot of log(I/IO) versus 103/T(°K) for the (PdC14)3- radical shows two linear portions which implies two modes Of decay O 0 O O I O O O O I O O O O O O O O O O O O O I 0 viii Page 54 62 68 70 71 75 78 80 81 85 Figure 12. 13. 14. Page (a) First-derivative X-band spectrum of a single crystal of KdeCl4 irradiated and observed at 77°K with Hllc, (b) angular variation of g when the magnetic field is in the ac plane, (c) angular variation of A(3SCl) when the magnetic field is in the ac plane. The solid curves of (b) and (c) were calculated with the parameters of Table 6. . . . . . . . . . . . . . . . . . . 88 The first-derivative X—band ESR spectrum of -CHCH3 in , (N(C2H5)4)2Pt2Br6 at 770K 0 O O O O O O ,. O O O O O O 0 O O 91 Possible molecular orbital energy level scheme for (Pt014)23- (d orbitals OHIY) o o o o o o o o o o o o o o o 97 ix INTRODUCTION Electron spin resonance (ESR) studies of transition metal complexes permit the identification of the paramagnetic Species and provide information concerning their ground-state electronic structures and symmetries.1 Complexes of the first-row transition metal ions in cubic, octahedral and tetrahedral crystal fields have been extensively investigated.2 Recent work has been increasingly directed toward less common oxidation states and crystal-field symmetries and toward problems involving second- and third-row transition metal ions.3'5 Many para- magnetic metal ions exist only as transient species and therefore are difficult to study by ESR. Thus, the stable oxidation states of plati- num and palladium are diamagnetic, M(II) and M(IV), having d8 and d6 electronic configurations, respectively, whereas the unusual paramagnetic oxidation states of M(I) and M(III) with d9 and d7 configurations, respectively are unstable transient species. It has recently been shown that high-energy irradiation of solid materials provides a method for obtaining such unusual Species and that their stability in the solid state is often adequate to permit ESR study.6’7 In this thesis, single—crystal ESR studies of several d7 and d9 complexes of platinum and palladium are reported. These species were produced by high—energy irradiation of the stable, d8 configuration, square-planar, diamagnetic compounds KdeCl4, (NH4)2PdC14 and KthC14 and have been identified from their Spectra. The crystal-field symmetry, coordination, and electronic structure of each species is discussed and compared with related transition metal complexes. HISTORICAL ESR Literature Reviews The literature of ESR studies of transition metal complexes has been reviewed up to 1965 in the Ph. D. thesis of H. A. Kuska,8 and three subsequent reviews by Kuska and Rogersz’Q’10 have continued the coverage up to 1971. McGarvey has written a review of theory11 and Konig has presented a useful general survey of the subject.12 A number of books on ESR have appeared including introductory surveys by Baird and Bersohn13, McMillan14 and Assenheimls; there is also an excellent textbook by Carrington and McLachlan.16 Experimental methods including the design and construction of spectrometers are discussed in several monographs.l7"19 A more advanced text by Ayscough2O and a review by O'Reilly and Anderson21 give up-to—date general treat- ments of the theory and applications of ESR spectroscopy. A comprehensive treatment of transition metal ESR by Abragam and Bleaney1 is the standard reference work on the subject, but a shorter monograph by Orton22 is useful because of a number of examples of typical calculations. Ligand—field theory has been treated by Figgis23 and Watanabe.24 Both the "Annual Reviews of Physical Chemistry"25-28 and the "Annual Reports of the Chemical Society"29’3O provide coverage of recent literature as do the proceedings of current ESR symposia.31"35 Specific topics are reviewed from time to time in the "Advances in Magnetic 36 Resonance" series. ESR Studies of Platinum and Palladium Species Platinum (II) and palladium (II) complexes have played a prominent role in the development of coordination chemistry. For example, the first reported organometallic compound of a transition metal was isolated over one hundred and forty years ago by Zeise. In this. salt, K(C2H4PtCl3), Pt is bonded to the ethylene N system by both a and N bonds.37 In 1893, Werner38 accounted for the existence of two forms (a and B) of Pt(NH3)2012 by postulating that the four-coordinate Pt(II) complexes were planar species and that the a- and B—forms were the trans- and cis- geometrical isomers, respectively, as has since been confirmed by X-ray crystallography.39’40 The trans-effect proposed by Tscherniaev41 in 1926 to rationalize the results of ligand substitution reactions in Pt(II) square—planar complexes was one of the first successful attempts to formulate an inorganic reaction mechanism. Because of this interest in Pt(II) and Pd(II) complexes, a substantial effort has been made to determine the d-orbital energy level schemes in these square-planar compounds from Optical spectroscopy42 and by theoretical calculations.43 The generally accepted d-orbital se- quences in KthCla and K2Pt(CN)4 are, in order of increasing energy, z2 xz, yz, xy, xz-y2 for the chloride42 and xy, xz, yz, 22, xZ-y2 for the cyanide salt.44 ESR provides another tool for determining the relative ordering of the d—orbital levels and at the same time provides information about the electron spin density distribution in the ground state. Paramagnetic Pt3+(d7) has been observed by ESR in single crystals of A1203,45:46 yttrium aluminum garnet (YAlG),47 and BaTiO3.l‘8 In each case the plati- num had inadvertently been leached out of the platinum crucibles used to grow the host lattices by the high-temperature flux technique. In all three lattices, the oxygen atoms form a distorted octahedron around the metal rather than a square—planar arrangement. ESR signals centered at 49 and palladium- g=2.000 have been reported from palladium-doped silicon doped KCl crystals50 but the paramagnetic species are not well defined. , The paramagnetic square-planar bis-maleonitriledithiolene (mnt) anion complexes51 (Pt(mnt)2)1‘ and (Pd(mnt)2)1-, and the related bis- chelate anion complexes (PtS4C4(CF3)4)1- and (PdS4C4(CF3)4)1-, have also been investigated by ESR. There has been a considerable controversy over the interpretation of the ESR and other data for these complexes,52 but they probably are reasonably well represented as d7 Pt(III) and Pd(III) species, in view of the magnitude of the 33S ligand hyperfine interaction observed in the nickel analog,53 rather than as d8, metal-stabilized, ligand-radical systems.54 By irradiation of diamagnetic Pt and Pd compounds with y-rays or high-energy electrons it should be possible to produce new M(I) and M(III) square—planar complexes in which the metal ion (M) has been re— duced to a d9, or oxidized to 3 d7, electron configuration. Indeed, Pd(I) has apparently been produced by X-irradiation of palladium—doped powders of MgO and CaO,55 and recently (Pd(I)(acac)2)1- has been detected by ESR in y-irradiated palladium acetylacetonate.56 The effects of high-energy irradiation are of three main types: changes in valency, changes in the point group symmetry of the species, and bond breaking. In a classic paper on the effects of radiation on transition metal ions substituted in LiF, NaF or KMgF3, Hall et. 31.6 noted that X—rays changed Fe2+(d6) into Fe3+(d5) and Fel+(d7), and in a similar manner Ni2+(d8) was converted to Ni3+(d7) and Nil+(d9). The sc0pe of the irradiation method is evident in the ESR study of X-ray irradiated single crystals of K3Co(CN)6.7 Since the original Co3+(d6) ion is reduced to C02+(d7) while one of the cyanide-metal bonds is ruptured, thereby drOpping the point group symmetry of the anion from octahedral, Oh, to tetragonal,C4v, all three major effects are seen in one problem. No d7 or d9 platinum or palladium complexes showing ligand hyperfine interaction in the ESR spectra have been reported; irradiation of K2Pt014 and KdeC14 accordingly was undertaken in an attempt to produce such species in a form sufficiently stable for study by ESR. This thesis is concerned with reporting the results of these experiments including identification of the products, a discussion of the energy levels and bonding in each new species, and some speculations on the nature of the reactions occurring. THEORETICAL Introduction The solution of the many-electron problem associated with tran- sition metal complexes has not been found exactly. Most of the important attempts to make non-empirical calculations of the eigen— values, eigenfunctions and physical observables for a transition metal complex have centered on the (NiF6)4- cluster in KNiF357'59, because this ion is known to have octahedral symmetry, its optical spectrum has been assigned60 and the fluorine hyperfine splitting has been observed by nuclear magnetic resonance (NMR)61 and ESR.62 Most of the remaining ESR experiments on metal complexes have been interpreted by the spin-Hamiltonian method of Abragam and Pryce.63 In this method a phenomenological Hamiltonian is developed that is restricted to terms containing the electronic-spin and nuclear-spin operators S and I, respectively, which arise in a power series of the form H = 2 z anm (5)“ 6)“ (1) 11:0 m=o where n and m are integers. Equation (1) permits the experimentalist to interpret ESR spectra in a relatively straightforward manner. At the same time, Abragam and Pryce have shown how to estimate the coefficients anm (usually tensor quantities) in terms of basic physical interactions such as the crystalline electric field, spin-orbit coupling, Zeeman energies, nuclear hyperfine splittings and quadrupole interactions. The basis of the calculation is to reduce the total Hamiltonian into segments according to the energy associated with each segment. Then, a sequential series of perturbations is performed in order of decreasing energy of the segments. Low64 gives typical energy ranges for the specific inter- actions as: potential and kinetic energy ~105cm'1, spin-orbit coupling N102-103cm'1, crystalline electric field ~102-104cm51, electron spin-spin interaction mlcm‘l, nuclear hyperfine splitting '\a10"1-10'3cm"1 and nuclear quadrupole effects ~10_3cm—1. In this thesis, the crystal-field approach65 will be followed. The ligands will primarily establish the symmetry and magnitude of the electric field. However, the magnitude of the field will be treated as an adjustable parameter since the optical spectra of the radicals pro- duced by irradiation were not measured. The crystal-field basis set will consist of the real metal 4d, and 5d atomic orbitals for Pd and Pt, respectively, neglecting the closed shells. The physical picture is that of a free metal ion perturbed by its nearest neighbors. Although this is only an approximation, the crystal-field technique has proven valuable in the past for determining the ground state electronic structures of paramagnetic species based upon their ESR spectra.3’6’7’66 The possible d-orbital energy level schemes in (PdC14)2- and (PtCl4)2_, displayed in Figure 1, can be predicted by considering symmetry arguments. In a six-coordinate octahedral field, the five independent d orbitals split into a lower-energy triplet, tzg, and a higher—energy doublet, eg, where the doublet is composed of the d22 and .o ou < Boum waamwuuuaa coauuoumwv Hmcowmuuou wmuuwaoau haamwxm cm sows macaw kuvonmuuo ow aw mflmuwnuo v u>wm ecu mo mcauovuo uapammom .H ounwfim U m < NN v// \\ N>.NX N>.NX Nm—NX.>X / m~ / / \ a / \/ x \ >x / \ / 9m \ / III I I I I / Um \\ NN / x z , \ . p . Nanx / x . w it x / a DNQ \ / \ ONO \ \\ \ IIIIII >X // UP“ - \ \ \ >x «N \ ~5qu ~>I~x «Tax «. 4.an 5‘0 :0 10 de-yz orbitals whose electron density is directed at the ligands; therefore, the doublet is destabilized by electron repulsion relative to the triplet. As one mentally removes the two imaginary ions situated along the positive and negative 2 axis, the d22 and dxz, dyz orbitals are reduced in energy relative to de—yz and dxy. The only point to be determined is to what extent d22 and dxz’ dyz are stabilized. The three possibilities that result as this tetragonal field increases are shown as cases A, B and C in Figure 1. As was pointed out earlier, case C gives the correct energy-level ordering for the parent (PtCl4)2- and (PdCl4)2- ions.42 It seems probable that ESR investigations of the irradiated parent ions will usually only detect the paramagnetic species formed by a one—electron oxidation or reduction of the initial (18 configurations to produce (17 or d9, respectively, since any other metal radicals would have to be created as a result of-a less probable three-electron change. It is also expected that the strong crystal field in the Pt and Pd complexes will require that the radical species have S=%. Therefore, neglecting the small nuclear quadrupole and Zeeman terms, the spin-Hamiltonian that one would expect to apply is m ll IE. 00" (Al + ml 3 HI :2 + ml L'IL (2) where B is the electronic Bohr magneton, and the electronic Zeeman term is linear in both magnetic field and electron spin, while the electron- 2 nuclear hyperfine interactions may be observed for both metal (KM) and ligand (XL) nuclei. Vector quantities are indicated by a single bar over the corresponding symbol while second-rank tensors are indicated by a double-bar overline throughout the thesis. 