4 Applications of Electron Resonance Spectroscopy By G . R. LUCKHURST Department of Chemistry The University of Southampton SO9 5NH ELECTRON resonance is now an extremely well understood branch of spectroscopy and there have been few if any new developments. Naturally an increasing number of app!.ications of electron resonance to problems in chemistry have been reported. The arguments for a review of such electron resonance studies in isolation from other techniques are mainly historical and should not be pushed too far. However this Report follows tradition and deals in some depth with a selection of the more interesting applications. Although the last comprehensive Report was for 1966,' only the literature for 1969 will be surveyed here. There have of course been Reports dealing with applications in organic chemistry.2 Numerous other reviews have also appeared, and these include electron resonance studies in molecular biology organic chemi~try,~,~ and inorganic chemistry,6 as well as two general review^.'.^ The application of electron resonance to triplet state studies has also been discussed.' The widths of the spectral lines are just as important as their positions and two reviews on the factors which determine linewidths have appeared.",' ' As we shall see the spectra of a large number of radicals in the condensed phases have been reported whereas new species in the gas phase are still rare.Although gas-phase electron resonance'2 will not be dealt with here a list of the recent successes may prove comforting. The following diatomics have been ' N.M. Atherton A. J. Parker and H. Steiner Ann. Reports 1966 63A 62. A. Horsfield Ann. Reports 1967 64B 29; C. Thomson ibid. 1968 65B 17. 0. H. Griffith and A. S. Waggoner Acc. Chem. Res. 1969 2 17. E. G. Janzen Acc. Chem. Res. 1969,2 279. I. N. Marov V. K. Belyaeva A. N. Ermakov and Yu. N. Dubrov Zhur. neorg. Khim, 1969 14 2640. M. C. R. Symons Ann. Rev. Phys. Chem. 1969,20,219. C. Thomson Quart. Rev. 1968 12 45. l o A. Hudson and G. R. Luckhurst Chem. Rev. 1969 69 191. ' I W. B. Lewis and L. 0. Morgan Transition Metal Chem. 1968 4 33. ' A. Mackor Chem. Weekblad 1969 65 13. ' A. Carrington and G. R. Luckhurst Ann. Rev. Phys. Chem. 1968 19 31. A. Carrington Inst. Petrol. 4th Conf. Spectroscopy 1968 157 38 G. R. Luckhurst reported :-SF SeF,' NS,14 and SeO l S The scope of this area was considerably increased by the observation of two linear triatomics NCO and NCS.16 Radicals.-The study of small neutral radicals has usually demanded the attachment of an electron beam to the spectrometer.l 7 This restrictive require-ment has now been removed'8*19 and a wide range of radicals R' can be produced in observable amounts by hydrogen abstraction from RH. The hydrogen atom is removed by the t-butoxyl radical which is conveniently formed by U.V. irradia-tion of di-t-butyl peroxide. Using this technique Krusic and Kochi have studied numerous alkyl radicals such as cyclopropylcarbinyl,20 cyclobutenyl,' and cyclopentyl.'8 The power of this technique is demonstrated by the following example. The two splittings of the c1 and protons in the allyl radical (1) are predicted" and found17 to be different.The coupling constants are in fact, 38.95 MHz and 41.50 MHz.17 By starting with either cis or trans but-2-ene the two methyl substituted allyl radicals can be generated.23 Analysis of their spectra shows that the larger splitting must be associated with the p position contrary to both molecular orbital calculations. 22 Similar non-equivalences in methylene splittings have now been observed in a number of radicals e.g. the 2- and 3- thenyl radical^,'^ although no assignments have been made. H Until recently few organometallic radicals had been studied. Presumably the large amounts of substrate required for hydrogen atom abstraction by hydroxyl radicals in a flow systemz5 is prohibitive.The use of the t-butoxyl radical has removed this difficulty and a variety of radicals have been observed. For example, tetramethylsilane yields the trimethylsilylmethyl radical Me3SicH, whereas l 3 A. Carrington G . N. Currie T. A. Miller and D. H. Levy J . Chem. Phys. 1969 50, l 4 A. Carrington B. J. Howard D. H. Levy and J. C. Robertson Mol. Phys. 1968 15, l 5 A. Carrington G. N. Currie D. H. Levy and T. A. Miller Mol. Phys. 1969 17 535. l 6 A. Carrington A. R. Fabris and N. J. D. Lucas J . Chem. Phys. 1968 49; 5545; '' R. W. Fessenden and R. H. Schuler J . Chem. Phys. 1963,39 2147. l 8 P. J. Krusic and J. K. Kochi J . Amer. Chern. SOC. 1968 90 7155. l 9 A. Hudson and H. A. Hussain Mol. Phys. 1969 16 199. 2 o J . K. Kochi P. J. Krusic and D.R. Eaton J . Amer. Chem. SOC. 1969 91 1879. '' P. J. Krusic J. P. Jesson and J. K. Kochi J . Amer. Chem. SOC. 1969 91 4556. "A. Hinchliffe and N. M. Atherton Mol. Phys. 1967 13 89; J. A. Pople D. L. Beveridge and P. A. Dobosh J . Amer. Chem. SOC. 1968,90 4201. 2 3 J. K. Kochi and P. J. Krusic J . Amer. Chem. SOC. 1968 90 7157. 2 4 A. Hudson H. A. Hussain and J. W. E. Lewis Mol. Phys. 1969 16 519. 2 5 W. T. Dixon R. 0. C. Norman and A. L. Buley J . Chem. SOC. 1964 3625. 2 6 A. Hudson and H. A. Hussain J . Chem. SOC. ( B ) 1969 793. 2726. 187; H. Uehara and Y. Morino ibid. 1969 17 239. A. Carrington A. R. Fabris and N. J. D. Lucas Mol. Phys. 1969 16 195 Applications of Electron Resonance Spectroscopy 39 with trimethylsilane the trimethylsilyl radical is formed.27 The radical con-centration is so high that silicon satellite lines are readily and in the radicals SiH3 and SiMe the silicon splittings are 745 and 507 MHz respectively, indicating a change from a pyramidal to a more planar structure.In contrast, alkyls of trivalent metals do not yield an organometallic radical but simply an alkyl radical :28 R3M + Bu'O' + R2MOBu' + R' Similar radicals can also be observed on U.V. irradiation of acyl peroxides.29 Unstable radicals are often postulated in many reaction schemes but unlike the systems just described it is not possible to establish a sufficiently high stationary concentration for detection by modern spectrometers. A technique, known as spin-trapping has been developed to overcome this difficulty. The basic idea is to trap the radical as it is formed as another more stable radical whose structure can then be determined by electron resonance.For example, the radicals react with nitrones or nitroso compounds to produce stable nitroxides. The analysis of the resulting nitroxide spectrum may then identify the scavenged radical.30 For example t-nitr~so-butane~' will react with R' to give the nitroxide RNOBu'. Nitrosobenzene gives a similar radical although the resulting spectrum may be more difficult to analyse. In contrast when phenyl-t-butyl nitrone is used as a trap the nature of the radical is inferred from the P-proton coupling in the nitroxide P~CH(R)NOBU'.~~ In a relatively short period of time this tech-nique has been used to study numerous reactions including nickel peroxide oxidation^,^ photolysis of organometallic~,~~ hydroxyl radical attack on sulph~xides,~~ N-bromosuccinimide oxidation^,^^ polymerisation of ~tyrene,~ and photolysis of indoles phenoles disulphides and thi01s.~~ The following application is of particular interest.When a solution of nitrobenzene in THF is U.V. irradiated an e.s.r. spectrum similar to that of the nitrobenzene anion but with an additional doublet splitting is ~btained.~' The radical responsible for the spectrum was thought to be the protonated nitrobenzene anion,j7 but it is now known to be the nitroxide (2) formed by addition of a THF radi~al.~'" The initial formation of the THF radical by U.V. irradiation has been demonstrated 2' P. K. Krusic and J. K. Kochi J . Amer. Chem. Soc. 1969 91 3938; S.W. Bennet, C. Eaborn A. Hudson H. A. Hussain and R. A. Jackson J. Organometallic Chem., 1969 16 P36. 2 8 P. J. Krusic and J. K. Kochi J . Amer. Chem. SOC. 1969 91 3942; A. G. Davies and B. P. Roberts Chem. Comm. 1969 699. 2 9 J. K. Kochi and P. J. Krusic J. Amer. Chem. Soc. 1969 91 3940. 3 0 C. Lagercrantz and S. Forshult Nature 1968 218 1247. " G. R. Chalfort M. J. Perkins and A. Horsfield J . Amer. Chem. Soc. 1968 90 7141. 3 2 E. G. Janzen and B. J . Blackburn J . Amer. Chem. Soc. 1969 91 4481. 3 3 S. Terabe and R. Konaka J . Amer. Chem. Soc. 1969 91 5655. 34 C. Lagercrantz and S. Forshult Acta Chem. Scand. 1969 23 81 1. 3 5 C. Lagercrantz and S . Forshult Acta Chem. Scand. 1969 23 708. 36 I. H. Leaver G . C. Ramsay and E. Suzuki Austral. J. Chem.1969 22 1891 ; 1. H. 3 7 R. L. Ward J. Chem. Phys. 1963 38 2588. 3 8 ( a ) D. J. Cowley and L. H. Sutcliffe Chem. Comm. 1968 201 ; ( 6 ) D. J . Cowley and Leaver and G. C. Ramsay ibid. 1969 22 1899. L. H. Sutcliffe Trans. Faraday Soc. 1969 65 2286 40 G. R. Luckhurst by the use of the spin trap phenyl-t-butyl n i t r ~ n e . ~ ~ In fact mono-protonated 2,3,5,6-tetrachloronitrobenzene anion has been ~bserved.~ 8b Alkali-metal reduction has been used to generate radical anions for many years. However recent papers have revealed that the chemistry of such systems is not always fully understood. For example sodium reduction of naphthalene dissolved in THF gives a spectrum originating from two radical anions.40 One species was the ion pair formed with the sodium cation while the other was thought to be the free anion.Measurement of the relative intensity of the two spectra as a function of temperature then gave the dissociation constant. However the relative intensity has been found to depend on the nature of the pretreatment of both the solvent and the sample tube.41 The spectrum thought to be caused by the free anion is clearly that of the ion pair with the potassium cation present as an impurity possibly from the glass of the sample tube. The unpaired electron in the benzene anion occupies the symmetric and anti-symmetric orbitals equally. However if the solution of the anion is warmed a 15-line spectrum is obtained which implies that the electron now occupies the anti-symmetric orbital.42 The degeneracy of the orbitals was thought to be split by the presence of a counter ion.42 Careful examination of the spectrum reveals a further splitting of each line into at least twelve component^.^^ Although the radical responsible for the spectrum was not identified it cannot be the benzene anion.The 15-line spectrum cannot always be although addition of lithium chloride is found to induce the change from the normal seven line spe~trum.