MAGNETIC RESQNANEE ST-U’Dlfié‘ {BF SOME MOLYBDENUMW) COMPLEXES Thesis for the Degree of M. S. M51213 tGAN STATE EJNEVERSW LAURAINE AMA DAL‘E'GN ' 19.6? $700807? ABSTRACT MAGNETIC RESONANCE STUDIES OF SOME MOLYBDENUM(V) COMPLEXES by Lauraine Anita Dalton A detailed study of the magnetic properties of a number of paramagnetic Mo(V) complexes has been conducted. Ligand hyperfine interaction as well as hyperfine interaction from the' Mo(V) nucleus has been observed for some fluoride, chloride, bromide, iodide, thiocyanate, and phosphorus-containing complexes. A careful study of the dependence of the hyperfine interaction upon the orientation of the external magnetic field with respect to the molecular axis of the Mo(V) complexes has permitted an evaluation of the relative importance of Fermi contact and electron-nuclear dipolar hyperfine interactions in these complexes. These observations have permitted a reexamination of molecular orbital theory for these complexes. Electron relaxation studies indicate that anisotr0pic and spin-rotational relaxation mechanisms are the dominant relaxation mechanisms in dilute solutions of Mo(V) complexes. In concentrated solutions electron-electron spin exchange is found to be the linewidth determining mechanism. An analysis of the anisotropic rotational relaxation mechanism has permitted the determination of the signs of the components of the hyperfine interaction tensors for molybdenum(V), fluorine, chlorine, and nitrogen hyper- fine interactions. The isotropic and anisotropic components of the molybdenum hyperfine interaction tensor are positive. The isotropic part of the fluorine, chlorine, and nitrogen superhyperfine interaction tensors is positive while the anisotropic components are negative. Detailed nuclear spin relaxation studies were carried out: They were interpreted in terms of nuclear relaxation through the modulation of electron- -nuclear and Fermi contact hyperfine interactions. Measurements of nuclear relaxation times at high concentrations of paramagnetic ions indicated that the rate of nuclear relaxation is determined by electron—electron spin exchange. Such interaction was taken into account theoretically and an expression predicting the appropriate relaxation behavior in the high concentration region was derived. The nuclear relaxation studies have also provided insight into the detailed nature of some of the Mo(V) complexes in solution. MAGNETIC RESONANCE STUDIES OF SOME MOLYBDENUM(V) COMPLEXES by Lauraine Anita Dalton A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemistry 1967 ii To my father, Mr. Alvin W. Nehmer ACKNOWLEDGMENTS The author wishes to express her sincere appreciation to Professor C. H. Brubaker, Jr. for his continued interest, counsel, and encouragement during the course of this investigation. iii TABLE OF CONTENTS INTRODUCTION HISTORICAL THEORETICAL I. Theory of Magnetic Resonance II. Magnetic Relaxation 111. Theory of Nuclear Magnetic Relaxation in Paramagnetic Complexes IV. Paramagnetic Relaxation in Inorganic Complexes EXPERIMENTAL I. Preparation of Samples II. Solvent Purification III. Crystal Preparation IV. Reference Standards V. Preparation of Samples for EPR VI. Instrumental VII. Computer Programs RESULTS I. Molybdenyl Halide Complexes II. Mixed Halide Complexes III. Mo(V) Complexes Containing Phosphorus IV. Mo(V) Complexes Containing Nitrogen V. Mo(V) Complexes with Ligands Containing Sulfur iv 13 13 24 26 39 46 46 51 51 52 53 53 55 57 57 90 90 108 119 TABLE OF CONTENTS - Continued VI. Nuclear Relaxation Results 127 VII. Electronic Relaxation Results 129 VIII. ENDOR Measurements 137 CONCLUSIONS 138 I. Halobxomolybdate(V) Complexes 138 II. Mo(V) Complexes with Ligands Containing Phosphorus 142 III. Mo(V) Complexes with Ligands Containing Nitrogen 144 IV. Mo(V) Complexes with Ligands Containing Sulfur 144 V. Zeeman and Metal Hyperfine Interactions 145 VI. Analysis of the Electron Paramagnetio Resonance Linewidths. 145 VII. Analysis of the Nuclear Relaxation Results 153 REFERENCES 165 TABLE II. III. IV. VI. VII. VIII. IX. XI. XII. XIII. LIST OF TABLES Magnetic Tensor Elements for Molybdate Complexes Values of for Mixed Complexes of Mo(V). Coefficients in the Kivelson Expression for Linewidth Coefficients of m I in the Linewidth Expression of Dye and Dalton Theoretical Expressions for Spin-Lattice Relaxation Magnetic Tensor Elements of Mo(V) Complexes Elements of the Ligand Superhyperfine Interaction Tensor Equilibrium Constants and Magnetic Tensors for Mixed Complexes Contact Frequency Shifts for Some Mo(V) Complexes Electronic Relaxation Times Spin Densities in Ligand Orbitals Exchange Polarization and Distortion Expressions for Molybdates Calculated from Electron and Nuclear Relaxation Values of To Studies vi page 11 40 42 45 65 68 93 130 136 140 146 157 Figure 10 11 LIST OF FIGURES page The Energy Level Diagram for the Interaction of a Para— magnetic Electron with Four Equivalent Fluorines in the Presence of a Static Magnetic Field 15 The Interaction of a Paramagnetic Electron with the Four Equatorial Ligands for Two Orientations of the External Magnetic Field with respect to the Axis of Highest Symmetry 19 EPR Spectra of [M00F5]2' 59 EPR Spectrum of [MoOBr5]2'in a Frozen Acid Class at 77°K 62 EPR Spectra of a Single Crystal of (NH4)2[MoOC15] in (NH4)2[InC15-H20] 74 The Variation of the Chlorine Superhyperfine Interaction as a Function of the Orientation of the External Magnetic Field with respect to the Quantization Axes of the Chlorine Superhyperfine Tensor 78 EPR Spectra of Polycrystalline (NH4)2[M00C15] in O (NH4)2[InC15 H20] at 77 K 80 EPR Spectra of Polycrystalline (NH4)2[MOOBrS] and K2[MoOFS] in Diamagnetic Hosts 87 EPR Spectra of a Single Crystal of KZIMOOFS] in . O K3T1F6 2H20 at 77 K 91 EPR Spectra of a Complex Formed by Adding (NH4)2[MoOC15] to H3PO4 95 EPR Spectra of Complexes Containing (Et0)2PO' as a Ligand 98 vii LIST OF FIGURES - Continued 12 13 14 15 16 17 18 19 20 21 EPR Spectra of Complexes Containing (EtOJZPSS' as a Ligand Nitrogen Superhyperfine Interaction in Mo(V) Complexes Containing Thiocyanate as a Ligand Solution and Frozen Glass EPR Spectra of [MoO(NCS)5]2' EPR Spectra of a Complex Containing Dimethylglyoxime as a Ligand EPR Spectra of Complexes Containing Pyridine as a Ligand EPR Spectra of M0203(SO4)2 EPR Spectra of Chlorine Superhyperfine Interaction in MoOClSO4 The Nuclear Spin-Lattice T1N and Nuclear Spin-Spin T2N Relaxation Times as a Function ofParamagnetic Ion Concentration and Radiofrequency Field Electronic and Nuclear Relaxation Times as a Function of Acidity of the Solution for [MoOClslz' in a Mixture of HCl and DCl Electron Spin—Spin Relaxation Time, T2e’ and Exchange Contribution to the Transverse Proton Relaxation NST2 ex H D D as a Function of the Mo(V) Concentration viii 103 109 112 116 120 123 128 131 134 159 INTRODUCTION Considerable interest has been aroused in the electronic structure and kinetic processes of molybdenum(V) complexes. Electron paramagnetic resonance (EPR) studies led workers to conclude that the unpaired electron was essentially a d electron with little spin polarization or hyperfine interaction with the 1,2,3 12' ligand nuclei. Chemical equilibria were first recognized in the [MoOCls system. This complex was shown to form paramagnetic and diamagnetic dimers in solutions of low acidity,2’4’S 4,6,7 while the [MoOBr5]2' system is less well under- stood. ]2' More recent studies on the molybdenyl system, [MoOX5 , where X may be F', Cl', Br', or HSO ', have shown ligand substitution equilibria to be Operatives’9 as well as indicating the presence of appreciable electron density on ligand orbitals.4’8’lo’11'12 However, the previous work has left several unresolved problems, such as the nature of the hyperfine interaction, nature of chemical equilibria, relative stability of ligands, the rates of ligand exchange and relation of the exchange rate to the stability of the ligand in the complex, the extent of solvent association within the inner coordination sphere, and the importance of the molybdenum-oxygen double bond in determining the kinetics of substitutional and electronic or nuclear processes. Dialkoxotetrachloromolybdates, originally synthesized by Funk, 23.23;}3' have recently been studied in detail by optical, infrared, and EPR techniques.14 These spectroscoPic measurements have led to interpretation of the structure of the [Mo(OR)2Cl4]' (R = CH3, CZHS) complex as characterized by C4v symmetry, and have shown the axial field to be comparable to the field in molybdenyl complexes. In this investigation, a number of complementary magnetic resonance techniques have been employed in an effort to extend the present knowledge of the structure of Mo(V) complexes and the dynamic processes in solution. Dialkoxomolybdate(V) as well as molybdenyl complexes have been studied by nuclear spin echo, electron spin echo, and NMR as well as EPR spectrosc0py in an effort to obtain a more precise estimate of the magnitude of the axial field gradient in these complexes. In addition, the development of a systematic means of detecting ligand hyperfine interaction has been sought and it is shown that the basis of such systematization lies in understanding relaxation processes. Studies in vanadyl and copper(II) complexes indicate that these relaxation processes are generalls'17 and may serve as a guide to the observation of ligand hyper- fine interaction. HISTORICAL Several methods for the preparation of molybdenyl pentahalide complexes- have been recorded. James and Wardlaw18 prepared (NH4)2[MoOC15] by electrolytic reduction of a hydrochloric acid solution of molybdenum trioxide, followed by. addition of NH C1 to the concentrated Mo(V) solution. The bromide salts were 4 prepared by an analogous method by Angell, James, and Wardlawlg, who found salts of the type [MoOBr ' to be more air-sensitive than the corresponding 5] chloride salts. The air—sensitivity of (NH4)2[MoOBrS] was also noted by Allena and Neumann6 who prepared this complex by dissolution of ammonium paramolybdate' in fUming hydrobromic acid, evaporation of solvent, and recrystallization from hydrobromic acid. Allen 23.21420 recently prepared salts of the type M(I)2[MoOXS], where M(I) = a univalent cation and X = C1' or Br', by separate dissolution of molybdenum pentachloride and the appropriate metal halide or amine hydrohalide in concentrated HCl or HBr followed by admixture of the solutions so that the M(I):Mo ratio was 2:1. Saturation of the resulting solution at 0°C with the corresponding hydrohalide gas caused the precipitation of the molybdenyl halide salts, which were filtered under nitrogen, washed with ether containing 10% thionyl chloride, rinsed with dry ether, and stored 22.222223 Comparable methods employed for preparation of Mo(V) complexes include the reduction of Mo(VI) in K MoO 2 4 precipitation of Mo(V) hydroxide.9 This MoO(OH)3 precipitate was washed with to Mo(V) with hydrazine in hydrochloric acid solution and subsequent . NH4OH and then dissolved in either concentrated HCl or HBr with formation of molybdenyl pentahalide species in solution; this method is also applicable to the 8,12 production of molybdenyl fluoride and thiocyanate11 complexes in solution. - 3 - Abraham gt a1.21 prepared [MoOClS]2' in solution by reducing a concentrated hydrochloric acid solution of molybdenum trioxide with excess Zn or Hg and characterized the resulting molybdenyl chloride anion in solution by EPR.A A solution of the molybdenyl thiocyanate was prepared by addition of NH4SCN and a solution of SnCl2 in concentrated HCl to a solution of MoO3 in HCl.21 The electron paramagnetic resonance of the molybdenyl chloride species was investigated as an aqueous solution of (NH4)2[MoOC15] by Garif'yanov and Fedotov22 at 77°K and 295°K. At 77°K a wide asymmetric line from the even. molybdenum isotOpes (92Mo, 94Mo,-96Mo, 98Mo, 100Mo;-nuc1ear spin quantum number I =-0) was superimposed upon a frozen glass pattern arising from inter- action of the odd isot0pes (gsMo and 97 Mo; I = 5/2) with the applied magnetic field. At room temperature the line from the even isot0pes of molybdenum is symmetric and centrally superimposed upon the isotrOpic hyperfine lines arising from the odd Mo isot0pes. The magnetic tensors for molybdenyl complexes are summarized in Table I. Garif'yanov and Fedotov reported dissolution of (NH4)2[MoOCls] in water; however, spectrOphotometric studies of [MoOC15]2' in varied concentrations of HCl by Haight5 indicated that the [MoOCls]2' species was monomeric only in concentrated acid solutions (10M to 12M) and dimerization predominates at acid concentrations lower than 6M HCl. Sacconi and Cini23 have reported that addition water to concentrated HCI solutions of Mo(V) results in reduced magnetic suscep- tibility.‘ Hare, Bernal, and Gray2 observed an EPR Spectrum of (NH4)2[MoOC15] in 22 and 10-12M HCl solution identical to that reported by the Russian workers, also observed the intensity of this spectrum to decrease markedly as the HCl concentration was reduced from 10M to 4M, and at HCl concentrations below 2M the paramagnetic species disappeared entirely. These workers concluded that the mN OH mm Hm .mom m.om ©.Nm mm +l 000 CM (*0 u.vn o.mh VD +| 001 l\ 0:» o‘u-i sf 4‘! c.0v +l thud v eem.~ mmo.~ ooem.~ «mam.a emm.H onm.H oomm.~ oam.a moo.on wmm.~ om.H moo.on eoo.oa mem.H mum.H as :m U moo.ow vma.~ moo.ow ema.H vmm.H hnvm.H omm.