ELECTEECN fiFflN RESONMQ’CE OF IRMEIAIED GRGANEC SINGLE CRYSTALS Thesls Eor {Em Dog-rec of DH. D. EEECEEEGM STATE WWEW Lowell Donalci Kispert i336 J g LIBRARY Michigan State University , This is to certify that the thesis entitled ELECTRON SPIN RESONANCE OF IRRADIATED ORGANIC SINGLE CRYSTALS presented by Lowell Donald KiSpert has been accepted towards fulfillment of the requirements for Ph. D. Chemistry degree in 77727177??? / Ma or [fprofesg’rm lm October 15, 1966 Date 0-169 ABSTRACT ELECTRON SPIN RESONANCE OF IRRADIATED ORGANIC SINGLE CRYSTALS by Lowell Donald KiSpert The w—electron radicals formed in several electron ir— radiated organic crystals were studied as a function of temperature. The radicals identified were: -CEs(77OK), -CF2CONH2(77-SOOOK) and CONH2(77OK) from trifluoroacetamide irradiated at 770K, °CF2COO-(SOO—77OK) from sodium chloro- difluoroacetate dihydrate irradiated at 5000K, ‘CH3(77OK), CH2COO—(ZOOOK) and -COO-(ZOO—SOOOK) from sodium acetate tri- hydrate irradiated at 770K, °CF2COO-(77OK) and various con- formations of EOCCFgéFCOO—(77—SOOOK) from sodium perfluoro- succinate hexahydrate irradiated at 770K, CeHSCOCHCOCFg (3000K) from benzoyltrifluoroacetone irradiated at 5000K and OOCCFCFZCF3(SOOOK)from silver perfluorobutyrate irradiated at 5000K. The complete carbon—13 tensors were evaluated for the 'CF3(77OK), -CF2c0NH2(5OO°K) and -CH3(77OK) radicals while only partial carbon-15 tensors were found for 'CF2COO-(SOOOK), -cnc1coon(300°1<) ,* and ~CF2CONH2(77OK) . The anisotropic drfluorine hyperfine splittings, A2 = 252, AX = 88, Ay = 90 gauss and the anisotropic carbon-15 hyperfine Lowell Donald Kispert splittings A2 = 518, AX = 238, Ay = 240—260 gauss, found for the ~CF3 radical lead to values of the isotropic fluorine and carbon-15 splittings which are in good agreement with the isotropic fluorine hyperfine splitting reported for the °CF3 radical in solution. This indicates that the same nearly tetrahedral structure as found in solution is present in single crystals. The defluorine hyperfine Splitting values were found to increase with decreasing temperature for the -CF2coo', -CF2CONH2 and ‘oocrgéFcoo' radicals while no temperature dependence was detected for the ~CF3 and the -CFHCONH2 radicals within experimental error. The larger carbon-15 isotropic hyperfine splitting (approximately 90 gauss) obtained for the 9CF2COO- and °CF2CONH2 radicals than for the 'CFHCONH2 radical (approximately 40 gauss) indicates that the radicals with temperature dependent hyperfine split- tings are slightly nonplanar while those with planar and tetrahedral structures have temperature independent hyperfine splittings. The proton hyperfine Splittings obtained for the methyl radical, A2 = 21.8, AX = 22.5, Ay = 22.5 gauss, are those expect- ed for a planar w-electron‘radical rotating in the plane of the carbon-hydrogen bonds. A comparison of the carbon-15 hyper- fine splittings A2 = 85, Ax = 15, Ay = 15 gauss with the carbon-15 splittings for other planar radicals indicates that the methyl radical is planar. Lowell Donald KiSpert The amount of water of crystallization was found to be an important factor determining whether a carbon-carbon bond was broken at 770K as in sodium acetate trihydrate or sodium perfluorosuccinate hexahydrate or whether molecular ions were formed as in succinic acid, glycine and draminoisobutyric acid. Diffusing oxygen was found to react with the 'CF2COO- radical in sodium chlorodifluoroacetate and the -00CCFCF2CF3 radical in silver perfluorobutyrate at 3000K but did not react with any of the other radicals studied. The variation in line widths at 5000K for the ESR spectra of the IOOCCFZCFCOO- radical was attributed to a fast oscil- lation between two conformations of the 8—fluorines which were distinguishable at 770K. In crystals irradiated and observed at 770K the radicals were in a single conformation and this differed from either of the two room temperature conformations. ELECTRON SPIN RESONANCE OF IRRADIATED ORGANIC SINGLE CRYSTALS BY Lowell Donald KiSpert A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of ChemiStry 1966 To - My Parents ii A. a "'2 i I \‘ -. ACKNOWLEDGEMENTS The author wishes to express his sincere appreciation to Professor M. T. Rogers for his suggestions, encouragement and continued interest during the course of this investi- gation. I would also like to thank Dr. D. H. Whiffen of the National Physical Laboratory, Teddington, England, Dr. J. A. Pople of Carnegie Institute of Technology and Dr. Y. W. Kim of Wayne State University for helpful discussions. The aid of the following people is gratefully acknowl—. edged: Dr. A. Tulinsky for experimental guidance in the crystallography work; Dr. M. Gordon for obtaining the NMR Spectra; Dr. W. G. Bickert and Dr. F. H. Buelow of the Agri- cultural Engineering Department for irradiation of the samples; R. A. Andrews at Wayne State University for obtain— ing the liquid helium Spectra and Dr. H. A. Kuska, G. Johnson and R. Drullinger for assistance with experimental problems. .Also, I would like to thank the Atomic Energy Com- mission and the Dow Chemical Company for financial support during the course of this investigation. iii TABLE OF CONTENTS Page INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1 HISTORICAL . . . . . . . . . . . . . . . . . . . . . 4 Theory of w-Electron Radicals . . . . . . . . . 5 arProton Splittings. . . . . . . . . . . . 5 8-Proton Splittings. . . . . . . . . . . 13 Proton Hyperfine Splittings in Unsaturated Organic Compounds. . . . . . . . . . . . 21 Inclusion Compounds. . . . . . . . . . . 21 Hyperfine Interactions from Protons of Inorganic Radicals . . . . . . . . . . . 23 Central Atom (13C, 14N) Hyperfine Inter- actionszth-Electron Radicals. . . . . . 23 N-H Hyperfine Proton Splittings. . . . . . 28 Fluorine Hyperfine Splittings. . . . . . . 29 Chlorine Hyperfine Interactions. . . . . . 32 Phosphorus Hyperfine Interactions. . . . . 34 Radicals Containing Sulfur . . . . . . . . 36 g Tensors of w-Electron Radicals with Quenched Spin—Orbit Interactions . . . . 39 g Tensors for Radicals with Partially Quenched Orbital Angular Momentum. . . . 39 THEORETICAL. . . . . . . . . . . . . . . . . . . . . 44 Spin Hamiltonians for Radicals in Single Crystals. . . . . . . . . . . . . . . . . . . 44 Treatment of the g Tensor. . . . . . . . . 45 Hyperfine Splitting Tensor to First Order. 47 Experimental Determination of Hyperfine Splitting Tensors. . . . . . . . . . . . 52 Forbidden Transitions. . . . . . . . . . . 53 Second-Order Perturbation Theory . . . . . 54' Electron Dipole-Nuclear Dipole Hyperfine Coupling. . . . . . . . . . . . . . . . . . . 56 Spin Flip Transitions . . . . . . . . . . . . . 