11 The remainder of the theoretical section will explore the crystal-field calculation of the g and AM tensors consistent with either a d7 or‘d9 configuration and with the three possible axially-elongated tetragonal field energy levels of Figure 1. The ligand hyperfine inter- action tensor, AL, will be treated by the molecular orbital approach. Spin-Orbit Coupling The metal ground state is subject to admixture of various excited states by spin-orbit coupling. The spin-orbit Hamiltonian is given by HLs = 2 6111'51 (3) 1 where Ci is the one-electron spin-orbit coupling constant (always a positive quantity), £1 and Si are the one-electron orbital and spin operators, respectively, and the sum is over the i valence electrons. The eigenfunctions of S2 and 82, where S is the total spin of the system, 6 , are written as |n8m> 7 such that SzlnSm> SzlnSm> s(s+1)|nsH> (4) mInSm> where m is the quantum number for the projection of S along 2 and n specifies information about the radial properties and the orbital angular momentum. The first-order energy correction to the ground state due to the spin-orbit coupling is 12 ELS . z <©Sm| ciii-Ei |osH> ‘ ' (5) 1 - where IOS@> is the ground-state function prior to the spin—orbit inter- action. The modified ground-state wavefunctions are laosfi> = losé> + z z z Ins'mi> . (6) n m' i Eo-En The second—order energy correction is of some considerable interest in the ESR of systems where S>1. One obtains Est = 2 z z z (bSmICiiilsillns'm9* (7) l n m i l,k=x,y,z Eo-En which may be identified with the spin—Hamiltonian term I an éu é: EZLS _ (8) that is, an expression, quadratic in spin, where D is a symmetric tensor. In the lower symmetry, strong crystal fields that often occur in the second- and third- row transition ion complexes, orbitally non-degenerate ground states are the rule. The electrons fill the metal orbitals with Spins paired, but if there is an odd number of electrons the highest orbital will contain a single unpaired electron and the paramagnetic species will have S=k; thus, Equation (8) should not be needed in this thesis since D, the dipolar interaction between two unpaired electrons, is then zero. 13 For a centrosymmetric atom68 the spin-orbit interaction is ; (r1) Ei-Ei = 232 (1.311.) Ei-Ei (9) _r1 3r1 where Vi is the potential arising from the interaction of the 1th electron motion with the nucleus and other electrons, and r is the inter- particle distance. Although many of the common crystal fields are considerably lower in symmetry than spherical, the factor (l—.§!1. r r is proportional to Z/ri3 and this latter term is large only In tie region close to the nucleus where the field is nearly spherical and the simple form of Equation (3) can be used. In complex ions the unpaired metal electrons can be found in the vicinity of the ligand nuclei, a fact confirmed by the observation of ligand hyperfine splittings. These splittings are one of the prime reasons that molecular orbital theory has been used to treat the bonding 69 In this theory, molecular orbitals are in transition metal complexes. constructed from metal atomic orbitals, I¢m>, and ligand group atomic orbitals, |¢L)g which transform in the same irreducible representation. The modified ground-state wavefunctions of Equation (6) will include terms having the following integrals7o <4’LI CIEI'EUIIL) - (10) The Z/r3 dependence of C1 means that the ligand spin-orbit coupling constant must be used in the integrals of Equation (10). The net effect in a molecular orbital description is to introduce terms in the g value 14 that depend upon the ligand spin—orbit coupling constant, especially if CchM. An extreme example of the ligand spin-orbit coupling influence on the g values can be found in the ESR study of (M(V)0X5)2- where M=Cr, Mo and W and X=F, Cland Br.71 When X is fluorine, gII gl, Manoharan and Rogers versal in order of the g-tensor elements to the increased contribution of CL in the case of the heavier ligands. For the Pd and Pt radicals discussed in this thesis CM is considerably larger than §C1=550 cm—1 so neglect of the ligand contribution should not alter the relative order of the g-tensor elements. In 1955 Owen72 noted that CM for metal ions in complexes is approximately 20-30% less than the corresponding free-ion value. He ascribes the reduction in CM to the d-electron delocalization in the molecular orbitals since the Z/r3 dependence will be reduced as the electron orbital is expanded. With CMOCZ/r3 it is clear that a reduction in Z will also pro- duce a reduction in CM. Murao73 correctly predicted that charge donation by the ligand to the metal in the bonding molecular orbitals would lower the effective charge, Z, by partially screening the antibonding electrons from the nucleus. Such effects will be more important for the first members of a transition row because their CM values are more strongly dependent on charge. Thus the results of extended HHckel molecular or- 693 carried to a self-consistent charge invariably show bital calculations that substantial electron density is transferred from the ligands. As an example, a calculation of charge-transfer effects in (Cr04)3- indicates that the metal charge is closer to +2 than to the formal charge of +5.74 In a similar manner, the two Hfickel calculations of (PtCl4)2- 43 both 15 find that the platinum ion probably has a charge close to +1. In the absence of the correct value for the metal charge, it is difficult to decide which free-ion value of CM to use in ESR calculations. Hazony75 has recently discussed the radial dependence of the 3d wave functions of iron complexes based upon Mfissbauer and ESR experi- mental spectra. He concludes that the tzg orbital triplet in octahedral symmetry undergoes radial expansion as the metal ion undergoes complex formation, whereas the eg orbitals contract. Moreover, the degree of radial expansion or contraction is a dynamic property that depends upon the internuclear metal-ligand distance and the degree of covalency. As covalent bonding increases, the expansion of the tzg orbitals becomes the dominant effect. In any event, the r"3 radial dependence of CM suggests that a somewhat different CM is apprOpriate for each separate type of d orbital in a complex. It is common practice in the analysis of ESR data to take the free-ion value of QM corresponding to the formal oxidation state of the metal. In the case of the radicals produced in irradiated KdeC14 and KthC14 one could use the free-ion C values of 1416 cm"1 and 3368 cm"1 1+ 1+ for Pd and Pt , respectively, since charge donation from the ligands will produce metal ions with approximate charges of +1. The above values 76 and are of CM were calculated from the optical data compiled by Moore based on the Russell-Saunders LS coupling scheme.69 However, in this thesis QM will always appear in a perturbation coefficient of the form (c/AE) where AB is a d-d energy separation. Because the optical spectra of the radicals are unknown, and in view of the difficulties noted above in selecting ;, the (c/AE) terms will be treated as adjustable parameters. 16 g Values The spin energy of an electron with a magnetic moment, i, in an external magnetic field, H, is E = -E-fi . (11) The fact that an electron has both spin and charge requires that the magnetic moment be proportional to the spinlé, ie., E = -gB§ = - Y(h/2N)§ . (12) where (h/2N)S is the spin angular momentum, B is the electronic Bohr magneton (lelh/4nmc), e is the electronic charge, g is the spectroscopic splitting factor and the negative sign demonstrates that the negative charge of the electron causes the spin and magnetic moment to be oppo— sitely directed. The quantum mechanical analogue of Equation (11), with the magnetic field in the z direction, is H = gBHzSZ . (13) The eigenvalues of Equation (13) are E = (S‘m'IHz|8é> = gBHzmés'Sdm'm , (14) where 63's is the Kronecker delta; 63's = 0 if S' + S and 63's =1 only if S' = S. 17 The resonance experiment is performed by inducing transitions between the energy states of Equation (14) by means of an oscillating microwave magnetic field which is usually oriented perpendicular to the applied static field. From time-dependent perturbation theory67, the transition probability for induced emission or absorption is proportional to the square of the matrix element of the magnetic dipole moment between the states of Equation (14). The perturbing Hamiltonian for the micro- wave field acting on the magnetic dipole is H = ‘UxHx coswt , (15) where t is the time and w is the oscillation frequency of the microwave field, Hx. If the value of “x from Equation (12) is substituted into Equation (15), P, the transition probability, becomes P a I|2 , (16) 2 where Sx has been replaced by its equivalent ladder operator.67 Then carrying out the indicated operations one obtains ngzHi coszwt P .. {(S(S+1)-m(m+1)) + (S(S+1)-m(m-l)) } . (17) Because the spin wavefunctions ISm> were chosen as an orthonormal set, one arrives at the ESR selection rule 8' = S,m' - mil. Thus, magnetic resonance will be observed when the microwave frequency v is equal to the 18 energy separation between the m and the (m + 1) or (m - 1) states. The Bohr condition then gives hv = Emil -Em = gBH . (18) Angular Variation of the giValue In the most general situation the g value is a tensor quantity. In the principal coordinate axis system of the g tensor, the magnetic dipole term becomes H = 8(gXXHXSX + gyyHySy + gzszSz) o (19) The evaluation of the matrix elements of Equation (19) are facilitated by converting Sx and Sy into their corresponding ladder operators67 to give H = 8{%(gxxHx‘18yyHy) S+ + 5 (gxxHx+18yyHy)S--+ gzszSz} (20) The secular determinant67 for an S = % example where Im = %>’E Im> and Im = 42>; I8) 1s m' “‘ i la) l8) h£> BgZZHZ -E gISXXHx‘igyyHy) 2 (21) I8) £(g H +1 H ) 2 XX X gyy y - Bgzsz ‘E 2 19 Solution of the secular determinant yields E = t 8/2 (ging + ggyflg + ggzflg)SE (22) If H is expressed in polar coordinates with respect to the principal g axes, then the magnetic resonance energy between the IQ) and I8>’spin states is AB = gBH , (23) where g = (gix sin2 6cos2 ¢ + g2 sin2 6 sin2¢ + ggz c0826)15 (24) YY Bleaney77 has treated the angular variation problem in a slightly different fashion. Equation (20) can be written H = (123+ + 13s_ + 1152) . (25) It may be recognized that the spinor78 1132 125+ is an Hermitian matrix operator whose coordinate axis system can be transformed by using a unitary matrix, Q, such that 20 11's,} 12's+' 1132 123+ <2“. (27) II .0 13's- ‘11'82' 13$- -llSz where QdI is the adjoint of Q. Now the transformed matrix of Equation (27) is diagonalized along the magnetic field vector by forcing 11' = 12‘ = O. The Hamiltonian of Equation (25) becomes H = BH11'SZ' , (28) where 11' is identified with g and has the same value as in Equation (24). Even though this exercise seems redundant, it is important for two reasons: Bleaney's technique leads directly to the anisotropic transition probability79 and, of greater interest, this same technique was employed by Bleaney77 to find the angular variation of the hyperfine interaction tensor in the form of an analytical function. Zeeman Effect The Hamiltonian Operator for the total electron magnetic dipole energy in a magnetic field is derived from the Dirac relativistic Hamiltonian.68 The crucial terms are .1 22 -- - ' H = 3;;2’{e A + 2ecA-p + 2e(h/2N)co~ curl A}, (29) 2 where me is the electron rest energy, p is the linear momentum, A is the vector potential and 01 (i = x,y,z), the components of 3, are the Pauli spin matrices. The vector potential of a uniform, unidirectional exter- nal magnetic field is given by80 21 X = - a? x i . (30) After substituting this relationship into Equation (29), the resulting expression can be simplified by vector identities to give a = (eh/4nmc) {(-2ne/hc)(r2fi-(E-N)E) + E + 2§}-fi . (31) The terms in the center brackets are the diamagnetic and paramagnetic moments induced by the external field and since they are quadratic in magnetic field strength, all of the states in the metal-ion ground term are shifted by an equal amount and, therefore, do not contribute to the spin Hamiltonian. The remaining expression is the familiar Zeeman Hamiltonian Hz = 3(I + 2;) - fi . (32) Slichter81 has shown that the orbital angular momentum is quenched for an orbitally non-degenerate ground state (orbital singlet). In other words, the expectation value of the orbital angular momentum over the ground state wavefunction, I£>, is (4411”) = 0 . (33) where ii is the x or y or 2 component of I. When the resonance condition between the orbitally non-degenerate spin states lu>Iand IS> is fulfilled one finds that AE - 28Hz . (34) 22 Comparing this result with the basic ESR equation (Equation (23)) shows that g = 2. Indeed, most organic free radicals do exhibit g values very close to 2, whereas the g values of most paramagnetic transition metal complexes deviate substantially from 2. This fact is of paramount importance to this thesis because it will be shown that the magnitude and sign of the deviation of the g value from 2 allows one to make an assign- ment of the ground state wavefunction. The goal of this section is to calculate the first—order Zeeman energies for an orbitally non-degenerate ground state using the spin- orbit augmented wavefunctions of Equation (6). Recalling the ESR selection rules AS = 0, Am = :1, it is obvious that one need only con- sider the matrix elements between the components of the ground state with different values of m. One then obtains E2 = (yosm"|Hz|a03m> , (35) which yields four terms, the first of which is z 2 HR . (36) k=x,y,z i If Equation (36) is recast into operator form by suppressing the matrix elements of 31k: and remembering that the orbital angular momentum is quenched for an orbital singlet, the first term becomes 22 Z Hksik . (37) k=x,y,z i 23 The second and third terms are equivalent and their sum is given by 282 E E )3 51—13-13- . (38) l,k n m' 1 EO'En Retaining terms to first degree in H and 8, Equation (38) reduces to 28 Z Z E-Z—Eflg <03m"|2,1klnS'm'> (39) n X Z l,k m' i where AEn = Eo—En. Equation (39) is further reduced by the ortho- normality of the spin functions to 7-8 3 ’32 2wé‘lliil?