~ moo.on mvm.a omm.H wvm.a nvm.a moo.OH hem.a NO0.0H omm.a anv -Nflmumooza Memm.mfiocH_~fie=zv as Hmaooozamnvmzv -Nflmsuooza xoamEou .moonmEou opmwnxfioz pom mucoEon howsoh uauocmmz "H mam HmHSOHpcomHom paw HoHHmamm EOHM woumHSOHmuw .mosHm> HoHHMHmm new OHmoagomH scam woumHsonuo .maonusm an mmsmm om xHoumEonpmmm mm vopmHmevn K EUOmHHHHHfi e-oH H- m p. Ha .aoseHucoo .H msmUoz mo moonmEou wotz How in mo mosHe> "HH mqm where ml and “2 are the two interacting dipoles, r is the midpoint-distance between the dipoles, and E is the unit vector along r. 12 If it is assumed that one dipole is a paramagnetic electron and the other is a nuclear dipole, the equation can be rewritten in slightly different form, introducing the electronic dipole field Hed —> + -> +-—> —> U E = H = -~ - e + 3? “e'reN ed ” “N ed “N — eN —— 1‘3 r3 For parallel spins the equation reduces to ueuN(1~- 3cosze) where e is the angle r -> + . . between reN and he. The dipole field Hed changes from 211e' at e = 0 to -ue' r3 r3 at 9 = fl/Z, since it is perpendicular to “e at 6 = 54°44'. It will also be noted that the dipole interaction is pr0portional to the inverse cube of the distance r. The contribution to the hyperfine interaction arising from Fermi contact 35,44 density* may be written as 2(§-‘I’)!w(rL)l2 r ,7: . 2 _. where Im(rL)! is the value of the electronic wavefunction at the ligand nucleus and the cmher symbols have their usual meanings. The state of lowest energy is the one ndth.the magnetic moments antiparallel. Visualization of this contact effect may'be facilitated by introduction of a "contact field" H wat the site fc of each ligand nucleus with a direction antiparallel to the magnetic moment of the interaction electron spin. _ 13 - It is to be noted that the functional dependence of w(r) upon r probably is exponential and hence Fermi contact hyperfine interaction will be expected to decrease with increasing electron-nuclear distance much faster than dipole-dipole interaction. The Fermi contact hyperfine interaction is isotropic. An analysis of the hyperfine structure for a typical Mo(V) ion in particular orientations with respect to the external field will next be con- sidered. It will be assumed that the complex is a tetragonally distorted octahedron (C4V symmetry) with four ligands on the corners of a.square and the Mo(V) ion in the center of the_square with the two ligands above.and below this square inequivalent with respect to the equatorial ligands. For simplicity the electron and nuclear dipoles will first be considered as point dipoles. The field generated by a paramagnetic electron is about three orders of magni- tude larger than the field generated by a ligand nucleus. For this reason it will be assumed that the electronic magnetic moment is polarized along the external magnetic field while the ligand nuclear moment is directed along the vectoral sum of the external field, electronic dipolar field, and Fermi contact field. First the case where the external field is parallel to the z-axis of the molecule will be considered. The four ligands in the xy plane are all equivalent with respect to the external field (see Figure 2). The total energy of the complex may be written as 4) -‘> pr} 7* V‘) + .y E = -ue Hext _ guli Hext - épI.(ch + Hed)' a u 0 + In this particular case all vectors are parallel to the z-ax1s and “e as well as :1 are quantized along that direction: - 19 - Figure 2. The Interaction of a Paramagnetic Electron with the Four Equatorial Ligands for two Orientations of the External Magnetic Field with respect to the Axis of Highest Symmetry of the Complex. (A) The external field parallel to the axis of highest symmetry. (B) The external field directed along one pair of molybdenum-equatorial ligand bond. (A) TIA E a -21- ll .4 :3: B uez e S 1112 YI I The case where I = 1/2 as occurs with fluorine nuclei, shown in Figure 2, will next be considered. The total quantum number MI = Zmli can assume the values 0, 21, :2. Each electronic spin level is Split into five sublevels, the Splittings being determined by the magnitudes of the external field interaction, the dipole interaction, and the contact interaction. Taking into account the selection rules AmI = 0, Ams = :1, this situation leads to five resonances with relative intensities 1:4:6:4:1. The transition energies are given by g||BHext - ZMIYIHCIHedI + IHfCI) (see Figure 2). If the external field is perpendicular to the z-axis of the molecule, application of the external field in the xy plane may-be either in an x- or y-direction on the one hand, or Hext may be rotated 45° with reSpect to the x-axis on the other. An inspection of Figure 2a shows that ligands at sites 1 and 3 are in equivalent environments, but the environment at sites 1 and 3 differs from the environment at sites 2 and 4. For a point dipole on the metal Site Hed = -2Hed . If M1 = mIl + m and M = m + m then M = 0, :1 l 2 13 2 12 14 1,2 for I = 1/2, as is the case for fluorine. Each level of the triplet of one pair is split again into a triplet by the other pair of ligands and as many as 9 resonances may be expected. It is easily seen that the resulting ligand superhyperfine structure is symmetrical around g1: It will be noted, however, that the nine signals are not spaced at equidistant intervals. The transition energies 5(M1,M2) between levels of specified M1 and M2 are given in Figure 2b. When the external field is applied at an angle 45° to the x-axis, higher symmetry results: the dipole fields on the four ligand sites are of equal - 22 - magnitude and different directions. All angles between the three types of fileds, H ch, and fied’ at the sites are also equal. The four ligand sites ext’ are thus equivalent, resulting in five equidistant resonance lines. The magni- tudes of the splittings depend upon the angle between fiext and fied45’ the local dipole field applicable in this case. In the point dipole approximation it is clear that the contribution to the superhyperfine interaction arising from dipole-dipole interaction is expected to depend strongly upon the angle betweeen the z-axis of the complex and the external magnetic field. In a frozen glass where all orientations are equally probable a rather complex superhyperfine structure is expected to be observed if the contribution to the superhyperfine interaction arising from dipole-dipole interactions is appreciable. The shape of this spectrum can be calculated by use of the computer program of Lefebvre.45 In solution the superhyperfine structure is expected to be unresolvable because of the averaging of the large number of spectral types corresponding to the different orientations. Since the Fermi contact interaction is isotrOpic, all orientations will,for I = 1/2 nuclei, give the same five line pattern with relative intensities l:4:6:4:l. Thus, if the hyperfine interaction is determined by Fermi contact-interaction alone, the superhyperfine pattern in solution is expected to be identical to that in the solid, if relaxation effects in the different states are neglected. This seems to provide a simple criterion for distinguishing between the-two types of hyperfine interactions. It may be noted that this criterion has been used for years by workers studying organic radicals. However, the validity of the point dipole approximation must also be con- sidered. Clearly, one should be able to approximate the ligand nuclei as point dipoles to a very high degree of accuracy, but if the paramagnetic electron is - 23 - in a dxy orbital, it would be highly doubtful that such an approximation is justified for the electronic dipole. For this reason the symmetry of the "electron cloud" must be taken into account. With the field along the z-axis of the complex the ligand nuclear dipoles are influenced by the same electronic dipolar field as in the point dipole approximation. 0n the contrary, when the external field is applied in the xy plane along the Mo-L bond there is a substantial deviation from point dipole“ l behavior. Although the exact values will depend on the true shape of the ground state wavefunction, the dipolar fields at ligands L1 and L2 will be given approximately by IHedll = 1°7|Hed| and [Hedzi = 0.7IHedI. When the external magnetic field is applied in the xy plane at an angle 45° from the x-axis, the electron moment yehS//2I At site 1 the xecomponent gives a field (2-k)Hed in l _I the x direction and the y-component gives a field (2 6)Hed in the negative y 2 direction. Combining these and using the above estimates for Hed and Hed , 'l‘ 2 a dipole field of the order of 1.25IHedl with an angle.of about 20° with the x-axis is obtained. Because of the equivalence of the ligands L', L2, L3, and L4, their local dipole fields are of equal magnitudes; their directions follow from those to be obtained for the point dipole case. The direction of quantization of KI is obtained by combining fid with fie and fiex Therefore, in the general expression of the energy, KI_is-no longer t' parallel to either Hg or H ex to Now the contact hyperfine interaction is considered in greater detail than: previously discussed. For a pure dxy orbital the ligands are located on nodes of this function. However, spin-orbit coupling will cause a.small amount of dX2_y2 to be mixed in, thus producing a small, but non-zero, value of IW(rL)I2 - 24 - at the ligand site. Hence if appreciable contact hyperfine interaction is; observed, it is expected to arise from n bonding of a fluorine p orbital with the Mo dxy orbital. For such bonding it would not be unreasonable to expect the overlap integral to be 0.05 to 0.10. Further Speculation could be made if further assumptions about the bonding were also to be made, but the essential result of this discussion is that the distinctions between contact~and dipole- -dipole hyperfine interaction remain even if the distribution of the electronic charge cloud over the molecule is taken into account. II. Magnetic Relaxation. At the outset of this discussion_it should be noted that two largely independent mathematical formalisms exist for treating relaxation phenomena in magnetic spin systems. The first derives from statistical thermodynamics and is structured around the concept of spin temperature. This method assumes that the spins are capable of transferring energy among themselves much more effectively or quickly than from themselves to the lattice, and thus the spins can be described as being in equilibrium. The system can then be described by the distribution functions (e.g., Maxwell-Boltzmann, Fermi-Dirac) of equilibrium statistical thermodynamics. Since the concept of thermalization or temperature broadening of the distribution of particles over the available energy levels is central to the method of equilibrium statistical thermodynamics, it is clear that spin temperature will be a convenient parameter for characterizing the particular distribution under consideration. Experimental systems having longitudinal or spin-lattice relaxation times of greater than a few milliseconds are capable of being described in terms of _ 25 - the spin temperature. The concept can be employed conveniently by using the phenomenological approach by Bloch.46 The second method of calculating relaxation times is that of the density matrix method of Redfield.47 This method complements the-spinetemperature method since it is most effective for the case where the rate determining relaxation process is the transfer of energy from one spin.to another rather than to the lattice. Processes where the rate of transfer of energy from the spin system to the lattice is fast and hence which are most effectively treated by the density matrix method include-systems undergoing chemical exchange, rapid Brownian movement, translational diffusion, rapid molecular vibrations or rearrangements, or notional narrowing.48"so The mathematical Operation of the density matrix method involves the solution of differential equations of motions characteristic of the particular system under consideration by using the formalism of matrix algebra.~ The particular restriction to physical systems where the rate of energy transfer from the spins to the lattice is faster than the rate of energy transfer among the spins themselves arises from the mathematical approximation ”Tc.<< l where w is the precession frequency of the given spin system under consideration and Tc is a correlation time characteristic of the rate of transfer of energy from the spin system to the lattice or the dynamic lattice process which causes this transfer. The question of deciding which method to use in a given experimental situation always exists. Experimentally there are two solutions to this problem. One is to measure the lattice times by the saturation or Spin echo methods. The spin-lattice relaxation time can be used as a criterion; times of a microsecond or less indicate that the density matrix method is preferable while times of greater than a millisecond dictate that the spin temperature - 26 - method should be employed. (In reality the popularity of the density matrix method arises from its mathematical convenience and similarity to perturbation theory in quantum mechanics and has.resulted.in its application to cases (solids, frozen glasses, and crystals) where the relaxation time may be on the order of seconds and where the above criterion certainly would-not predict its applicability. The good agreement obtained between theory and experiment in these eases is somewhat puzzling.) A second method of determining the desir- ability of the respective theoretical methods is to perform an-analysis of-the shape of the particular absorption under consideration.. The density matrix method predicts Lorentzian shape while the spin temperature-method may result in either Gaussian or Lorentzian line shapes. Since the details of the two mathematical methods.have-been-adequately 33,35-38,51,52 reviewed elsewhere it will not be done here. III. Theory of Nuclear Magnetic Relaxation in Paramagnetic Complexes.’ The influence of paramagnetic electrons of a substance on nuclear resonance manifests itself in the decrease in the longitudinal, T1, and transverse, T2, relaxation times of the nuclear magnetization M, and also in the shift 6 of the nuclear resonance frequency-w These effects are due to the action of I' the magnetic field of the paramagnetic atoms on the nuclear moments. This action varies in time as the result of free precession, electron spin relaxa- tion processes, exchange, and thermal motions. In a number of theoretical papers‘ts’sy’"64 these effects were studied in substances with a low concentration of paramagnetic ions and without taking the interaction between these electrons. into account. A consequence of this approximation was the derivation of the theory of additivity of effects of paramagnetic ions on the relaxation times T1 and T2: T1 and T2 are prOportional to the reciprocal of the concentration -27.. of paramagnetic ions, N Experiments-carried out at low concentrations of S' paramagnetic materials have confirmed this conclusion. At high concentrations of paramagnetic ions exchange interactions can arise between the ions which result in exchange of electron spin orientations and give rise to changes in the internal fields simultaneous with changes due to precession, electron spin relaxation and thermal motion. As a result, the internal fields must average out to a greater degree than in the absence of exchange, and are manifest in a decrease in the effectiveness of the influence on the relaxation times T1 and T2 by additional paramagnetic atoms newly added to the substance. Under these conditions the relation Tl'l, Tz'1 a N8 must break down. In the subsequent paragraphs an attempt is made to develop a theory of the shape and of the width (Tz'l) of the resonance line due to nuclei in para- magnetic media, taking into account the exchange interactions between the paramagnetic ions, which are in turn modulated by the thermal motion in the system. In the limit of dilute solutions (i.e., the absence of electron exchange) these equations reduce to those develoPed by other workers.48’53"64 This deve10pment is important for three reasons. First, it permits an analysis of relaxation data at all concentrations from which one may obtain spin echoes (or free precession tails) or reasonably wide NMR lines. Second, it facilitates a better understanding of the approximation of non-interaction electron Spins 48,53-64 made in the earlier calculations, and finally, the result permits a better correlation of nuclear relaxation data with electron relaxation data. The calculations were carried out utilizing the method of Kubo and Tomita.65’66 According to Kubo and Tomita65 the half—width Awk = l/T2 of a magnetic resonance line and the spin-lattice relaxation time T are determined by the 1 - 23 - formulas #1 2 , -1 _ 2 , (T2) 7 §°1e T18 ’ (T1) ' EOOBTOB (1) T68 = Reggelwerfia8(t)dt (2) 5202 f (T) = <{[I H (1)][H' I ]}>/ (3) dB a8 ' a’ 8 ’ -o o fa8(0) = 1; {AB} = (l/2)(AB + BA) IC) = 12,111 = I; my. (4) where the notation is standard density matrix notation.65’66 Formulas (1) through (4) are valid for (EL - Eh) << kT and are < 1. EL and Eh are the energies of the magnetic sublevels of the particles; Tc is a parameter having the meaning of a correlation time of the perturbation H'(r). The indicatedinequalities are almost always fulfilled for liquids. The angular brackets in Eq. (3) signify averages over the Spin and lattice variable with the density matrix of the system. Next the autocorrelation function for the nuclear magnetization in a system which contains N identical magnetic-nuclei and NS paramagnetic ions I per.unit-volume will be.considered. The shape of the absorption line, I(m), is given by-the Fourier transform of the autocorrelation function G(t) of the component of the magnetic moment parallel to the direction (x) of the variable-(radiofrequency) magnetic field: (1/2h)f”c(t)e'i”tdt (5) ICw) G(t) x ~99 <{Mx(t)Mx(0) }> (6) The angle brackets in Eq. (6) denote averaging of the_symmetrized product. {Mx(t)Mx(O)} by use of the density matrix p.‘ Since the gaps between the mag- netic sublevels are small (hm << kT), it can be assumed that 65' -29- p = l/{(Zl+l)(NI)}{(ZS+1)(NS)} (7a) so that Mx(t) = exp(itH/h)Mxexp(-itH/h) (7b) where H is the total Hamiltonian for the system without the variable radio- frequency field which in the case under consideration includes the Zeeman energies_ “ I _ c A z _ c 2 Hz . YIHogIh - gIBNHogIh (7C) A S c 2 Hz - YSHOESZ . z gBHOXSK (7d) K of the nuclear and electronic moments in a constant magnetic field HO (Ho I! z), the energy of interaction of nuclear and electronic moments, h - Z r'3[i é - 3r‘3(i f )(s f )] + h 2 A i g (7e) IS ‘ YiYs hr h i at h hi i ht hf h z h>£ h>£ where the first term represents the through-space or dipolar spin-spin interaction and the second term represents the scalar coupling or Fermi contact hyperfine interaction, the energy of the exchange interaction of electron spins among themselves, He = h 2 Jij(rij)SiSj , (7f) 1>J the kinetic energy of the system HK and the energy HSK of interaction of the electron spin system with fih' The Hamiltonian H may be separated into three parts: A H. A I. A A S A A A 0 Al .. A. Hl — Hz ’ H2 + H2 + HSK + HK + He’ H _ HIS (8) where H' is to be considered the perturbation. These Hamiltonians 49,50 (H1, H2, H') satisfy the commutation relations A A 1, H2] = [H2. Mx] = 0 (9) - 30 _ Upon substitution of the solution of the Heisenberg equation into (6) 2'1th? [Mx(t), H'l‘fHé'd-H’] ' (10) the first terms of the series G(t) = Gh(t) are obtained Go(t) = (l/6)NIYIZI(I+1)[e(iwIt) + . . .] (11) G1(t) = 0 (12) 62(t) = (-1/6)NIyI21(1+1)[e(i“1t) x §0Y2£Et(t-t)e(iwyT)fy(t) + . . .] (13) where 0,2 = 5"2)/. MEO) = vléch * 11%). (14) fy(t) = h<[h§°), h;(r)][fi:$°), fif°)]>, (15) H'(t) = 2e(i“yT)n'(r) = Zeciwy‘)exp(irfi2/h)fi;exp(-irn2/fi). (16) Y Y Here 0Y2 is the contribution to the second moment of the resonance line (in frequency units) due to H; (the contributions of the individual terms in the perturbation H to the second moment are additive); fY(T) is the IS correlation function for the quantities H;(r) which vary in time under the influence of H2 (modulation of the perturbation by "motion"). N is a formal operator defined by the relation NA(t) = A(t)/A(O). It is to be noted that G0(t) describes the unperturbed motion of the nuclear magnetization--the free precession. - 31 - In order to obtain fy(1) of the form (15) one must evaluate A A A ‘ _ '. -1 * s “ * -1 * s * “ H;(T) - exp[ih 1(Hz + HsK + HK + He)] x H;expEdfi 1(Hz + HSK + HK + He)] (17) A The electronic Zeeman Hamiltonian, st, in (17) yields time factors of the A form exp(i8wsr), B = 0, t1. HsK describes relaxation processes for the com-. ponents of the electron spin, so that fy(r) is equivalent to N = exp(-|Tl/TB) B a 0' T1, 8': *1 (18) T = { a 1,. Further, it is assumed that the time variation of the exchange energy He(T) = exp(itHK/h)Héexp(-irHK/h) under the influence of thermal motion in the system HK is characterized by the correlation time 19: fi<fie(r)fie(o)> . exp(-|tl/te) (19) Considering the limiting condition ‘ 2 2 <|He| > << <|HK| > (17) may be.expanded into a series in powers of He.- The effect of He on the correlation function for the perturbation is manifest in the term in~ the expansion quadratic in He (the term linear in He gives zero upon averaging). Taking into account the preperties of H;(r) and fy(r), the result of calculation is fY(r) = + ' (iBw r)< “(0) “IS 2 2 (20) x (1 - weYB,aF(t))exp(-IrI/TB), -32- _ A . -1 A_ _B i _' '1 A Ya'B fYB’1(t) _ Nh§£, (21) “ B y,-B Nh§£<§g£(r)§;£ (0)>. fYB,2(T) = NhX£; 3 F(T) = £ET-T')dT'eXp(-lT|/Te), (22) 2 _ “ “(0) HIS 2 (0) IS 2 weYB,“ - <|[He. [M+ 1)! >/u2 x (23) Here HI; alare the terms in the expansion of the energy of interaction between nuclear and electron spins in terms of the Zeeman frequencies of nuclear and electron spins “, HIS “128(fivfi,lHyB,2) Y8 HIV[Z}YB,1§Z£ hZ£{h£}YB,2AhE] Yes The subscript a distinguishes quantities which refer to the dipole (o = l) and the hyperfine (a = 2) interactions. The shape of the resonance-line is of concern out to distances from the center of the line of the order of its width. Information with respect to this part of the line will be obtained if the integration in (13) is carried out.up tO-t = T20, where T o is the 2 transverse relaxation time of the nuclei in the absence of motion.65 It can be shown that F(r) = 12/2 for T 0 << _ O 2 re and F(t) - lrlre for T >> 1 , 2 e Then following the procedure of Ref. 65 and denoting “e33 a = wez, one can 2 . write - 33 - 2 weYB,aF(I) z exp[—wezF(T)] exp (-12wez/2), T20 << re . (24a) 2 0 exp (-Itlreme ), T2 >> I 8 (24b) The quantity “e33 (23) has the meaning and the dimensions of the square of the exchange frequency. For the correlation function (21) of the coordinate part of the perturbation “:21 which varies under the influence of the classical thermal motion of ”K 3 one can take48 fYB,1(T) = eXPC-ITI/Tl) f (25a) With respect to the hyperfine interaction energy two cases must be distinguished. If one intends to consider the interaction of the electron and nuclear spins belonging to different particles moving independently, then one can set fYB,2(T) = eXp(-|T|/12), f (25b) where 12 represents the lifetime of the diamagnetic particle in the solvate- shell of the paramagnetic ion. Obviously in a solid 1 '1 = 0, but if the 2 isotropic interaction of the nuclear moment of the ion with its own electron is considered (the anisotroPic part is customarily not very great and its 2 1 (25c)' effect is negligible), then T = O, and fYB.2 = since this interaction is not modulated by thermal motion. Upon substitution of (21) into (13) and employing the relationships (24) and (25) one obtains for Go(t) + 62(t) the expression (omitting a constant factor) . 2 t (1w t)(1 — Z 2 o f dr(t-r)exp[i(yw +Bw )1] x exp[-|T|T;1 - |T|TB'1 - mezF(t)]) + . . . (26) _ 34 _ which can be approximately represented in the form. . 2 t . exp [iwlt - “El 2 YZBOYB,G g dr(t-r)exp[1(ywI + BwS)T x exp[-Itlr;1 — ITITB'I - we2F(T)]] + . . . (27) The next consideration is the calculation of the line shape for two limiting cases-~fast motion (liquids) and slow motion (viscous liquids, solids)--of the system. A. Fast thermal motion: T2°>> Te In order to find the line shape I(w) near its maximum one should (in the case T2o >> re) evaluate the Fourier transform of the~autocorrelation function (27) making use of (24b). A Lorentz line of half-width Am,/2 and with its center at the frequency67 ”1 + 6 is obtained: _ 2 -l -2 2 -1 -2 2 Awlé — S(S+1)OIS[(1/3)R01 + (1/2) (Ru/[R11 + 008]) + (1/4)(R01/[R01 + wI]) + (1/2) (Rfi/[Rfi + (“’5 + wI)2]) + (1/12)(Rfi/{Rfi+ (w, - “92“] + (1/3)[S(S+1)] [R02 + Rig/[Rig + (mI - wS)2]] (28) -5 = scsmofS [(1/2MwI/R5f + mi) + (ImamI + wSI/[Rfi + (“’1 “”532” + (1/12)([wI - wSI/[Rfi + (w, - w5)21)] 2 -2 2 .. . ,. + 5(S+1)([wI - wSI/[R12 + (”I - ms) 1) (29) -1 -1 -1 2 . -1 _ -1 -l 2 R0,“ - Ta + T1 + Tewe , R1,a- Ta + T2 + Tewe (30) A brief discussion of formulas (28) - (30) follows. First, it follows from the definition of R"1 R-1 0 a , I a in (30) that the half-width and the shift of - 35 - the resonance line due to nuclear spins are determined-by the velocities~ofg thermal motion, by the electron relaxation or by the electron exChange-motion depending on which process proceeds at the greatest rate: ra'l, TB'I, or temez. For paramagnetic ions of the type Cu2+, V02+,'etc., Tl'l, T2"1 2 108 sec-1; for other paramagnetic ions(TiS+, Fe2+, Co2+ from the iron group and the rare earth ions) the relaxation times are very short, and apparently, one can estimate T1- > 1010 sec-1. In nonviscous liquids rl'l =~1011 sec-1. One can suppose that the value5« of Te-1 will be somewhat greater than the values-t l sensitivity of the exchange energy to the variations in the distances between the paramagnetic ions. For-rough calculations one can assume that te'l = tl'l. in view of the greater The lifetime of a particle in the solvate shell of the ion, 12, as~a rule will be greater than the relaxation times-T and T. and the effect of thermal motion 1 2 on the hyperfine interaction will become unobservable. Moreover, in concentrated solutions, ois >> , since the internal field amount to approximately 103 to 104 gauss, while lAI = 10 to 102 gauss. In concentrated solutionswe can attain values of 1010 to 1011 sec-1. \> These estimates show that very different situations can be realized in practice. One case of interest occurs when the dominant terms in R31 are the 3 -l 2 0 0 O O 0 0 terms we Te + Ta . It 15 realized in solutions of relatively high concen- trations of paramagnetic particles with not too short relaxation times T1, T2. Then 2 RB,Y - Ta/(l + TaTewe ) and for R '1 >> wI’ w the following expression is obtained from (28) for the B,a half-width S - 36 _ 2 Am = (20/12)S(S+l)oIStl/(l + r remez) + (2/3)S(S+1)12/(1 + tzrewez) 1 1 /2 (31a) For large values of we2 one obtains by neglecting in the denominators of expression (31a) unity in comparison to TaTewe 2 2 2 Awk - S(S+l)[(20/12)oIS + (2/3)1/Tewe. (31b) 0 2 2 2 O I O I Since 018’ we , = NS (the hyperfine interaction with an electron spin belonging to a different ion is under consideration), then it follows from (31a) that in this range the dependence of Am,é on concentration will be due to the variations in Te which increases as the concentration is increased; therefore, Am,/2 will decrease. Further, in accordance with (28), the line width will gradually diminish as the external field increases.. In. weak fields.