57 Optical Crystallography . . . . . . . . . . . . 60 Crystal Symmetry and Alignment. . . . . . . . . 64 iv TABLE OF CONTENTS - Continued EXPERIMENTAL . . . . . . . . . . . . . . . . . . . . ESR Spectrometer. . . . . . . . . . . . . . . . Crystal Holder. . . . . . . . . . . . . . . . Standard Samples. . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . CCngCOONa°2H20. . . . . . . . . . . CClaCONHg and CC lgCONDg. . . . . . . . . . CF3CF2CF2COOAg . . . . . . . . . . . . . N300CCF2CF2COON6.’ 6H20: . . . . . . . . . . CF3CONH2 . . . . . . . . . . . . . . . . . NaOOCCHs- 3H20. . . . . . . . . . . . . Na0013CCH3, Naooc13CH3 . . . . . . . . . Crystal Growing . . . . . . . . . . . . . . . . Irradiation Procedure . . . . . . . . . . . . Gas Reactions of Radicals in Crystals . . . . . Crystallography . . . . . . . . . . . . . . . . Techniques for Obtaining Single Crystal ESR Spectra . . . . . . . . . . . . . . . . . . . RESULTS. ESR Study of Irradiated Sodium Chlorodifluoro- acetate . . . . . . . . . . . . . . . . . . . Space Group Determination for Sodium ’ Chlorodifluoroacetate. . .,. . . . . . Identification and Angular Dependence in vacuo . . . . . . . . . . . . . . . . The 137CF2COO- Radicals. . . . . . . . . Irradiasion and ESR Observation in vacuo at 77 K. . . . . . . . . . . . . . . . . Temperature Dependent Fluorine Hyperfine Splitting. . . . . . . . . . . . . . . Reactions of the -CF2COO‘ Radicals with Air. . . . . . . . . . . . . . . . . . . ESR Study of Irradiated Trifluoroacetamide. . . Assignment of the Crystal Axes for Tri- fluoroacetamide. . . . . . . . . . . . . Interpretation of the Spectra. . . . . . . The 'CF2CONH2 Radical. . . . . . . . . . . Linewidth Variation in the Spectrum of the -CF3 Radical . . . . . . . . . . . . . . Determination of the Hyperfine Splittings. The -NH2CO Radical . . . . . . . . . . . Unidentified Radicals. . .'. . . . . . . . The ~13CF3 Radical . . . . . . . . . . . . The '13CF2CONH2 Radical. . . . . . . . . . ESR Study of Irradiated Sodium Perfluoro- succinate . . . . . . . . . . . . . . . . . . Page 81 81 81 92 94 96 98 101 101 102 107 111 114 115 116 116 118 118 TABLE OF CONTENTS - Continued Page Crystal Axes for Sodium Perfluorosuccinate Hexahydrate. . . . . . . . . . . . . . . 118 Identification of the Radicals formed in Sodium Perfluorosuccinate Irradiated and Observed at 770 K . . . . . . . . . . 118 Spin-Flip Transitions at 770 K. . . . . . . 130 Change in the Conformation of the Room Temperature Radical as a Function of Temperature. . . . . . . . . . . . . . . 133 Radical Formed in Irradiated Silver Perfluoro- butyrate at 3000K . . . . . . . . . . . . . . 140 The CF3COCHCOC6H5 Radical . . . . . . . . . . . 148 ESR Study of Irradiated Sodium Acetate Tri- hydrate . . . . . . . . . . . . . . . . . . 148 The Crystal Axes for Sodium Acetate Tri- hydrate. . . . . . . . . . . . . . . . . 148 Interpretation of Spectra at 770K. . . . . 150 Interpretation of the ESR Spectrum of the -CH2COO Radical at 2000K. . . . . . . 154 Identification of the -C00 Radical at 3000K. . . . . . . . . . . . . . . . . . 158 Effect of Water of Crystallization on C-C Bond Breakage. . . . . . . . . . . . . 160 ESR Study of Irradiated Trichloroacetamide. . . 160 Crystallography of Trichloroacetamide. . . 160 Measurement of the Hyperfine Splitting Constants at 770K. . . . . . . - . . . 163 Measurement of the Hyperfine Splittings at 5000K. . . . . . . . . . . . - . . 164 13C Hyperfine Splitting Values for the HCClCOOH Radical at 3000 K. . . . . . . . . . . . - . . 169 Reactions of Radicals with Absorbed Gases . . . 170 DISCUSSION . . . . . . . . . . . . . . . . . . . . . 174 Electronic Structures of the 'CF2COO_ and 'CF2CONH2 Radicals. . . . . . . . . . z . . . 174 Near Neighbor Interactions of the-CF2COO Radi— cal in Irradiated Sodium Chlorodifluoroace- tate. . . . . . . . . . . . . . . . . . . . . 176 Structure of the °CF3 Radical . . . . : . . . . 180 The Electronic Structure of the FOOCFgCFCOO‘ Radical . . . . . . . . . . . . . . . . . . . 182 B-Fluorine Hyperfine Splittings in the OOCCFgCFCOO' Radical . . . . . . . . . . . . 184 Barrier to Rotation. . . . . . . . . . . . 192 Temperature Dependence of the OhFluorine Hyper— fine Splittings . . . . . . . . . . . . . . . 194 vi ‘4‘ TABLE OF CONTENTS — Continued Page The -CH3 Radical . . . . . . . . . . . . . . . 201 Electron Densities for Some Radicals . . . . . 205 Chlorine Hyperfine Splittings:nlthe ‘CClg Radical. . . .2. . . . . . . ... . . . . . . 207 Hyperfine Interactions in the CONH2 and NH2CO- Radical. . . . . . . . . . . . . . . . . . . 208 A Comparison of the Geometry of Some Aliphatic Radicals . . . . . . . . . . . . . . . . . . 210 Failure to Observe y-Fluorine Hyperfine Split- ting Constants . . . . . . . . . . . . . . . 212 Relative Saturation Properties of Several Radicals . . . . . . . . . . . . . . . . . . 214 Effect of Water of Crystallization on Radical Formation. . . . . . . . . . . . . . . . . . 216 Peroxide Radicals. . . . . . . . . . . . . . . 217 SUMMARY . . . . . . . . . . . . . . . . . . . . . . 221 REFERENCES. . . . . . . . . . . . . . . . . . . . . 224 APPENDIX. . . . . . . . . . . . . . . . . . . . . . 239 vii LIST OF TABLES TABIE Page 1. Hyperfine Interactions with arProtons (Gauss) . . 8 2. Hyperfine Interactions with 8—Protons . . . . . . 14 3. Hyperfine Interactions with B—Protons for C-CHg—X Type Radicals O C O O O O O C O O O O C O O O O O 16 4. Hyperfine Interactions with 8-Protons for C-CH-XY Type Radicals . . . . . . . . . . . . . . . . . . 18 5. Hyperfine Interactions with 8-Protons for C-Nfis . 18 6. Hyperfine Interaction with B-Protons for C-OH Type Radicals . . . . . . . . . . . . . . . . . . 19 7. Hyperfine Interactions wits 8—Protons for C- -CH-X, C- S-CHX and C- C’ —NH2 Type Radicals . . 19 8. Delocalized Proton Hyperfine Interactions in Un- saturated Compounds . . . . . . . . . . . . . . . 22 9. Hyperfine Interactions with Protons in Inorganic Radicals. . . . . . . . . . . . . . . . . . . . . 24 10. Hyperfine Interactions with Nitrogen. . . . . . . 26 11. Hyperfine Interactions with Carbon-13 . . . . . . 27 12. as and B-Fluorine Hyperfine Interactions. . . . . 30 13. Hyperfine Interactions with Chlorine. . . . . . . 33 14. Phosphorus Hyperfine Interactions . . . . . . . . 35 15. Hyperfine Interactions with 338 and g Tensors for the Corresponding Radicals. . . . . . . . . . . . 37 16. Typical Principal Values of g Tensors in W-Elec- tron Radicals with Quenched Spin-Orbit Coupling . 40 17. dLElectron Radicals . . . . . . . . . . . . . . . 41 I viii LIST OF TABLES - Continued TABLE 18. Hyperfine Interactions with Other Nuclei. . . . 19. Hyperfine Splitting Constants and 9 Values for NO, N02, N02,N033ndN03 ........... 