~’ These experiments do not provide any evidence for removal of the degeneracy by an external perturbation. However in the solid phase at 77K the spectrum of the benzene anion contains seven lines whereas at 4.2K only five lines are observed with a spacing of 15.7 MHz. The unpaired electron now occupies the anti-symmetric orbital because the degeneracy is removed by either the Jahn-Teller effect or more probably the crystal field of the 3 9 E.G. Janzen and J. L. Gerlock J . Amer. Chem. SOC. 1969,91 3108. 4 0 N. M. Atherton and S. I. Weissman J . Amer. Chem. SOC. 1961 83 1330. 4 1 P. Graceffa and T. R. Tuttle jun. J. Chem. Phys. 1969 50 1908; G. E. Werner and 4 2 W. Kohnlein K. W. Boddeker and U. Schindewolf Angew. Chem. Internat. Edn., 43 P. Wormington and J . R. Bolton Angew. Chem. Internat. Edn. 1968 7 954. 44G. L. Malinoski jun. and W. H. Bruning Angew. Chem. Internat. Edn. 1968 7 953. 4 5 K. W. Boddeker G. Lang and U. Schindewolf Angew. Chem. Internat. Edn. 1968, 7 954. 4 6 ( a ) M. T. Jones R. D. Rataiczak and I. M. Brown Chem. Phys. Letters 1968 2 493; ( b ) M. S. de Groot I . A. M. Hesselmann and J.H. van der Waals Mof. Phys. 1969, 16 45 61. W. H. Bruning ibid. 1969 51 4170. 1967 6 360 Applications of' Electron Resonance Spectroscopy 41 Analogous distortions have been observed in the photo-excited triplet states of benzene in perdeuteriobenzene and 1,3,5-trimethylbenzene in B-trimethyl b o r a ~ o l e . ~ ~ ~ The distortions were detected by the departure of the zero-field splitting from cylindrical symmetry. The experiments were however unable to distinguish between a lattice induced or a Jahn-Teller distortion. ENDOR NMR and ELD0R.-ENDOR. The wealth of lines in a solution electron resonance spectrum leads to unnecessary complications and can confuse the analysis. For example the complicated spectrum from the [2,2]paracyclo-phane anion4' had been attributed to the free anion whereas correct analysis shows it to come from the ion pair with potassium.48 The determination of the coupling constants can often be simplified by measuring the electron-nuclear double resonance49 (ENDOR) spectrum of the radical.50 In this experiment the intensity of the electron resonance signal is monitored as the frequency of a radio source is swept.The ENDOR spectrum of a radical containing only protons will consist of pairs of lines centred on the free proton frequency and separated by the appropriate hyperfine splitting. Since each group of equivalent nuclei yields a pair of lines the ENDOR display is readily analysed and has better resolution than the e.s.r. spectrum. The literature has not however been flooded with solution ENDOR spectra because of instrumental problems.ENDOR has been used to measure the coupling constants in substituted triphenylmethyl radicals5 which because of their low symmetry give complex electron resonance spectra. Although the ENDOR spectrum yields the coupling constant the number of nuclei responsible for the coupling is not easily determined. This difficulty can be removed5' by measuring both the ENDOR and e.s.r. spectra. The e.s.r. spectrum is then simulated with the ENDOR coupling con-stants for different numbers of equivalent nuclei until a fit with the experimental spectrum is obtained. In principle the fluorine-substituted radicals studied by Allendoerfer and Maki52 should give fluorine ENDOR lines. These were not observed presumably because of the short nuclear relaxation time for these nuclei,53 although a triple resonance experiment has been suggested to avoid this diffi~ulty.~~ The relaxation time is determined by the rotation of the radical coupled to the anisotropic hyperfine tensor.The pseudo-secular terms (S I *) are the most important for nuclear relaxation and will be large for fluorine bonded directly to a n-system. In contrast fluorine ENDOR has been observed for the kis-(trifluoromethyl) benzene anion52 where the fluorine4ectron dipolar coupling is small. The high resolution of ENDOR makes it possible to study small couplings often unobserved in the e.s.r. spectrum. In the 2,6-di-t,butyl-4 7 A. Ishitani and S. Nagakura Mol. Phys. 1967 12 I . 4 8 F. Gerson and W. B. Martin J . Amer. Chem. Soc.1969 91 1883. 49 G. Feher Phys. Rev. 1956 103 834. 5 0 J. S. Hyde J . Chem. Phys. 1965 43 1806. 5 1 L. D. Kispert J . S. Hyde C . de Boer D. LaFollette and R. Breslow J . Phys. Chem., 5 2 R. D. Allendoerfer and A. H. Maki J . Amer. Chem. Soc. 1969 91 1088. 5 3 J. H. Freed J . Chem. Phys. 1965,43 2312; 1969 50 2271. 1968,72,4276 42 G. R. Luckhurst 4-cyclohexylphenoxyl radical the y protons which can be axial or equatorial do have slightly different ~ p l i t t i n g s . ~ ~ The difference may indicate an angular dependence in the y splittings similar to that encountered for /3 ~ p l i t t i n g s . ~ ~ The ENDOR spectra of biradicals could also be used to determine the triplet-singlet splitting J . The conditions which result in a dependence on J are the same in both e.s.r.and ENDOR spectra.55 The only advantage in using ENDOR would be if the e.s.r. spectrum contained many lines. This is indeed the case for solutions of Tschitschibabin’s hydrocarbon said to have the triplet structure (3).56 However analysis of the ENDOR spectrum shows quite clearly that the para-magnetic species in solution is a substituted p-biphenyldiphenyl radical.55 In the solid phase an e.s.r. spectrum characteristic of a triplet state with D = 404 MHz and E = 14MHz has been observed and attributed to (3).57 In contrast the triplet state spectrum of Schlenk’s hydrocarbon has not been observed.58 The behaviour of this type of hydrocarbon which has been known for many years is not well understood. The use of polarographic techniques for their controlled production from the appropriate dichloride may well help to solve the problem.59 ENDOR presents fewer problems in the solid phase which may be examined at very low temperatures thus increasing the electron spin lattice relaxation time.The paramagnetic product of y-irradiated single crystals of anthracene was shown6’ to be dibenzocyclohexadienyl by measuring the ENDOR spectrum. This identification would have been quite impossible if only the electron resonance spectrum had been available. Provided a methyl group in a radical rotates classically the spectrum will contain a quartet but if the group tunnels between configurations a septet can result.61 The barrier height can therefore be deter-mined from the temperature dependence of the electron resonance spectrum.5 4 R. F. Adams and N. M. Atherton MoI. Phys. 1969 17 673. 5 5 H.-D. Brauer H. Stieger J. S. Hyde L. D. Kispert and G . R. Luckhurst Mol. Phys., 5 6 P. C . Reitz and S. I. Weissman J . Chem. Phys. 1960 33 700. ” H.-D. Brauer H. Stieger and H. Hartmann Z . phys. Chem. (Frankfurt) 1969 63 50. 5 8 E. Ulusoy H. Hartmann and J. Heidberg 2. Nuturfarsch. 1969 24b 249. 5 9 W. Summermann G. Kothe H. Baumgartel and M. Zimmermann Tetrahedron 6 o U. R. Bohme and G. W. Jesse Chem. Phys. Letters 1969 3 329. 6 1 J. H. Freed J . Chem. Phys. 1965 43 1710. 1969 17 457. Letters 1969 3807 Applications of Electron Resonance Spectroscopy 43 Similarly tunnelling is also evident in the ENDOR spectrum and in the 4-methyl-2,6-di-t-butylphenoxyl radical the barrier is found to be 1.2 -t 0-3 G H z .~ ~ The high resolution of ENDOR is valuable in probing the ligand spin distribu-tion in transition metal complexes. Thus an ENDOR study of copper 8-hydroxy-quinolinate yields not only the nitrogen hyperfine tensor but also evidence for ligand proton couplings.63 In solid-state electron resonance the quadrupole coupling is best determined from the line positions of transitions involving both an electron and nuclear spin. Quadrupole couplings for copper in a variety of complexes,64 and for nitrogen in peroxylamine di~ulphonate~' have been measured using these transitions. The accuracy of this technique is limited, whereas in ENDOR the quadrupole coupling appears as a splitting of the lines which can be determined quite a ~ c u r a t e l y .~ ~ It is often difficult or impossible to grow a magnetically dilute single crystal and in electron resonance a powder sample is often used. Provided the aniso-tropies in the magnetic interactions are large the powder spectrum exhibits singularities.66 These may be thought of as originating from radicals with their principal axes parallel to the magnetic field. Use of the singularities in an ENDOR experiment should produce a single crystal spectrum.67 This is indeed the case for the copper 8-hydroxyquinolate complex.68 For organic radicals the poor resolution may make it impossible to select molecules by monitoring a single electron resonance peak. However under these conditions the ENDOR spectrum is found to contain singularities from which the hyperfine tensor may be deter-mined.69 It may also be possible to study the state of aggregation of the solvent molecules using ENDOR techniques.The ENDOR spectrum of the tris(p-toly1)-methyl radical in a toluene glass does not contain a line at the free proton frequency. If the glass is crystallised then an intense peak appears which originates from the dipolar coupling between the unpaired electron and the protons in the matrix.70 The observation of the matrix ENDOR presumably results from the absence of motion in the polycrystalline sample. The line shape might further be used to study the aggregation of the matrix.70 The proton hyperfine tensors in triplet states can also be studied by ENDOR.7' The power of the technique is illustrated by the elegant work of Hutchison and his colleagues in their determination of the spin distribution in the triplet state, from the hyperfine tensors as for example in bi~henylmethylene.~~ Their work 6 2 S.Clough and F. Poldy J . Chem. Phys. 1969 51 2076. 6 3 G. H. Rist and J. S. Hyde J . Chem. Phys. 1969 50,4532. 6 4 H. So and R. L. Belford J . Amer. Chem. SOC. 1969,91 2392. 6 5 D. M. Close and H. N. Rexroad J . Chem. Phys. 1969,50 3717. 6 6 R. Neiman and D. Kivelson J . Chem. Phys. 1961,35 156; B. R. McGarvey Transition 6 7 J. S. Hyde 'Magnetic Resonance in Biological Systems' Eds. A. Ehrenberg B. G. '* G. H. Rist and J. S. Hyde J . Chem. Phys. 1968,49 2449. 6 9 A. L. Kwiram J . Chem. Phys. 1968,49 2860. ' O J. S. Hyde G. H. Rist and L. E. G . Eriksson J . Phys. Chem. 1968 72 4269. 7 1 e.g. P.Ehret and H. C. Wolf Z . Najurforsch. 1968 23a 1740. 