(S'm'I811ISm><0I£1kIn> - (40) l,k n m' i AED Recasting Equation (40) into operator form by suppressing the matrix element (S'm'lsill8m> one obtains CilHkSil 28 2 2 Z (Winch) “—5“— . (41) l,k n 1 En The fourth term has the form 1:12:32 , (42) which is quadratic in magnetic field strength and will be omitted as was done in the reduction of Equation (31). When the first three terms are collected (Equations (37) and (41)) and compared with the leading term in 24 the spin Hamiltonian of Equation (2) the following identification may be made glk=22(61k+ X X i l,k n . _ <43) §P|£11I€> ) AE n . where 81k is the lk'th element of the g tensor and 61k is the Kronecker delta. This result was first obtained by Pryce82 in 1950. It is possible to calculate the g tensor directly from Equation (43), but in the case of strong crystal-field problems it is better to perform the sequential perturbations of spin—orbit coupling followed by the Zeeman interaction. This thesis is concerned only with S=k spin systems so, if Id) and Ié> are the doublet ground state wavefunctions, the principal g tensor elements of Equation (35) can be equated with the tensor elements of the phenomenological Hamiltonian of Equation (21) to give 8xx = 2 i <§I£ix + 2SixIB> gyy = 21 2 <§|21y + 2siy|é> (44) 1 gzz = 2 i ° Sign of the g,Shift It is convenient to define a quantity known as the g shift, Aglk, where Aglk = (Elk-2) - (45) 25 From Equation (43) 2: 22 <0|211In> Yam£(9.¢) . (47) where, as usual, n is the principal quantum number, 2 is the orbital angular momentum quantum number, m2 is the component of 2 along the z axis, R is the radial function, and the spherical harmonics ngz describe the angular portion of the wavefunction. In considering the d orbitals (i=2), the radial portion an is assumed to be the same for each. In magnetic resonance one is interested in the matrix elements of the orbit- al and spin angular momenta which are assumed independent of an. Whenever a radially dependent quantity occurs, the following type of relationship is implied: 26 C1 = (C1) = fo°°R*n251Rn2r2dr - (48) In the absence of detailed information concerning the radial wave- functions radially dependent terms are treated as adjustable parameters to be evaluated by experiment. In the notation for the d orbitals which will be employed in this thesis one writes (22)+ Id22,a:> (22)“ |d22,s> . (49) where a,8 are the spin function and dZZ is the spatial function. The angular portions of the real d—orbitals are (22) = 822 = do (x2-y2) = dx2-y2 = 1//2(d2+d_2) (xy) = dxy = 1/1/2(dz-d_2) (50) (xz) = dxz = l//2(d1-d-1) (yz) = dyz = -1/i/2(d1+d_1) where do = Y20 = /5/16N(3c0326-1) 9:1 = Y211 = /15/8N sinecosee11¢ (51) d+2 — Y2-2 = 715/32n sinzeei21¢ and 22 and d22 will be used interchangeably. 27 As an example of a typical calculation the case of a complex with an axially symmetric g value (gzz = 8|]: gxx ' Byy ' 8L), 8 d7 configura- tion, S=%, the energy level scheme A of Figure 2 and the unpaired elec- tron in dZZ will be examined. The ground state in the hole formalism65 is (dx2-y2)2(d22). The calculation is facilitated by the use of two tables; the first, the effect of the operator E‘E on the d-orbital set of Equations (50) is presented in Ballhausen's bookégb; the second, giving the matrix elements of the orbital angular momentum within the d— orbital set is compiled in McGarvey's reviewll. The zero-order Kramer's doublet is I (xZ-y2)2(zz>+> [(x2-y2)2(22){> (52) I 0+) I 0") where Id> refers to the ground state wavefunction. The first-order improved configurational wavefunction Id> obtained by introducing the spin-orbit interaction (Equation (6)) is IQ) = NI(x2-y2)2(22)£>'+iall(X2-y2)-(Xy)-(Zz)f> -ia1I (XZ-y2)+(XY)-(22)+> 33% (xZ-y2>‘‘+> -ia4/2| (xz-y2)+(y2)+(zz)+> :Z'Z‘I (xz-yz)‘(xz)'(zz)+> —a4/2I (x2_y2)+(xz)+(22)+> 3%‘31I (xz-y2>2(xz)‘> -1/3a3/2|(x2-y2)2(yz)f> , ' (53) where 28 a1 = c/E(0) - E{(x2-y2)’(xy)+(zz)+} a2 = c/E(0) - E{(x2-y2)'(e)'(zz)+} (54) a3 = c/E(0) - E{(x2-y2)2(e)'} a. = c/E(0) - E{(x2-y2)+(é)+(zz)+} . I The orbital, e, can be either dxz or dyz: C is the one-electron metal spin-orbit coupling constant, N is a normalization constant and the denominators are the configurational excitation energies. Normalization gives the equation <§I€> = 1 = N2 + 2a? + ag/Z + aZ/Z + 333/2 . (55) The first—order IS) function is found from I(x2-y2)2(22)€> in a like manner. The Zeeman spin-Hamiltonian expressions of Equation (44) lead to 2 2 2 2 2 2N + 4a1 - a2 + 334 - 3a3 2N2 + 6a3N + 4a? + 2a2a4 g|| EL (56) The obvious problem is that one has five unknowns and only three equa- tions (including normalization). However, the perturbation coefficients, a1, are usually small enough (>O.1) that any product of two coefficients can be ignored. When this is done, Equations (56) become 8II = 2N2 2 (57) g-L =3 2N + 683N 29 Since the g shift (gli2) is due to the excitation of an electron from one of the filled orbitals dxz or d into the partially filled dZZ orbital, yz its sign is positive such that g1) gll = 2. The calculated g values for the other two possible ground states of the Pt and Pd radicals reported in this thesis are shown in Table I with the normalization constant suppressed. TABLE 1.~- g Values calculated from ligand field theory8 Ground State Configuration (hole formalism) g|| gl- 87 (dx2_y2)2(dxy) 2 - 8c/AE1 2 + 2c/AE2 d7 (dx2_y2)2(dzz) 2 2 + 6§/AE3 d9 (dx2-y2) 2 + 8c/AE1 2 + 2c/AE4 a) AEl = E(xz-y2)-E(xy); AEZ = E(xz,yz)—E(xy); AE3 = E(xz,yz)-E(z2) AE4 = E(xz,yz)-E(x2-y2). If there is a low-lying excited state not coupled to the ground state by the spin-orbit interaction the resonance signal will be strongly temperature dependent because of the thermal distribution of electrons between the two orbitals. If the low-lying state is coupled to the ground state, the perturbation coefficients, a1 = g/AE, will be very large. In this situation one must simultaneously diagonalize the crystal- field and spin—orbit interactions to obtain the correct ground state wavefunctions (the g shifts will still be large but calculable). Fortunately neither of these two cases occurs in the Pd radicals. But 30 in the Pt—containing radicals the large spinjorbit coupling constant may require a higher-order perturbation treatment. Tippens83 gives analyti- cal expressions for the second-order spin-orbit coupling correction to the g value. Atkins and Jamieson84 have generalized Tippens' method to insure that the g value remains gauge invariant. Hyperfine Interactions Introduction When a nucleus with a non-zero nuclear magnetic moment, in, is placed in a magnetic field, H, the associated nuclear spin vector, I, takes one of (21+1) quantized values, I, (I-1), °°°°, -I, and the energy becomes HN = ’Un ° H = -ganH-I (58) where 3n is the nuclear magneton, eh/4NMc (M is the proton mass), gn is the nuclear g factor and I has all of the properties ascribed to a gener- alized spin angular momentum. The hyperfine energy term S°Z~I (Equation 2) arises from the mutual interaction between the nuclear magnetic moment and the spin-plus- orbital magnetic moments of the unpaired electrons. This interaction may be viewed in two equivalent ways: either the electrons produce a magnetic field at the nucleus thereby lifting the (21+1)-fold nuclear spin degener- acy; or, the nucleus produces a field at the electron that adds to the external magnetic field. From either point of view the magnetic field at the electron, which is being examined by the ESR experiment, has (21+1) values. The ESR selection rules A880, Amatl state that the quantum of 31 angular momentum imparted by the microwave field is used to "flip" an electron spin and as a result of the conservation of angular momentum I cannot be simultaneously changed. Thus the ESR spectrum will show (21+1) lines of equal spacing and intensity since the nuclear energy levels are essentially equally populated. If the electron interacts with n magnetic nuclei of spin Ii, the number of lines becomes n (211+1)(212+1) ~.-- (21n+1) = n (211+1) . (59) i=1 while the relative intensities can be found by summation. Should j nuclei of spin I be magnetically equivalent, the combined nuclear spin _ 3 vector is I = 211 and the j nuclei produce (2jI+1) lines. The scizi and utility of the structural information from the hyperfine splitting is now apparent. One can often identify radicals by the number and intensity of the lines in the ESR spectrum. The nuclear spin of previously unexamined isotopes can be determined or, alterna- tively, if I is known, then the magnetic moment can be estimated from the hyperfine splitting. The extent of covalent bonding may also be judged from the magnitude of the interactions. The Hyperfine Hamiltonian The objective in this section will be to develop two expressions for the hyperfine interaction. It is desirable to have a phenomenol- ogical spin Hamiltonian (Equation 1) that will allow the spin parameters to be easily extracted from the experimental splittings. It is also desirable to have an equivalent Hamiltonian expression that is directly 32 related to the basic physical interactions which can then be used to give a molecular structure interpretation to the splittings. This latter expression can also be used to identify the ground state or confirm the identification made from the g values. The relevant portion of the Dirac equation for a one-electron atom in a magnetic field 1365268 an = e/mc {Z . 5 + (h/ZN) a - 6 x X} . (so) .The vector potential A for the nuclear dipole is given by80 A = in x r/r3 (61) where r is the distance between electron and nucleus. Substitution of Equation (61) into Equation (60) yields {_—___<‘7‘§>'i + “imfih (62) r 1'5 Hn = 8e8n88n where as before I is the orbital angular momentum for a single electron, § is the spin angular momentum for a single electron and ge = 2.000. This dipolar Hamiltonian integrates to zero for the spherically symmetric s orbitals which is fortunate, since a singularity develops in Equation (62) when r = r0 (r0 is the nuclear radius); yet, p, d and f electrons that do exhibit dipolar hyperfine interactions have nodes in their electron distributions at the nucleus. The fact that s electrons show an isotropic hyperfine splitting is attributed to the Fermi contact interactionl'22 which may be written 33 Hf = (an/3) gegnsen|w(0)I2 ' (63) where I‘I’(0)I.2 is the s-electron spin density evaluated at the nucleus (r=0) for the orbital W. In operator form the contact term becomes Hf = (aw/3) gegnsen 6(?>i-§ (64) where the delta function requires that r=0 for the integration over the electron coordinates. The total hyperfine Hamiltonian is -Hh = Hn + Hf = SegnBBn {if§§2.