(R§ aw: << 1) the observed width is-given by (31a). In strong fields (a: aw: >> 1, butkg aw: << 1) the following expression is obtained _ 2 2 Atu,/2 - (7/12)S(S+1)°ISRB,1 + (l/3)S(S+l)RB,2 (31c) In the absence of exchange (low concentration of paramagnetic ions), (28) together with (30) become similar to the well known formulas of Bloembergen57 and of Conger and Selwood.68 0f some interest are the investigations of the line shift -6 (formula (29) gives the shift in units of rad/sec). As can be seen from (29), -6 1 passes through a maximum (as the external field is varied) at ”I = R6; and ms +wI = Rlll’ At the same time the shift diminishes-as the velocity of the motion R'1 increases. B,a . B Slow thermal motion: T2o << Te The condition T2o << Te, r1, r2 corresponds to a slow modulation of the exchange, hyperfine and dipole interactions with the thermal motion. The: - 37 - nature of the phenomenon is in this case determined by the exchange and the relaxation motions in the electron spin system. The nuclear absorption line near ist maximum has-a Lorentz shape, since the approximate autocorrela- tion function assumes-the following form for T20 << re: exp{iwIt - t 2 o2 ImeXp[-T[T'1 - i(ymI + Bws)] - 12m2/21dr} + . . .,- Y’s YB 0 B e 2 2 2‘ 0a8 - O016,1 + O018,2 (32) The factor multiplying f in the exponent of the exponential determines- the position of maximum intensity_w +16 67, while the factor multiplying I [-t] determines the half-width Auk _1 1 1 2 Aw% = (n/z) me via sé-ioYBReLCZYB) (33) _1 1 1 2 ml + o = n1 - (n/Z) we yéo B§-10YBImL(ZYB); lvl + Isl 7‘ o (34) zYB = (on + Bws - 1TB'1)/oe/§ (35)- L(Z) e exp(-ZZ) — i2W(z)//F', W(Z) = exp(-Zz)£zexp(x2dx) (36) A brief analysis of formulas (33) - (36) is given. In a number of 3+, V02+) the-electron-relaxation times TB =‘T1,h 7 to 10'8 seconds, so.that T cases (Mn2*, Cr T2 are' comparatively long, about 10' '1 << ”S #-0; 8 therefore in ZY the imaginary part Can be neglected if B i 0. Moreover, B if TBwe >> 1, then the formula for the half-width of-the line (33) assumes the following form: - 33 - -l 2 2 2 2 Am = (n/Z) w [o + o + X o exp{-(yw + Bo ) /2w }] k e 00 10 Y=0,1 8=11 vs I S e (37) analogous to the well known formulas for the half-width of the electron resonance line.65 For the line shift 6 one obtains in the present case -1 (TB «lawsl. :3 i‘ 0) 2 w —o = /§'o Z 2 o W[(yw + 8w )//§'n ] (38) e 7:0 B=*1 v8 I S e When the relationship wa + Bws = Bus is taken into account, expression (38) may be rewritten as -5 = Ji'oe'15(3+1)[(5/12)ois - (1/3)]exp(+y2)fyexp(x2dx) (39) 0 which reaches a maximum at yE.wS//2 we = 0.925. Thus by measuring the width (35) and the shift (39) one can find the-exchange-frequency we. a 1 5| Then the shift 6 =‘0, since in such an approximation In the opposite case T >> lyw + Bo (weak fields) one can.set YBequal to -i/§'neTB. L(ZYB) is real, while the half-width of the line AwfiLdoes not depend upon. 2 the constant magnetic field, but will vary markedly as the concentration of the paramagnetic ions is varied: ‘ -l 2 2 2 Aw,é = (w/Z) we [SCS+1) [(7/12loIS + (1/3)]8Xp(u ) u 2 2- 2 2 x [1 - (2/V?)I exp(-x dx)] + [(13/12)oIS + (1/3)]exp(u ) o x [1 -(2/¢?)£pr(-x2dx)]] , u = 1/«2'T1ne,- v =_1//§'T2we (40) In the case of weak exchange, when the exchange in the electron spin system is slower than the relaxation motions (Tl-1, Tz'1 >> we), formula (40) is inapplicable and the calculation must be repeated neglecting in - 39 - (32) the quantity wesz/Z in comparison to T/TB; the formulas obtained are- not reproduced here since in this case they coincide exactly with (28) and 8-: = TB-l' In the case me = TB'1 one should utilize formula (40) and tables of functions for estimating the line width. (29) with R Finally, in calculation one could also have taken into account the symmetry of the complex ion as Woessner69 has done; however, in inorganic complexes this calculation does not appear to be necessary to obtain good agreement between experimental results and theoretical calculated values. IV. Paramagnetic Relaxation in Inorganic Complexes. In this section a general review of paramagnetic relaxation in inorganic complexes is not attempted, but rather a brief consideration of the theory necessary for interpretation of the spectra.of Mo(V) complexes is presented, making reference to the apprOpriate literature for the mathematical develop- ment. For clarity spin-Spin and spin-lattice relaxation processes will be treated separately. Spin-spin processes are further divided according to their dependence on the nuclear spin quantum number m1. A. Spin-spin_or Longitudinal Relaxation Processes. 1. Nuclear Spin Dependent Relaxation. Nuclear spin dependent relaxation arises from a distribution of Zeeman- and/or hyperfine interactions. The first such nuclear spin dependent relaxae tion process, observed by McConnell,70 arises from the averaging of anisotropic Zeeman and hyperfine interactions by the molecular tumbling of the paramagnetic complex in solution. This case has been treated in detail by 1(ivelson.15-17’71 The result of the Kivelson derivation modified for the case of an axially symmetric complex is given in Table III. - 4o - IWBLE III. Coefficients in the Kivelson Expression for Linewidth. -1 _ , 2 3 T2 - a + BmI+-ym1 + GmI a' = (1/45)w02(Ag/g)2'rR[4 + 3n] - (1/30)mo(Ag/g)b1(1+1)(a/w03TR[1 + n] + (1/ 40)b21(1+1)TR[3 + 7n - Suf(a/wo)] B = (1/15)bwo(Ag/g)rR[4 + 3u] - (1/45)w02(Ag/g)2(a/wo)tR[8 +~6u + 6uf] - (1/20)bZI(I+1)(a/wo)tR[4 + 3n + 7uf] + (1/40)b2[21(I+1)-1](a/mo)rR[3 + Zu] Y = (1/40)b2TR[5 - u + 5uf(a/wo)] - (l/30)bwo(Ag/g)(a/wo)rR[7 + 5n + 12uf] 6 = (1/20)b2(a/wG)TR[1 + u +uf] AH = (2/v’3')(n/ge)12'1 where uz = microwave frequency Ag = 8" - 81.: anisotropy of electronic Zeeman tensor .4 II R rotational correlation time b =.A - B = anisotropy of the hyperfine tensor I = nuclear spin quantum number _ 2 2 u - 1/(1 + mo TR ) f==w 21 2u o R _ 41 - The second mechanism giving rise to nuclear Spin dependent linewidths (Tz'l) is chemical exchange between two species having the same nuclear spin quantum number but different Zeeman and/or hyperfine interactions. A mathematical interpretation of this phenomenon was first attempted by Freed 72 and Fraenkel. ‘ More recently Dye and-Dalton73have considered relaxation involving chemical exchange for species involving large hyperfine interaction. Their expression for T2'1 is reproduced in Table IV. A final mechanism capable of giving rise to nuclear spin dependent linewidths involves either a static or dynamic distribution of resonance frequencies arising from a distribution of hyperfine or superhyperfine inter- . 73 actions. 2. Non-Nuclear Spin Dependent Relaxation Processes (Residual Linewidths). a. Spin-Rotation. This mechanism was first proposed by'Hubbard74 and has been shown by 16’71 to be an important contributor to residual‘ Kivelson and coworkers linewidths in dilute solutions of inorganic complexes. The expression derived by Kivelson is as follows: a" = (Agl l2 + 2Agi2)kT/121Tr3n where Agll =.g|| - 2.0023, Agl.= 81.- 2.0023, r-is the hydrodynamic molecular radius, and n is the viscosity. b. Ligand Exchange. The contribution to T2'1 from ligand exchange may be represented as -1 ' 2 where k is the rate constant for the formation of the complex and [X] is T = k[X] TABLE a = [ B = 2 Y = [ 6 = 2 e = 2 where Fl = F2 = F3 = F4 = - 42 _ IV: Coefficients of mI in the Linewidth Expression of Dye and Dalton. -1 2 2 2 3 4 T2(m1) ' pA/TZA + PB/sz + PA PB (TA + TB)[“ + 8mI * YmI * 6111I + emI ] F + F I(I+1)]2 1 3 [F1 + p31(1+1)][.1=2 + %F4 - I(I+1)F4] 2 1 - F2 + 4F4 — I(I+1)F4] 2F3[F1 + F31(I+1)] 1 - 1:4[Fl + F31(I+1)] - 2F3[F2 + 4F4 I(I+1)F4] 2 1 F4[F2 + 4F 3 4 - I(I+1)F4] + F - (aA - 38) 2 2 -aA /2wA + aB /2wB 3 2 3 2 -aA /2wA + aB /2wB and pA and pB are the fraction of the two species, A and 8; TA and TB are the mean lifetimes of A and B; T trans A and T B are the exchange-independent 2 2 . . o o ' . . i . . verse relaxation times; “A and ”B are the tranSition frequenCies in the absence of hyperfine interaction; w and ”B are the frequencies of A transition involving the hyperfine component mI; and aA and aB are the hyperfine splitting frequencies. _ 43 _ the concentration of the ligand undergoing_exchange._ c. Electron Exchange and Dipolar Broadening. The mechanisms discussed previously determine T2 and hence the paramag- netic resonance resonance linewidths in solutions of low paramagnetic ion concentrations. In solutions where the concentration of paramagnetic ion is 1 molar or higher the linewidth is determined by dipolar and exchange interactions. The exchange interaction between electrons*was~first considered by Dirac,7S who demonstrated that the exchange coupling is approximately equiva- lent to a potential of the form -2 ZJ...(s.-s.) ij 1] 1 J The effect, electrostatic in origin, is dictated by symmetry of the orbital wave functions in the representation of the permutation group. 76 66’78 have-calculated Van Vleck, Pryce and Stevens,77 and Anderson the combined effect of exchange and dipolar interaction on the linewidth. Since the nature of these calculations has already been demonstrated in the section on nuclear relaxation the tepic will not be further pursued. B. Spin-Lattice or Longitudinal Relaxation Processes. 1. Processes Independent of Hyperfine Interaction. Until recently spin-lattice relaxation times were thought to be indepen- dent of hyperfine interaction and capable of being represented in the most. general form by the following expression: T -1 1 = AT + BT“(Jn_1)[9/T] + C exP[*9/T] where T is the temperature in degrees Kelvin, e is the Debye temperature, - 44 _ Jn-l is a transport function and A, B, and C are arbitrary coefficients. The first term in the above expression arises from the Van Vleck direct relaxation process.79 This process involves a phonon-induced spin flip in the ground electronic (orbital) state. The second term arises from the Van Vleck second-order Raman process.79 This process describes a spin flip resulting from a two-phonon interaction. The third term in the expression for T1.1 is due to Orbach80-and is similar to the Van Vleck process except that the spin flip is accompanied by the simultaneous excitation of the electronic state. The theoretical expressions for the relaxation probabilities for these three processes are given in Table V."It'may-also be pointed out that a particularly instructive application of these theories to relaxati . . . . . . ' . 81 tion in inorganic complexes is given by Kivelson. 2. Processes Dependent on Hyperfine Interaction. Recently-it has been shown that the modulation of either isotrOpic hyperfine interaction or anisotropic hyperfine interaction can be-an impor- tant means of spin-lattice relaxation.'82'86 In these processes the spins. -lattice relaxation occurs through the modulation of the hyperfine interaction tensor by phonon or molecular collisions. The process depends upon the difference in magnitude of the tensor representing interaction between the final and initial states, whether or not they are vibration or electronic. The most important mechanisms of this type are a direct vibrational process in which the incoming phonon or colliding molecule excites a vibrational mode of the molecule and simultaneously induces a Spin transition, and an Orbach type of mechanism in which the incoming phonon or molecule excites the paramagnetic species electronically and simultaneously induces a spin transition. - 45 - TABLE V: Theoretical Expressions for Spin-Lattice Relaxation. Van Vleck direct process (Tle)-1 = 64(A/A)2(¢'qo/Aro)2[(worcizrc‘il/(l +w02rc2) Van Vleck-Raman process (T1e3'1 e szcx/A)2(¢'qO/Aro)4rc'1 Orbach process ('rIe)‘1 = 16(1/1)2(o'qo/1r0)2(A/oon)2(1c‘1/[exp(hoon/kr)-1]} where the symbols are defined in Reference 81. EXPERIMENTAL 1. Preparation of Complexes. [Mooc1512’ Ammonium ox0pentachloromolybdate(V) was prepared both by the electro- lytic method of James and Wardlaw18 and by the method of Allen, 33 al.20, with preference for the latter method. In addition, the method of Allen was 2+. CSH6N+(pyridinium), and Zn2+ employed for preparation of analogous K+, Cu oxopentachloromolybdate complexes. This series of complexes was dissolved' in D20 (Merck Isot0pic Products) saturated with HCl gas for nuclear spin relaxation studies; the concentration of molybdenum in-these solutions ranged from 0.01M to 2.0M. [MoOX5]2- ' where X = F', Br', and I- were conveniently prepared 2- Solutions of [MoOXS]2 by dissolution of the [MoOCl salt in the appropriate acid followed by S] bubbling of the corresponding hydrohalide gas through the-solution at 0°C for fifteen minutes. K2[MoOF5] for "dOping" in a diamagnetic salt was prepared both by ligand replacement and by the method of Allen, gt_al.20 Solutions 2+, NH4+, and an+ and X = F' for nuclear spin echo studies with cations K+, Cu were prepared by ligand replacement. [Mo0(NCS)5]2' Ammonium ox0pentaisothiocyanatomolybdate(V) (assignment of structure based upon observed EPR spectra to be discussed in the Results section) was - 46 _ - 47 - prepared by the method of Abraham, gt al.21, a well-known analytical method for Mo(V).82 [MoO(NCS)5]2- could also be prepared by adding KSCN, NaSCN, or NH4SCN to an alcohol solution of (NH4)2[MoOC15]. 