7 2 C. A. Hutchison jun. and B. E. Kohler J . Chem. Phys. 1969 51 3327. Metal Chem. 1966 3 89. Malmstrom and T. Vanngard Pergamon Press Oxford 1967 63 44 G. R. Luckhurst also illustrates the difficulty in understanding the factors which determine the ENDOR intensities. ENDOR transitions within the 10,) state of the triplet levels should occur at the free proton frequency.” However they are not ob-served in the spectra of ground state triplets,72 but do appear in the spectra of photo-excited triplets such as benzene.73 N.M.R. It is convenient to think of ENDOR as an n.m.r. experiment in which certain spectral lines come from n.m.r. transitions of those radicals with c1 electron spin whereas those with p spin produce the remaining lines.Then any process which reduces the lifetime of an electron spin state will produce a fluctuating field at the nucleus and so reduce the ENDOR intensity. In particular electron spin exchange caused by radical collisions can decrease the spin-lattice relaxation time TI and lead to the loss of an ENDOR When the spin lifetime is extremely short the nuclear transitions can be observed with an n.m.r. spectro-meter. The transition frequency vp shows a shift from that vD observed in a comparable diamagnetic compound because of the Boltzmann distribution of the electron spins. In fact the shift is7’ where ai is the coupling constant of the ith nucleus with magnetogyric ratio yi. Since each group of equivalent nuclei produces just one line the n.m.r.spectrum will be considerably simpler than the electron resonance spectrum. Further, since the absolute magnitude of the shift is measured experimentally the sign of the coupling constant can also be determined unlike ENDOR. The technique is, however limited by the large linewidths which can make peaks unobservable. Under certain conditions the width AHi is given by The relaxation time T’ decreases with radical concentration and the lines in the spectra of pure liquid free radicals such as the n i t r ~ x i d e s ~ ~ are sharp. Radicals cannot always be studied under these ideal conditions but an ingenious solution has been provided.77 The values of both Tl and the linewidth are reduced by using a free radical such as di-t-butylnitroxide as a solvent. This technique has been used to study the effect of substituents on the spin distribution in phenoxyl radicals.78 The ability to measure small coupling constants with n.m.r.has demonstrated the angular dependence of the y proton splitting in an alkyl chain attached to a phenoxyl radical.79 The nitronylnitroxide (4) contains ” A. M. Ponte Goncalves and C. A. Hutchison jun. J . Chem. Phys. 1968,49 4235. 7 4 J. H. Freed J . Phys Chem. 1967 71 3 8 . 7 5 D. B. Chesnut and H. M. McConnell J . Chem. Phys. !958,28 107. 7 6 N. A. Sysoeva V. I. Sheichenko and A. L. Buchachenko Zhur. strukt. Khim. 1968, ’’ R. W. Kreilick J . Amer. Chem. SOC. 1968 90 27 1 1 5991. ’’ W. Espersen and R. W. Kreilick J . Phys. Chem. 1969 73 3370. 7 9 F. Yamauchi and R. W. Kreilick J . Amer. Chem.SOC. 1969 91 3429. 9 1083 Applications of Electron Resonance Spectroscopy 45 an asymmetric centre and so the methylene protons are expected to be magnetic-ally non-equivalent. The resulting inequality of the methylene proton splittings is revealed in the n.m.r. spectrum of (4) dissolved in di-t-butylnitroxide.80 0 Me 1. Me I 0-The form of the relationship between the fluorine coupling constant and the spin distribution in the radical would seem to be a particularly thorny problem.81 A reasonable relationship is QF = QcPc + QFPF. ( 3 ) but the question in dispute is the relative importance of the two terms. The attempts to estimate the two Q values usually rely on calculations of both pF and pCg2 This procedure is unsatisfactory and in fact pF can be estimated from the widths of the "F n.m.r.lines.83 When the electron-nuclear dipolar coupling is large equation (2) for the linewidth must be m ~ d i f i e d . ~ ~ ~ ~ The width now depends on the hyperfine tensor which for fluorine is dominated by the local spin density pF. Measurement of the line position and width eventually gives both aF and pF.83 Since pc can be calculated fairly accurately measurements for a series of fluorinated phenoxyl radicals show QF to be greater than Qc, although of the same sign.83 On the other hand unrestricted Hartree-Fock calculations appear to reach the opposite conclusion. 82 N.m.r. can be used to study the structure of biradicals. However when the triplet-singlet separation J is comparable to RT equation (1) must be modified to :85,86 - -aiyehS(S + 1) - -Av vp 3kTyi[l + exp(J/RT)] (4) By measuring the shift as a function of temperature it is then possible to determine the absolute magnitude of J .For example bis-galvanoxyl has been shown to have a singlet ground state with a thermally accessible triplet.86 A complementary technique involves measurement of the shift of the solvent peak as a function R. W. Kreilick J. Becher and E. F. Ullman J . Amer. Chem. SOC. 1969 91 51 21. Lewis J . Chem. SOC. (B) 1969 531. N. K. Ray Chem. Phys. Letters 1969 3 261. '' J. Sinclair and D. Kivelson J . Amer. Chem. SOC. 1968,90 5074; A. Hudson and J . W. 8 3 W. G. Espersen and R. W. Kreilick Mol. Phys. 1969,16 577. 8 4 H. S. Gutowsky and J. C. Tai J . Chem. Phys. 1963,39 208. W. D. Horrocks jun.J . Amer. Chem. SOC. 1965 87 3779. 8 6 P. W. Kopf and R. W. Kreilick J . Amer. Chem. SOC. 1969 91 6569 46 G. R. Luckhurst of the concentration N of the paramagnetic species. This shift is proportional to the susceptibility x of the solution8’ which is 3kT + 1 + exp(J/RT) x = so for a given solute the solvent shift is determined by the spin multiplicity S. This multiplicity is not always well defined. For a biradical where the hyperfine interaction is greater than J the system behaves as two monoradicals with S equal to one half. At the other extreme when J/a >> 1 the molecule is a triplet state (S = 1). A range of states exists between these two extremes because the triplet and singlet states are mixed by the hyperfine interaction. An indication of the extent of the mixingcan be obtained from the electron resonance spectrum,88 but if this cannot be analysed the concentration dependence of the solvent shift should give similar information.86 ELDOR.The analysis of an n.m.r. spectrum can often be simplified by the applica-tion of a host of multi-resonance technique^.^^ The close relationship between electron and nuclear magnetic resonance implies that these multi-resonance techniques should also be valuable in electron resonance. The difficulty lies not so much in devising the experiments but in the short electron spin relaxation times which create extreme instrumental problems. These have been overcome for ENDOR and experiments have recently been reported in which the sample is irradiated with two microwave frequencies.This technique which is known as electron-electron double resonance or ELDOR has been applied to solids at liquid helium temperature” and to fluid solution^.^^^^^ In order to appreciate the scope and significance of ELDOR consider a simple example. There are three allowed electron resonance transitions for a nitroxide radical corresponding to the nitrogen nuclear quantum number 1 0 and - 1. At constant magnetic field the transitions would occur at the frequencies wl coo and w- 1. The observing microwave frequency is held constant at wl say the frequency of the pumping microwave source is then swept and the intensity of the electron resonance line at col is monitored.93 When the pump frequency is wo the populations of the two levels involved in this transition will change.This because of nuclear spin relaxation results in a population change for the col transition and produces an ELDOR response when the frequency difference is w1 - coo the nitrogen coupling constant. Similarly when the pump frequency is w- there is another 8’ E. de Boer and C. MacLean J. Chem. Phys. 1966,44 1334. 88 H. Lemaire J . Chim. phys. 1967,64 559; S . H. Glarum and J. H. Marshall J. Chem. 8 9 R. A. Hoffman and S. Forsen Progr. N. M. R . Spectroscopy 1966 1 15. 90 P. P. Sorokin G. J. Lasher and I. L. Gelles Phys. Rev. 1960 118 939; W. P. Unruh and J . W. Culvahouse ibid. 1963 129 2441; P. R. Moran ibid. 1964 135 A.247. 9 1 J . S. Hyde J . C. W. Chien and J. H. Freed J. Chem. Phys. 1968 48 421 I . 9 2 J. S. Hyde R. C. Sneed jun. and G.H. Rist J . Chem. Phys. 1969 51 1404. 9 3 J. S. Hyde L. D. Kispert R. C. Sneed jun. and J. C. W. Chien J. Chem. Phys. 1968, Phys. 1967 47 1374. 48 3824 Applications of Electron Resonance Spectroscopy 47 ELDOR response at twice the coupling constant. In general this combination line will be less intense than the primary line because the population changes have to be transmitted through two spin levels. Clearly ELDOR should be invaluable in unravelling overlapping spectra produced by two or more radicals. The observing frequency would be set on a line from just one of the radicals then only the ELDOR spectrum of that species would be obtained. This is because although the pump changes the spin popula-tions of the other radicals if nuclear relaxation is purely intramolecular there is no means of transferring this change to the monitored transition.The validity of this analytical application has been demon~trated~~ for y-irradiated malonic acid which contains three radicals.94 The intensity of an ELDOR response depends on the ratio of the electron to the nuclear relaxation times,” and may therefore vary from one nucleus to another. As we have seen the principal nuclear relaxation process for radicals in solution results from the perturbing pseudo-secular terms S I * . Those nuclei with large anisotropic hyperfine tensors will therefore give the greatest response, whereas other nuclei may not give an ELDOR signal. It should be possible to determine large coupling constants when they are obscured by many smaller couplings.For example the two nitrogens in DPPH are not quite equivalent, although analysis of the multi-line electron resonance spectrum is unable to yield the difference with any great accuracy. In contrast the ELDOR spectrum contains only two primary lines one from each of the two nitrogens corresponding to coupling constants of 22.246 and 27-307MH~.’