+.212:§25.. (8w/3)6(E>§}-i . (65) Additional unpaired electrons and/or nuclei can be included in Equation (65). If Equation (65) is expanded into its components, the result can be represented in tensor form by ah = a-K-i' (66) where E is a symmetric tensor. Equation (66) is the phenomenological expression used to interpret experimental spectra. Abragam and Pryce63 have cast the hyperfine Hamiltonian into a form that is more convenient for computing matrix elements. Within states where L, the total orbital angular momentum, is constant, which includes the ground state and lowest—lying excited states, the Cartesian coordinates of Equation (65) can be replaced by appropriate orbital angular momentum operators. The validity of this replacement is based on the Wigner-Eckhart theorem.81 Proper combinations of the (x,y,z) 3:. coordinates are related (apart from a constant) to the spherical harmon— ics whose rotations are covered by the Wigner-Eckhart theorem. The angular momentum operator equivalent must transform in the same way as the combination of Cartesian coordinates assuming that allowance is made for the non-commutivity of 1x. 1y, and 12; for example, xy transforms the same as 3(1ny + lylx). The constant of proportionality is determined by evaluating the same matrix element for both forms of the Operator. In this manner Abragam and Pryce showed that the hyperfine Hamiltonian for a single electron is “I. = gegnBBn (r3) {E-i - «5.2) + £2(2+1)(§~I) —3z/2(I i) -3a/2} (67) where €=2/ (22+3) (22-1) is the constant of proportionality, is the expectation value of r"3 over the radial portion of Hh and K is the s- orbital contribution to the hyperfine interaction and is defined by (Bu/3)6(?) ‘ a , 68 K (If-3) ( 7 The utility of Equation (67) is now apparent. The involved integrals have been replaced by simple algebraic relationships depending upon the well-known matrix elements of angular momentum operators. Isotr0pic Hyperfine Interaction One of the most striking hyperfine interaction problems is found in the case of half-filled d-shell ions such as high-spin an+ (with con- figuration 3d5 and ground state 6S) in an octahedral crystal field where 35 no hyperfine splitting would be expected. With L=O there should be no orbital contribution to the hyperfine splitting while the spherical symmetry eliminates any dipolar contribution and the absence of half- filled s orbitals rules out splittings arising from the Fermi contact term. Yet, an appreciable splitting is Observed and this splitting is 87:88 of the inner s electrons. Thus. an attributed to core polarization unpaired d electron with its spin up i will have different electrostatic repulsion and exchange interactions with inner s electrons whose spin is up + than with those whose spin is down I . In the conventional Hartree- Fock closed-shell calculations the spin properties of paired electrons are exactly equal, but opposed in sign, leading to a net cancellation of spin density at the nucleus due to filled s shells. The Hartree-Fock 87.83 does not have this restriction, method employed by Watson and Freeman so that electrons with the same values of the n and A quantum numbers but different values of the ms quantum number are allowed to have different radial wave functions. The result is that the s-orbital core electrons may be polarized to give a net spin at the nucleus which has a sign Opposed to that produced by the unpaired d electron. Any spin density at the nucleus contributed by s electrons in the valence shell, or further removed from the nucleus than the d level, yields a core polarization term of the same sign as that of the unpaired d electron. Although these spin density differences are quite small, the contact hyperfine inter- action for a single 5 electron is very large and produces isotropic splittings which usually dominate the observed metal hyperfine splittings. As a measure of the core polarization, the parameter x is defined as the unpaired spin density at the nucleus per unpaired electron: x = 411/28 £II¢1+(0)I2 - I‘M-(0H2) 1 (69) 36 where I¢1+(O)I2 is the positive spin density (m=+%) in the 1th 3 oribtal evaluated at the nucleus and S is the total spin of the system. Pre- dictions of x and by spin-unrestricted Hartree-Fock calculation887’88 have been quite successful despite the fact that x is the sum of several large terms which may have Opposite signs. This success is particularly surprising since the calculated metal hyperfine interaction energies are approximately 10'2cm-l approximately 105cm'1. , while the total energy Of the complex ions is McGarvey89 has summarized the experimental trends among values of x. He shows that x gradually decreases across a transition series from -2.0 atomic units (an) to -3.4 an as one goes from a 3d1 to a 3d9 con— figuration. Similarly x runs from -4.0 to -9.0 an across the 4d series and from -10 to —15 au across the 5d series. Experimentally x is related to K by (see Equations (68) and (69)) K = -(2/3)x . (70) A number of workers have shown that K is relatively constant for a given metal ion in a variety of complexes. However, as the complexes become more covalent the unpaired electron becomes more delocalized and decreases while x approaches zero, a result supported by McGarvey's89 compilation. This linear correlation of x with covalency is observed for d1, d3, (15 and d7 cOnfigurations. 2+ In the case of the (19 configuration, particularly Cu complexes, the linear correlation of x with covalency breaks down implying that K is 90,91 not constantgo’gl. Kuska st 31. attribute the lack of correlation in copper complexes to a small admixture of 4s electron density into the 37 ground state. They believe that molecular vibrations reduce the symmetry restrictions which prohibits direct mixing of 43 with the dx2_y2 ground state 89 says that spin density is induced orbital. On the other hand, McGarvey into the 43 copper orbital by exchange interaction with the ligands. Recently McMillan92 has discussed the contribution to the metal core polarization induced by unpaired spin density on the ligand nuclei which will increase with increasing covalency as one goes from the 3d to the 4d to the 5d transition series and as sigma bonding between metal and 8 ligands increases. Therefore, ions with d9 or d configurations, or a strong-field (17 configuration, where the unpaired electrons are in pre- dominately o—type orbitals will experience "anomalous" core polarization and x cannot be easily correlated with covalency. In certain point-group symmetries, it is possible for one of the d orbitals to belong to the totally symmetric irreducible representation as do the s orbitals. Mixing can then take place between the nd and (n+1)s orbitals and, as noted earlier, spin density in s orbitals in the valence shell (or beyond) will cause x to become more positive. For example, (CO(II) phthalocyanine),65 which has a low-spin 3d7 configuration of D4h symmetry with the unpaired electron in a (3d22 +43) hybrid orbital, has an isotropic hyperfine field at the nucleus of x=+2.2au where as the great majority of 3dn ions have negative values of x clustered about a value of -3 an. The reason for the extensive discussion of x is that in this thesis two of the three possible ground states of the Pt and Pd radicals have either d9 or low-spin d7 configurations. Since the molecular orbitals containing the unpaired electrons form o-type bonds with the ligands, these ground states are the ones most likely to exhibit "anomalous" core polarizations. The consequences are: (1) the magnitude 38 and even the sign of x cannot be assumed to agree with that calculated from spin—unrestricted Hartree-Fock calculations for the metal ions since those are based solely on dn core polarization; (2) the inability to interpret x restricts the use of hyperfine splittings to assign the ground states of the radicals; (3) x (or K) cannot be used to estimate the degree of covalency. Because the isotropic hyperfine splitting, as measured by -gegn88n K in Equation (67) , does not necessarily follow changes in (K3), the hyperfine Hamiltonian in this thesis will be written uh = «(E-i) + pal-'1') + 52(2+1)(§o'1') _ - _ _ _ _ _ _ (71) -3/2§(2-s)(£-I) —3/2g(2-I)(2-s)} where P = gegnBBn and K now has units of energy. In the ESR literature of transition metal complexes, energies are usually expressed in units of cm'l. To find x in atomic units from K (cm-1) the following equation89 is used: x(au) = -3/2(hcag/gegnBBn)K(cm'1) (72) where so is the Bohr radius. Analysis of Metal Hyperfine Interactions For transition metals Equation (71) may be transformed by putting £=2l21 since, for d electrons, i=2. In the crystal-field approximation, (:r‘3>h is assumed to have the same value for all of the valence d elec- trons and one obtains 39 “I. = «(I-Sol") + 1303 + 5/7»? (73) where a = 4§ -(I°§)E - E(I-E). The relationship between the experimental principal A values (Equation (66)) and the principal values of Equation (73) can be determined by examining the corresponding matrix elements between the ground state spin wavefunctions Ii) and Id> (@I-KSZIZ+P(£z+az/7)IZI€> (74) and Azz/2 <§IIzIé> (bl-KSZ+P(£z+az/7)I€>> <6I12I€> (75) or -K + 2P <§I£z + az/7I€> and similarly —K + 2P (bllx + ax/7Ié> (76) W - -.< + 21? (ally + ay/7IB> . :> I The calculated hyperfine splitting values for the three possible ground states of the Pt and Pd radicals studied in this work are reported in Table 2 based upon an axially symmetric hyperfine interaction tensor (Azz = All, Axx = Ayy = A1} where the unique axis is z). The ground state wavefunctions I€> and Id) are the same spin-orbit augmented functions used earlier to calculate the g values reported in Table 1. 40 mmoo.~ -.4w n.aw< muoo.~ I __w u __w< mamas 3.38:: + 28m + or MES)” + :3 + 26:: + V? Amsumxev me mawasa\ma + K\~-Va + g- AaNawa I K\3Va + y- Amuevaamsumxev as mum/ES: + Cu: + 6.: 2.9:? + :3 + 2.7: + V... ARENANTNxB as .Aw. __< hamaamsuom OHosv cowumuswfimcoo Oumum vapouu H Oohum was Bowmun< mo >uomzu Ozu mp wmumasoamo A - a'l¢L(x2-y2)> I") = Bldxy> - B'|¢L(xy)> ' (77) IW1>=81Idxz yz>" BII¢L(x2.y2)> where the ligands lie along the tx and iy axes. The I€> orbital contains the unpaired electron and ¢L(x2-y2), ¢L(xy) etc. are the symmetry-adapted wavefunctions constructed from linear combinations of ligand atomic orbitals. The squares of the coefficients represent the electronic spin density in that atomic orbital. If a2 = 0'2, the covalency is maximized 2 since the electron spends equal time on the metal and ligands. As a +1, the electron is more nearly localized on Cu2+ and the bonding is more nearly ionic. The value of a2 can exceed unity depending upon the value of the overlap term found on normalization, eg., 1 = oz + 6'2 - Zaa'S (78) where S is the group overlap integral. The ESR spectra of the Cu2+ complexes can be fitted to the following axial spin Hamiltonian: = g] IBHzSz+giB(HxSx+HySy) + Al IIzSz+Ai(IxSx+IySy) (79) 42 which gives All = -K -(4/7)a2P+Ag|IPZ||+(3/7)A§1PEL’ , AL = -K +(2/7)62P+(11/14)AgLP2L 2" = aBi{qu -a'els—aa'<1-e§>kr(n)} El.= OB'IOB —O'BS-(1//2)a'(1-82)kT(n)} I (80) s = (Hx2_y2I¢L(x2-y2i> I T(n) = n-(I-n2)%égh8(zpzs)5/2(zs—zp)/(zs+zp)5 Agll = gII - 2.0023 Agi = gi — 2.0023 where Zp and Z8 are the effective charges for p and s electrons on the ligand, R is the metal-ligand internuclear distance and n2 is the fractional p character of the ligand orbitals making up ¢L(x2-y2). Often, as in the case of the Pt and Pd radicals, there is a lack of good wave functions, information about effective charges, spin-orbit coupling con- stants and excitation energies which prevent one from using the complete expressions of Equations (80). McGarvey points out that by setting 2" = 2L.- 1 Equations (80) reduce to the much simpler pair All = -K +P(-4/7a2+Ag||+3/7Ag1) (81) 21.: "K +P(2/7a2 + 11/142gL) . 43 Fortunately substitution of experimental values of A||, Al, Agll, AgL into Equations (81), along with a value of P based on from unre- 2 stricted Hartree-Fock calculations, leads to values of a and K(Or x) that are substantially the same as result from more extensive treatments employing Equations (80). Angular Variation of the HyperfineSplittingli93.94 For a microwave frequency of N10,000MHz (X-band), the Zeeman energy is E/hc 2 0.3cm-1 . (82) Using the point-dipole approximation, the hyperfine interaction energy is about E/hc « (BBn/hcr3) = 0.004cm’1 (83) O where r is taken arbitrarily as 0.5A. In terms of magnetic fields, the external field at X-band when g=2 is approximately 3600 Gauss at reso- nance. Again, within the point-dipole approximation (r=0.5X), the magnetic field at the nucleus due to the electron is an a e/r3 = 80,000 Gauss (84) while the field at the electron due to the nucleus is Re « Bn/r3 = 40 Gauss . (85) 44 These observations illustrate the so—called high-field approximation in which the larger energy Zeeman term is diagonalized with the electron spin quantized along the external field. The smaller hyperfine term is treated next with the nuclear spin quantized along the resultant magnetic field which is primarily due to the field produced by the electron. Consider the following Hamiltonian: Hz = BEE-'3' . (86) If the unit vector 5 along the external magnetic field direction (H=Hfi) has direction cosines cosasinB, sinesinB, and cos B with the (x,y,z) principal axes of the g tensor, then the energy eigenvalues are E = gBHm (87) where m is the projection of S along the magnetic field direction and 2 yysinzosinZB + ggzcoszB (88) g2 = (n §)(§-fi) = ggxcoszesinzs + g and one obtains (28+1) equally spaced levels of interval gBH. Since the experimentally determined g tensor will always be positive and symmetric, no information is lost by dealing with the g2 tensor. The orientation of the g-tensor axes is not usually known beforehand so one chooses a right- handed Cartesian coordinate system (1,2,3) located in the crystal (Often the crystallographic axes). Then the unit magnetic field vector 3 has direction cosines cos¢sin6, sin¢sin6 and cosO with the chosen crystal 2 axes and g becomes 45 2 2 2 2 g = sin 9(G11cos O + 2G1251n¢cos¢ + Gzzsin O) + 23in6cosO(Gl3cos¢ + G23sin¢) + G33cosze (89) 2--tensor elements in the (1,2,3) axis system. where the G13 are the g To evaluate the tensor it is usual to perform three mutually perpendicular rotations of the crystal in the magnetic field and if the three rotations are made about the orthogonal crystal axes (1,2,3) one obtains 2 g = ngsinze + 2623sin6cosO + G33cosze for rotation around 1, since 0 = N/2 and H is in the 2-3 plane; g2 = G11 sin26 + 2613sin6cose + G33cosze (90) for rotation around 2. Since 0 = O and H is in the 1-3 plane; and 2=c 12 2 .2 g 118 n ¢ + G13sin¢cos¢ + G2251n O for rotation around 3, since 6 = N/2 and H is in the 1-2 plane. As Schonland94 has noted each of these equations is of the form g2 = a1 + 81 cosZOl + 71 sin261 (91) (for rotation about axis 1) where 46 a1 ' 3(033 + G22) 81 = 5(033 - G22) Y1 = G23 with similar results for the other two rotations. As the magnetic field makes its excursion there will be a maximum and a minimum in g2 in each of the three planes. If gi and g3 represent the extrema in each plane, there result six equations in the six independent tensor elements Gij- In each plane two unique parameters arise a=afi+g5 (92) 6 = Mg}. - 33) and it may be shown that the g2 tensor elements are G11 = (012 + a3 - 0:1) (93) 612 = t{(03 + 01 - 02)(03 - 01 - (12)}g5 . Cyclic permutation of the indices will give the other four elements. The g2 tensor can be diagonalized by an orthogonal (similarity) transformation to give the principal values gfix, 33y and ggz as follows: I» I-1 (lkicidljk = 8§k513> (94’ where (lki) a (11k).1 are the orthogonal direction cosine matrices re- lating the experimentally chosen crystal axes (1,2,3) to the principal g axes (x,y,z), and 613 is the Kronecker delta. 