2- [MoO(HSO4)S] A solution of the oxopentabisulfatomolybdate(V) anion (assignment of structure based upon observed EPR Spectra and electrostatic charge considerations) was conveniently prepared by dissolving (NH4)2[MoOC15] in an excess of concen- trated sulfuric acid. A solution giving an identical EPR spectrum was prepared gby reduction of K2M004 (Alfa Inorganics) or (NH4)6Mo7024-4H20 (Mallinckrodt Analyzed Reagent) in hydrochloric acid solution with hydrazine hydrate in HCl solution. The Mo(V) was precipitated as MoO(OH)3 by addition of NH4OH. The: washed precipitate was then dissolved in concentrated sulfuric acid. M0203(SO4)2 Molybdenum trioxydisulfate was prepared both by electrolysis with plati- nized platinum electrodes of a concentrated sulfuric acid solution of [M002(SO4)2]2- and more conveniently by reduction with a stream of H23 gas of a concentrated sulfuric acid solution containing 14.4g (0.1 mole) molyb-. denum trioxide (Merck and Co.). MoOClSO4 Molybdenum oxochlorosulfate, characterized by chlorine hyperfine lines in the EPR spectrum, was prepared by adding to the sulfuric acid solution of M0203(SO small amounts of saturated aqueous NaCl, KCl, or concentrated HCl 4)2 so the the Cl—/SO42— ratio was between 1/20 and 1/10. MoOCl3 Molybdenum oxytrichloride was prepared by solvolysis of MoClS (K G K - 43 - Laboratories) in liquid sulfur dioxide. 5.5g (0.02 mole) MoCl5 was placed in a 300-ml 3-necked round bottom flask equipped with dry ice condenser and- inlets for prepurified nitrogen and sulfur dioxide. The flask was placed in an acetone-dry ice bath and $02 gas was admitted until about 100 ml of condene sate had accumulated. The excess SO2 was then allowed to evaporate, the flask' being swept with prepurified nitrogen until the solid MoOCl3 was dry. The MoOCl3 was dried at room temperature under reduced pressure for 24 hours before~ being used. Commercial MoOCl3 (Climax Molybdenum Co.) was used in later experi- ment 5 . 2- [MoO(H2PO4)5] A Species tentatively characterized on the basis of EPR spectroscopy and electrostatic charge considerations as the oxopentakis(dihydrogenphosphato)- molybdate(V) anion resulted upon dissolution of (NH4)2[MoOCls] in concentrated phosphoric acid. C5H6N[Mo(OCH3)2X4] Pyridinium tetrachlorodimethoxomolybdate(V), as well as the corresponding tetramethylammonium and quinolinium salts, was prepared by the method of McClung, g£_al;}4 The preparation of [(CH3)4N][Mo(0CH3)zBr4] and [(n-C4H9)4N][Mo(OCH3)ZI4] as well as (NH4)[Mo(0CH3)2F4] by procedures analoe gous to those employed for the synthesis of [(CH3)4N][Mo(OCH3)2C14] were attempted, yielding crystalline solids, but EPR examinationlof N,N-dimethyl- formamide (DMF) solutions of the solids (bromide and iodide) indicated mixed halide ligand substitution. The solid obtained from addition of a dry methanol solution of ammonium fluoride to a methanol solution of molybdenum pentachloride was insoluble in organic solvents, and EPR examination of the solid showed it - 49 - to be diamagnetic.- The synthesis of a thiocyanato complex was attempted by a method analogous to that for the preparation of [(CH3)4N][Mo(OCH3)2Cl4], by employing NH4SCN (Baker Analyzed Reagent) instead of [(CH3)4N]C1. 5.5g (0.02 mole) MoCl5 (Climax Molybdenum Co.) was placed in a SOO-ml 3-necked round bottom flask which was swept with helium. Methanol which had been refluxed over magnesium turnings was distilled with helium sweep into the flask containing MoCl and was also distilled into a flask equipped with 5 sidearm stopcock containing 7.6g (0.1 mole) NH SCN which had been dried 4 under vacuum. The NH4SCN solution wasadded dropwise to the MoCl5 solution which had been immersed in an acetone-dry ice bath. The solid product-was filtered under helium, washed with cold ether, and dried under vacuum for 24 hours. EPR examination of this complex showed it to be isotrOpic, the nitrogen superhyperfine lines indicating the presence of three 14M nuclei in the coordination sphere. A formula consistent with the observed EPR spectra is [Mo(NCS)3Cl3]', but this-characterization must be regarded as tentative. . Thiocyanate complexes with axial symmetry were prepared by adding NaSCN, KSCN, or NH SCN (in excess) to methanol or dimethylformamide solutions of 4 pyridinium tetrachlorodimethoxomolybdate(V). Solutions of sulfate and phosphate complexes possessing axial symmetry, were prepared by dissolution of C N[Mo(0CH3)2Cl4] in concentrated sulfuric 5H6 and phosphoric acids respectively. The composition of such complexes was not determined in the solid state, but the ligands in the xy plane (z is the axial molecular axis) apparently are bonded to the molybdenum through the oxygen, on the basis of EPR characterization of the solution species. - 50 _ Mo(V) Complexes with Ligands Containing Phosphorus Addition of molybdenum pentachloride (Climax Molybdenum Co.) to tri-n-butylphosphate (Eastman Organic Chemicals) resulted in the formation of complexes tentatively characterized as [Mo[(BuO)3PO]C15] and [Mo[(Bu0)3PO]2Cl4]+ on the basis of EPR data. Dissolution of molybdenum pentachloride in diethylhydrogenphosphite (Victor Chemical Co.) resulted in the formation of a series of complexes differing in ligand substitution. The concentration of each species (as measured by EPR) varied in a regular manner as the concentration of MoCl5 was changed. Tha nature of the equilibria of this series of complexes- will be discussed in later sections. Addition of molybdenum pentachloride to diethyldithiophosphoric acid (abbreviated DDPA) (Aldrich Chemical Co.) or the addition of DDPA to a hydrochloric acid solution containing [MoOClS]2' resulted in the formation of a complex the EPR spectral features of which are consistent with the formula [Mo(Cl)SSPS(0C2H5)2]', both phosphorus and chlorine superhyperfine' structure being observed in the EPR spectrum. Extraction of this latter complex with ethanol resulted in the disappearance of chlorine superhyperfine structure, an effect which may be attributed to the replacement of chloride- ligands with ethoxide ligands. Addition of DDPA to a sulfuric acid solution 5]2' resulted in the formation of a complex giving an EPR spectrum consistent with the formula [Mo(HSO4)SSPS(OC2H5)2]-. containing [MoO(HSO4) No attempt to characterize these complexes by chemical means was made. _ 51 _ II. Solvent Purification. Methanol, ethanol, acetone, and dimethylformamide were purified for preparation of EPR samples. Dimethylformamide (DMF) and acetone were purified and degassed by a repetitive melt-pump-freeze technique and subsequently distilled into a vessel which was swept with prepurified nitrogen. Methanol was dried by refluxing with magnesium turnings and subsequent distillation in a nitrogen-swept storage vessel; ethanol was dried by refluxing with sodium and distillation into a similar storage container. Ether was dried by refluxing over sodium followed by distillation. III. Crystal Preparation. For EPR and Spin echo studies, crystals of molybdate salts substituted into diamagnetic hosts were prepared. Crystals of (NH4)2[InClS-H20] containing a range of concentrations of (NH4)2[M00C15] from 0.1 mole percent to 1.9 mole percent as an impurity were grown by cocrystallization of the molybdate and indate from hydrochloric acid solution, crystals of (NH4)2[InBr5-H20] with (NH4)2[MoOBr5] being prepared by an analogous procedure. Crystal structure information is given by Wentworth and Piper.24 Crystals containing about 0.01 mole percent to 0.1 mole percent [MoOF5]2' in KszOFS-KHF2 were made by dissolving K2[MoOCls] in concentrated HF, then bubbling HF gas through the solution at 0°C for conversion of [MoOC15]2' to [MoOF5]2-, followed by cocrystallization of [MoOF5]2' with the apprOpriate- 88 amount of KZNbOF -KHF2 (prepared by the method of Balke and Smith ; Commercial 5 KZNbOF obtained from Alfa Inorganics was used in later experiments). Crystals 5 identical in appearance and EPR spectral features were obtained by use of K2[MoOF5] solid prepared by the method of Allen, g£_al.20 as the source of molybdenum impurity in the host crystal. _ 52 - K2[MoOF5] was also substituted into a KZSnF6-2H20 host (KZSnFG obtained from Alfa Inorganics) at a concentration between 0.1 mole percent and 1.0 mole‘ percent. Since a high concentration of was necessary to suppress polymerization of the potassium hexafluorostannate (at 48 to 72 hour intervals during the crystallization period HF gas was bubbled gently through the crystallization solution by means of a gas dispersion tube) and since the host crystallizes in monoclinic plates89 only small crystals were obtained. The most satisfactory host for the [MoOF5]2- in this investigation was found to be K3TlF6-2H20. By cocrystallization of K2[MoOF5]-with this-host, crystals larger in Size than the fluorostannate crystals were obtained with a molybdenum concentration between 0.1 mole percent and 1.0 mole percent. IV. Reference Standards. Five reference standards were commonly employed for calibration of magnetic field and-frequency-and monitoring of passage conditions.’ Potassium peroxylamine disulfonate, K2N0(SOS)2, was prepared by the method of Palmer;90 potassium pentacyanonitrosylchromate(I) hydrate, 91 K3Cr(CN)5NO°H O, was synthesized by the procedureof Griffith, g£_al. 2 In addition, an aqueous solution of vanadyl sulfate (Fisher Scientific Co.) and a 0.1% pitch in KCl as well as a 0.00033% pitch in KCl standard Varian reference standards were employed. Diphenylpicrylhydrazyl (DPPH) (Aldrich Chemical Co.) was conveniently used by gluing small crystals of the free radical to the outside of sample tubes. Pertinent magnetic tensors for these standards are recorded in the literature.26’92’93 -53- V. Preparation of Samples for EPR. For EPR relaxation and equilibrium studies, a weighed quantity of molybdate was placed in a glass container similar to that described by Dalton92 so the solution could be prepared without exposure to air. An alternate technique for filling EPR tubes consisted of temporarily sealing the tubes filled by'a hypodermic syringe in the dry box with wax or with polyethylene caps. The tubes were then sealed with a torch bGIOW'the temporary seal. For spin echo studies the solution samples were prepared in the-dry box, since the sample tubes were of a diameter too large for convenient sealing with a torch. VI. Instrumental. A. Electron Paramagnetic Resonance Measurements. Electron paramagnetic resonance measurements were made at frequencies from 9.2 to 9.5 ko by using a Varian X-band Spectrometers. Measurements-at 35.0 to 35.5 ko were made by using a Varian K-band spectrometer. Measurements at 77°K were made by using the Varian nitrogen dewar assembly. Variable temperature measurements were made by using the Varian variable temperature accessory. When searching for ligand superhyperfine structure, special care waS~ taken to assure that there was no distortion of the-resonance lines from instrumental effects. Consequently, for these studies microwave power and modulational amplitudes were kept at a minimum. Slow passage conditions were employed and dielectric loss was minimized as much as possible by judicious choice of solvent. _ 54 - B. Electron Spin Relaxation Measurements. Electronic relaxation times were measured by both the saturation and electron spin echo techniques. The saturation measurements were performed at 9.2 ko on a Varian EPR spectrometer. The electron spin echo spectrometer employed permitted electron Spin echo measurements to be made-either by the classical 90°-180°-90° pulse sequence technique or by the "picket" technique. The picket technique delivers a string or picket of 10 to 20 pulses instead of the initial 90° pulse of the classical sequence. This-insures complete saturation in the initial step of the sequence, thus combating such spurious 94-97 Unlike the relaxation processes as cross relaxation or Spin diffusion. nuclear Spin echo experiment to be described later, the pulse angle could be varied only by changing the pulse amplitude. ‘Care was taken to ensure that the first pulse was a 90° pulse. The angle of the other pulses is less crucial. Measurements were made at 4.2°K, 77°K, and 298°K by using the appropriate dewar assembly and refrigerant. C. Nuclear Spin Relaxation Measurements. Nuclear spin-lattice relaxation times (TIN) were measured by a 90°el80°-90° pulse sequence. In these experiments the pulse angle could be varied by changing either the pulse amplitude or pulse-width. Molecular diffusion pre- vented use of this method for measurement of nuclear spin-spin relaxation times (T Nuclear spin—Spin relaxation times were measured by either the Spin 2N)' echo ”picket" technique of Carr and Purcell98 or by wide line.NMR with Varian 60 Mc/sec and 100 Mc/sec instruments. The nuclear spin echo Spectrometer employed was a variable frequency spectrometer-permitting measurements to be made at 3.09, 4.4, 16.33, and 28.7 Mc/sec. - 55 - D. Electron Nuclear Double Resonance Measurements. ENDOR measurements were made at 4.2°K. Varian EPR spectrometers served to provide the saturating microwave field. The radiofrequency