~ The measurements do indicate the potential of the technique although the precise structure of DPPH is not particularly important. The dependence of the ELDOR signal on both electron and nuclear relaxation times means that relaxation processes may be studied by ELDOR.9’ The results of a preliminary study” are in qualitative agreement with the theory developed for high power multi-resonance experiment^.^^,^^ Information about these relaxation processes may also be obtained from the linewidths of low power electron resonance spectra.” Further ELDOR studies are thus required to see whether their complicated theoretical analysis can provide any chemical informa-tion not contained in the linewidths of an electron resonance spectrum.Weak Molecular Interactions. Liquid Crystals. The isotropic rotational Brown-ian diffusion in a solution averages the anisotropic magnetic interactions to zero. As a consequence only the scalar interactions can be obtained from a solution electron resonance spectrum. This limitation can be removed by studying a magnetically dilute single crystal but for most organic radicals this is impractical. Measurements in a nematic liquid-crystallineg5 solvent can often provide a partial solution to the problem.96 The magnetic field in an X-band spectrometer is sufficient to align the nematic liquid crystal with the long molecular axis parallel y 4 A.Horsfield J. R. Morton and D. H. Whiffen Mof. Phys. 1961 4 327. 9 5 A. Saupe Angew. Chem. Internat. Edn. 1968 2 97 ’‘ A. Carrington and G. R. Luckhurst Ma/. Phys. 1964 8 401 48 G. R. Luckhurst to the field. The anisotropy in the solute-solvent interaction then results in partial alignment and hence shifts in both the g factor and coupling constant :97 The ordering matrix 0 in equations (6) and (7) describes the partial alignment of the solute.98 The g and hyperfine shifts for perinaphthenyl triphenylmethyl, and pentaphenyl cyclopentadienyl have been determined by measuring their electron resonance spectra above and below the nematic-isotropic transition point of 4,4'-dimethoxyazoxybenzene.99 The results for perinaphthenyl are in good agreement with previous measurements.loo The hyperfine shifts were used to confirm the positions of negative spin density. Surprisingly'00 the hyperfine shifts were found to be in good agreement with their theoretical values obtained from the McConnell and Strathdee equations. The component of the g tensor perpendicular to the molecular plane was found to be close to the free spin value in agreement with Stone's theory."' This theory has also been tested'" by measuring the isotropic g factors for a number of phenyl substituted aromatic radicals. The g tensors have been calculated for a number of nitroxide radicals but there are few measurements with which to compare them.'03 The electron resonance spectrum of perchlorodiphenylmethyl has been measured in both phases of 4,4'-dimethoxyazoxybenzene in an attempt to determine the chlorine hyperfine ten~or."~ The tensor component can only be determined from a partially aligned spectrum under certain conditions.For example if the ordering matrix is axially symmetric about the 3 axis then equation (7) reduces to97 i - a = O,,A;, (8) and if fi33 is known A i 3 can be determined. In the case of perchlorodiphenyl-methyl its ordering was obtained from the carbon-13 hyperfine shift.'04 The component of the chlorine tensor along the 3 axis i.e. the axis parallel to the carbon 2 p orbital was found to be k47.0 MHz.The other components of the tensor cannot be determined using this technique although they have been esti-')' G. R. Luckhurst Mol. Crystals 1967 2 363. 98 A. Saupe Z. Naturforsch 1964 19a 161. 99 M. Mobius H. Haustein and M. Plato Z. Naturforsch. 1968 23a 1626. l o o S. H. Glarum and J. H. Marshall J . Chem. Phys. 1966,44,2884; H. R. Falle and G. R. Luckhurst Mol. Phys. 1966 11 299. A. J. Stone Mol. Phys. 1963 6 509; 1964,7 31 1 . ihid. 1969 24a 1083. l o ' K. Mobius and M. Plato Z. Naturforsch. 1969 24a 1078; M. Plato and K. Mobius, l o 3 0. Kikuchi Bull. Chem. SOC. Japan 1969,42,47 1472. I o 4 H. R. Falle G. R. Luckhurst A. Horsfield and M. Ballester J . Chem. Phys. 1969, 50 258 Applications of Electron Resonance Spectroscopy 49 mated by combining the results for a number of chlorine-containing radical^.'^' The sign of the component A i 3 does depend on the sign of the isotropic chlorine splitting.If the chlorine spin density is taken to be positive then the liquid crystal results show that the isotropic splitting is also positive in agreement with the single crystal studylo5 and linewidth measurements.'06 The chlorine quadrupole tensor could not be determined in these liquid crystal experiments because of the axial symmetry of the alignment about the field direction.'04 Destruction of the axial symmetry would lead to the retention of the I IT terms in the spin Hamiltonian and hence a dependence of the spectrum on the quadrupole tensor. Nematic liquid crystals can be alignzd by an electric field'07 and if this is applied perpendicular to the magnetic field the axial sym-metry would be destroyed.Electron resonance experiments involving both electric and magnetic fields have been described but the vanadium quadrupole splitting of the solute vanadyl acetylacetonate was too small to be determined. lo* Alternatively if the anisotropic hyperfine tensors are known from solid-state studies the shifts can be used to study the anisotropic properties of liquid crystals. A convenient paramagnetic probe for such measurements is vanadyl acetyl-acetonate. The g and hyperfine tensors are essentially axially symmetric about the 1 7 - 0 bondlo9 and so the shifts determine the degree of order O, for the V - 0 axis, (9) where cp is the angle between the symmetry axis and the magnetic field.'' The solute order has been determined as a function of temperature for a wide range of nematogens.' l o This dependence can be used to test the form of the angular pseudo-potential U which is the potential of one molecule resulting from its interaction with all the others. The degree of order is calculated by taking the appropriate Boltzmann average.' ' When dispersion forces are dominant U takes the form"' 0 3 3 = (3 cos2 4p - 1)/2 6&0 2 v2 u = - 4 3 cos2 cp - 1). The presence of a single parameter JE implies that the order should be a universal function of the reduced temperature T/TK where TK is the nematic-isotropic transition point. The potential is found to be qualitatively but not quantitatively correct.' l o l o ' R. P. Kohin J. Chem.Phys. 1969 50 5356. l o ' E. F. Carr Ado. Chem. Ser. 1967 63 76. A. Hudson Chem. Phys. Letters 1969 4 295. D. H. Chen and G. R . Luckhurst Mol. Phys. 1969 16 91. R. Wilson and D Kivelson J. Chem. Phys. 1966,44 154. ' I ' D. H. Chcn P G 7dmes and G. R. Luckhurst Mol. Crystals and Liq. Crystals 1969, 8 7 1 . ' I 1 W. Maier and A. Saupe Z. Nuturforsch 1959 14a 882 50 G. R. Luckhurst Similar measurements have been reported with nitroxide radicals (5) as the paramagnetic probes' 12a although no detailed analysis of the ordering matrix was presented. In principle these experiments are of interest because the probe, like a liquid crystal is rod-like. Indeed equation (10) for the pseudo-potential assumes a cylindrically symmetric liquid crystal. In practice a liquid-crystalline molecule is not cylindrically symmetric but may achieve it through rapid rotation about the long Unfortunately it is not possible to confirm this for the nitroxide probes since all the diagonal elements of 0 have been determined in the principal axis system for the g and nitrogen hyperfine tensors.It is not possible therefore to obtain the principal components of the ordering matrix to see if it is cylindrically symmetric. Intriguing experiments with L-shaped nitroxides have been reported which claim to demonstrate the alignment of each arm of the L.l12' The rate of exchange between these orientations is slow and so a superposition of spectra is observed. These results are unexpected and one would like to be quite certain of their reproducibility.The addition of a non-mesomorphic solute to a liquid crystal produces the expected depression of the nematic-isotropic transition point.' l4 It was not known whether the order was also decreased. Determination of the order for vanadyl acetylacetonate dissolved in mixtures of 4,4'-dimethoxyazoxybenzene and numerous solutes shows that the order is not decreased.l15 Indeed the order at a given reduced temperature is found to be independent of the nature or concentration of the solute a result which can be rationalised using the pseudo-potential in equation Determination of the temperature dependence of the probe's order is not the most satisfactory way of testing the pseudo-potential. In particular it is unable to distinguish between errors in the angular part of the potential or in the form of the coefficient.Knowledge of the probability distribution function p(cp), would be more useful since A d a exp ( - U / W (11) Fortunately p ( q ) can be determined when the probe tumbles slowly enough to give a polycrystalline spectrum."' By assuming that the intensity of an A peak of the vanadyl acetylacetonate spectrum is determined entirely by the ''' ( a ) P. Ferruti D. Gill M. A. Harpold and M. P. Klein J . Chem. Phys. 1969,50,4545; (b) G. Havach P. Ferruti D. Gill and M. P. Klein J . Amer. Chem. Soc. 1969,91 7526. H. Lippmann Ann. Phys. (Leipzig) 1957 20 265. J. S. Dave and M. J . S. Dewar J . Chem. SOC. 1954,4616. D. H. Chen and G. R. Luckhurst Trans. Faraday SOC. 1969 65 657. 'I6 C. F. Schwerdtfeger and P. Deihl Mof.Phys. 1969 17 417 Applications of Electron Resonance Spectroscopy 51 number of molecules with their V-0 bonds parallel to the magnetic field the pseudo-potential was shown to exhibit a simple cos2 cp dependence.' Although the basic assumption in the analysis is in error the qualitative conclusion still holds. ' Suspensions of colloidal copper complexes behave in many ways like nematic liquid crystals and the particles are aligned by a magnetic field.' '' However the size of the particles prevents rapid molecular motion and a polycrystalline copper spectrum is observed."' The intensities and shapes of the lines in the spectrum are determined by the anisotropic distribution function. By analysing the spectral lineshapes theoretically it should be possible to determine the coefficients in the distribution function.The accuracy of the present analysis may be severely limited by the numerous approximations in the lineshape calculations. 