47 If the Hamiltonian now includes the hyperfine interaction, and the principal axes of the hyperfine tensor coincide with those of the g tensor, then H = BH for the 3d87, 4d88 and 5d transition metal ions. Ligand Hyperfine Interactionsl’85 Ligand hyperfine splittings provide the most striking demon- stration of covalency in transition metal compounds and also provide the best criterion for finding the extent of covalent bonding. There are two alternate theories for picturing the ligand hyperfine interaction. If one examines an isolated metal-halogen bond composed of two paired 50 p—electrons on the ligand and one unpaired electron on the metal, the two approaches may be compared. In the molecular orbital (MO) approach two orbitals 0A and OB are constructed: , IPA a NA(d"AP) and ' (100) ¢B " NB(P+Bd) . The lower energy p electrons on the ligand constitute the major component Of the bonding orbital OB while the singly occupied antibonding orbital ¢A is largely the metal d atomic orbital. NA and NB are the normalizing coefficients (NA=NB=1) and A and B are small admixture constants. After bond formation the bonding orbital drops in energy below that of the original atomic p level and the antibonding orbital is raised in energy above that of the atomic d level, but the net energy of the system is lowered. Normalization gives NA . (1-2As+1\.2)l5 (101) N3 =- (1+212.s+132)15 where S = . The orthogonality condition yields <¢AI¢B> = o = B-A+S-ABS (102) and by neglecting the small term ABS, one obtains A - B+S . (103) 51 There is a fraction N%(B2+BS) of two electrons transferred from the negatively charged ligand to the positively charged metal via the bonding function 63. A fraction Ni(A2—AS) of one electron is transferred in the Opposite direction via the antibonding orbital to give a net electron transfer Ni(A2-AS) from p to d. Since the orbitals with Spin up + are each singly occupied, the only measurable electron transfer is that associated with the bonding electron with spin down +, or alterna- tively with the antibonding hole with spin up +. Because the hyperfine interaction drops off as 1/r3 the overlap contribution is small and the fractional spin density transferred to the ligand is f = AzNi . (104) That is, the transferred spin is just the square of the antibonding ligand coefficient. In the configuration interaction (CI) approach the ionic nature of the complex is emphasized. The ground state is considered to be (M+n)(L') and the wavefunction is a many-electron Slater determinant a +-+ Wg = (3) Ipde (105) where the spin is represented by the superscript + or - for m = ik. A small amount of the excited state consisting of (Mn-1)(L°), where the ligand has completely transferred one electron with spin down + to the metal, is admixed into the ground state by configuration interaction leading to a new wavefunction 9g - N(9g + owe) (106) 52 +_+ where N=1, C is small and We = (3)8IpddI. The fraction of unpaired spin on the ligand is f = CZNZ , (107) a result that is formally analogous to the MO method. In the past decade, the relative merits of the molecular orbital and configuration interaction methods have been explored by performing a host of non—empirical calculations on the (NiF6)4- "cluster" ion. In the "cluster" ion approximation, the remainder of the crystal is ignored except in that it creates a Madelung-type electrostatic potential at the ion. Table 3 gives a comparison of the 10Dq, fo(%) and f3(Z) values determined experimentally with those calculated from the crystal-field (CF), molecular orbital and configuration interaction theories. 10Dq for (NiF6)4- is defined as the energy separation between the ground (t6e2)3A2g state and the first excited state (t5e3)3T2g. TABLE 3. -- Comparison of calculated with experimental parameters for (N1F6)4' Method 10Dq(cm-1) fo(%) fs(%) Reference Experiment 7250 3.8 0.5 (1963)60’61 Calculated CF 1514 (1970)57 Calculated CF -3572 (1971)58 Calculated MO 2800 1.0 0.3 (1964)97 Calculated CI 5400 2.9 1.0 (1966)98 Calculated M0 6089 4.8 0.4 (1970)57 9 Calculated MO 7210 3.3 0.4 (1971)5 53 The crystal—field calculation gives values of 10Dq too small and can even reverse the known energy levels. Earlier calculations seemed to favor the CI approach over the M0 technique. However, larger and faster computers have allowed workers to include the closed shell orbitals, to calculate directly the energies of excited states and explicitly include three- and four-center integrals. Thus, recent MO calculations have shown good agreement with the experimental observables. The successful MO calculations are appealing to chemical intuition because complexes such as the dithiolate compounds,53 where = 50% of the unpaired spin density is on the ligands, are difficult to picture in the CI framework. Also, the bulk of experimental ESR results has been analyzed by the MO tech- nique; therefore, the MO scheme will be followed in this thesis to analyze the ligand hyperfine splittings. Sample Calculation The analysis of ligand hyperfine splittings in the complex ion (PdCl4)3- will serve an example. The ion is assumed to have the same square-planar arrangement of chlorines about the central metal atom as in the parent (PdCl4)2- ion. The ground state in D4h point-group symmetry should be (d9)ZBl with the unpaired electron in the dx2_y2 orbital. A metal coordinate axes system (XYZ) for this radical is defined so that the Z axis is the unique C4 rotation axis. Each chlorine nucleus is assumed to have its own local right-handed Cartesian coordinate system (xyz) with each x axis directed toward the metal atom (Figure 2). The blg antibonding orbital containing the unpaired electron is Iblg) = aIxz-y2> - 1501' I01-02+O’3-O’4 > (108) 54 .I @3me a mac . a . m V a on As a xv pamwaa pan AN.» xv Hmuma mom amumuw mwx¢ .N oupme 55 where the chlorine O orbitals are I01> = nI3px>1 + (1-n2);’I3s>1 . (109) Normalization gives 1 = 02 + a'2 — 4aa'S (110) where S is the overlap integra1¢A The ligand hyperfine spin Hamiltonian for the o orbitals is expected to be axially symmetric with the x axis being the unique axis: HL = AIISxIx + Al(sny + szIz) . (111) By symmetry, it is possible to focus attention on one of the ligands and simply multiply the spin density obtained for that ligand by four to get the total transferred spin density. The expectation value of BL for blg retaining only those terms containing 01, is lib-11> 2 (blgIHLIb1g>= -aa''2IHLI01>+ %'<01IHLI01>+' 5%. <°jIHLI°1>~ j 2 (112) The third term, involving integrals of C11 with the other three chlorine nuclei, is dropped because the r"3 dependence of the hyperfine splitting makes the term vanishingly small. The first term would be dropped for the same reason except that the coefficient a is large; that is, the majority of the unpaired electron density resides on the metal. To the ligand nucleus, the spin in de-yz appears to be concentrated at the 56 metal nucleus and the interaction behaves as a direct dipole term which can be written Hd = Ad(2$xIx"Sny‘SzIz) (113) where Ad = ggn88n R'3 and R is the metal-ligand distance. The second term is evaluated with the hyperfine Hamiltonian of Equation (71) where i=1, g=2/5, P=gegn88d3p for a chlorine 3p electron and the (I-I) contribution is zero for an orbital singlet. There results HL = —t(§-i)-3/5P{-4/3(E-i)+(E.§)(Ioi)+(I-i)(I.§)} . (114) The components of the second term for S=2 are 12 2 %‘ <01+I (HL)XI 01+) '2 22 %’ (bl'l{(n2-1)K— —%—'P}snyI01£> (115) <91’I(HL)yI01f> 2 12 2 = %‘ <§1'|{(n2-1)K- —%‘P}szIz|oI£> If one adds the direct dipole term of Equation (113) to Equation (115) and compares corresponding elements with the phenomenological Equation (111), one finds A'I = A8 + 2(Ap + Ad) (116) 21.: AS - (AD + Ad) , 57 where (117) All and Al are known experimentally, and Ad can be calculated if R is known, hence AS and Ap may be computed readily. The transferred spin densities to the first chlorine are As a'2 f = ——'= —' (1-n2) 5 A3 4 (118) f _fp=n201'2 p 11.3 4 ’ where 8 _ _ Agc3501) = (—§)gegn88nlw3s(o)|2 = 1570 x 10 4cm 1 (119) Ag(35c1) = (2/5)gegn88n<}'3)3p = 46.75 x 10"‘Icm'1 are Obtained from I‘I’33(O)I2 and 3p which, ‘in turn, have been taken from the Hartree-Fock calculations for free chlorine atoms with con- figurations (3S3p6) and (3823p5), respectively.99 The coefficients n2 and 0'2 are also obtained, as is the hybridization ratio p/s = n2/(1-n2). The most serious approximations in the ligand hyperfine inter- action are: a) Core polarization of the chlorine Is and 25 orbitals by the unpaired electron spin in the 3px orbital has been neglected b) C) 58 and the entire isotropic hyperfine component has been attrib- uted to spin density in the valence shell 3s orbitals.100 This suggests that only the anisotropic ligand term should be used to estimate spin densities and covalency just as was done in estimating covalency from the metal hyperfine splitting. Since the chlorine is essentiallyCl', I‘l’38 (O) I2 and 3p should be evaluated for the ionic species.101 However, in this thesis the usual convention of taking I‘l’3s(0)l2 and 3p from the Cl0 wavefunctions will be followed. This facilitates making comparisons with ESR studies in the literature. The point-dipole correction, Ad, is only the leading term in a multipole expansion and is only rigorously correct for a spherical electron charge distribution on the metal102 (132,, a half— or completely—filled shell). EXPERIMENTAL ESR System The ESR system and the techniques employed have been discussed in the Ph.D. thesis of Kuska.8 The measurements were performed on a Varian Associates (VA) X-band, Model V-4500-1OA ESR spectrometer with IOOkHz modulation and a 12—inch VA electromagnet. The magnetic field was measured with a marginal—oscillator NMR probe103 and the resulting NMR proton frequency was counted on a Hewlett—Packard (HP) Model 524C electronic counter. The magnetic field for protons in a water sample is calculated from the following equation: H(Gauss) = (2.3487465 x 10'4)v(Hertz). (120) Microwave frequencies were measured by either a calibrated TS-148/UP U. S. Navy spectrum analyzer or with a Hewlett-Packard Model 5245L frequency counter equipped with a Hewlett-Packard Model 5257A transfer oscillator. All of the spectra were recorded on a Moseley XY recorder. 