equipment was largely "homemade". In general, the best ENDOR signals were obtained from the central or outermost components of the hyperfine spectrum. VII. Computer Programs. A. Programs to Calculate Hyperfine and-g Tensors from EPR Spectra. Several computer programs were employed to obtain A and g values from EPR Spectra. The data reported in-this thesis were obtained by using a program written by Mr. Vincent A. Nicely of this laboratory. This program is based upon the modified Breit-Rabi equation discussed in the Theoretical section. B. Program to Obtain Linewidth Parameters from EPR Linewidth Data. The nuclear spin dependence othhe EPR linewidths-was determined by evaluating the coefficients of the following expression; -1 2 3 T2 - C0 + Clml +szI + CSmI . A least squares fitting sequence of the above expression to the experimental» data was employed. This program was obtained from Mr. Jay D. Rynbrandt99 of this laboratory. C. Program to Obtain Linewidth Parameters from Magnetic Anisotropy. Data and Solution Viscosities. Several programs were written which calculate o', a", B, y, and-6 from- experimental values for , gll, gl, , A, B, ms, n, r, and T, which are in the notation of Kivelson.15'17 A plotter subroutine which presents the respective hyperfine components as derivatives of Lorentzian absorptions permits comparison of the experimental and theoretical spectra. - 56 - D. Program to Synthesize the EPR Spectra of Frozen Glasses and Polycrystalline Samples. Lefebvre and Maruani45 have written a rathergeneral and effective program to accomplish this task. Their program, document 8275, was obtained from ADI Auxiliary Publication Project, Photoduplication Service, Library of Congress, Washington, D. C., and modified to synthesize Mo(V) Spectra. E. Program to Synthesize the ENDOR Spectra of Frozen Glasses and Polycrystalline Materials. A program taking into account nuclear dipolar, electron-nuclear hyper-- fine interaction through second order, and quadrupolar interactions was‘ written, but further work must be done before this program can be used for effective analysis of experimental Spectra. F. Additional Programs. Additional programs were written for calculation of molecular orbital 14,100,101 coefficients from various methods in the literature and symmetry constants for a series of molybdates were evaluated by the method of Culvahouse, g£_al.102 1 RESULTS 1. Molybdenyl Halide Complexes. A. Solution and Frozen Glass Spectra. [Mo0F512‘ The EPR spectra of [MoOF5]2- in 38% hydrofluoric acid are Shown in, Figure 3. Fluorine superhyperfine structure is observed on both the central line from the molybdenum isotOpes.92Mo, 94M0, 96M0, 98Mo, and 100Mo (1 = 0) and on the hyperfine components arising from interaction of the paramagnetic electron with 95Mo and 97Mo nuclei (I = 5/2). As shown in Figure 3, the superhyperfine structure consists of five equally spaced lines; however, the signal heights of the superhyperfine lines are not in the ratio;l:4:6:4:l. The variations in signal heights occur because the linewidths of the super- hyperfine components depend upon the nuclear spin quantum number ml. The m idependence of the linewidth results from averaging ofvg tensors and'SuperL W I hyperfine interaction tensors by tumbling of the complex in solution, as is discussed by Kivelson and coworkers.15-17 If the areas rather than the signal heights of the superhyperfine components are considered, the intensity ratios l:4:6:4:l, as is theoretically predicted, are observed. The number of components together with the fact that_their intensities are in the ratio l:4:6:4:l indicates that the paramagnetic electron interacts with the four equatorial fluorine nuclei of the [MoOFS]2- complex. The observed fluorine superhyperfine interaction is only Slightly dependent upon temperature, the concentration of [MoOFS]2-, and the pH of the solution (the electron paramagnetic resonance spectra were examined in HF _ 57 - - 53 - and mixtures of HF and DF prepared by bubbling HF gas into D20) and vary only from 12.4 to 13.5 gauss over the entire range of conditions under which spectra were recorded. A typical Spectrum of [MoOF5]2- in a frozen acid glass is shown in Figure 3. The spectra of acid glasses is rather sensitive to the concentration of [MoOF5]2- and the pH of the solution used to prepare the glass. Although fluorine superhyperfine interaction is observed in the frozen glasses it is too complex to permit first order analysis, 143;, the intensity ratios cannot be determined without the aid of computer Simulation of the spectra. [Mo001512’ The solution and frozen glass Spectra of this complex are-in good agree- ment with those already reported:4’10 [MoOBr512’ Bromine superhyperfine interaction in solutions of the [MoOBr5]2' complex was-not observed; however, in agreement with Kon and‘Sharpless10 and Dowsing~ and Gibson4, bromine superhyperfine structure for this complex in frozen acid glasses was observed. The Spectra did not appear to be.particularly~sensitive* to the concentration of [MoOBr - or the pH of the solution used to prepare 5] the glass. A typical Spectrum Showed no detectable superhyperfine interaction of the molybdenum parallel hyperfine components or on the 81' absorption; however, the g1 absorption di5played a bromine superhyperfine structure-con- sisting of thirteen nearly equally spaced lines (see Figure 4). Dowsing and Gibson4 suggest that the paramagnetic electron interacts with four equivalent bromine nuclei. However, the hyperfine interaction may be interpreted as arising from two equivalent bromine nuclei. ‘Then the thirteen lines may be _ 59 _ Figure 3. The EPR Spectra of [MoOF5]2- in Solutions and Frozen Glasses of Hydrofluoric Acid. (A) A first derivative presentation of the fluorine superhyperfine structure- on the central line corresponding to the electron in complexes containing 92M0, 94M0, 96M0, 98M0, or 100Mo nuclei (I = 0). The spectrum was taken at -80°C. (B) A second derivative presentation of the spectrum in (A). (C) A second derivative presentation of the fluorine superhyperfine structure on the mI = +5/2 and mI = +3/2 components of the 95Mo and 97Mo hyperfine com- ponents. (D) First derivative presentation of the spectrum of [M00F5]2- in a frozen acid glass at 77°K. (A) (8) Ho = 3367.93 gauss -60- HO = 3485.31 gauss r) -6l- _ 62 - Figure 4. EPR Spectrum of [MoOBrS]2— in a frozen acid glass at 77°K. First derivative presentation. _ 64 _ shown to arise from the near degeneracy of the molybdenum perpendicular hyperfine components and the bromine superhyperfine components. [MoOIS]2- Although ligand superhyperfine interaction was observed for this complex in concentrated HI solution, the separation of the molybdenum hyperfine compo- nents was smaller than for other molybdenyl halide complexes. This resulted in considerable overlap of the superhyperfine components, making quantitative measurements of either the molybdenum hyperfine interaction or iodine super- hyperfine interaction impossible. The values of the magnetic tensor elements measured from solution and frozen glass spectra of the molybdenyl halides are given in Tables VI and VII. B. Single Crystal and Polycrystalline Spectra. Prior to discussion of the single crystal EPR spectra of molybdenyl halide complexes, it is necessary to indicate clearly the coordinate system to which the magnetic tensor elements refer. The Zeeman and metal hyperfine interaction tensors can be thought of as having their origin at the molybdenum nucleus. To calculate the theoretical expressions for the elements of the Zeeman and hyperfine interaction tensors from molecular orbital theory, it is convenient to take the-z axis-alongthe molybdenum-oxygen bond. The x and y axes are located in the plane formed by the four equatorial halide ligands. This coordinate system permits unambiguous specification of Zeeman and metal hyperfine tensor elements but does not perm t unambiguous specification of ligand superhyperfine tensor elementSt“ To consider ligand superhyperfine interaction a coordinate system which has its origin at the ligand nucleus rather 65 o.Hn m.cv o.mm e.wo m.ee m.we n.ma N.mo m.we w.mm e.mo 0.0m o.oo m.Hv o.om 0.00 B.Hv H.n¢ H.on 0.0m m.om o.en o.ne o.mm m.en c.0e X EU e-oH H- m < Adv wmm.H evm.H mam.H me.H mvm.H mvm.H ovm.H wmm.H oovm.H .Hn ooo.N Nmm.H www.H vuw.~ omo.m omo.N mom.H onm.H mmom.H __m mmm.~ ovm.H wmm.~ wmo.m mom.H oom.H mam.H mmm.~ mvm.H mvm.H nuvm.~ Aw dmfiOHOUN + GEO en Heuuflmmoovozgzozmu (Hmflmuzvmuuoza -Nflmflmuzuoozg -NHmHoozH am 0 -N no 2_ mampmxho “mo: ofipocmmsmwe ca mmoozmx - ”memoozu N HON: memeHHNfiezzv an Hmnmoozammezzv MH0002 - Hmnuoozu m HON: mfiueHHNnezzU on Hmnuoo2_mnezzm onmEou .moonmEou m>voz mo mpcoaofim Homcob ofipocmmz .H> mqm mHmohnnm 0:» ma uzom .v-oH x H-.Eo m.o ecu mo.o :oozuon omcmh mosHm> ocflmnomx: one :a mofiucwmuaooc: . ecu ecu mooo.o one Noo.o coozuoc omcma mosHm> m esp ca mofiucflmuaoucs och 67 eoHesHom :OdNHOmINuV eH m.om N.eN H.me Nee.H oom.H mem.H -HmHuHOdNHOmmNuVHoEH coHHsHoo onmnosmv :H N.mm e.mN w.oe mmo.H oom.H oem.H HmHuHoanoomVHoza K EU e-oH H- m < Amv Aw __w va .onmEou .eoseHoeoo .H> mHmae Hme.Hmmn manpmxho oncflmV H0.00 H0.NH-0 H0.NHO 0.0 H.om 0.0 .00 HmnmoozHNHe:20 e00N=\H0oz eH . . e O 00 0 HUNm H000 omHuo z COHHS v N . How 00 :HHug 0H . . e 0 m0 0 Huem H0mm omHuo z eoHosHom e00NH mqm 0H0 000oeeee mH <000o .pmo: ofiuocmmswfiv a“ onmEoo oumenHHoE mo mHmpmHHo oncfim m: wnfivcfihm Ha voummonm hoezomeoqufiae .HHuooHHe 0093mmoa menu Heaven woumHSUHmo ma ous> on“ was» oumofieafi momocuconemo .mecmeH Hmfinoumsco 0:» 09 whomoh .cm a .cofiuompoucfi ocfimuomxnuomzm on» GM uo>Ho>:H HoHos: ucmmflH echo HuNm H000 m m N.N .00 H H0H00 HosmvHozH COHHS m N . Hon mHm Keq 1 [Mo[(EtO)2PO]C15]_ 1.945 48.1 1.61 x 10'2 2 [Mo[(EtO) P0] 01 ]’ 1.938 52.5 2 2 4 -3 5.57 x 10 3 [Mo[(EtO) 90] Cl ]‘ 1 929 55.9 2 3 3 _3 1.45 x 10 4 [Mo[(EtO)2PO]4C12]- 1.919 60.9 3.15 x 10'4 s [Mo[(Et0)290]501]' 1.910 Species Complex Isotr0pic Zeeman Tensor, |pp|. The Spin density in the halide p orbitals was calculated by using this equation. The results are presented in Table XI. Next the implications of the spin densities calculated in Table X1 in terms of molybdenum-ligand bonding will be considered. Spin density in the ligand pk orbital can most logically arise from in-plane n bonding involving the molybdenum b2(primarily dxy) and ligand b2(primarily py) orbitals. Since the paramagnetic electron is assumed to be localized primarily in the ground state b2(dxy) orbital it is reasonable that a fairly large paramagnetic denSity would be expected to reach the ligand b2(py) orbital. The explanation of Spin density in the ligand px orbital cannot be ration- alized in terms of bonding involving the b orbitals. The ground state b2 2 orbital is of the wrong symmetry to overlap appreciably with the ligand px orbitals. Therefore configurational interaction involving an excited molybdenum bl(dx2-y2) orbital must be considered. Bonding for such a case would be 0 rather than n. It is logical to expect that this type of bonding would be considerably less effective than in-plane n bonding involving the metal and ligand b2 orbitals and would be less effective for the chloride and bromide ligands than for the fluoride ligands. The results in Table XI appear to be consistent with this analysis. Metal- -ligand overlap integrals of 0.01 to 0.10 could easily-account for the observed distribution of electron-density. Such overlap integrals are certainly reason- able from the quantum mechanical standpoint by analogy witherigorous Hartree- -Fock calculations carried out for other complexes. — 14o -. moo.o ooo.o moo.o mHo.o ooo.o ooo.o ooo.o moo.o ono.o moo.o Nvo.o mvo.o mmo.o mmo.o mmH.o ooo.o mmH.o nvo.o neo.o ovo.o moo.o ooo.o Hoo.o Hoo.o oeewHH -HNH... mNoovmamm Heomm0oz- -HNHmrN000mdmmHH00ozH -HmHmuz0mH0ozH -HeHmuzUN m -NH -HeH0N 1N .mHmpHnHo ccmwflq cfi mofiuflmcom :Hmm 1N H00000ozH HmuzvoozH HmaoozH NHmemoozH eomHuooz HmruovoZH HmHuoozH onamm .Hx mqmo0 .mHea .eomea: .0 .0 0:0 c0500am .0 .o0 .0000 .oeHeHenoH .2 one .oeoreoom .0 .0 .0 .HoeoEoH0 .0H.4mm.mm .HeeoEoH0 H0 MH.HN00H0 00N 0m ..0H00 .Hoz .eo00H02 .0 .0 0:0 .moeoH3o0 .0 .0 .eoonoz .0 .0 .0Honmeo0 .< .Hneeae0 .2 .0H.4mm.mm .Hneeoe0 H0 eouoHn0oe H000M0 0o mosHe> oHEoum 0:0 0:0 04 mo 003H0> 00>H0mco 0:0 0:00: an eopeHonmo 0903 H_00_ mo 002H0>-0>onm 0:9 .H.H000H0 00NN .00 ..0H00 .Eo00 .0 .eoeH000 .0 .0 0:0 ezomeom .00 eoeH000 0:0 croonom He 000 141 .1. 0 . H.He00H0 00 .00 ..>00 .0H00 .00H00 .