2o Electron resonance studies of the smectic phase have been reported.12' The high viscosity of the smectic phase prevents its alignment by a magnetic field, although a macroscopically ordered phase can be obtained by employing the following device. A compound such as 4,4'-di-n-heptyloxyazoxybenzene which exhibits both a nematic and smectic phase is used as a solvent. The nematic phase is first aligned by a magnetic field and the order is then frozen in by lowering the temperature below the nematic-smectic transition point. l 2 ' This type of solvent matrix may be important in structural studies because the orientation of the solute with respect to the field can be readily changed.The order of the probe, vanadyl acetylacetonate was found to be less in the smectic than the nematic phase. Analogous experiments have been performed using n.m.r. but with a purely smectic solvent.'22 The observation of alignment is unexpected. It may result from the depression of the smectic transition point below a nematic transi-tion by the large solute ~0ncentration.l~~ Alternatively the fluid may adopt transitory nematic characteristics prior to the formation of the smectic meso-phase. Isotropic Interactions. The anisotropic solute-solvent interactions in liquid-crystalline solvents are responsible for the changes in the spectrum when the solvent is aligned. The scalar couplings may also change when there is an iso-tropic solute-solvent interaction.The nitrogen coupling in the nitrobenzene anion increases with the polarity of the s01vent.l~~ This and the concentration dependence in mixed solvents has been interpreted on the basis of the formation of a hydrogen-bonded solute-solvent adduct :' ROH + X- ROHX-' I ' P. Diehl and C. F. Schwerdtfeger Mol. Phys. 1969 17 423. "* P. G. James and G. R . Luckhurst Mol. Phys. in the press. ' I 9 J . R. Wasson C. Trapp C. Shyr and D. Smith J . Chem. Phys. 1968 49 5197. C. Trapp D. Smith and J. R. Wasson J . Chem. Phys. 1969 51 1419. P. D. Francis and G. R. Luckhurst Chem. Phys. Letters 1969 3 213. 1 2 ' C. S. Yannoni J . Amer. Chem. SOC. 1969,91 461 1 . 1 2 3 J . S. Dave P. R . Patel and K.L. Vasanth Mol. Crystals and Liq. Crystals 1969 8 93. 1 2 4 J. M. Gross J. D. Barnes and G. N. Pillans J . Chem. SOC. ( A ) 1969 109. 1 2 5 J. Gendell J. H. Freed and G. K. Fraenkel J . Chem. Phys. 1962 37 2832 52 G. R. Luckhurst The equilibrium constant for adduct formation can then be obtained from the concentration dependence of the coupling constants. At high alcohol concentra-tion the fluorenone ketyl exhibits a departure from the predicted behaviour which may be caused by changes in the solvent sheath surrounding the adduct.'26 In many studies the solvent activity has been replaced by its concentration and this may have produced deviations from the simple theory. The p-chloronitrobenzene radical anion has been studied in mixtures of acetonitrile and alcohols for which activities are a~ailab1e.I~' In order to obtain complete agreement with theory it is necessary to invoke equilibria between a range of solvated anions X(S,) .. . X(S,)(S,) . . . X(S,) which also increases the number of adjustable parameters. The analysis ignores any equilibria with counter ions which may not be valid, for there is strong evidence for the existence of ion pairs in acetonitrile'24 and ethereal solvents.'28 Indeed the structure of the ion pair has been shown to undergo changes on solvation.'28 The variations in the coupling constants are readily interpreted in terms of an increase in the Coulomb integral for the oxygen atom on formation of the adduct. The problem is not so easy for the solvent dependence of the coupling constant in vanadyl acetylacetonate.' 29 Originally the solvent dependence was thought to be caused by chelation at the six position.' 29 Although this is certainly true for solvents such as pyridine an exhaustive study in 41 solvents has shown that solvation of the vanadyl oxygen is also important.130 The formation of an ion pair may be regarded as an extreme case of anion solvation. The cation perturbs the spin distribution and for the nitrobenzene anion the nitrogen splitting is found to depend on the cationic radius.124,'31 This dependence is to be expected if the electric field generated by the cation perturbs the spin distribution. Unlike solvation there are strong forces holding the ion pair together and so its long lifetime often results in the observation of metal hyperfine structure.The magnitude of the metal coupling and the sym-metry of the spin distribution makes speculation about the geometry of the ion pair possible. Thus in the m-dinitrobenzene anion the sodium cation is in the plane of the ring and symmetrically placed with respect to the oxygens of a given nitro For the caesium cation however the observation of an alter-nating linewidth effect implies that the cation exchanges rapidly between the two nitro groups. A similar situation is suggested for the 1,2-semiquinones, although an alternating linewidth effect is only observed with the barium salt.'33 Possibly the most detailed study of the geometry of an ion aggregate has been made for the triplet dianion of triphenylene which is associated with two counter ions.Calculations of the zero-field splitting parameters as a function of geometry, suggest that the cations are ca. 2-3 8 above and below a non-central ring.' 34 G. R. Luckhurst and L. E. Orgel Mol. Phys. 1964,8 117. Sr. M. T. Hertrich 0. P. and T. Layloff J . Amer. Chem. SOC. 1969 91 6910. K. Nakamura and N . Hirota Chem. Phys. Letters 1969,3 137. 1 2 9 I. Bernal and P. H. Reiger Znorg. Chem. 1963 2 256. I J 0 C. M. Guzy J. B. Raynor and M. C. R. Symons J . Chem. SOC. ( A ) 1969,2791. I J 1 J. M. Gross and J. D. Barnes J . Chem. SOC. ( A ) 1969 2437. l J 2 R. F. Adams and N. M. Atherton Trans. Faraday SOC. 1969 65 649. 1 3 3 E. Warhurst and A. M. Wilde Trans. Faraday SOC. 1969 65 1413. J. L. Sommerdijk J. A. M. van Broekhoven H. van Willigen and E. de Boer J .Chem. Phys. 1969 51 2006 Applications of Electron Resonance Spectroscopy 53 The results of ion-pair studies have shed considerable light on the structure of these species. However the number and nature of the species present in solution may be more complex than previously imagined. Thus fluorenone ketyl in methyltetrahydrofuran has been shown to exist as an ion pair three ion quartets, and an aggregate of numerous ions.'35 The nature of the solvent can alsa have a profound effect on the structure of the ion pair as experiments with tetraglyme and ethereal solutions of the sodium-naphthalene system have shown.' 36 The smallest cation is the proton which it is claimed,' 37 forms a stable adduct with 2,2,6,6-tetramethylpiperidine N-oxyl. The electron resonance spectrum shows the expected doublet splitting of 9.3 MHz an increase in the nitrogen split-ting to 61.2 MHz and a decrease in the g-factor to 2.0042.A similar adduct is formed between the nitroxide and aluminium trichloride which has an aluminium splitting of 24.7 M H z . ' ~ ~ The change in the nitrogen splitting might provide a convenient probe of strength of the Lewis acid. In fact these strengths have been estimated from the electron resonance spectra of adducts with titanium cyclo-pentadienyl c~mplexes.'~~ Such a scale can only be established on an empirical basis because of the many complex factors which determine an isotropic coupling constant. Molecular vibrations can and do lead to the temperature dependence of coupling constants as for example in the methyl radi~a1.l~' If the vibrational frequencies are solvent dependent then the coupling constants will exhibit an apparent solvent dependence.Thus the methylene coupling constant in the phenoxyl radical (6) is temperature de~endent'~' presumably because of the torsional vibrations as in the 4-amino-2,6-di-t-butylphenoxyl and other radi-c a l ~ . ' ~ ~ The observed solvent dependence possibly results from a change in the barrier height. The model used to interpret the experiments involves solvent-solute charge transfer to modify the spin distrib~tion'~' and is probably incorrect. 1 3 5 K. Nakamura and 1 3 ' K. Hofelmann J. 4645. CH2 I 0 (6) 'Me N. Hirota Chem. Phys. Letters 1969,3 134. Jagur-Grodzinski and M. Szwarc J . Amer. Chem. SOC. 1969 91, 1 3 ' B.M. Hoffmann and T. B. Eames J . Amer. Chem. SOC. 1969 91 2169. 1 3 * B. M. Hoffmann and T. B. Eames J . Amer. Chem. SOC. 1969,91 5168. 1 3 9 G . Henrici-Olive and S. Olive J . Organometalic Chem. 1969 17 83. 14' H. Fischer and H. Hefter Z. Naturforsch. 1968 23a 1763; J. M. Riveros and S. Shih, I4'S. Aono and M. Suhara Bull. Chem. SOC. Japan 1968,41 2553. 1 4 ' A. J. Stone and A. Carrington Trans. Faraday SOC. 1965 61 2593; P. D. Sullivan, J . Chem. Phys. 1969 50 3 132. J . Phys. Chem. 1969 73 2790 54 G. R. Luckhurst The hyperfine shifts for a paramagnetic probe dissolved in a liquid crystal could be used to study the nature of the order-disorder transition. Clearly other spectral parameters can be employed to investigate phase transitions. Indeed, this is the basis of the spin-labelling technique for investigating bimolecule~.~ Few other studies have been reported although the ferroelectric phase transition in Rochelle salt has been detected by changes in the spectrum of copper ions added to the The reversibility of the transition induced by an electric field has also been demonstrated by monitoring the spectral changes.The phase transitions in ammonium nitrate have been detected as changes in the intensity of the spectrum of added manganese ions.'44 Of course phase transitions in the paramagnetic ion-radical salts of for example tetracyanoquinodimethane have been studied by electron re~0nance.l~~ The formation of triplet dimers in a pure free radical galvanoxyl is suspected and a transition is observed at 81K.Pressure has long been a neglected variable in electron resonance spectroscopy. The solvent viscosity has been increased by the use of pressure in order to study line broadening produced by molecular reorientation 47 and radical collisions. 14* More recently equipment has been developed to generate pressures as high as 400 atm'49 and used to investigate the equilibrium : eS&. + Ph $ Ph-The electron resonance spectrum is found to be extremely sensitive to pressure because of the large volume change - 71 ml mol-' for the equilibrium. This suggests a large molar volume of the solvated electron. States of Higher Multiplicity.