59 60 Sample Preparation Samples of K2PdC14 and (NH4)2PdC14 were Obtained from both Engelhard Minerals and Chemicals and the Matthey Bishop Company. KthC14 104 to give was prepared from platinum metal by oxidation with aqua regia HthCl6, and K2PtC16 was then precipitated by addition of KCl. The K2PtC16 was reduced with hydrazine hydrochloride to give K2PtCl4.lOS All residues were saved and reworked when necessary. Single crystals were grown from slightly acidified (HCl) aqueous solutions Of the salts by using seed crystals. K2Pt(CN)4:3H20 was prepared from K2Pt014 in aqueous solution by addition of KCN followed by filtration and repeated recrystallizations from water solutions. Single crystals were grown by slow crystallization from.water solution and had to be stored in a high-humidity atmosphere to prevent loss of water. The bromine bridged complex, tetraethylammonium tetrabromo-uu' dibromoplatinum II, (N(C2H5)4)Pt2Br6106a was prepared by the method of Harris g£_§l,106b and single crystals were grown from acetone solutions of the salt. Crystal Structure of K2(Pd,pt)314107 K2PdCl4 and KthCl4 are isostructural: the space group is D4h- O O P4/mmm with Z=1 and a0 = 7.04A, Co = 4.103 for Pd and a0 = 6.98A, o co = 4.13A for Pt. Each metal atom is surrounded by four equivalent o chlorines at a distance of 2.33A. These square-planar units are stacked along the c axis in alternate lamellae with the potassium cations 61 (Figure 3). The crystals almost always grow as rectangular needles with the c axis the needle axis and (100) and (010) forming the faces. Irradiation Methods Crystals suitable for irradiation (approximately 2 x 2 x 4 mm) were optically selected with the aid of a polarizing microscope with crossed Nicol prisms. In this manner, crystals that were twinned or had large imperfections could be discarded or cleaved perpendicular to the c axis. Crystals to be irradiated with the 60CO y-ray source were placed in glass vials and immersed in a Dewar of liquid nitrogen. The 60Co Dewar was placed in the center of the Michigan State University y-source and subjected to 6 x 106 rads. Crystals to be irradiated by electrons were placed in Saran-wrap Containers which were buoyed up by foamed polystyrene balls weighted to just float on liquid nitrogen in a Dewar. If the crystals were allowed to sink in the liquid nitrogen the electron beam was severely attenuated. The Dewar was placed approximately four inches below the tip of the l-MeV electron source at Michigan State University and then subjected to a dose rate of 3 x 106 rad/min for three minutes. A lower dosage gave a reduced paramagnetic signal intensity whereas doses above 3 x 107 rads produced appreciable crystal fracture and crumbling. The same crystal could be reirradiated at least twice before the physical damage was too severe to allow handling without breakage. Experiments were conducted to measure the change in the ESR spectra of y-damaged crystals upon exposure to ultraviolet irradiation. The beam Of a General Electric BH6 mercury lamp was focused through the 62 .eaoummx use «Hopmwm mo oupuosuum Hmummhu .m mupmfim 63 port of a VA Model V—4531 general purpose ESR cavity and onto the crystal which was cooled to liquid nitrogen temperature (both the lens and Dewar were quartz). Sample Handling The sample handling technique was similar to that used by Kispert.108 Because of the temperature sensitivity of the paramagnetic radicals formed in irradiated crystals of K2PtCl4 and K2PdC14 (no radicals remain at room temperature), sample transfer, mounting and other manipulations of the crystals were all performed under liquid nitrogen. The crystals were clamped between two brass clips which were glued to the end of a quartz rod and then the entire assembly was immersed in a glass Dewar filled with liquid nitrogen. The bottom of the Dewar had a quartz finger of the prOper dimensions to just fit into the Varian Associates general-purpose, T102 mode, X-band cavity, Model V-4531. The rod was held centered in the Dewar by a cylindrical foam insert at the top of the Dewar while the sample was centered vertically in the cavity until the signal was maximized. The initial setting of the crystal in the plane of rotation was done by visual alignment of the external crystal faces with the quartz rod. This alignment was refined by phys- ically reorientating the sample. The oscilloscope mode of signal diSplay was also used occasionally to refine the alignment or to find a principal axis of the radical. The angular variation in each plane Of rotation was measured by either rotating the Dewar in the cavity and measuring the angle of rotation on a machined protractor or by rotating the calibrated magnet. Normally, three independent planes of rotation are employed to 64 obtain the magnetic tensors; however, in this case, the high degree of crystal symmetry reduced the necessary rotations to two. Accordingly, the spectra were recorded at 100 intervals with the external magnetic field in the ac and aa' planes. Error Analysis The error introduced into the measured g values may be estimated by taking the total derivative of g = hv/BH dg = (3g/3H)VdH + (8g/3v)Hdv (121) which reduces to Ag = ig(I2AH/HI + IAv/vI) (122) where the factor of two arises because the magnetic field must be measured both up and down field from the center of the pattern. The proton resonance from the marginal oscillator provides an absolute field measurement limited by the precision of the fundamental constants and the accuracy of the HP 524C counter (:20 Hz). At a microwave frequency Of 104 MHz and a g value of 2, the proton resonance will occur at approxi- mately 15 MHz :20 Hz, a very small percentage error compared to that arising from the field inhomogeneity. Since the water probe of the marginal oscillator was located outside the cavity on the magnet pole face it was important to estimate whether the field at the sample differed from that at the NMR probe. For 65 this purpose a dual-probe assembly was constructed which permitted a comparison of the field at the two positions; this revealed a field difference of about 0.25 Gauss which was neglected. The error in frequencies measured with the spectrum analyzer is less than 10.5 MHz. Thus, for a spectrum centered at g - 2.00 with H==3500 Gauss and v (microwave)==10,000 MHz, Equation (122) gives Ag==i0.0001 . (123) A larger error is introduced in the magnetic field measurement because Of the finite linewidths in transition-metal ESR spectra. In a first- derivative presentation of the absorption spectrum, the point of inflec- tion (crossover point) mid-way between the peak and valley becomes successively more difficult to determine exactly as the line width in- creases. Actually, in this research the limiting error is the error in crystal orientation which arises because crystals must be mounted under liquid nitrogen without the aid of a polarizing microscope or of X-ray methods for establishing the location of crystal axes. The error Ag in the g value of a radical with axial symmetry based upon an angular error, A6, in orientation is .8 = iI{(Ri - gT|)/g}cosesin6A6I (124) o or 20 in where g2 is given in Equation (99). As an example, let A6 = 1 the data for the determination of gll, where g|| = 2.500 and $1.: 2.000. Then 66 A6 = 1°, Ag = a 0.0035 0 (125) A0 = 2 , Ag = i 0.014 . Clearly, the larger the anisotropy (gi - gf'), the larger is the poten- tial error in Ag. For a fixed angular error, the maximum error in Ag occurs with 6 = 45°. It is difficult to assess the angular error in a single measurement by the technique described earlier; hence, to minimize and bracket the error, replicate measurements on many crystals were made. Therefore, the errors in the spin-Hamiltonian parameters are reported as standard deviations, D, given by n 2 n 2 5 p = 2: A1 - (1: A1) In , (126) i=1 i=1 ,, (n-l)‘ where A1 is the ith-individual Observation of the n Observations made. If there are less than six independent observations, the mean experi— mental deviation is reported. RESULTS K2PtCl4 Introduction At 770K four distinct groups of ESR lines are observed in irra- diated KZPtCl4 crystals. The two strongest sets are shown in Figure 4 with HIIa. The intense group of six lines at low field (Set A) which is also seen with HIIC, must belong to a radical containing two magnetically equivalent platinum nuclei; in the absence of experimental information concerning the ligands or charge, this radical will be designated as (Ptz). The second set of intense lines shown in Figure 4 at higher field (Set B) is also seen when HIIc and is a triplet, each component of which shows superhyperfine splitting into ten lines. On the basis of these nuclear hyperfine interactions, this second radical is presumably (PtCl3)o or (PtC13)2_ and will, therefore, be tentatively designated (PtCl3)n‘. A third set of lines of low intensity has ESR parameters essentially identical with those observed for (PdCl4)3— (see the Results and Discussion sections on KdeCl4), but in Figure 4 the lines are ob- scured by the lines of Set B. This radical is attributed to palladium impurity which appears to be present in all available samples. A fourth feature of the spectrum is a weak, single line at g = 2.000 which, on warming, seems to resolve into a triplet of separation 6 Gauss; there is 67 68 ...__e suw3.M um um «Hoummx mo mamumhuo OHwnHm woumapmuuw mo suuuoonw «mm pamnlx O>Hum>fiuop umuHm.OnH .q Oupwfim o 69 insufficient evidence to identify it and it will not be discussed further. This fourth feature is too low in intensity to be seen under the condi- tions of Figure 4. On warming the crystals from 770K to about 108°K the (Pt2) lines slowly decrease in intensity and a new set of lines of lower intensity starts to grow in. At 1250K the (Pt2) lines are gone and the new set (Figure 5a), which shows hyperfine interaction with one platinum and one chlorine nucleus, has reached maximum intensity; this radical is tenta- tively designated as (PtCl) and its probable structure will be discussed later. With further warming the (PtCl3)n- lines disappear above 1900K. The (PtCl) spectrum is also gone by room temperature, where no stable radicals exist. On irradiating the crystals at 770K with the mercury vapor lamp the (Pt2) lines disappear rapidly and the (PtCl3)n- lines decrease in intensity slowly; the (PtCl) species was, however, never observed on illumination as it is on warming. (Ptz) Radical The first-derivative spectra of the axially symmetrical radical (Ptz) are shown in the parallel (Figure 6a) and perpendicular (Figure 6b) orientations. Only a single magnetic site is observed for this radical. These spectra can be interpreted with the spin Hamiltonian of Equation (79) where S=%. Hyperfine coupling of the Odd electron to two equivalent nuclei necessitates some care in constructing suitable nuclear spin wave- functions.109 In order to account for the second-order hyperfine inter- actions one must introduce the total nuclear spin operator I=(I1+I2) and associated representations II, mI>where 70 9n? 1.942 ”‘1 16013 (a) Mile OIZGH I 9:240: 13.32.. W (b) l-llla Figure 5. The first-derivative X-band ESR spectra of (PtC15)2—: (a) with HIIc, (b) with HIIa. 71 e) .1921 Hllc In) Fifi/2) I19 "1‘ 9‘: 2.723 g“ 3 1.770 Iv) IRE) l1°> I90) ILA/e lac» I357!» It“) I‘d: ‘4) IM) Figure 6. The first-derivative X-band spectra of (PtCl4)23- in irradiated single crystals of K2PtCl4: (a) with HIIc, (b) with H%c. The feature marked X in (a) is centered at g = 2. 00 and is from an unidentified species. 72 I 3 II + 12, II + 12 - 1, . . . . , II - 12 = O mI = 1, 1 - 1, . . . . , -1 . (127) The spin functions, representations, and degeneracies, along with the calculated and experimental relative intensities for the six-line (Ptz) radical, are given in Table 4. The line associated with the singlet product function (OB—Ba)//2 is not shifted by either the first- or second- order hyperfine interaction and is therefore under the strong central line which is dominated by the radicals containing the non-magnetic platinum isotopes. The principal values of the g and A(195Pt) tensors that are listed in Table 5 under (Pt2) were calculated from Equations (99). UV-Photobleaching Experiment An ultraviolet (UV) photobleaching experiment was performed on y-irradiated crystals of K2PtC14, maintained at 770K, with the light beam incident on the (100) face. The decrease in (Ptz) concentration was measured by recording the decrease of the ESR signal intensity as a function of UV exposure time. If the decrease in signal intensity (radical concentration) with time is assumed to be proportional to the instantaneous signal intensity (radical concentration) raised to some power, n, then -dI a Indt (128) where I is the signal intensity and t is the time. A plot of the in- tegral form of Equation (128) for n=2, that is (l/I - 1/10) versus t, yields a straight line (see Figure 7) which implies that each reactive 73 .moaHm> some can mmwuwmamucw Housmafiuoqu nonuo «£8 .wmsam> vmumasoamu onu saws nomwummaou you wq.o~ on cu ammono was A@.o_ mafia HouauawquXm 0;» mo %uwmaouaa o>wumaou 039 n .HmSm: mm Am_N\HI .- AENH was Asa—N} u Ans—NH 0.3m m a 9.3 8 3.2 3.2 a 9.2 Q23 1 ms 84 84 H Aoi $23 + as 3.0 84 H 01.: mm 8.0 8; a A1: 8 Saw 2: N A2722: 8 8 mm; 3; N A212: . so 06 nmowuumamuaH mmfiuwmamucH . m>wumamm 958m?