20. Anisotropic Splittings for Two and Three Unequal- ly Coupled Nuclei . . . . . . . . . . . . . . . . 21. Nonequivalent Sites Occurring for Various Crystal Symmetries. . . . . . . . . . . . . . . . . 22. Hyperfine Splittings and g Tensors for the 'CF2COO' Radicals in Irradiated Sodium Chlorodi- fluoroacetate . . . . . . . . . . . . . . . . . . 23. Hyperfine Splittings (A) and g Tensors for the 'CF3, 'CFgCONHg and OCNHg Radicals. . . . . . . . 24. Hyperfine Splitting Tensors for the Various Con- formations of Perfluorosuccinate Radicals . . . . 25. Hyperfine Splitting Tensors for 'CH3. . . . . . . 26. Hyperfine Splittings Occurring Along Specific Directions. . . . . . . . . . . ’.' . . . . . . . 27. Production of Methyl Radical as a Function of Water of Crystallization in Irradiated Poly- crystalline Acetates. . . . . . . . . . . . . . 28. Comparison of the Mean Magnetic Moments (u) for Various Isotopic Combinations of Chlorine in 'CCls...................... 29. Hyperfine Splitting Tensors for the 'CC13, ~CHC1COOH and '0CNH2 Radicals . . . . . . . . . 30. Studies of Gas-Radical Reactions. . . . . . . . . 31. Oxygen and Hydrogen Addition to Various Irradi- ated Single Crystals. . . . . . . . . . . . . . . 32. Breakdown of the dsFluorine Hyperfine Splitting Tensor . O O O O O O O O O O O O O I O O O O 0 ix Page 41 45 51 66 89 108 128 152 155 161 167 168 170 173 175 LIST OF TABLES - Continued TABLE 33. 34. 35. 36. 37. 38. 39. 40. 41. Components of the Fluorine Superhyperfine Split- ting Tensor for both Possible Choices of Rela- tive Sign. . . . . . . . . . . . . . . . . . . . Electron Spin Density Distribution for the 'OOCCFZCFCOO- Radical. . . . . . . . . . . . . . Undiagonalized 8-Fluorine Hyperfine Splitting Tensors for the 'OOCCFgCFCOO' Radical at 300 K and 770K . . . . . . . . . . . . . . . . . . . . Comparison of the Twist Angle_y and Bop” for Various Conformations of the 'OOCCF2CFC80‘ Radical. . . . . . . . . . . . . . . . . . Undiagonalized chFluorine Splitting Tensors for the 'OOCCF2CFCOO— Radical. . . . . . . . . . . . Possible Isotropic thluorine Hyperfine Split— tings. O O O O O O O O O O O O O O O O O O O O 0 Electron Density on the ahCarbon Atom. . . . . . The Structures of Various Radicals . . . . . . . Attenuation (Varian High Power Arm) Needed to Initiate Saturation. . . . . . . . . . . . . . . Page 177 183 187 189 197 199 206 213 215 LIST OF FIGURES FIGURE 1. The origin of the anisotropic osproton hyper- fine interaction. . . . . . . . . . . . . . . 2. Positions of extinction for triclinic, orthor- hombic and monoclinic crystals. . . . . . . . 3. Adjustable single crystal holder. . . . . . . 4. Definition of the orthogonal abc* reference axes and the monoclinic abc crystal axes with respect to the sodium chlorodifluoroacetate crystal morphology. . . . . . . . . . . . . . 5. Spectrum of the radicals produced in sogium chlorodifluoroacetate irradiated at 300 K with a H H. . . . . . . . . . . . . . . . . . 6..Spectrum of the radicals produced in sodium chlorodifluoroacetate_irradiated at room temperature with b IIH. . . . . . . . . . . . 7. The angular dependence of the defluorine hyperfine splittings in the c*a plane.. . . . 8. The angular dependence of the defluorine‘ hyperfine splittings in the bc* plane . . . . 9. The angular dependence of the dhfluorine hyperfine splittings in the ba plane. . . . . 10. The upfield 13c satellites for the ocrgcoo' radicals (a), (b), (c). . . . . . . . . . . . 11. Temperature dependent superhyperfine split- tings in the -CF2COO radicals. . . . . . . . 12. Temperature dependence of the Az thluorine hyperfine splitting for the -CF2COO radical. 13. ESR Spectra at 3000K of the peroxide radicals W, X, Y, Z in irradiated sodium chlorodi- fluoroacetate after one day in contact with air 0 C O O O O O O I O O O O O O O O O O O 0 xi Page 64 70 82 84 85 86 87 88 93 95 97 99 LIST OF FIGURES - Continued FIGURE Page 14. Angular dependence of the peroxide lines for the radicals X, Y, Z, W of Figure 13. . . . . . 100 15. The a*bc reference axes with reSpect to the trifluoroacetamide crystal morphology . . . . . 101 16. Trifluoroacetamide with a* EH irradiated at 770K. . . . . . . . . . . . . . . . . . . . . . 103 17. Angular variation of the chfluorine splittings for tsifluoroacetamide irradiated and observed at 77 K . . . . . . . . . . . . . . . . . . . . 104 18. Angular variation of the defluorine hyperfine Splittings for trigluoroacetamide irradiated and observed at 77 K. . . . . . . . . . . . . . 105 19. Angular variation of the csfluorine splittings for tgifluoroacetamide irradiated and observed at 77 K . . . . . . . . . . . . . . . . . . . . 106 20{ ESR spectrum of the oCF2COO- radical at 770K showing the nonequivalence of the two fluorines 109 21. ESR spectrum of tr'fluoroacetamide irradiated and observed at 77 K with b Ilfi'and 15 db attenuation . . . . . . . . . . . . . . . . . . 109 22. Temperature dependence of the defluorine hyper- fine splitting (A) for the -CF2CONH2 radical with a*lIH. . . . . . . . . . . . . . . . . . . 112 23. ESR spectrum of the -CF3 radical at 770K with c IIH and 2 db input attenuation of the micro- wave power. . . . . . . . . . . . . . . . . . . 113 24. The ESR Spectra of the 13-CF2CONH2 radical at 3000K . . . . . . . .'. .'. . . . . . .'. . . . 119 25. The a*bc reference axes and the abc crystal axes for sodium perfluorosuccinate hexahydrate. 120 26. ESR spectrum with a* [H ofosodium perfluoro— succinate irradiated at 77 K. . . . . . . . . . 122 xii LIST OF FIGURES - Continued FIGURE 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. ESR Spectrum, with bIlH, of sodium perfluoro- succinate irradiated at 77 K. . . ; . . . . . ESR Spectrum, with cIIH, 08 sodium perfluoro- succinate irradiated at 77 K. . . . . . . . . Angular variation of the hyperfine splittings for the radical produced when sodium per- flgorosuccinate is irradiated and observed at 77 K. . . . . . . . . . . . . . . . . . . . . Angular variation of the hyperfine splittings for sodium perfluorosuccinate irradiated and observed at 77 K. . . . . . . . . . . . . . . Angular variation of the hyperfine splittings for sodium pergluorosuccinate irradiated and observed at 77 K. . . . . . . . . . . . . . . Change of the ESR Spectrum as the irradiated crystal is allOwed to warm from 17 K to 300 K (at 15 db attenuation) when a*||H . . . . . . Variation of the intensity of the Spin-flip transitions with angular setting. . . . . - - The height and width of peaks in the second- derivative spectrum of the ‘OOCCFCFgCOO- radical plotted versus temperature. . . . . . The height and width of peaks in the second- derivative spectrum of the ‘OOCCFCFECOO‘ radical plotted versus temperature. . . . . - The height and width of peaks in the second- derivative Spectrum of the ‘OOCFCFQCOO‘ radical plotted versus temperature. . . . . . Variation of the csfluorine hyperfine split- tings with temperature in various crystal orientations. . . . . . . . . . . . . . . . . Variation of the B-fluorine hyperfine split- tings with temperature for various crystal orientations. . . . . . . . . . . . . . . . . xiii Page 123 124 125 126 127 131 132 134 135 136 137 138 LIST OF FIGURES - Continued FIGURE 39. 