-The scalar spin Hamiltonian required to analyse the solution spectra of biradicals is'" (12) Although there is now some d o ~ b t ~ ~ ~ ~ about the structure of the biradi~als'~' which this Hamiltonian was proposed to analyse there can be no doubt about the form of %.The mixing of the triplet and singlet states by the hyperfine inter-action when J is comparable to a'') has been observed for a wide range of nitrox-idelS and iminoxyl biradicals.'52 The paramagnetic units contained in the biradicals are usually separated by alkyl chains. Recently stable conjugated = [g(l)s,(l) + g ( 2 ) ~ ( 2 ) ] p ~ + Ca(i)s(iI. p i ) + js(1) ~ ( 2 ) I 1 4 3 M. Schara and M. Sentjurc J . Chem. Phys. 1969 50 1493. 1 4 4 S. D. Pandey and G. C . Upreti Chem. Phys. Letters 1969 3 526. 14' I. M. Brown and M. T. Jones J. Chem. Phys. 1969 51 4687; J. C . Bailey and D. B. ' 4 6 K. Mukai Bull. Chem. Soc. Japun 1969 42 40.14' N. Edelstein A. Kwok and A. H. Maki J . Chem. PhyA. 1964 41 179. 14' N. Edelstein A. Kwok and A. H. Maki J. Chem. Phys. 1964 41 3473. 14' K. W. Boddeker G. Lang and U. Schindewolf Angew. Chem. Internat. Edn. 1969 8, I s " D. C . Reitz and S. 1. Weissman J. Chem. Phys. 1960 33 700. 15' R. Briere R. M. Dupeyre H. Lemaire C . Morat A. Rassat and P. Rey Bull. SOC. Chesnut ibid. 1969 51 51 18. 138. chim. France 1965 3290. E. G. Rosantsev and V. I . Suskina. Doklad-v Aknd. Nauk SSSR 1969 187 1332 Applications of Electron Resonance Spectroscopy 55 nitroxide biradicals with triplet ground states have been synthesised with struc-tures (7),' 53 (8),' 54 and (9).' 5 4 The solution spectrum of each biradical contains a broad line presumably because of the large zero-field splitting.Indeed, measurements in a polycrystalline matrix have confirmed the large value of D, which is cu. 370 MHz. Molecular orbital calculations of the zero-field splitting suggest that the biradicals adopt a conformation which minimizes electron delocalisa tion. 0 I-'But 0 -0 0 Inorganic polyradicals are also known. Vanadyl pyrophosphate has a solution spectrum characteristic of a complex containing three vanadyl units.'55 The spin Hamiltonian needed to interpret the spectrum is obtained by a simple extension'56 of equation (12). Transitions involving two doublet states and a quartet state must now be considered. In vanadyl pyrophosphate the quartet-doublet separation is large (cu. 30 cm- ') and only the quartet state is populated.'" The positions of the hyperfine lines are determined by transitions within this state and are given by'56 in agreement with experiment. Dinuclear vanadyl tartrate complexes are known. Their spectra have been measured in the solid phase,'57 where the metal-metal distance is 4-4 A and in solution. The well-resolved solution spectrum exhibits weak triplet-singlet transitions and is completely compatible' 5 8 with the dimer 1 5 3 A. Calder A. R. Forrester P. G. James and G. R. Luckhurst J . Amer. Chem. SOC., 1 5 4 E. F. Ullman and D. G. B. Boocock Chem. Comm. 1969 1161. 1 5 5 A. Hasegawa Y. Yamada and M. Miura Bull. Chem. SOC. Japan 1969 42 846. 1 5 6 A. Hudson and G. R. Luckhurst Mol. Phys. 1967 13,409. 1969 91 3724. R. L. Belford N. D. Chasteen H. So and R.E. Tapscott J . Amer. Chem. SOC. 1969, 91 1675. 1 5 ' P. G . James and G. R. Luckhurst Mol. Phys. 1970 18 141 56 G. R. Luckhurst in solution having the same structure as in the solid contrary to an earlier analysis.' 59 Copper acetate is probably the best known paramagnetic inorganic dimer and was studied in the early days of electron resonance spectroscopy.'60 The solid-state spectrum is exceptional because the Zeeman and zero-field splittings are comparable. The large value of D for copper acetate and benzoate16' is not dipolar in origin but is a consequence of the enormous triplet-singlet separation and spin-orbit coupling which combine to give a pseudo-dipolar coupling. 6o Recently copper dimers have been observed in which J and hence D are much smaller than the Zeeman splitting.In principle analysis of their spectra should yield the dipolar coupling and hence the metal-metal separation. The starting point for the analysis is the spin Hamiltonian for the dimer in a given orientation. Only zeroth and second rank magnetic interactions are important and so In this Hamiltonian F r > q ) denotes the anisotropic g and hyperfine tensors for the two units as well as the zero-field splitting. is the appropriate spin operator and &2) is a second rank Wigner rotation matrix which relates the molecular and space-fixed axes. The positions and intensities of the electron resonance transi-tions are obtained by diagonalising the Hamiltonian matrix using a convenient spin basis. This procedure is feasible for a single crystal study but to calculate the polycrystalline lineshape the matrix would have to be diagonalised for each molecular orientation.In order to reduce the cotnputational time it is necessary to make certain approximations. The principal axes of all interaction tensors are taken to have cylindrical symmetry about a common axis the zero-field splitting is assumed to be small compared with the Zeeman splitting and the integration over all orientations is replaced by a summation.'62 These and the use of perturbation theory make it possible to calculate the polycrystalline line shapes for both the Am = 1 and Am = 2 transitions. The Am = 1 transition is predicted to give a broad line whereas the half field Am = 2 transition should show hyperfine structure in agreement with observations on copper citrate and malate.' 62 The zero-field splitting determined by fitting the experimental spectra can then be used to calculate the metal-metal separation.This determination assumes that the electrons behave as point charges and may not always be valid. The technique has been applied to a wide range of copper dimers. For complexes with NN-bis(2-hydroxyethyl) glycine the two copper atoms are held in the same complex although J is negligible.'63 The copper-copper distance is found to be ca. 5 A. Dimers are also formed when the ligand is unable to accommodate two R. H. Dunhill and M. C. R. Symons Mol. Phys. 1968 15 105. B. Bleaney and K. D. Bowers Proc. Roy. SOC. 1952 A 214 451. F. G. Herring R. C. Thompson and C. F. Schwerdtfeger Canad.J . Chem. 1969 47, 555. J. F. Boas R. H. Dunhill J. R. Pilbrow R. C. Srivastava and T. D. Smith J . Chem. SOC. ( A ) 1969 94. 1 6 3 J. F. Boas J. R. Pilbrow and T. D. Smith J . Chem. SOC. ( A ) 1969 723 Applications of Electron Resonance Spectroscopy 57 metal atoms. ' 6491 The spectrum of copper(I1) protoporphyrin-IX contains a well-resolved spectrum from the monomer as well as the broad Am = 1 line and the structured half-field line characteristic of the dimer. Analysis of the line shapes gives the copper-copper distance as 4.3 8 in contrast to an earlier estimate'66 of 3.5 A. The solvent appears to play an important although poorly understood role in stabilising the dimer. Addition of toluene to a chloroform solution of copper(@ diethyldithiocarbamate increases the extent of dimerisation.' 67 It would be interesting to see if dimer formation is restricted to the solid state by making solution linewidth investigations. Dimer formation is not restricted to copper complexes. Iron(rI1) forms an oxo-bridged dimer'68 whose spin multiplicity in principle could range from S = 1 to 5 but in fact only the quintet state is populated.'68 Surprisingly although J is large (190cm-') the zero-field splitting is determined by the electron dipolar coupling. ' Electron resonance has proved to be valuable in identifying the molecular fragments produced by radiation damage.8 Often the radicals are trapped in pairs and analysis of the triplet state spectra yields the inter-electron separation which may then provide further information about the reactions following irradiation.The spin Hamiltonian required in such analyses is given by equation (14) which has been discussed by Itoh et They consider in detail the complications in the spectrum which can occur when the electron-electron inter-actions are comparable to the electron-nuclear couplings. Under these condi-tions there is considerable mixing of the triplet and singlet states as observed in solution studies.88,' 5 1 Their theoretical treatment is then used to interpret'69 the triplet-state spectra obtained from y-irradiated dimethylglyoxime crystals. ' 70 Identical theoretical concepts have been used to analyse the spectra of exchange-coupled pairs of praseodymium(II1) and cobalt(II1) ions in crystalline lattices. " ' The radical pairs formed by U.V.photolysis of tetraphenylhydrazine have been the subject of a particularly elegant investigation.'72 The spectra do not exhibit hyperfine structure and so there is no triplet-singlet mixing. The spectra do, however contain many lines because the dimers can adopt various orientations with respect to the crystal lattice. In fact two types of dimer are formed ; in one both diphenylamino-radicals are linear whereas in the other one radical is linear while the other is bent as in tetraphenylhydra~ine.'~~ A radical pair is also formed on U.V. irradiation of 2,3,4,4-tetrachloronaphthalene-l(4H)-one. ' The 164 R. W. Duerst S. J . Baum and G. F. Kokoszka Nature 1969 222 665. 1 6 ' J. F. Boas J. R. Pilbrow and T. D. Smith J. Chem. SOC. ( A ) 1969 721. 1 6 6 A.MacCragh C. B. Storm and W. S. Koski J. Amer. Chem. SOC. 1965 87 1470. 16' J . R. Pilbrow A. D. Toy and T. D . Smith J . Chem. SOC. ( A ) 1969 1029. 1 6 ' M . Y. Okamura and B. M. Hoffman J. Chem. Phys. 1969,51 3128. 1 6 ' K . Itoh H. Hayashi and S. Nagakura Mol. Phys. 1969 17 561. 0. E. Yakimchenko G. P. Doroshina and Ya. S. Lebedev Khim. vysok. Energii 1969, 3 242; Y . Kurita Bussei 1968 9 87. J. W. Culfahouse D. P. Schinke and L. Pfortmiller Phys. Rev. 1969 177 454. D. A. Wiersma J. H. Lichtenbelt and J . Kommandeur J. Chem. Phys. 1969,50,2794. D. A. Wiersma and W. C. Nieuwpoort Chem. Phys. Letters 1968 2 637 58 G. R. Luckhwst compound dissociates into a chlorine atom and a phenoxyl type radical which is responsible for the phototchromism of the substance.Radical dimers are formed during X-irradiation of hydroxyurea in which the radicals H,NCONHO are ca. 6.4 8 apart and apparently in adjacent molecular layers.' 