“ AHE.H_ «muowuuaam swam Housmafiumnxm vmumHSUHmo komumamwmn macaumuammmuamm unavoum Hmoaoaz .soa -mNAQHoumV was you moauamamuss «mm was mcoaumsammmuaam -- .q msm10 Gauss peak-to-peak) would seem to indicate that the radical is undergoing restricted rotation at 77°K to produce a broadened but virtually isotropic spectrum. K2Pt(CN)4°3H20, (Pt(NH3)4)ClZ and K(Pt(NH3)Cl3)’H20 Irradiation of single crystals of Kth(CN)4°3H20 at 77°K gave no usable spectrum when examined by ESR since the fragile needles powder either on irradiation or on cooling. (Pt(NH3)4)C12 and K(Pt(NH3)Cl3)°H20 single crystals behaved in a similar manner and no satisfactory spectra were obtained, although there was evidence for a chlorine-containing platinum radical in the case of K(Pt(NH3)Cl3)'H20. KZPtBr4, KZPdBr4 and K2Pt016 91 .Mohn um eummumuaaammmovzv aw mmomwl mo asuuuomm «mm vsonix 0>Hum>auovlumuwm may .m~ ouswah 92 Irradiation of single crystals of Kthqu, K2PdBr4 and KthC16 has been carried out at 77°K without permitting the crystals to warm up. No evidence for any platinum- or palladium—containing radicals was noted. DISCUSSION KZPt014 (Ptz) Radical l. g Values Since the unique axes of the A and g tensors coincide with the c crystallographic axis, the (Pt2) radical must have a point—group symmetry no lower than C4v° It is highly unlikely that any gross re- arrangement of the ten nuclei that comprise the two original neighboring (PtCl4)2- anions can occur and still preserve the C4 rotation axis. Therefore, it is proposed that the (Pt2) species is either ((PtCl4)2)n- or ((PtC14)Cl(PtCl4))n-, the latter unit having an additional bridging chlorine midway between two adjacent square-planar units along the c axis. Since the (Pt2) radical converts on warming to the (PtCl) radical, which is believed to be (PtC15)2-, it is tempting to postulate the pre- sence of a bridging chlorine in the dimer unit since that would also explain why the unpaired spin is confined to two platinum nuclei rather than being further delocalized along the infinite array of (PtCl4)2- units stacked along the c axis (Figure 3). However, there is no detectable chlorine hyperfine interaction in the spectra of this species (Figure 5) to confirm the presence of a chlorine bridge; also, not all the (Pt2) radicals transform to (PtC15)2— on warming and, on cooling, the (Pt2) 93 94 species does not reform as would be expected if a bridging chlorine were involved. Therefore, it appears more likely that the (Ptz) radical is simply a dimer of the type ((PtC14)2)n- in which an electron has been lost or gained from an adjacent pair of (PtCl4)2- units. On this assumption we have computed approximate values of the components of the g tensor as_outlined below. The metal orbitals that may contain the unpaired electron, and also are consistent with a C4 rotation axis parallel to c, are 5d22, 5dxy: 5dx2_y2 and 6pz. The g values for these possibilities can be calculated by the crystal-field method. Starting wavefunctions are eon- structed from the symmetric and antisymmetric combinations of the real metal d-orbital basis set. For example, |a1g> = 15> '32u> = '32) {Id.2>1 +Id22>2W2 H.122)1 -|dzz>2}//2 (132) where the functions are denoted by their symmetry under D4h’ the sub- scripts 1 and 2 refer to the two Pt nuclei, and overlap has been neglected. The g values for the four possible orbitals are given in Table 7, where only terms linear in C, the one-electron spin-orbit coupling constant, are retained (t is always positive). Although the exact ordering of the orbital energy levels is unknown, the relative order may be estimated from symmetry and the criterion of maximum overlap. Experimentally one observes g1? 2>g|| which eliminates 6pz and 5dx2-y2 from further consideration. Regardless of the oxidation state of platinum, t is of the order of112 2000 to 5000 cm"1 which means that, in the case of gll for the £1 ground state, E(xgzy2)-E(§y) is approximately 95 __w A N A.Hw N A 4w A __w __w n N A Aw HWAN u __w Hovuo u u u + + + .. u + + Russians": + N Amsumxvmnfisgém + Sevmuaamevm Aaevmlseémvu .mw u .. + + AmxvmlAmh1Nxvm Auhlmxvm1azxvm __ um I N um + N N N w mm %+ I u+ N (Na Nu m Hmuefio Amumv Mom moaHm> w woumasoamo II .s mam0H amuoao Hmuwpuo umHnumHoa wanammom .qH shaman \fll, \\IAu—mw )fhfiil I «N (s 1’s «N 1|.lll\z ~IIIIIII ~>.~x “(Gailona 911 :JVH u .5. >x 31:“? ”new .\\r.. xx 0015.111 > ks adNfiw .rk\ \H ¢ I \.|.|. .u—n— .l.l.l ”7" ‘0‘”! N\anJNK IIMflflfiu )HAHV1 11‘ N‘a.JNI 98 The Optical transition, AE, can be estimated from the value of the spin- 1+ 76 orbit coupling constant for Pt (C = 3368 cm-l). If the percentage change in C for platinum is similar to that exhibited by nickel in going from Ni1+ (C = 565 cm-1) to Ni3+ (C = 705 cm—1)112 then C(Pt3+) N 3368 (ggg) = 4203 cm-1. But the coupling constant in transition metal complexes is reduced by 25% to 30% from its free-ion value by covalency and charge dOnation by the ligands; hence it is reasonable to choose C = 3000 cm"1 which leads to AB = 16,000 cm-l. The ESR parameters observed for the (Pt2) radical are thus con- sistent with those expected for a dimer (PtCl4)23' with configuration d15 in a 2A2u ground state and with the unpaired electron delocalized over two nearest-neighbor platinum ions through the interaction between their 5d22 orbitals. 2. Pt Hyperfine Interaction The crystal field platinum hyperfine tensor elements are All -K + P{4N282 + 1232 - 6aN}/7 Al (134) -K + P{-2N282 - 9a2 + 45aN}/7 where K is the isotropic hyperfine interaction, P = gegn8e8n5d, N is as before, a = (t/AE) and 82 is the total spin density in both 5d22 orbitals. If the covalency is ignored (82=1), and the experimentally determined All and A1 are assumed positive, the solution to Equations (134) results in a value for P that agrees in sign and order of magnitude with the values computed by Freeman g£_§l,96 by the Hartree-Fock method. The resulting parameters are 99 P - 470 x 10-4 cm-1 K a -239 x 10-4 cm"1 x - 9.37 a.u. where x, the isotropic hyperfine field at the nucleus, is obtained from K by Equation (72). The covalency can be estimated from Equations (134) if the value of P is taken from the Hartree—Fock calculations of the free ion. Using the value P = 509 x 10‘4 cm"1 for Pt3+(d7) obtained by extrapolation from the recent calculations of Freeman96 (Table 8) one obtains 82 8 1.04. The fact that the hyperfine magnetic field produced at the nucleus (as measured by x) is positive in (Ptz) is unusual for transition metal complexes. However, as noted earlier, positive signs for x have been obtained in the ESR studies of Co(II) phthalocyanine65 and Co(II) in irradiated crystals of K3Co(CN)6.7 In both systems the Co2+ ion is in a low-spin, (17 configuration with the unpaired electron in an orbital com- posed of 3d22 and 43. An analogous situation appears to exist for (PtCl4)23' such that the half-filled a2u orbital (Equations 132) under D4h symmetry, where s and d22 have the same irreducible representation, should read a2u e B{(5d22 + u6s)1 - (5d22 + u6s)2} (135) where u is the degree of mixing and B is the normalization constant. Although it is difficult to say anything quantitative about x, the hyper- fine fields at the nuclei in various Pt species (Table 9) indicate that Pt3+ in BaTiOg,"8 YAlG47 and particularly (PtCl4)23', have substantial 63 character in their ground states. 100 TABLE 8. -- Hyperfine interaction parameters for platinum species by spin- unrestricted Hartee-Fock calculations.96 O... M iv .. w*-----... .fl~ ....—. . - p - crow" -q System x(a.u.) '5d (a.u.) P(x 10'l‘cm'l) Pto 5d86s2(3F) -4.4 11.8 451.5 Pt° 5896s(3n) +53.6 11.1 424.7 Pt+ 5d9(2D) -18.3 11.2 428.5 Pt++ 583(3F) -18.1 12.2 466.8 Pt+++5d7(4r) —17.98 13.38 5098 .V ”— ”-— p_-——-—. —.’—“d—.-—_— n F- —‘ V ——'—w a Values obtained in this work by linear extrapolation. TABLE 9. -- Hyperfine fields at the Pt nucleus (Hn = -K/2gn8n) in various platinum species. “t— . - on..- —- -—.--o. Substance Hn (kilogauss) Ref. (Pt(111)015)2’ in K2Pt014 -863 a Pt3+ in BaTiO3 D —376 48 Pt3+ in YAle :124c 47 (PtCl4)23' in KZPtCl4 +394 a Pt metal -1180 115d Pt3+ (free ion) -754 96 This thesis YAlG B yttrium aluminum garnet K = 2 (Ag + Am + An)/3 Estimated from Knight shift measurements 101 3. Linewidths1 The ESR shapes for (PtC14)23- are exactly Guassian and broader than those noted for most of the other species in irradiated K2PtCl4 and K2PdCl4. This broadening may be attributed to unresolved hyperfine splittings from the planar chlorine ligands. There also appears to be an anisotropic, mI-dependent linewidth. In the parallel orientation (Figure 7a) the linewidth decreases from ~45 to ~19 Gauss as m1 goes from -1 to +1, while just the opposite trend is observed in the perpendicular orientation (Figure 7b) where the linewidth increases from N16 to ~30 Gauss with increase in m1. Closer inspection reveals that the transi- tions at highest field in the parallel direction, and at lowest field in the perpendicular direction, are really doubled. This doubling does not seem to arise from nuclear spin flips (AMS=1, Am1=11) because, in that case, it should occur symmetrically about the usual transitions. For the same symmetry reason, spin-spin interactions from nearby radicals and/or splitting from two magnetically different sites should broaden the II, tmI>pairs to the same extent. Neither does the doubling seem to be a. result of an error in orientation since a complete rotation with the mag— netic field in the aa' plane gives no change in the position or intensity of the split lines. Moreover, the spectrum of irradiated K2PtCl4 powder, in which orientation effects are averaged, still shows the mI-dependent linewidth. Anisotropic spin-lattice relaxation could account for the residual linewidth difference in the parallel and perpendicular orienta- tions, but the dependence on m1 may indicate a time-dependent mechanism. It is possible that the hole in the d manifold of (PtCl4)23' might migrate along the c axis but the spectra at 77°K demand that the hole be localized on just two platinum nuclei so if the hole does hop it 102 must do so in a time peroid slower than the reciprocal of the hyperfine splitting frequency. 4. Structure It is believed that the (PtCl4)23- radical is an example of a dimeric species with a one—electron metal—metal bond. It was noted many years ago that certain d8 square-planar metal complexes show evidence of metal-metal bonds. Thus, the crystal structures often show columnar stacking of the square-planar units with the metal ions in infinite chains, although such an arrangement does not permit closest possible packing of the ions,116 and the metal-metal distances may become quite short. The Pt-Pt distance, which is 4.133 in K2PtC14, is only 3.252 in Magnus' green salt117 {Pt(NH3)4}{PtCl4} and 3.093 in Sr{Pt(CN)4}'3H20.116 Also, Amax of the absorption band polarized parallel to the metal chains increases as the Pt-Pt distance decreases in a series of platinum cyanide 118 in solution, these are colorless. crystals with different cations; It was suggested by Rundle,119 and later by Miller,120 that in the complexes with short Pt-Pt distances the nd and (n+l)p orbitals on adjacent metal ions overlap to give a pair of 32u and a pair of “Ig molecular orbitals and that configuration interaction lowers the energy of the occupied (mostly nd22) orbitals, thus accounting for the observed interaction. For a chain of metal ions, these discrete levels are re- placed by energy bands and, if the metal-metal distance is small, the bands broaden and the separation between the highest occupied nd22 band and the lowest unoccupied (n+1)s band decreases. It has indeed been shown that the (18 system {(CO)21r(acac)} exhibits semiconductivity, with the ratio olI/ql > 500 for the dc conductivity parallel and perpendicular 103 121 while the compound K2Pt(CN)ABr0.3°2.3H20 shows metallic to the chains, conduction along the direction of the chains of metal ions.122 Monomeric d8 (Pt014)2' units have the energy level scheme C (Figure 1). Loss of an electron from one of these units, followed per- haps by a shortening of the Pt-Pt distance to a neighboring (PtCl4)2- unit would give d15 dimers (PtCl4)23- with an energy level scheme as in Figure 14. The stability of this species would arise from removal of an electron from the antibonding aZu orbital and configuration interaction stabilization of the 31g orbital. The Pt-Pt bond could then be described as a one-electron metal-metal bond; such a bond has recently been re- ported123 in the cation {Fe(h5-06H5)(CO)(SR)};. (PtCl) Radical (195 1. g and A Pt) Values The g tensor for the (PtCl) radical (Table 5) is almost axial, with the unique axis parallel to the c axis of the crystal, indicating that the radical has nearly retained the tetragonal symmetry of the (PtCl4)2- ion. The magnitude of the g shifts suggests that the odd electron is largely associated with the platinum ion. If this small deviation from axial symmetry is temporarily ig- nored one should be able to distinguish whether the Pt2+(d8) ion has captured an electron to form Ptl+(d9) or lost an electron to give Pt3+(d7) by comparing the experimental g values with those calculated from crystal-field theory (see Table 1). The experimental order gxx = gyy > 2 > gzz corresponds to the d7 configuration with the unpaired electron in the 5d22 orbital. 