40. 41. 42. 43. 44. 45. 46. 47. 48.- 49. 50. 51. Angular variation of the hyperfine splittings at 77 K for the radicals (R) and (P) of 0 sodium perfluorosuccinate irradiated at 300 K. Angular variation of the hyperfine splittings at 77 K for radicals (R) and (P) of godium perfluorosuccinate irradiated at 300 K . . . . Angular variation of the hyperfine splittings at 77 K for the radicals (R) and (P) of 0 sodium perfluorosuccinate irradiated at 300 K. The orthogonal abc* reference axes for silver perfluorobutyrate crystals . . . . . . . . . . The first-derivative ESR Spectrum 03 Silver perfluorobutyrate irradiated at 300 K. . . . . The first-derivative spectrum ofosilver per- fluorobutyrate irradiated at 300 K . . . . . . The peroxide line which obscures the fluorine hyperfine splittings in the spectrum of irradiated silver perfluorobutyrate. . . . . . The abc* reference axes with respect to the sodium acetate trihydrate crystal morphology . ESR Spectra of the radical produced by irradi— ation of sodium acetate trihydrate at 77 K . . ESR Spectra of isotopically substituted sodium acetate trihydrate, irradiated and observed at 770K . . . . . . . . . . . . . . . . . . . . . The ESR spectra 8f sodium acetate trihydrate irradiated at 77 K and observed at 200 K at low microwave power (input attenuation 24 db). The ESR-spectrum of the 'CHgCOO- radical at 200°K as a function of input microwave power . The first-derivative ESR Spectra of sodium acetate trihydrate irradiated at 770K and ob- served at 3000K. . . .'. . . . . . . . . . . . xiv Page 141 142 143 144 146 146 146 149 151 153 156 157 159 LIST OF FIGURES - Continued FIGURE 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. The second-derivative Spectra of powdered acetates. . . . . . . . . . . . . . . . . . . The abc* reference axes and the abc crystal axes for trichloroacetamide . . . . . . . . . The second—derivative ESR spectrgm for tri- chloroacetamige irradiated at 77 K and ob- served at 300 K with a IlH and 10 db attenu— ation . . . . . . . . . . . . . . . . . . . . The ESR Spsctrum of trichloroaceSamide irradi- ated at 77 K and observed at 300 K with b llH The ESR spgctrum of trichloroaceSamide irradi- ated at 77 K and observed at 300 K with c*H H The decrease in intensity fgr the lines in the ESR Spectrum of -CF2COO radical upon re— action with H2 or 02. . . . . . . . . . . . . Diagram of the possible fluorine p-orbital configurations associated with various super- hyperfine Splittings. . . . . . . . . . . . . Correlation diagram for the 770K (radicals R and P),and the 300 K spectra (Z) of the ‘oocrgcrcoo- radicals with b Ira. . . . . . . Conformations of the 8-fluorines with reSpect to the pz arcarbon orbital for the various 'OOCCFCFchO' radicals. . . . . . . . . . . . The hi h-field lines of figure 11 at 3000K and 77 K (after warming to 3000K and cooling again). . . . . . . . . . . . . . . . . . . . XV Page 162 163 165 166 166 172 179 186 191 198 INTRODUCTION ESR studies of irradiated single crystals containing trapped oriented radicals have been of much importance Since they yield both isotropic and anisotropic hyperfine splittings from which the detailed structures of the radicals may be de— duced. The spectra of polycrystalline samples usually yield comparatively little information on the hyperfine interactions since the anisotropic interactions broaden the resonance lines and the weak transitions are obscured; liquids yield only the isotropic interactions. The existence of oriented organic radicals was first demonstrated in 1956 when Uebersfeld and Erb (1) irradiated glycine single crystals. The importance of this work was not realized until 1958 when the work (2) was repeated with im- proved resolution demonstrating that a high degree of orien— tation was present. This slow beginning in the study of oriented radicals is surprising since in 1951 Schneider, Day and Stein (3) studied randomly oriented free radicals by ESR in irradiated samples of polymethylmethacrylate and the exist- ence of oriented transition metal ions had been known for years (4-6). At present a great deal of data has been accumulated (7) from studies of the ESR spectra of crystals of carboxylic acids, amino acids and amides irradiated at room temperature. Irradiation of these crystals at room temperature usually 1 produces radicals in which a hydrogen atom has been lost from the carbon atom adjacent to a carboxyl or amide group. Recently it has been shown that when these materials are ir— radiated at low temperatures and the ESR spectra observed with— out permitting the temperature to rise that molecular ions are produced initially (8-14). Bond breakage may then occur on warming with the production of secondary radicals. Box, Freund and Lilga (8) proved the presence of molecular ions by irradiat- ing succinic acid-1,4-13C at 770K. The 13C hyperfine lines were found, along with methylene proton splittings, in the resulting ESR Spectrum. From this, it was deduced that the electron was mainly on the carboxyl carbon and that the structure of the radical was -OOC-CH2-CH2-C C—Qfi ,”/ \\\ H l/ \ // // _ Figure 1. The origin of the anisotropic asproton hyperfine interaction. The x, y and z principal axes used in this study are defined in (a). The magnetic field (H) is parallel to the ~C-H bond in (b), perpendicular to the C-H bond and to the p-or ital in SC) and perpendicular to the rgdical plane in (d). If 0.3 9.3 55 then 1-3 c0329 is negative and if 55 < 9 §;125°, then 1-3 c0529 is positive. This results in positive, negative and near zero anisotropic hyperfine splittings for the magnetic field orientations shown in (b). 