> .z 0:0 000000 .0..0H 000nm 000 noeeom H0 eoeoHsnoe Hx0mnv 0o m0sHm> 0:» 0:0 m< mo 003H0> 00930005 0:» wcfims Ha e0umH30000 0003 H_mq_ mo 003H0> 0>ocm 0:0 . . e N 0 N00 0 H000 H000 +H H0 H00 H000-0020 000.0 000.0 00H.0 0H0 -HNH00N0000000H00N000ozH 0 x0 0 0 0 0 _ 0_ _ 0_ ‘0‘ Emu-E 0Hm-H-0m .0oseH-eoo .Hx 00000 - 142 - B. Discussion of the Complex Superhyperfine Structure Observed in Frozen Glasses. Measurement of the spectra of single crystals and of polydrystalline powders has greatly facilitated the interpretation of the frozen glass spectra of [MoOBr§]2-. A discussion of the more complex frozen glass spectra of [MOOF5]2- follows. Upon close examination it may be noted that’the'major peaks of the frozen glass Spectra (indicated by arrows in Figure 3) are separated by 50 to 55 gauss. Neither the molybdenum perpendicular hyperfine lines-nor the Ay(L) components of the fluorine superhyperfine interaction have the correct inten- sity ratio to account separately for the observed structure. The studies on 97Mo) crystals and polycrystalline samples of K2[MoOF5] indicatethat Al(95Mo, and Ay(19F) are of the same order of magnitude. Hence the overlap of fluorine 'Superhyperfine components from the central molybdenum line and-from the molyb- denum-perpendicular hyperfine components may account for the unusual intensity ratios observed. II. Mo(V) Complexes with Ligands Containing Phosphorus. Phosphorus superhyperfine interaction will be discussed first. The spin densities in the s and p orbitals of phosphorus are given in Table XI. The large paramagnetic densities in the phosphorus s orbital indicate that the bonding of the DDPA ligand to molybdenum is through phosphorus; although the possibility of Mo-S=P: bonding cannot definitely be ruled out.' The isotropic nature of the superhyperfine interaction also indicated that the bonding is through phosphorus, which implies that the bonding iS'O in nature. Since the ground state b2(dxy) orbital of molybdenum has"the wrong symmetry for this - 143 - type of bonding, configurational interaction involving promotion of an electron to the first excited a1 orbital must be invoked. The small electron density in the phosphorus p orbitals also requires configurational interaction for its explanation.. In this case metal and-ligand e orbitals are involved. The strong, anisotropic.chlorine superhyperfine interaction observed in 53?, the [MoClSSPS(OC2H5)2]' complex indicates very strong in-plane n bonding involving the molybdenum b2(dxy) orbital. The greater strength of this interac- tion in phosphate complexes than in oxOpentachloromolybdate complexes probably arises from the reduction of the amount of in-plane w bonding to the equatorial ligands by the strongly covalent molybdenum-oxygen bond. As is evident from an inspection of Table VI, the Zeeman and hyperfine' tensors indicate that the complexes studied fall into two categories. The large differences in the magnitudes of g and A tensors for the complexes of Mo(V) with DDPA as compared to the magnitudes of g and A tensors for the complexes with other phosphorus-containing ligands are interpreted as further indication that a molybdenum-phosphorus bond lies along the highest axis of symmetry in the complex containing DDPA while in the other complexes, a molybdenum-oxygen bond lies along the highest axis of symmetry. It is to be remembered that in terms of molecular orbital theory, g values approaching the free electron value of 2.0023 and increasing metal hyperfine coupling constants indicate increasing covalency in metal-ligand bonding. Since the Zeeman and metal hyperfine interaction tensors have been observed in this investigation to be determined primarily by the nature of the equatorial ligand,-the replace— ment of the stronger molybdenum-oxygen bond by the molybdenum-phosphorus 0 bond has been interpreted to result in more effective in-plane r bonding of - 144 - molybdenum to the equatorial ligands. This conclusion drawn from a consideration of Zeeman and hyperfine interaction tensors is in agreement with the observation of increased chlorine superhyperfine interaction in the complex containing DDPA. III. Mo(V) Complexes with Ligands Containing Nitrogen. The observed nitrogen splittings in the thiocyanate complexes of Mo(V) would tend to indicate that the bonding involves a Mo-N bond rather than a Mo—S bond. It may be argued that sufficient electron density could carry through the SCN- system to the nitrogen as‘a result of the strongly covalent nature of all the bonds involved in this ligand (3:2;3 the multi-centered nature of the molecular orbitals). However it is doubtful that this amount of electron density could travel through three bonds, even though they are strongly covalent. It may be noted that 13C enrichment would be one clear-cut means of resolving this problem, since, if -SCN bonding is involved, an appreciable electron density at the 13C nuclei would be expected.. An attempt was made to observe such interaction by examining the spectra at high gain. No 13C lines were detected. However, until the resolution of this problem is accomplished, no detailed interpretation of the bonding can be made other than to note that in-plane w bonding involving the b2(dxy) orbital of molybdenum is probably involved. IV. Mo(V) Complexes with Ligands Containing Sulfur. The anisotrOpic nature of the chlorine superhyperfine interaction (as indicated by the strong mI dependence of the linewidths in the EPR spectrum of MoOClSO4) indicated that strong in-plane n bonding involving the b2 orbital of molybdenum is probably present, although the location of the chlorine in the coordination sphere remains uncertain. - 145 - V. Zeeman and Metal Hyperfine Interactions. As can be seen from consideration of Table VI, the large variation in. the values of the Zeeman and metal hyperfine interaction tensors with changes in equatorial halide ligand do not apparently arise from changes in metal- -ligand bonding. Therefore, the conclusion may be drawn that the variations most reasonably arise from changes in the exchange polarization of the ground state dxy and inner S orbitals of molybdenum. The theory of exchange polari- zation applicable to molybdenum d1 complexes has recently been extensively 3,100,101,103 reviewed. The exchange polarization parameters have been cal- culated by using the methods of both McGarvey3 and Low.101 The results of this calculation are tabulated in Table XII. The results imply that the most recent spin-polarized Hartree-Fock calculations of Freeman, gp_gl;}oq give rather good agreement with experiment. In particular, the results of this investigation indicate that the calculated value for the core polarization is only about 10% to 20% smaller than the value (approximately -400 to -500 kG) which was estimated from experimental data. When the limitations of the calculations are taken into account, such agreement is rather encouraging. VI. Analysis of the Electron Paramagnetic Resonance Linewidth. The analysis of the EPR linewidths leaves little doubt that the anisotrOpic 15’16 are the dominant relaxation and spin-rotational mechanisms of Kivelson mechanisms in Mo(V) complexes in dilute solutions in non-coordinating solvents (acetone, DMF, chloroform, carbon tetrachloride, benzene, acetonitrile, etc.). Other important mechanisms include electron exchange in solutions in which the concentrations of the paramagnetic species exceeded 5 x 10'2M and ligand exchange in certain solvents which engage in rapid exchange with the ligands (methanol, ethanol, hydrochloric acid, hydrobromic acid, etc.). 146 - wo.00- n.0HNn 0.0001 wm.0w wm.0m mm.w0 00.NH 0H.o0- om.wm N0.omu mm.m0 I... mNH.H mm0.o mmn.o mw0.o mw0.o wa.o omw.o Hno.H 000.0 owm.o mnw.o on w.Ho v.wm m.00 n.5m 0.0m v.w0 m.w0 m.wm o.mm m.mm m0.o wm.0 nn.m mN.m mm.m N0.m 0N.m 0N.n 0w.0 no.0 wm.m 0.om 0.Hm H.mv 0.00 0.H0 c.00 o.H0 m.0m h.mm o.o0 00000 :0 HeH0NH00000o2020000 NH000000Noz e00H00oz 00000\z000:z eH H0H0NH00000oszom00 0 -NH H00z0ooz- -NH0H00ozH -NH0000ozH -NH000ozH 0H00o: mampmxho “mo: owuocmmemfi0 =0 ammoozamx H0N0 0H00HHNH0020 m N 0 0H H H00o20 H :20 x0HmEou .00p00anoz Mom mcoflmm0hmxm cofiuhoumfla 0:0 COMHMNfihmHom 0mcmcoxm .HHx mam00 .0200 .ooHem .0 .0 0:0 .0000: .a .2 .onoo005Hs0 .2 .0 0H HHAwV\mfim 1 AMVVH n HAMV\mAmV u __MVHH\HmAmV\mm u ANVVH 1 HAmV\mAmv I 0o2 onmsou .0oseHoeoo .HHx 0000o2 .xowmsou 000N0 eH H0H0NH00000o2020200 H.0000 0H HeH0NH00000oz-20000 x0HmEou .0oneHoeoo .HHx 000<2 150 - .H00 0:0 .H00 .HHO .000 none voooHsoHo0 m .H200H0 00 .<0N .mnoeeoH moHnHen .2o0 .2 seem ood0o .H00 0:0 HN0 .000 aonm 0oeoH=oH00 0 .H00 0:0 HHO .000 aonm eneoHeoHe0o 00.00 N0N.0 000.0 N0N.0 000.0 02.20 00.00 0H.0N 00.00 0H.0N 02.00 0N.00 .0N.00 0N.00 0N.00 00.00 00.00 00.00 00.00 00.00 00.00 H0.H0 00.00 H0.H0 00.00 0N.Ho H0.H0 00.00 H0.H0 00.00 00 EU 0-0H H- Hml Hm.- SQI MQI Mal .HNO .00 seem 0oenH=oHo0 n .3oHon :0>0m .HHV .cm scam 0090Hsonue 000N0 0H H0H0NH00000o2H20000 00000 :H H0H0NH00000oszom00 NH000000No2 000H00oz 00020\2000zz eH H0H0NH00000o2020000 -NH0H00z00o20 onmEou .0oocHenoo .HHx 00000 151 000 000 000 000 000 000 000 0500» m0 mzu on n 0000000 afinm voaflmmcn mo 0030005 0 u m N .ucwpmcou mcflamsou,u0nno 0090 u 0 kuoaanmm m000900mm umofim Hmcowmupou u 0 000:: 0\0 u : 00-0vz00020 0000.0 0 0 0. . . 00:00\20 - 0000 - 000000000 + 0000000 - 0200000 u 0 0. . . 00000\20 - 0000 - 00000\000 - 002000 - 02000-00 u < . . . .INr . IMI,- . + 000 000 + 0000 000 .. ..+mlww-lm-w-00- 000 +IhI-u2.0< .. 0 : s 5 a N ma 0 .N 00 00 N N . . . + 0000\00 - 00 - 0000.0 «.00 0 may wafiuuoccou 05000 00000 Magma: + N500\HN0 . mNoo.N n __m .000 .cm 500m 00000300000 .000 000 .000 .000 .000 0000 00000000000 .000 000 .000 .000 .000 0000 00000000000 .000 000 .000 .000 .000 0000 00000000000 .000000000 .HHx 000<0 - 152 - As has been pointed out by Fraenkel,104’.105 when both hyperfine and superhyperfine structure are determined by anisotrOpic tumbling, one may use an analysis of the nuclear spin dependence of the linewidths to determine the sign of the hyperfine and superhyperfine coupling constants. Such was the case for [MoOF5]2-, [MoO(NCS)S]2-, [Mo(OCH3)2(NCS)4]-, and MoOClSO complexes 4 and the signs of the fluorine, chlorine, nitrogen, and molybdenum hyperfine interactions were determined. The sign of the isotropic and anisotropic parts of the molybdenum hyper- fine interaction were found to be positive. The isotropic and anisotropic parts of the ligand superhyperfine interactions for the ligands giving the superhyperfine structure were found to be Opposite in sign with the isotropic parts positive and anisotrOpic parts negative. The analysis of electron paramagnetic resonance linewidths has demonstrated that the search for ligand hyperfine interaction can be conducted systematically by following a few simple rules. The key to the resolution of ligand hyperfine interaction lies in obtaining sufficiently narrow EPR linewidths, i;g;, suffi- ciently long electronic relaxation times. Since chemical exchange broadens lines, measurements should be made in non-coordinating solvents. Concentration of the paramagnetic ion should be kept sufficiently low that the lines are not broadened by electron-electron dipolar interaction or spin exchange but sufficiently high so that large modulational amplitudes and excessive microwave power are not required to obtain detectable signals, conditions usually met for about 0.01M paramagnetic ion. Since the anisotropic and spin rotational mechanisms have different dependences upon temperature and viscosity, one should perform a careful temperature study. These machanisms result in the linewidth reaching a - 153 - minimum value over a very small temperature range (10° to 30°). Corres- pondingly, in this investigation detection of ligand hyperfine interaction in solution over only a small range of temperatures was achieved. In single crystals linewidths-are theoretically expeCted to decrease with decreasing temperature so that a general rule is the lower the tempera- ture,_the better the resolution of ligand-superhyperfine lines. VI. Analysis of Electron Spin-Lattice_Relaxation Results. Since, in all mechanisms proposed to date, the electron spin-lattice relaxation times depend upon the magnitude of the splitting of the b2(dxy) and e(dxz, dyz) energy levels, it may be concluded that the long relaxation times observed indicate a rather large magnitude for this_sp1itting. The long times indicate that-there are no low-lying electronic, rotational, or vibrational excited states strongly coupled to the ground state. Sufficient information is not available at this time to determine the cause of the anisotr0py of the observed relaxation times. VII. Analysis of the Nuclear Relaxation Results. A. [Mooc1512' Concentration of Paramagnetic Ions less than 0.01M. For this case, the nuclear spin-lattice relaxation times for both hydrogen isotopes are inversely pr0portional to the concentration of Mo(V) with the quantities NSTIH and NST1D having the values 5.2 x 10'3 msec and 10'1 msec, respectively in a field of 6730 gauss. The nuclear spinqspin relaxation times measured by the wide line NMR technique were also inversely proportional to Mo(V) concentration. However, the nuclear spin-spin —154- relaxation times measured by the normal 90°-180°—90° spin echo pulse technique did not obey this relationship. This discrepancy arises as a result of molecular diffusion in the nuclear spin echo technique.