104 Not only has Pt2+ been oxidized to Pt3+, but the energy levels in the parent (PtCl4)2- anion (Case C in Figure 1) have been altered by an axial compression to the level scheme of Case A in Figure 1. Thus, the chlorine that is responsible for both the chlorine hyperfine splitting and the axial compression in the (PtCl) radical must be positioned nearly along the c axis to give (PtC15)2-. If this chlorine were exactly parallel to the c axis the g tensor should be axial. Instead, the dxz’ dyz orbital pair is split in energy, presumably by a slight tipping (<5°) of the fifth chlorine away from the c axis in the (110) plane. The C4 rotation axis of the crystal generates four mag- netically inequivalent sites, but the small tipping angle effectively reduces the inequivalence to two sites related by a 900 rotation about c. The fifth chlorine interacts with the metal d22 orbital to give a sigma antibonding orbital, 0: |¢> = A|5d22>Pt ' x"€>Cl 9 where ' (136) Io>C1 a ml3pz + (1-m2)%l3€> . If the constraint of axial symmetry is now removed, a more accurate description of the platinum spin-Hamiltonian parameters can be calculated from crystal-field theory. Maki g£_§l,66 have solved this problem for a nearly axial, d7, strong—field example with a (dx2-y2)2(d22) ground state (hole representation). In a slightly modified form the pre- sent results are: 822 ' 2N2 gxx - 2N2 + 6Na1 gyy - 2N2 + 6Na2 (137) 105 pand‘ _ - AZZ = -K + P(4N2A2 - 3N(a1 + 82)}/7 Axx = -K + P{-2N2A2 + 6Na1 + 3N321/7 Ayy = -K + P{—2N2A2 + 6Na2 + 3Na1}/7 (138) where the symbols K,P are as before, a1 = C/{E(dyz)—E(d22)}, a2 = C/{E(dxz)—E(d22)}, A is the MO coefficient of Equation (136), and N is the normalization coefficient of the zero-order ground state, (dx2_y2)(d22), following first—order perturbation by the spin-orbit coupling operator. Only when A|l(195Pt) and Al(195Pt) are both negative does one obtain a -magnitude and sign for the parameter P in agreement with the Hartree- Fock calculations for platinum.96’124 As a result of the high symmetry of the host crystal it is not possible to label gxx and gyy uniquely so gxx = 2.417 is arbitrarily chosen. By suppressing the covalency (setting A2 = 1) and making the approximation Alfexperimental) = (Axx + Ayy)/2, Equations (137) and (138) can be solved. Substitution of the spin-Hamiltonian parameters of (PtC14)2- yields N = 0.985 P = 321 x 10" cm-1 a1 = 0.0805 n = 525 x 10" cm'1 a2 5 0.0751 x = -20.5 a.u. Allowing covalnecy, and using the value of P for Pt3+ from Table 8, one obtains AZ = 0.88 and Xexp = ~22.6 a.u. The relatively close agreement between Xexp and the theoretical value of x from Table 8 implies that the hyperfine field at the Pt nucleus results mainly from 106 core polarization and not from any appreciable 6s involvement in the ground state, while 12<1 confirms the obvious fact that the unpaired electron is delocalized onto the ligands. 2. Chlorine Hyperfine Interaction A direct measure of the covalency may be obtained from an analysis of the chlorine hyperfine interaction. The spin Hamiltonian of Equation (114) operating on the ground MO of Equations (137,138) gives A||(35’37Cl) = (1-m2)1'2Ag + 4m21'2P°/5 Al(35’3701) = (1-m2)A'2Ag — 2m21'290/5 . (139) The direct dipole interaction, Ad = gegnBeBnR-3, between the unpaired electron in the 5d22 orbital of platinum and the chlorine nucle- us has been neglected because the numerical value of Ad for any reasonable Pt-Cl internuclear distance, R, is less than the experimental error. Since the hyperfine splittings for 35C1 and 37Cl could not be resolved, the weighted arithmetic mean of Ag and 3p for both isotopes was taken from the tabulated Hartree-Fock parameters.99 The spin densities can then be estimated as fp(%) e 1'2m2 x 100 and fs(%) = 1'2(1-m2) 100 (140) Substitution of the expirimental splittings into Equations (139,140) leads to A' a 0.57 f3(%) = 2.0 m - 0.97 fp(%) ' 30.6 with a hybridization ratio p/s - m2/1-m2 = 16. 107 Table 10 compares the axial ligand spin densities of low-spin, d7 complexes in examples where the anisotropic splittings are available. The exceptionally large spin densities on chlorine in (PdC15)2‘ and (PtC15)2- are probably a reflection of the abnormally short M—Cl dis- 0 tance (R<2 A) demanded by the crystal structure. Thus, the unpaired spin in (PtC15)2- is rather delocalized in the o antibonding molecular orbital which is composed primarily of a 5d22 orbital on platinum and a 3pz orbital on chlorine. TABLE 10. -- Axial ligand spin densities.a Substance Nucleus %fp %fS (%fp + %fS) Reference CoPc°Pyridineb N(Pyridine) 2.9 2.4 5.3 125 Fe(CN)5N0H 2“ N(NOH) 4.2 2.9 7.1 126 PdC15 2‘ c1 34.7 1.7 36.4 c PtC15 2‘ c1 28.1 1.9 30.0 c Rh(II)(CN)4C12 4’ CI 11.4 1.2 12.6 127 orbital. Pc = phthalocyanine c This thesis Low-spin, (17 complexes with the unpaired electron in the metal d22 108 (PtCl3)n- Radical The presence of the ten hyperfine lines characteristic of three equivalent chlorines for both Hllc and Hlla (Figure 8) indicates that three chlorine ligands lie in the aa' plane occupying three of the four chlorine positions of the (PtCl4)= ion. While the platinum need not lie in this plane the symmetry of the host lattice favors a planar species. The symmetry would then be D2h and the energy levels of Figure 1, Case C, would be scrambled with dxz: dyz split in energy; dxz-yZ’ which is directed at the ligands, would remain highest in energy. Consideration of the possible d7 and d9 configurations suggests that d9, (22)2(xz)2(yz)2(xy)2(x2-y2)1 is the only reasonably acceptable ground state. Under D2h symmetry, dx2_y2 and d22 transform together as A1. Taking the ground state in the hole formalism as Ixz-y2>= oldx2_y2> + 8|822> , (141) where a2 + 82 = 1, the g values are calculated to be gzz - 2N2 + 8N02 a1 gxx = 2N2 + 2Na2 (o + /38)2 g),y - 2192 + 2Na3 (o - /3B)2 , (142) where 2 sou/38 o-/38 I‘N +q2a§+a§ (T)+a§ (Ty? and a1 3 c/E(xy) - E(xz-yz) s2 - t/E(y2) - E(x2_y2) a3 - C/E(x2) - E(xz-yz) 109 There is insufficient information to solve these equations; however, the order is predicted to be gzz >> gxx > gyy = 2 as observed. A rough analysis of the available metal hyperfine splittings using P . 430 x 10"l'cm'1 (Table 8) yields a positive value for x which suggests that the platinum 6s orbital contributes to the ground state as was noted in the case of the (Pt2) radical. The chlorine hyperfine interaction results from transferred spin density in the 0 molecular orbital which is formed from a chlorine 3p orbital and the Ixz-y2> metal orbital. Reaction Scheme A possible mechanism to account for the observed radicals and their decays may be given, beginning with the assumption that the initial step on y-irradiation at 770K is (PtCl4)2- + (PtCl3)2‘ + c1 . The neutral chlorine atom could move into the potential well at the center of the unit cell (Figure 3) eventually abstracting an electron from (PtCl4)2- to form (PtCl4)-. This could then form the (Pt2) radical by combining with a neighboring undamaged ion of the lattice ' (Pt014)2' + C1 + (PtCl4)- + 01' (PtC14)' + (Pt014)2' + (PtCl4)23- . On warming, the hole centered on the (Pt2) radical could then migrate parallel to the c axis until it encounters either (PtCl3)2-, forming a diamagnetic species, or Cl- forming (PtC15)2-: 110 3- 2- 2- - (Pcc14)2 + (PtCl3) + 2(PtCl4) + (PtC13) (PtCl4)23- + Cl‘ + (PtCl4)2- + (Pt015)2’ . K2PdC14 Radical I l. g Values The ESR spectra (Figure 10) show that Radical I is (PdCl4)n- where n = 1(d7) or n = 3(d9), corresponding to the loss or gain of an electron by the original (PdCl4)2' ion. These two possibilities are distinguished by comparing the observed g values (Table 6) with the calculated g values of Table 1. Only the d9 configuration of Table 1 is consistent with the observed order g||>glf2. The energy separations AEI = 23,000 cm"1 and AE4 = 27,500 cm—1 reported by Basch and Gray43 for the parent (PdCl4)2- ion are based on the optical spectra of Day ggngl.128 If these numbers and the value of th = 1416 cm"1 76 are used in the theoretical expressions for gll and g1 for d9 in Table 1, one obtains gll - 2.483 and gl'= 2.105; these are in fair agreement with the experiment considering the many approximations that have been made which include neglect of the change in metal charge_ from +2 to +1 in estimating the AE values, neglect of the reduction factor in the free-ion palladium spin-orbit coupling constant, neglect of covalent bonding and other smaller terms.85 2. Pd Hyperfine Interaction The anisotropic hyperfine interaction arises from the coupling of an electron in the dx2_y2 antibonding orbital with the palladium 111 nucleus. Only the magnitude is observed experimentally but the sign may be obtained by the method of Fortman;95 a positive contribution of the dipolar term with Hllc is predicted. The sign of the isotropic hyperfine term is also predicted to be positive since it must arise solely from the core polarization of the s orbitals (s orbitals cannot mix with dx2_y2 under D4h symmetry in the molecular orbital treatment). Calculations of the core polarization for 4d ions with spin-polarized Hartree-Fock wavefunctions predict that the isotropic hyperfine interaction a = %(All + 2A1) will be negative when the nuclear magnetic moment is positive, and vice versa.87 Since u (lnSPd) = -O.639 nuclear magnetons,129 it is likely that both Al I (10596) and A i(105Pd) are positive. For (PdC14)3' with the unpaired electron in a dx2_y2 orbital one employs Equations (81) for the metal hyperfine splittings. One finds that P a -58.4 x 10"4 cm"1 for the Pd+ ion based on an estimate of<zd of 7.17 a.u. obtained by extrapolation.87 The solution to Equations (81) shows that approximately 78% of the unpaired spin density is localized in the metal dx2-y2 orbital. Table 11 lists the spin densities calculated in this manner for other palladiumrcontaining species reported in the literature. 0n the basis of the anisotropic couplings, the acetylaceton- ate complex is slightly more covalent than the chloride. However, as has been observed in other d9 systems, the covalency found from the isotrOpic magnetic field at the nucleus per unit spin (x/xo) bears no simple re- lationship to oz obtained from the anisotropic hyperfine coupling constants. 3. Chlorine Hyperfine Interaction The principal values of the chlorine superhyperfine interaction tensor for (Pd014)3- are given in Table 6 where the coordinates are 112 TABLE 11. -- Isotropic hyperfine fields and covalency parameters for palladium complexes.a Substance x x/xo a Reference (PdCl4)3- (in KdeClA) -7.66 0.83 0.785 b (PdCl4)3' (in (NH4)2PdC14) -7.55 0.82 0.78 b Pd(acac)2 ’ (in Pd(acac)2) -10.00 1.09 0.725 56 Pd° (in Pd metal) -8.2 0.89 129 Pd84C4(CF3)4 ' -1.58 0.17 51 8 x0 and x is the experimental value. b This thesis = -9.2 a.u. for Pd+ ion from the calculations of Watson and Freeman 87 113 defined in Figure 2. Although there are eight possible sign combinations for the principal elements, it is probable that the correct set is that with all signs positive, since only that choice is consistent with the assumptions that (a) the transferred spin density is positive (b) the dx2-y2 metal oribtal forms 0 bonds with a hybrid of the 38, 3px chlorine orbitals so that Ay = A2, and (c) the isotropic chlorine hyperfine inter- action should be large and sign determining because the chlorine 33 orbitals are directly involved in the bonding. The principal elements of the chlorine hyperfine interaction tensor may be written in terms of the isotropic contribution As, the direct dipolar interaction Ad between the electron in the dx2-y2 orbital of Pd and the chlorine nucleus, the dipolar interaction A0 between the electron in the 3px orbital of chlorine and the chlorine nucleus, and the dipolar interactions Any, Anz between an electron or hole in the chlorine py and pz orbitals and the chlorine nucleus. As a result of the relation- ship between the direction cosines of the three chlorine p dipolar terms only two independent values (AU - Any) and (Anz - Any) can be determined, such that Axoo 100 200 0 AyO -AS 010 +(Ad+AO-Aflx) 0-10 0071, 001 00-1 -1 0 0 + (Aflz — Any) 0 “'1 0 o 0 0 2 (143) Ad - 0.2 x 10-4 cm"1 is estimated from Ad - ggnBBnR"3 using the Pd-Cl distance observed107 for (PdC14)2-, R - 2.332. The three observed 114 principal components lead, by the use of Equation (143), to A8 a 12.3 x- 10"4 cm"1, (A0 - Any) - 3.7 x 10" cm"1, and (A1,z - Any) 8 0.3 x 10'4 cm"1. Both ANZ and Any presumably arise from configuration interaction;130 that is, the approximate treatment given by the one-electron molecular orbitals should be augmented by mixing in small amounts of excited states which occur in the many-electron theory.85 In view of the fact that the experimental tensor is nearly axial with Ay(35Cl) = Az(35Cl), and the experimental error in Ay(35C1) is large, one can set Any 8 Aflz = 0, in this way neglecting the small configuration interaction terms. One can then obtain information about the blg antibonding molecular orbital (Equation 108) that contains the unpaired electron. The analysis of the chlorine hyperfine interaction for (PdCl4)3_ follows the sample calcu- lation presented in the Theoretical section, Equations (108-119), and yields f8(%) 0.78 0'2 = 0.35 fpx(%) 7.9 n2 = 0.91 with a hybridization ratio p/s a 10. Even though nitrogen-bonded ligands generally produce larger crystal fields than chlorine ligands, many of the d9 ESR studies on Cu++ and Ag++ have involved nitrogen-bonded ligands. In Table 12 we compare the spin density of Radical I with the well-characterized ESR results for Cu(II) and Ag(II) tetraphenylporphyrins.132 The total ligand spin density {(f8(%) + fpx(%))} , which is a direct measure of the covalency of the metal-ligand bond increases in the order Cu++de+