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EU. //oo\\\¢m //00\\\ mm m.a- m.m- 0.4 mm: acacaummso .mmm ocom Op 4. mcmHm 41 osom cu: mmm Hmoaomm Hmumano mum camouuomacd . oamouuomH oddcaunou I a magma 12 In Table 1, it is apparent that arprotons also exhibit characteristic anisotropic interactions with typical principal values of 10.7, 0 and -10.7 gauss. This can be explained by first considering the energy equation for the classical interaction of the electronic and nuclear dipoles. The anisotrOpic part (52) is < 1‘5 COSZO‘ > (1-2 c0826) W = 2 r3 Av oC B (1-3 cos2 6) where r is the distance from the unpaired electron to the nucleus, a is the angle between this line and a principal axis, a the angle between H (magnetic field)and the principal 1-3 cos2a axis; < r3 >av is zero for s electrons and non-zero for electrons with p or d character;\the anisotropic split- ting results from"the (1-3 c0329) term. From this term, the anisotropic hyperfine interaction B between an unpaired electron in a p orbital of an atom and the magnetic nucleus of that atom is found to be ZB parallel to the p—orbital direction (2) and -B perpendicular to it (x or y). The iso- tropic parameter A associated with the 5 character can be added to the above to give the total interaction, i,§,, the hyperfine interaction due to 13C would be expected to be cylindrically symmetric. We now consider a planar R2CH fragment in which the unpaired electron occupies the carbon 2p orbitalvand there is a dipole-di— pole interaction with the hydrogen nucleus. The three principal — . , 4 ~ ___,.._____.__---.,. 1,, - .1. —- ,1 13 directions x, y, z and the direction of H. are shown in Figures 1b-1d. The proton hyperfine interaction is positive, negative and near zero when the electron density is in the Wblume for which (1-3 c0529) iS negative, positive and near zero,respectively. The change in signs reflects the fact that the electron magnetic moment is negative. Thus the positive proton Splitting value is found parallel to the C-H bond, the negative Value is perpendicular to the C-H bond in the plane of the radical,while the near zero value is found perpendicular to the plane and the C-H bond. Using this information, the angles between the various protons can be deduced. 8-Proton Splittings The hyperfine Splittings between the unpaired electron and the B-protons are given in Tables 2-7. The results can be rationalized by two methods; the valence bond method (100) where admixture of states such as H%C = CgH into the ground state for the ethyl radical are invoked andimolecular orbital theory (101) where hyperconjugation is postulated between the 2p orbital on Ca and a pseudo w—System of the proton group. Both calculations predict positive density on the B-protons. Theoretically (100,102,103), the isotropic coupling B constants of the B-protons, a can be calculated from the relation afi3= R(9)pZ where p: equals the spin density in the jpz orbital on the orcarbon atom, R(e) can be approximated by (104) R(G) = A0 + B0 cosae ' (1) o . where A is equal to zero on jnjzifiJ Hag) 14 cozy mmUIU. 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Iooomwom - 000.4400000004 40 0.00. 0.4H 0.04. 0.00 Iooomoom 000000004 00 0.00. 0.4H 4.00 0.00. mooomoom 000000004 .000 000 04000000400. 0H0 040040004 4004000 Hmummu“ llil« 04004000 0009 00I0 400 msououmIm 0443 004000400c4 00400000 I .0 04908 'A‘:“, Ar .v0ug‘v.. ‘ IV V "“f‘ 0 '0 ~ ~.C. Q .n F ‘9 :‘Dv ‘ s ‘7“ 20 theoretical grounds (100,126). For radicals with two B-protons attached to the same carbon atom e = 500 i.v or 600 1'7 depending on the conformation of the molecule; where y is the angle of twist, e is the angle between the projection of the C bond onto a plane which is perpendicular to the -H B B CQrCB bond and the axis of the pz orbital on C07 If free rotation about the COL-CI3 bond occurs, then R(e) must be replaced by an average value which equals approximately 50 gauss. For the case of restricted motion (by lowering the temperature or steric interaction) Stone and Maki (127) have used the’free rotor and harmonic oscillator approximations to evaluate . The value obtained was used to explain the B—proton hyperfine Splittings in irradiated alanine at 770K. The effect of molecular motion on the B-proton hyperfine c0nstants has also been c0nsidered by other authors (1284130). The effect of motion constrained between two extreme values using different probability distributions has been calculated by Griffith (151) to be of the form = A + B 0052(50 I y) (2) where A (BO-B)/2 and.1& approaches zero as the motion decreases. From Tables 2 and 5, B is somewhat less than 50 gauss for several cases where no rotation is involved; the reason for this is not fully understood. 21 Proton Hyperfine Splittings in Unsaturated Organic Compounds , The v-orbital for the radicals formed from irradiated aliphatic compounds given in Tables 1—7 consisted primarily of a carbon atom 2p orbital. However, in irradiated olefinic compounds a delocalized w-orbital can occur. For example furoic acid (152) and thiophene 2-carboxylic acid (155) add a hydrogen atom to the ring with a resultant hyperfine inter— action with four protons (Table 8). In glutaconic acid (154), a C—H bond is broken and the electron delocalized over three carbon atoms but not over the carboxyl groups while potassium hydrogen maleate (155) contains an electron delocalized over the entire molecule. In the irradiation of fumaric acid (85), ita- conic acid (118) and acrylic acid (119) however a proton adds and typical arproton hyperfine interactions are observed. Inclusion Compounds Griffith (151) has studied X—irradiated single crystals of the inclusion compounds formed between long-chain alkyl esters, ketones or esters and urea. Because irradiated urea gives few radicals, only ESR lines from the irradiated esters, ketones or ethers are observable, so the anisotropic hyperfine splittings are easily measured. These radicals lie in an ex- tended planar zigzag configuration with their long axes parallel to the c axis and are enclosed in tubular cavities formed by Spirals of hydrogen—bonded urea molecules. Because of the resulting symmetry an A2 hyperfine Splitting parallel to the c hexagonal axis and an isotropic m.m- «.0- m.a mma m.mu a.ou N.w m.mu "mm nooomoqqqmoooom mooomoumoooom m+ m: o o.¢ H mm ama m.m: o m.m s.maummuam mooommuqqqmmoqumfloooom mooommomo n moooom «.5- o «.5 a.m u mm m.«: o m.