- Molecular diffusion as well as, relaxation processes can cause the precessing Spins to lose transverse phase memory; hence, if accurate measurements of T rare to be made by transient 2N pulse techniques, the problem of molecular diffusion must be overcome.98 When this was done.by use of the "picket" technique,98 good agreement between nuclear spin echo and wide line NMR results were obtained. The observation that the relationships NSTlN’ NST2N equal constant values for any given complex indicates that electron-electron spin exchange is negli- gible in solutions less than 0.01M in paramagnetic Mo(V). Thus the general equations derived in the Theoretical section reduce to T1‘1 = (4/30)s(5001232821266)[SrC + 7rc/(1 + wszrc2)1 + (2/3)S(S+1)A2p(fi-2)[re/(1 + mszrez)] (41) T2'1 = (4/60)s(S+1)v,2g282p(r'6)[7rc + larc/(l +0521c2)1 + (1/3)scs+1)Azp(fi‘2)[re + re/(l + wszTez)] (42) where To is the correlation time for the dipolar interaction and Te is the correlation time for the exchange interaction. It is to be noted that l/Tc = l/Tr + l/TS_ (43) and l/T l/r e h + l/TS (44) where Tr is the correlation time for the "tumbling” of the paramagnetic complex, and is the same Tr used in the anisotropic and Spin.rotational-mechanisms of Kivelson,15’16 Is is the electron relaxation time (15 = T = T tin solution), - 2e. 1e - 155 - and r is the lifetime of the resonant nuclei in the complex. Note that p is h given by p = NS'n/m where NS is the concentration of paramagnetic ions, m is the concentration of resonant nuclei in the solution and nvis the number of sites occupied by. the resonant nuclei in the paramagnetic complex. The other symbols are defined by Gutowsky, g£_§l;é. To interpret the data, one must decide whether the measured times are determined_by magnetic interaction or by the lifetime of the hydrogen and deuterium nuclei in the first coordination shpere of the paramagnetic complex. In other words, one must determine which of the three correlation times Tr, Ts’ or Th is the shortest. This problem can be resolved by a comparative study of the relaxation of both isotopes of hydrogen. The ratios of the mag- netic relaxation times of protons and deuterons in [MoOClS]2' solutions were /NST = 38.5 and N T /NST 39. NSTlD 1H s 20 2H = These values correspond, within experimental error, to the theoretical ~“2/~bz = 42.5 and imply that the nuclear relaxation is determined by the modulation of electron-nuclear dipolar interaction. If the relaxation times are expressed as -1 _ -1 -1 (TN1,2) ‘ (TN1,2)a + p{(TNl,2)b + Th} where (T and (T are the relaxation times of the resonant nuclei N1,2)b Nl,2)a in the first coordination shell of the paramagnetic ion and outside this shell respectively, the ratio of spin-lattice to spin-spin relaxation times indicating 4 that (T >> I is less than 1.3 x 10' sec. N1,2)b h and the upper limit for Th - 156 - The nearness of the ratios of NSTlD/NSTlH and NSTZD/NSTZH to 42.5 indicates that the relaxation times given in Figure 20 are represented by the equations (Tl'l) = (4/30)s(S+1)v12gzezp(r'6)re[3 + 7(1 + wszrcz)’1] (45) and (Tz'l) = (4/6O)S(S+1)yIZg282p(r-6)tc[7 + 13(1 + 0521c2)'1] + (1/3)S(s+1)p42(n'2)re(1 + (1 + mszrez)‘1) (46) and that the first term in the expression for (Tz'l) dominates. Next, the correlation time To is found by comparing the relaxation rates of either protons or deuterons at several frequencies. For example, if the proton relaxation times are examined at frequencies of 4.4 and 28.7 Mc, the 11 roots of the resultant quadratic equation give Tc1'= 6.8 x 10' sec and 1 = 1.2 x 10-11 sec at 300°K. The choice between these values can be made c2 by measuring T1 or T2H for some third value of the field Ho (or radiofrequency 11 H field frequency). Results indicate that Tc = 1.2 x 10' sec is the correct value. In addition, on heating a solution, T1H becomes longer, the rate of the rise depending upon whether or not wsTc is comparable to unity. Experi- ments which compared the influence of heating on T1H for the two frequencies 4.4 and 28.7 Mc/sec showed that, of the two values found for the correlation time, the relevant one is To = 1.2 x 10"11 sec. It is interesting to compare this value of Tc' with the value of Tc calculated from electron spin relaxation studies (see Table XIII). Similar comparisons have been made by Lewis, g£_al;}06 who have also found good agree- ment between correlation times calculated by electron and nuclear resonance methods. - 157 - TABLE XIII. Values of Tc Calculated from Electron and Nuclear_Relaxation Studies. a b Complex Temp. :2. :2 [Mooc1512' 300°x 2.0 x 10‘11 1.2 x 10'11 [Mo(OCH3)2C14]’ 300°K 5.0 x 10'11 5.0 x 10'11 [M00F512‘ 273°K 2.0 x 10'9 1.8 x 10’9 Units of To are sec. aCalculated from nuclear relaxation results. bCalculated from electronic relaxation results. - 158 - By setting Tc = 1,2 x 10-11 sec and r = 2.7 A 48,60,61 in the above equa- tions, it is found that p = 0.045; i;g;, n, the number of protons or deuterons in the innermost shell of the paramagnetic complex is 4.3, or to within experi- mental error, 4. This means that in approximately lZN HCl the paramagnetic molybdenum species is either [MoOClS(H20)2]z- or [MoO(HC1)S]S+. This latter species may be visualized as follows, E;,_ .. ”CI . It is impossible to differentiate conclusively between these two possibilities at this time. The best method of testing the possibilities would-be to use H2170 or 02170 instead of water containing a natural abundance of-16O. Several 2+ such studies of this-type.have been performed on solutions of-Mn2+ and Cu 62,107 complexes. Concentration of Paramagnetic Ions Greater-than~0.0lM.-- Figure 21 is a plot of-NSTex H’ the exchange contribution to the transverse-> .9 relaxation, and the electron spin-spin relaxation time, in acidified aqueouS‘ solutions (about 12M) versus the Mo(V) concentration. The exchange contribution was calculated from the rigorous expression given in the Theoretical section and the expressions (41) and (42) and also from the values of T and T at 28.7 1H 2H Mc/sec. As the solution is diluted TE: decreases and reaches a limit of l x 108 sec-l. The value of NST2 ex H also decreases with increasing dilution, and .9 3 causes NST2N to be non-constant. The Similar behaVior of NST2,ex,H and T2e leaves no doubt that the electron relaxation time, 15’ appears as.the correlation - 159 - Figure 21. Electron Spin-Spin Relaxation Time, T2e’ and Exchange Contribution to the Transverse Proton Relaxation N T as a Function of the Mo(V) S 2,ex,H Concentration. Circles indicate T2;1 Squares indicate NST2,ex,H° 00000\00005 :0 HuNfimHUoosz m.N 00.0 m.o mN.o 0.00 mod . - . D 0 o o 0 1. .m D 3 O m a x 0 l O C 0 a 0 w u ,@ ' _ a o 2 0 T m NS 0 a - w I O a 2.xo.Nm o . 0: l .02 n o 0-0 000 o (12°)'1, sec'l x 10'8 - 161 - time for exchange interaction between ions and hydrogen nuclei in acid solution. Assuming that the EPR lines are of Lorentzian form, the limiting value was found 'T2e = 10'8 sec. Next the exchange interaction constants for protons and deuterons are calculated to be 3.5 x 105 cps and 5.0 x 104 cps respectively. to be’r s This-is in excellent agreement with—the measured NMR shifts (see Table IX). Upon comparing AH with AD it is found that the density of unpaired electrons of the M003+ ion for protons |w(0)lH2 is somewhat higher than for deuterons: 2 ~ 2 IwcoHH - 1.06lw(0)ID. Since Te = T5’ the lower limit of the residence time of.a hydrogen nucleus. in the paramagnetic complex is 10"8 sec. Relaxation Times as a Function of Acid Concentration. It is well-known that the paramagnetism of Mo(V) ions in aqueous solution 2’4’5'6’7’23 It is interesting to observe depends upon the acid concentration. how the pH affects the relaxation rates of protons and deuterons. Such studies were performed, the results being shown in Figure 21. All solutions used in these experiments contained 0.2M Mo(V). The pH was altered by varying the- concentration of HCl gas in D 0. It was found that the longitudinal relaxation 2 times of protons and deuterons remained constant between 12N and SN HCl (and DCl). With acid concentrations less than 5N, the longitudinal relaxation time rose sharply due to the decreased concentration of paramagnetic ions: Mo(V) either is oxidized to Mo(VI) or it forms a diamagnetic dimer. The transverse relaxation times behave quite differently. As the acidity decreases they decrease, pass through a minimum, and then increase rapidly. This increase begins at the same~ concentration as for the nuclear T times, and is also caused by the decreased 1N concentration of paramagnetic ions. To draw any conclusions about the cause of - 162 - the decrease in TZN’ one needs to compare the effects of pH on the EPR line- width and on the exchange contribution to T This comparison is made in 2N° Figure 21 for protons. There is no correlation of-any kind between variations of T2;1 and T The relaxation times of deuterons are determined by 2,ex,H' quadrupolar relaxation; thus the construction of a similar graph for T2 ex D S 9 was not possible. On comparing the minimum values of T2H and T2D (the latter is 27 msec), it was determined that (TZD/TZH) = 42. Since this figure is close to the ratio of the squares of the magnetogyric ratios, (yH/YD)2 = 42.5, one can infer at this point (5N HCl) that neutralization of the exchange inter- action between a paramagnetic ion and a hydrogen nucleus is not due to the loss of a hydrogen nucleus from the complex. It must be noted that the increase in T is not caused only by the 2H increase in concentration of hydrochloric acid. It also occurs when LiCl is added to a solution containing 6N HCl. For example, addition of six moles of LiCl also increases T2H by a factor of 12. Thus it is the change in C15 . + . . concentration rather than of H concentration which affects the transverse relaxation time. Changes in T can also be caused by formation of other 2N monomeric complexes of Mo(V) in the solution. In these complexes, the electron transverse relaxation time, T , remains constant because it is largely deter- 2e mined by the Mo-O bond. Reduction in the number of chlorine atoms in the complex probably leads to an increase in n, the number of resonant nuclei in 2H1 (since there the first coordination sphere, and thus the relaxation rate T are two protons in H 0 but only one in HCl). 2 2- B. [MoOFS] The interpretation of the relaxation times in solutions containing the ' complex. [MoOFS]2' anion is essentially the same as for the [MoOClS]2 - 163 - For protons and deuterons in solutions reasonably dilute in paramagnetic ions the longitudinal relaxation times TlH and T1D decrease with increasing temperature and do not depend on the acidity of the medium, i.e., on the rate of chemical exchange of protons or deuterons. Moreover NSTlD/NSTlH = 39. These 1 -nuclear dipolar interaction modulated by the Brownian rotation of the complex. results correspond to the conditionsiunder which T is determined by electron- The quantity NST1 was found to be independent of the cation for solutions of the complexes (NH4)2[MoOF5], K2[M00F5], Zn[MoOF5] and Cu[MoOF5]. NST1 was found equal to 2 x 10.5 sec'mole/liter. The transverse relaxation times for protons and deuterons (after correction of the effect of quadrupolar interaction) were observed to decrease with increasing temperature. In general, the transverse relaxation times were found to obey Eq. (46) for solutions dilute in [MoOF5]2-. The ratio of T for protons and deuterons varies from 2.42 at 273°K lN/TZN to 3.24 at 335°K. When the solution pH is increased, the ratio TIN/TZN also increases somewhat. The rates of relaxation for fluorine nuclei do not depend upon the pH of the solution and increase six-fold as the temperature is raised from 273°X to 335°K. However, the ratio TlF/TZF remains constant and is equal to 2.67. For solutions of the complexes (NH4)2[M00F5], K2[MoOF5], and Zn[MoOFS] the ratio NSTZH/NSTZF = 1.2, which corresponds within experimental error to the value of YFZ/YHZ. These results indicate that the nuclear relaxation times are determined by electron-nuclear dipolar interaction and that the lifetimes of hydrogen nuclei (protons and deuterons) and fluorine nuclei in the first coordination Sphere are fairly long (> 10’ssec). - 164 - For solutions of Cu[MoOFS], the ratio of NSTZH/NSTZF equals 200, due to the relaxation of the F_ ions in the first coordination sphere of Cu(II). From the data for solutions of this complex the lifetime in the first coordination Sphere of Cu(II) is calculated to be 10"7 sec. For concentrated solutions of 2N was [MoOFS]2- in aqueous hydrofluoric acid the nuclear relaxation time T found to be determined by electron exchange. An evaluation of the relaxation times yielded values of the correlation times and electron—nuclear coupling constants in good agreement with EPR and~ NMR frequency shift data. Further calculation yielded a value for n, the number of resonant nuclei in the first coordination sphere, of approximately four. Thus the [MoOF5]2' complex may be formulated as (MoO(HF)5]5+ or [MoOFS(H20)2]2-. C. [Mo(OCH3)2C14] Complex. The relaxation times for dilute solutions of the complexes C5H6N[Mo(OCH3)2C14], [(CH N][Mo(OCH3)2C14], and C9H8N[Mo(OCH3)2C14] in methanol can be interpreted 3)4 by using Eqs. 45 and 46. The nature of the cation had no effect upon the observed relaxation rates. An analysis of the experimental data yield values for the rotational correlation time in good agreement with values obtained from EPR line- width measurements. Calculation yielded a value for n of approximately 6, which is in good agreement with the formula [Mo(OCH3)2Cl4]T Comparison of nuclear and electronic relaxation results indicated that for solutions above 0.1M in [Mo(OCHS)ZCl4]' the relaxation times are determined by electron exchange. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. K. REFERENCES DeArmond, B. B. Garrett, and H. S. Gutowsky, J. Chem. Phys., 423 1019 (1965). C. B. J. R. Hare, I. Bernal, and H. B. Gray, Inorg. Chem., 1, 831 (1962). R. McGarvey, J. Phys. Chem., 11, 51 (1967). . D. Dowsing and J. F. Gibson, J. Chem. Soc., 1291, 655. . P. Haight, Jr., J. Inorg. Nucl. Chem., 23'1612 (1964). . P. Allen and H. M. Neumann, Inorg. Chem., 23 1612 (1964). . Wendling, Bull. Soc. Chim. France, 1292, 413. . I. Ryabchikov, I. N. Marov, Yu. N. Dubrov, V. K. Belyaeva, and N. Ermakov, Dokl. Akad. Nauk SSSR, 169, 1107 (1966). I.-Ryabchikov, I. N. Marov, Yu. N. Dubrov, V. K. Belyaeva, and N. Ermakov, Dokl. Akad. Nauk SSSR, 165, 842 (1965). 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