74 Phenoxyl radicals formed by irradiating resorcinol appear to form two kinds of dimer.17' In one pair the separation is 7.25 A whereas in the other it is only 5.2 8,. Phenoxyl radicals can also be trapped as pairs in certain clath-rates.' The formation of radical pairs has been detected in irradiated high polymers by the observation of a half-field line.'77 The Am = 1 transition was obscured by the monoradical spectrum. Unfortunately no attempt was made to determine D and hence the radical separation from the position of the Am = 2 transition. The situation is slightly better for irradiated crystals of n-paraffins.17* Here the Am = 1 transitions are observable as satellite lines from which the inter-radical separation is found to be 5.758,.The radicals are again in adjacent layers. Hyperfine structure is also observed with a spacing equal to half the p proton coupling constant as expected for D >> a. Relaxation.-The static properties of the spin system determine the line positions in an electron resonance spectrum. On the other hand the dynamics of the system influence the line shapes; linewidth studies have yielded a wealth of kinetic data."." The first problem in any linewidth investigation is to identify the relaxation process and then formulate the time-dependent spin Hamiltonian. It is particularly useful to write the perturbation in irreducible tensor notation 1 7 9 Then under most conditions,' 8o there are no cross terms between perturbations of different rank L and we can discuss these individually.Scalar Interactions. The scalar interactions with L = 0 which determine the line positions in a solution spectrum may be subjected to a time-dependent perturbation. The resulting linewidth variations within the spectrum may take many forms but alternating linewidths l o caused by an out-of-phase modulation of the coupling constants for two equivalent nuclei are often observed. Redfield theory" can only be used to calculate the linewidth when the modulation is fast. In the slow exchange region the line shapes may be calculated using a variety of essentially equivalent theories provided the modulation is the result of discrete jumps between a finite number of sites.The computation involved is often 1 7 4 K. Reiss and H. Shields J . Chem. Phys. 1969 50 4368. 1 7 ' D. Campbell and M. C. R. Symons J . Chem. Soc. ( A ) 1969 1494. 1 7 6 H. Okigashi and Y. Kurita J . Magn. Resonance 1969 1 464. 1 7 7 M. Iwasaki T. Ichikawa and T . Ohmori J . Chem. Phys. 1969 50 1984. 1 7 * M. Iwasaki T. Ichikawa and T . Ohmori J . Chem. Phys. 1969 50 1991. 1 7 9 M. E. Rose 'Elementary Theory of Angular Momentum,' 1957 p. 80 John Wiley and Sons Inc. New York. J . H. Freed and G. K. Fraenkel J . Chem. Phys. 1963,39 326 Applications of Electron Resonance Spectroscopy 59 lengthy but the time required may be reduced by reformulating Sack's equation using Green's functions.' 81 The hydroxymethyl radical exists in two conformations at - 130 "C in which the methylene proton splittings are 49.6 and 52-4 MHz.lg2 At higher tempera-tures there is rapid interconversion and the linewidths alternate.The energy barrier of 9-5 +_ 1.5 kJ mol- ' is slightly smaller than for protonated semi-quinones.' 83 Linewidth alternation is also observed' 84 in the proton hyperfine lines in the spectrum of (10). Presumably the complex can exist in a configuration in which the hydrogens are unequally bonded to the titanium. The standard linewidth analysis yields an activation energy of 17 kJ mo1-'.'84 The spectra of the radical cations of tetrathioalkoxyethylene exhibit an alternating line-width. The low temperature spectrum of the methyl compound shows that the exchange is between configurations with just two groups of six equivalent pr0t0ns.l~~ The barrier between these configurations is estimated to be 36.0 kJ rnol-'.l8' Any process which results in the exchange of coupling constants corresponds to an out-of-phase modulation.Thus ring inversion should produce alternation in the widths of the fi proton quintet. This has been observed for many aliphatic nitroxides and in piperidine N - o ~ y l ' ~ ~ the barrier was found to be 25 kJ rnol-' in agreement with earlier results.18' O/H H,O H*H H*H Linewidth alternation is often observed in the spectra of radical anions of 1,4-disubstituted benzenes. ' The fluctuations in the coupling constants are produced by migration of a counter ion from one substituent to the other. Provided the cation is located above the molecular plane it is fairly easy to visualise this process.However extended Hiickel calculations for the pyrazine anion locate the cation in the molecular plane and adjacent to the nitrogen.18* R. Yaris and A. L. Shain Chem. Phys. Letters 1969 3 597. A. Hudson J. Chem. SOC. ( A ) 1969 2513. P. D. Sullivan and J . R. Bolton J . Amer. Chem. SOC. 1968 90 5336; T. E. Gough, Canad. J . Chem. 1969,47 3 3 1 . G. Henrici-Olive and S. Olive J . Organometallic Chem. 1969 19 309. D. H. Geske and M. V. Merritt J . Amer. Chem. SOC. 1969 91 6921. l B 6 J. C. Espie H. Lemaire and A. Rassat Bull. SOC. chim. France 1969 399. A. Hudson and H. A. Hussain J . Chem. SOC. (B) 1968 251. l S 8 T. A. Claxton Trans. Faraday SOC. 1969 65 2289 60 G.R. Luckhurst It is now hard to visualise the cation motion and it is suggested that the cation forms part of the solvent sheath in which the anion rotates.'" In principle the spectral changes caused by electron transfer from a para-magnetic to a diamagnetic species can be calculated for all rates of transfer." Time-consuming spectrum simulations can often be avoided by restricting the rate experimentally to either the slow or fast region where analytic forms of the linewidth are available. The limiting form in the fast transfer region derived by Piette and Anderson has been modified to increase its range of applicability.' 89 The line broadening in the n.m.r. spectrum of a system in the fast transfer region can also yield the rate constant. Further if the appropriate coupling constants are known from electron resonance measurements the difficult problem of determining the radical concentration may be avoided.' 90 Experimentally, electron transfer between pyridine and aryl substituted pyrylinium salts has been studied.'" Formation of appreciable amounts of ion pairs in solvents of high dielectric constants is unexpected.The detection of the cation dependence on the electron transfer rate between the mono- and di-anion of cyclo-octatetraene in liquid ammonia is therefore ~urprising.'~~ The effect on the transfer decreases in the order Li > Na > K which is the reverse to that found in ether solvents.'93 The broadening of a 1 2 1 triplet by electron transfer is exactly the opposite to that produced by the alternating linewidth effect.The combination of slow electron transfer and an out-of-phase modulation of the coupling constant might result in the equality of the three linewidths. Conceivably this might suggest the absence of dynamic processes in the system. This esoteric combination has been observed for potassium 2,5-di-t-butyl p-benzosemiquinone and analysed using the Kaplan-Alexander theory.' 94 Relaxation via electron transfer is also im-portant in solutions of alkali metals in liquid ammonia although spin-orbit interactions do contribute to the linewidth. The linewidth has been measured at low frequency 7MHz and could provide more information about these fascinating liquids.'95 Unfortunately the exact nature of the relaxation processes is not formulated clearly. Electron exchange like electron transfer limits the life-time of a particular spin state and so results in line broadening." The linewidths in the limit of slow exchange are proportional to the rate of radical collisions.This prediction has been tested by studying the concentration dependence of the linewidths for solutions of peroxylamine disulphonate.' 96 The agreement with theory was not exact and this is attributed to the different ionic strengths of the solutions which will affect the exchange rate constant. '97 The rate constant for different solutions l S 9 C. S. Johnson jun. and J. B. Holz J . Chem. Phys. 1969,50,4420. 190 W. G. Williams Mol. Phys. 1969,16,69. 19' M. FBrcasiu and D. Farcasiu Chem. Ber. 1969 102 2294. 1 9 2 F. J. Smentowski and G. R. Stevenson J .Phys. Chem. 1969,73 340. '93 F. J. Smentowski and G. R. Stevenson J . Amer. Chem. SOC. 1967 89 5120. L94 R. F. Adams N. M. Atherton and A. J. Blackhurst Trans. Faraday SOC. 1969,65,2967. 1 9 5 D. E. O'Reilly J . Chem. Phys. 1969 50 4743. 196 M. T. Jones J . Chem. Phys. 1963,38 2892. 19' H. Alibhai A. Hudson and H. A. Hussain J . Chem. SOC. ( A ) 1969 678 Applications of Electron Resonance Spectroscopy 61 shows the expected proportionality to the ionic strength. Further the slope is consistent with a transition state involving two doubly charged anions. '97 A less detailed study of spin exchange in peroxylamine disulphonate solutions ignores this c ~ r r e c t i o n . ' ~ ~ A general theory of electron spin exchange has been formulated and applied to the tetracyanoethylene anion and di-t-butylnitroxide.' 99 The spin-lattice relaxation time is predicted and found to show a rapid decrease with increasing radical concentration before reaching a limiting value.This behaviour is unlike that of the linewidths which exhibit an increase. Spin exchange has been employed to investigate the structure of ionic fluids with manganese(r1) tetrachloride as a paramagnetic probe. In the eutectic of potassium and lithium chloride the concentration of manganese required to reach the fast exchange region is much less2" than that required in tri-n-butylbenzyl phosphonium chloride.201 The lower rate of bimolecular collisions in the latter is taken to indicate a more ordered structure in this fluid. Anisotropic Interactions. The vast majority of anisotropic magnetic interactions are of second rank.As the molecule rotates the perturbation induces transitions between the spin levels as well as modulating their energies. It is of course quite misleading to think as some authors do that the resulting linewidth is caused by incomplete averaging of the anisotropic couplings. If the radical contains a single magnetic nucleus the width of a line depends on its nuclear quantum number m," T,-'(m) = A + Brn + Cm2 (16) The linewidth coefficients are determined by the anisotropic g and hyperfine tensors as well as the details of the molecular motion. The formula for the coeffi-cients adopt simple forms when the rotational diffusion conforms to the Debye model. '' The linewidth coefficients can be used in a variety of ways e.g.they can yield sign information or rotational correlation times. Experimentally the sign of B is determined by the sign of the isotropic coupling constant whereas theor-etically B depends on the anisotropic g and hyperfine tensor. Knowledge of two of these quantities allows the sign of the third to be obtained. The spectra of fluorinated semiquinones enriched in I7O exhibit pronounced asymmetric line broadening. Measurement of the linewidth coefficients and a theoretical estimate'" of the g tensor shows that both u F ~ F and acpc are positive, whereas aopo is negative.202 If reliable estimates of the signs of the spin densities are available then the absolute magnitudes of the isotropic coupling constants can be obtained. Sign determination with liquid crystals is however more general since it does not require knowledge of the g - t e n ~ o r .