¢ m.m- u «m m m m . I . . I m mma s.. «.o a.a a.mm u mm m m m\\ /m M m.a| a.ou m.a N.N H mm _ _ . . I . I I .l w. _ m a a o s e m n m o . as o \ m \m mma oadouuoma e.am H mm mooo mm a m mooonln / \ mamam Cu 4. m /m m\ /m .mwm . mmm oamouuomwcfl mum camouuomH amounomm Amunhuo mocsomfiou Umumusummco CH wCOHuumuwucH msflmummwm cououm UoNflHmoonn .m magma .25 splitting value Axy in the plane perpendicular to the c axis are obtained. Normal hyperfine splittings for the dr and B— protons and splittings of 2 gauss or less for the iF-protons are obtained where the convention for labeling the protons is R‘ng-EHg-gHg-Coo-gHgR'. Excellent tables of hyperfine splitting constants for several inclusion compounds can be found (156) and those will not be repeated here. Hyperfine Interactions from Protons of Inorganic Radicals For comparison, inorganic radicals with proton hyperfine splittings have been included (Table 9) with the organic radicals above. The magnitude of the proton hyperfine Split- ting (502 gauss) due to the electron localized on the hydrogen atom is characteristic of the large Splittings observed between eleCtron and nucleus of the same atom. Since a very good review of the inorganic radicals is available (7), little discussion of this tOpic will be given. However, since the hyperfine splittings depends on the radical geometry it is important to compare various substituents in organic v-radicals with the same substituents in inorganic w-radicals and thus in the re- maining tables various inorganic radicals with their hyperfine splittings and g values will be included. However, a complete listing of all known inorganic radicals has not been included. _§§ntral Atom (13C,14N) Hyperfine Interactions _;Q7W-Electron Radicals Schrader and Karplus (145) have used a semi-empirical rusn-ionicrvalence bond theory with different degrees of carbon mad mmoo.m u .m o.mm mam Mom.a swam was «oao.m u m msao.m u m o.ma ammo som.¢ coumsux an ammo maa mmoo.m u m mmoo.m u m N.@ mmflm som.« coumsnx an amflm flea a.mH. 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QMB 25 sigma orbital following to estimate the isotropic proton and 13C splitting values as a function of e where e = 00 for a planar radical and in general is the angle between the nodal plane of the pz orbital and the C-H bond direction. A drastic increase in the central atom splitting value occurs even for values of e as small as 50. From Tables 10 and 11 the isotropic hyperfine interaction with the central 13C of hydrogen-bonded W-radicals is about 45 gauss and about 16 gauss with the central 14N of several radicals. Comparing these values with the 1109.7 and 549.5 gauss splitting values for 13C and 14N calculated for an electron in the 25 orbital of each shows that the odd electron occupies an orbital with only a few percent 25 character (neglecting ls polarization) in these radicals. This implies that the orbital occupied by the odd electron is nearly a pure p orbital and that the radical should be nearly planar. For the °COO- radical, the 13C isotrOpic splitting is 157 gauss which indicates that ps = 0.15 and therefore the radical should be nearly tetrahedral. The mechanism for the isotropic contri- bution to the central atom hyperfine interaction has been treated theoretically (144,145). The hyperfine splitting tensors found in Tables 10 and 11 for 14N and 13C show some deviations from cylindrical symmetry. The non-axial symmetry indicates that the O'bonds of the central atom are not identical. An answer may lie in the observation that the anisotropic l4N interaction tensors of the radicals 26 66 6.6- 6.6- 6.6 6.6 umzoombmmooOZNm mmzoommommooozmm 9663/ vimmoo/ 66 6.6- 6.6- 6.6- 6.6- mm/xmz\\mo «mo/xmz\\\6o 666 6.6 6 6.6 6.6 -ooofl+6mzomoomxmmoo mooofimmzvmomomimmov 66 6.6- 6.6- 6.6 6.6- -ooommp+6mz 6660660662 666 6.6- 6.6- 6.66 6.66 mmzmo¢626moo 6626662626660 0 0 WWW 6.6- 6.6- 6.66 6.66 +¢wwo - o// mo 662/6 - 66m.66 660 //zom mmo\ //zom 666 6.6- 6.6- 6.6 6.66 z 6cosm6m\z 666 6.NH 6.6”. 6.6% 6.6A66 -62 626 66 6.6- 6.6- 6.6 6.66 +662 6666662 66.66 6.6- 6.6- 6.6 6.66 +662 6660662 666 ----- 6.66 662 666.6 66666 66 662 666 ----- 6.66 662 606.6 60666 :6 662 666 066066066 66 662 666.6 60666 c6 662 666 6.6- 6.66- 6.66 6.66 +26immov -mo+_666066626xmmoo. 666 6.66- 6.66- 6.66 6.66 +26immov -ooommo+26immov 666 6.6-. 6.6 6.6 6.66 +26immov 6626Ammov 66 6.6L 6.66- 6.66 6.66 uvmm 6ommmi6mzo 66 6.66- 6.6- 6.66 6.66 Am66vmz 6662666 66 6.666 6.66- 6.66 6.66 minmomvz mimomvzmmx 66 6.6- 6.66- 6.66 6.66 mmzmom 6666662 .mm& 6mm UHQOHuOchd mmm oamouuomH 6606©mm Hmummuo cmmouuHZ £663 mGOHuomumuCH wCHMHmmxm .OH magma vi‘ q)‘ i a. V. .>©566 66:8 + _ 6.6 6.6 6.6- 6.6 6 6 _ 6 ma 1 _ 66 6.66- 6.66- 6.66 6.66 6 6o -o.mflo.o. 6666 66666 38606 . 66 - a 666 6.66- 6.66- 6.66 6.66 omH 66606666 6608666\z M 666 6.66- 6.66- 6.66 6.666 -666+mz 626666 I 666 6666.6 6666.6 6666.6 ".mw _ 666 6.66- 6.66- 6.66 666 -ooo. 6666.6 6666.6 6666.6 u 6Mv 6 666 6.66- 6.6- 6.66 666 6666. 6666 666 6.6- 6.6- 6.6 6.66 -666. 66066 7. 6 166-666- 66- 66 666 666. 66266666 2 6 66- 6.66- 66 66 66266666. 66266666 6 6.66- 66- 66 6.66 666. 6666.62666666 66 66- 66- 66 6.66 mi-momomo. 6566666666 666 66- 66- 66 66 -666+6mzmo. 6666666662 666 66- 6 66 66 A-oooommo. 6666666662 666.666 66- 66- 66 66 mimoouvmo. mimooovmmo .mmm mmm odd-306656 6mm UHQOHuomH 660666666 666666660 mausonumo nuflz mGOHuomumucH mCHmHmmmm .66 magma 28 NH(S03-) (89) and NH:(S03-) (91) approach axial symmetry at 770K. Thus the deviation from axial symmetry at 5000K is due to hindered rotation of the -NH2 and -NH groups about the S-N bond. Further variable temperature studies to measure the 13C hyperfine interaction at 770K must be done to determine the exact cause of non-cylindrical symmetry. The nitrogen 14N and 13C hyperfine Splitting tensors have a large component along the direction of the orbital containing the unpaired electron. Thus the p-orbitalS of the carbon and nitrogen atoms lie parallel to the intermediate principal value and perpendicular to the radical plane. N-H Hyperfine Proton §plittings The anisotropic hyperfine proton Splittings for NH are larger than for C—H (Table 1). By using the theory of McConnell and Strathdee (160), the splittings can be crudely matched with bond lengths of 1.05 X and an effective nuclear charges of 5.7 to 5.8 (89) for the NH(SOa-) radical indicating that the anisotropies are sensitive to nuclear charge and bond lengths. The failure to exactly predict the anisotropies is thought to lie in the fact that as the temperature was lowered, the rotation about the N-S bond decreased and more nearly <2y1indrical symmetry was noted in the nitrogen coupling con- StEintS so that effects such as hindered rotation should also be taken into account. 29 Fluorine Hyperfine Splittings Fluorine interactions, listed in Table 12, Show that the isotropic fluorine hyperfine splitting is positive in contrast to that of a similarly placed hydrogen. The fluorine tensor for the 'CFHCONHa (82) radical and -CF2CONH2 (20) radicals,“ have a large Splitting perpendicular to the plane and nearly cylindrical symmetry with approximately 11% Spin population in the 2p” fluorine orbital. This shows that considerable C-F double-bond character exists. The departures from cylindri- cal symmetry are a combination of the dipole—dipole (160) effect from the 80% Spin population in the carbon 2p” orbital with the fluorine nucleus and the polarization (20) of the C-F bond. For the proton case, Spin polarization of the C—H bond produces the isotropic proton Splitting with the anisotropic component resulting from the dipole—dipole effect. A small amount of 5 character in the C-F G’bond results in a negative isotropic contribution; however, a larger positive isotropic coupling is observed. The variation in the isotropic fluorine hyperfine Splitting indicates that the geometry of the fluoro radicals varies considerably from planar 'CFHCONH2 to tetra- hedral -PF4 (165). Work on perfluorosuccinic acid (19) Shows hyperfine splittings from all three fluorine atoms indicating consider- able delocalization of the odd electron; the B-fluorine pr spin density is approximately 5%. 5O .mpsum 66:6 CH Umscflucoo 6 6 666-6 666-6 66666 666666 -ooommb 6666 mzooommommoooomz 6- 6- 66 6 "36 I I "6 66 66 66 66 6 Am 6666 6 66- 66- 666 66 ".6 -ooommmmoooo- 6666 mzooommommoooomz 6- 6- 6 6 "66 I I ".6 66 66 66 66 6 Am 6666 6 66- 66- 666 66 "66 -ooomommoooo- 6066 mzooommommoooomz 66- 6 6 66 "66 l I la 66 6 66 66 I 6 66-6 6666 6 66- 66- 666 66 u 6 -ooomommoooo- 6666 mzooommommoooomz 6.66- 6.66- 6.66 6.66 "66 6.66I 6.66I 6.66 6.66 "66 66 6.66- 6.66- 6.66 6.66 n 6 -ooomommoooo- mzooommommoooomz 66- 6.66- 666 6.666u66 66- 6.66- 666 6.666n6.6 666 66- 66- 666 666n66 666660666 66666606 6066 662660666 666 66 6- 66 6.66 n 66 N6 66 666 66- 66- 666 6.66 n 6 mmzoomwmmo mmzoommommo 666 66- 66- 666 66 u 6 6mzooommo. 662660660 66 66- 66- 666 66 n 6 mmzoommo. mmzoommo 66 6.6- 6.66- 6.666 6.66 n 6 mmzoommo mmzoommmo .mmm mmm Uflmouuomfla4 mmm UHQOHuOmH Hmoflpmm .QEGB Hmumhuo mco6uomumuc6 6:6mummmm oGHHOSHmIm U26 lo .N6 magma l .mpsum mflsu CH 6 066066066 6.666 m 666 066066066 6.666 6.66 066066066 6.666 666 666662 666 66 6.62 6606. 6 600663 6.62 N 6.662 666 6.66- 6.66- 6.666 666 6pm 606.6 oo 06 66o 6 66- 66- 606 666 u 0 660. 6066 66260660 6 66- 6.66- 6.666 06 n 0 An 6666 -ooommb 6266066600 .mmm mmm 0666066606656 6.6m 06mouuomH 660666666 .9659 66666060 Umscflusoo I N6 mHQme 52 Chlorine Hyperfine Interactions Very little work has been done on crystals containing a radical with chlorine hyperfine interaction. This is due to the fact that a complication arises because the magnetic moments ofthe two chlorine isotopes 35C1 (in 75 percent abundanod and 37C1 (in 25 percent abundance) are not equal so that a separate set of hyperfine lines for each results. The existence of a chlorine nuclear electrical quadrupole moment means that there are a total of eleven unknown ele- ments to be determined versus the usual Six elements for nuclei of Spin 1/2. However, results are available (Table 15) for the HCClCOOH (167) and HCClCONHg (168) radicals which Show that the largest principal hyperfine Splitting of 19.6 gauss for the chlorine tensor lies parallel to the smaller 9 value. This direction is thus perpendicular to the plane of the radical indicating that the chlorine atom possesses un- shared electrons in its p orbital so thatmthertructure Cl+-EHCOOH is somewhat important. This large value is be- lieved to dominate the trace of the tensor and the isotropic coupling of the chlorine must be positive for the following reasons. 'If the C-Cl bond were to Show the Same polarization as that in C-H, the negative contribution to the chlorine iso- tropic coupling would be much less than the above value be- cause the bond orbital is nearly pure 5p-. In addition, calculations Show that the electron dipole—nuclear dipole negative contribution to Az is negligible and good agreement 55 666 660306 6.66 66066 60666 66666 6600.6 6660.6 6600.6 u 6 666 6.66- 6.66- 6.666 6.66 63066 600.6 600.6 600.6 u 6 mm 6.M6I 6.m6I m.mm 6.6N6 6060 60606mz 6mmo.m mm6o.m Nmmm.6 u m 066 6.66- 6.66- 6.66 6.66 WHo 6066 6666662 mm6 6.6m m.mMI 6.m6 m.6m 666 6.66- 6.66- 6.66 6.66 mmfi 6.6MI 6.6MI m.m6 0.0m 666 0.66- 0.66- 6.66 6.66 m6o 6066 666 666 6.6 6.6- 6.66 6.6 mmzoo6oom mmzoomm6oo 666 6.6 660 6.66 6.6 mooo6obm mooommHUU .mmm mmm oflmouuomflc¢ 66m 06mouuomH HMUHpmm .mEoB Haumwuv. msHHOHQU SuHB wGOHuomumucH mCHMHmmmm .m6 magma 54 with Dixon and Normanfs(174) isotropic chlorine hyperfine 3'5 gauss) for HClCCOOH results if AC1 is Z positive and the small in-plane Splittings are negative. . . Cl splitting (aiso Because the complete tensor has not been determined,2a more exact description of the bonding can not be given. PhOSphoruS Hyperfine Interactions Only a few radicals have been studied in which Splitting from phOSphorus has been observed (Table 14). A large 31P hyperfine Splitting (aiso = 472 to 1544 gauss) was observed for HPdé (157,158), 'PF4 (165) and ~90; (175-178) radicals as consequence of the unpaired electron occupying essentially an Sp3 hybrid o'orbital. AS compared to the w-radicals men- tioned above, the hydrogen coupling in HP02- is quite large. Adrian gt al. (179) and Brivati g; _l. (180) report that a large positive proton coupling is found (157 gauss) in the formyl radical with configuration interaction between the ground state and a low lying excited state (He + C0) being used to explain the large 157 gauss proton splitting. Thus the unpaired electron density on the proton is taken as positive. The 9 tensors of both the nearly tetrahedral radicals 'P03= and HP02 show cylindrical symmetry, the direction of the minimum 9 being parallel to the spa-G'orbital of the unpaired electron with about 55% unpaired Spin in the 5p phosphorus orbital, 15% in the SS orbital and 16% on the proton. Because the geometries of the above radicals are close to tetrahedral, they can not be thought of as w—radicals in the 55 666 ----- 6.66 6. 606.6 66 :6 6mm Hm.“ lllll 0.0m mo VHON0¢ .HVH G...” NEW 666 ----- 6.06 666. 606.6 HM 06 666 666 0.66- 0.66- 6.666 0.666 660306 "666. 6666.606662 666 6.66- 6.66- 6.66 6.666 "666. 066.6666666626 006.6 u 6 06 6 . 6 .6 6 666 0.66- 0.66- 6.606 0.666 6 6603 u 06 0 m6 066 2 6600.6 6606.6 000.6 6000.6 n 6 6 . 6 6 6 6 6 666 6.66- 6.66- 6.666 0.666 66030 n 06 60666 0 6 6 A 626 666 66666606 666666 0.066 666. 666 66666606 666666 6.6666 666. 666662 0600.6 0600.6 6600.6 6 6.66- 6.66- 6.66 6.666" 666 m m . 666 0.06 6.66- 6.666 6.666" 666 6-66066- 660_ 60666666626 666 6.66- 6.66- 6.66 6.666" 6666 6.66- 6 66- 0.606 6.666" 6666 "60696-6660 60666662 6660.6 6666.6 6600.6 6660.6 n 6 66 306 6 66 066.6666662 666 0.66- 6.66- 0.666 0.666 6 0 - 6. 6660.6 6660.6 6600.6 6660.6 u 66 306 6066 6 60666 60 666 6.06- 6.06- 6.666 6.666 6 - . A v 666 6660.6 6660.6 6660.6 6060H6 u 6 660306 6066 666066666: 6.06- 6.06- 6.666 6 066 - . 