~ ' ~ l g 8 S. Fujwara and K. Sakioka Bull. Chem. SOC. Japan 1969 42 2120. M. P. Eastman R. G. Kooser M. R. Das and J. H. Freed J . Chem. Phys. 1969 51, 2690. 'OOT. B. Swanson J . Chem. Phys. 1966,45 179; L. Yarmus M. Kukk and B. R. Sund-heim ibid. 1964 40 33. ' O ' B. R. Sundheim J. Flato and L. Yarmus J . Chem. Phys. 1969 51 4132. W. E. Geiger jun. and W. M. Gulick jun. J . Amer. Chem. SOC. 1969 91 4657. ' 0 3 A. Carrington and G. R. Luckhurst Mol. Phys. 1964 8 401 62 G. R. Luckhurst The theory required to analyse linewidth variations is more complex when the transitions are degenerate for then the components of a line may have different widths.These differences could destroy the Lorentzian shape of the line and so complicate the analysis. Under certain conditions it is possible to average over the widths of a degenerate line.204 By employing these averages when interpreting the linewidths for the NN'-dimethylpyrazine cation the nitrogen and methyl proton splittings were found to be positive.205 The C coefficient depends only on the hyperfine tensor and if this is known the rotational correlation time z, can be measured. According to the Debye model of rotational diffusion and by measuring z as a function of temperature the size r of the radical can be determined. The radius of the NN-dimethylpyrazine cation in methanol is found to be 3.2A. Analysis of an asymmetric linewidth effect has been employed to locate the sodium cations in the triple ion of p-benzosemiquinone.206 The isotropic sodium splitting was assumed to be positive and the g-tensor was taken from a previous linewidth in~estigation.~" This information gives the sign of B and of one component of the hyperfine tensor.Calculations of the tensor for various posi-tions of the cation then show that the cation must be in the plane of the ring and at least 0.6A from an oxygen.206 The linewidth variations in the spectra of the radical anions of naphthalene, anthracene and tetracene have been subjected to a particularly thorough investi-gation.208 The average linewidth approximation is used in the analysis together with hyperfine tensors calculated from the McConnell and Strathdee equa-t i o n ~ . ~ ~ ~ The quantitative agreement is poor even when allowance is made for anisotropic rotational diffusion2 and modulation of the isotropic coupling constants.The reasons for the discrepancy may be the inaccuracies in the theor-etical hyperfine tensors which have been detected by liquid crystal measure-ments,'" or in the average linewidth approach. When the anisotropic tensors are known the linewidth coefficients can be used to measure the rotational correlation time within the framework of the Debye model. This technique has been used to investigate the structure of fluid o-ter-phenyl with vanadyl acetylacetonate as the paramagnetic probe.2' Near the melting point the high viscosity had been attributed to cluster formation.212 However the rotational correlation time obeys the Debye equation (17) exactly, '04 A.D. McLachlan Proc. Roy. SOC. 1964 A 280 271. ' 0 5 M.-K. Ahn and C. S. Johnson jun. J . Chem. Phys. 1969,50 632. ' 0 6 T. E. Gough and P. R. Hindle Canad. J . Chem. 1969,47 3393. ' 0 8 B. G. Segal A. Reymond and G. K. Fraenkel J . Chem. Phys. 1969 51 1336. *09 H. M. McConnell and J. Strathdee Mol. Phys. 1959 2 129. J. W. H. Schreurs and G. K. Fraenkel J . Chem. Phys. 1961,34 756. J. H. Freed J . Chem. Phys. 1964,41 2077. G. R. Luckhurst and J. N. Ockwell Mol. Phys. 1969 16 165. 2 1 2 E. McLaughlin and A. R. Ubbelohde Trans. Faraday SOC. 1958,54 1804 Applications of Electron Resonance Spectroscopy 63 which argues against the existence of clusters. A planar molecule such as vanadyl acetylacetonate cannot rotate isotropically.If however its anisotropic motion is taken into account the approximate cylindrical symmetry of the tensors about the V-0 bond ensures that the equations for B and C are unaltered. But now the correlation time is for the end-over-end motion.2 '' Asymmetric linewidths are observed in solid-state spectra and have been used to investigate the motion of the trapped species. The germanium trichloride radical is formed by irradiation of the tetrachloride and found to rotate in the solid.213 An approximate analysis of the temperature dependence of the line-widths yields an activation energy for reorientation of 6.3 kJ mole-'. A more accurate analysis was attempted but incorrect theoretical expressions were used for the linewidth coefficients. The asymmetric line broadening shown by the spectra of most nitroxide radicals has been used to probe the molecular motion in polymer^.^'^,^^^ The activation energy for molecular motion of the probe in polyisoprene is 22.38 kJ mol- in comparison with 17-45 kK mol- ' in p~lybutadiene.~ l4 These values are in accord with the lower glass transition point for polybutadiene.The wrong linewidth theory has been employed in interpreting the linewidth effects observed in the spectra of irradiated high polymers.216 The polycrystalline nature of the spectrum shows that the motion is slow and yet Kivelson's linewidth expres-sions," valid only for rapid motion are used to analyse the linewidths. When the g factor deviates from the free spin value spin-rotation is often a dominant relaxation process.' For example in tetramminocopper(I1) the spin-rotational contribution to the linewidth is as important as that from the aniso-tropic g and hyperfine tensors.217 There is reasonable agreement between the experimental and theoretical widths calculated using the Debye model to deter-mine the correlation functions." The discrepancies which are greater than those found for copper acetylacetonate,218 may be caused by fluctuations in the ligand arrangement2' or by ligand exchange. The sulphite radical-ion SO2- contains no magnetic nuclei and so spin-rotation is likely to be the dominant relaxation process. According to the Debye model the linewidths should be proportional to kT/q and this dependence has been confirmed for SO,- in a wide variety of solvents.219 This result is surprising for a small radical and may be indicative of considerable solvation.The ionic radius of 0.91 A obtained from these results is likely to be incorrect because the theoretical expression used for the linewidth is only correct for an axially symmetric spin-rotation tensor. In contrast the ' l 3 J . Roncin and R. Debuyst J . Chem. Phys. 1969,51 577. ' 1 4 A. Rosseau and R. Lenk Mol. Phys. 1968 15 425. 2 1 5 A. M. Wasserman A. L. Buchachenko and A. L. Kovarskii European Polymer J . , ' I 6 S. Moriuchi H. Kashiwarba J. Sohma and N . Yamaguchi J . Chem. Phys. 1969 51, ' l 7 G . Nyberg Mol. Phys. 1969 17 87. 2 1 8 R. Wilson and D. Kivelson J . Chem. Phys. 1966,44,4445. ' 1 9 L. Burlamacchi Mof. Phys. 1969 16 369. 1969,473. 298 1 64 G.R. Luckhurst widths of the chlorine dioxide spectrum show a marked deviation from direct proportionality to k7’/q.220 The deviation is caused by a precessional effect resulting from the lack of high molecular symmetry. The values of molecular radius obtained from the Debye and Stokes-Einstein equations are found to be solvent dependent.2209221 In fact these equations require modification to allow for the anisotropy in the solute-solvent potentia1.220y222 The apparent solvent dependence of r then reflects the changes in the anisotropic potential. Even with this modification the theory is still only valid for large solute molecules dissolved in small solvent molecules or a highly anisotropic solute-solvent potential. When these conditions are not satisfied the extended diffusion model of the liquid should be The advantage of this approach is that it does not separate the orientational and momentum correlation functions when dealing with spin-rotation.22 Redfield’s formulation of relaxation theory is particularly valuable because it can handle a wide range of complicated fluctuations in a simple way.224 The elements of the relaxation matrix are obtained using perturbation theory and are only correct to second order in X’(t)7.The higher order terms have been evalu-ated.225,226 One treatment is specific toproblemsinvolvingrotationaldiffusion226 whereas the other based on a cumulant expansion is more Although both treatments provide a valuable extension to Redfield’s theory neither can treat the slow rotation problem [X’(t)7 4 13. The slow motion problem can be treated if it involves jumps between a discrete number of sites.” Indeed this approach has been used to interpret the line shapes of slowly rotating ground state triplets.227 Good agreement with experiment is obtained by treating the rotation as a jump process between only fifty orientations. The triplet state problem does not involve the pseudo-secular terms which are so important in relaxation by an anisotropic hyperfine tensor. These terms are difficult to handle and are apparently neglected in one complex treatment of slow rotation of nitroxide radicals.22 * ”O R. E. D. McClung and D. Kivelson J. Chem. Phys. 1968,49 3380. 2 2 1 R. Wilson and D. Kivelson J. Chem. Phys. 1966,44 4440. ’” H. Friedmann and W. A. Steele J. Chem. Phys. 1964 40 3669. 2 2 3 R. E. D. McClung J. Chem. Phys. 1969 51 3842. 2 2 4 A. G. Redfield Adu. Magn. Resonance 1965 1 33. 2 2 5 J. H. Freed J. Chem. Phys. 1968,49 376. 2 2 6 H. Sillescu and D. Kivelson J. Chem. Phys. 1968 48 3493. 2 2 7 J. R. Norris and S. I. Weissman J. Phys. Chem. 1969 73 31 19. ’” N. N. Korst and A. V. Lazarev Mol. Phys. 1969 17 481