6 6 6 666 0.66- 0.66- 0.666 6.666 -6666 06 m 62 .mmm mmm Uflmouuomflcfl mum UflmouuomH HMUHUmm anumhuu I‘ 'III‘ 56 same sense as planar w-radicals. The coupling mechanism for planar radicals according to molecular orbital theory in— volves excitations from filled to unoccupied orbitals whereas for bent radicals excitation into a half-filled level occurs. It is interesting to note that the phOSphorus isotropic hyperfine Splitting varies from 674 gauss for tetrahedral P03- to 23.8 gauss for the P atom. It appears that the phos- phorus splittings are very dependent on the geometry of the radical. The suggestion (158) that replacement of oxygen by hydrogen results in a decrease of the angle between the X-H bond and the unpaired electron density axis has not been in— vestigated. It is also possible that the large proton split— ting is a direct measure of the s—character on X (X = P here) for radicals such as H-i-A and H-i-Ag. In view of the limited data on phosphorus little can be said about organo-phosphorus splittings. Radicals Containing Sulfur Sulfur-52 (99% natural abundant) has a zero Spin and thus Table 15 shows only the g value variation. By comparison with other organic free radicals where the free electron is localized on the H, C and N atoms, the difference between g (max) and g (min) is approximately .007 or less while for those radicals where the electron is localized mainly on the sulfur Ag = .05. This can be explained by considering an electron in a p orbital of the sulfur while spa hybrid bonds form the d‘bonds. If the x axis is along the p orbital axis, .Aomdv Umflwsum smog m>mn 856cmamm no HSMHSm Hmnuflo 0:6:6mpcou mHmUBOQ 0626060 mo HmQEdc 4 .x. 6.6- 6.6- 6.66 0.066 "0666 666 0660.6 6660.6 6600.6 u 6 -6066 0666.6066662 666 660.6 6666.6 6606.6 u 6 666 66666 66666666666 - - - 606.6 u 6 6660666266 666 6.66- 6.66- 6.66 6.666 "0666 -606 6662666 666 -606+6mz 6666.6666662 666 6060.6 6666.6 0660.6 +606 6666.6666662 666 6600.6 6600.6 0660.6 -666 0666.6666662 N 666 660.6 06 600.6 u 6 660306 -606 6066662 666 600.6 660306 -606 6666.6666662 666 66.6 66.6 66.6 .66666666626666006 666.666666666626666666 666.66.66 -- -- 660.6 066666660666 60066 666.66.66 666.6 660.6 606.6 066666660666 6066 666.66.66 660.6 660.6 600.6 6-666-6 60006 666.66.66 060.6 660.6 006.6 6-660-6 60066 666466.66 666.6 666.6 660.6 -m-6-m 0666606 6066 66-666666666266006666 666 666.6 660.6 600.6 6060666666666666 66666666666666666 66 666.6 060.6 606.6 n 6 66666666666666 mooo6mom6moooom .mmm U6Q066066c¢ amoflwmm 6666660 66606066 mafloaommmuuou 6:6 606 wuomsma 6 0:6 666 zuHB chHuomumuCH mCHunmmhm .66 66666 58 the z axis along the C-S bond and the y axis in the plane and perpendicular to the C-S bond, then by perturbation theory the following equations can be derived (185): 9x. = 9f (5) .___ _ _;__ 1 2 9y 9f [ 1 ”/6[(E2-E1) + (Es-El) + (E4—E1)]} (4) _ _ A. ___2;__. .___4___ 92 - 9f [ 1 (2) ((E2_El) + (E3_El)) } (5) as an example IJ-cystine dihydrochloride (15)has gy = 2.025 ' gz = 2.055 gX = 2.005 which results in Eg-El = 15,000 cm“l and E4—E1 = 45,000 cm‘1 where E1, E2, E3 and E4 are the energies-forhthe unpaired electron in the pX orbital, each of the two non-bonding Spa hybrids and the bond- ing 6‘ orbital. This type of partially quenched Spin-orbit coupling adequately accounts for the large g values present in sulfur-containing compounds. The non—axial symmetry in the g value is thought to be due to the non-bonded sp2 hybrids interacting with atoms not bonded to sulfur plus the F- character of the odd electron orbital preventing the rotation about the C-S bond. An exception to the large variation in g value in sulfur radicals occurs in the $03- (189) radical where g = 2.004. Here the sulfur hyperfine Splittings suggest Sp3 hybridization at the central atom which is consistent with an expected pyramidal (191) structure for the $03— radicals and.with the observed geometry of the P03: and C103_-radicals. 59 ngensors of w-Electron Radicals with Quenched Spin-Orbit Interactions McConnell and Robertson (192) have explained the small 9 shifts in w-electron radicals in terms of spin—orbit interaction which mixes V and d‘excited states with the ground state. If the unpaired electron is contained mainly in the 2% 2pz carbon orbital, then g = gX = gy is reduced by —wE: from gfree radical with promotion of the odd electron from a F-orbital to a d”*-orbital and increased-gg-by promotion of a d’electron to pair with the odd electron in the w-orbital, where E; and E2 are the energy separations for each case. gz is affected only slightly by the promotion of a 6'electron to a 6* state because this transition is highly energetic. Since Eg‘l — E1_l varies from 8000 to 800 cm-1, g = 2.009 to 2.005 in agreement with experiment (Table 16). The 9 value will deviate further from the g2 value as the spin-orbit coupling increases. In addition hetero groups like N = 0 and C = 0 in N03" and C03_ have low energy n-—-)-W transitions 'which reduce E2 and thus increase g . q; Tensors for Radicals with Partially mienched Orbital Angular Momentum XeF, KrF, and F2_ and o’- electron radicals (Table 17) i.e., the unpaired electron occupies a 6’orbital of the mole-' cule. The deviation in the g values from the free electron 9 value could be accounted for by spin-orbit interactions between ground 6'— state and w-states of the molecule. 4O 666 A66 6600.6 6660.6 66006060. 666060066 66 0606.6 6600.6 6606.6 -ooomw6moooo- 6266066066006662 06 6600.6 6606.6 6600.6 66260660. 66260660 666 6600.6 6600.6 6660.6 A-ooomoqumovooom Mooomoumoooom 06 6600.6 6600.6 6600.6 hvmm 6066666626 66.06 6600.6 6600.6 6600.6 600060660666606 6060660660666606 606 6600.6 6600.6 6666.6 6Amooovwmmo 666660660660 mm 6600.6 mmoo.m 6600.6 mfimooovmu. mfimooovomm 6m 6600.6 6600.6 0600.6 mooommo. NASOOUVUmm .mmm msmHm CH 66m manam ou Havapmm Hmumhuo m 666906ucmmuwm mcflamsoo uflnuolc69m Umnocmso nuHB 66606©mm couuowamlh :6 muomcme m 60 mmSHm> Hmmflucflum Havamha .66 06968 mom UHQOHuomH 6.66 H wd. xHHumE H& CH 6mm< 0 - 606 6.66- 0.66- 6.66 6.066 n 66 -6066 6066662 600.6 600.6 600.6 u 6 . - ma 6 6 . mm 006 6.66- 6.66- 6.606 6 666 - 6 n 066 0666 2 666 6.66- 6.66- 6.66 6.6606 u 666 "6066. 6064666 .mmm mwm U6monuoch¢ 6mm oamoqumH HMUHUmm HMumhno 6m6052 umnuoasuHB mGOHUUMHmucH mCHMRmmmm .m6 $6968 1 4 666 0660.6 0660.6 . 6600.6 "6 . - m 666 -666 6.666- 6.666- 6.666 6 666 - mm - m . _ 660.6 660.6 000.6 , "6 - 6 6666 666 066- 066- 066 006 - m6 6 m 6066 6.666- 6.666- 6.666 6.666 "6x6 6666.6 6666.6 0666.6 u6 . m 6 u x x 66x 666 6.066- 6.066- 6.606 6 666 66 m 066 .mmm mmm uflmouuomflcd 6mm UflmouummH HMUHUmm .mEmB 6mum>60 mamo6©mm couuumHmub .66 66969 42 The remaining inorganic type radicals are w—electron type \Tables 18, 19). In general these radicals have partially quenched orbital angular momentum and their 9 values can be calculated by equations derived by Kanzig and Cohen (195) A2 6 92 - go + 2(X2132) fl (6) A2 Ii- )\ k2 A2 % 9y — 90 (12:52) - IE [ + (12:32) - ($2132) - 1 ] (7) A2 i. )\ )\2 % A2 9X ‘ go ($2132) - EDI - (12:32) - (iz:zz) + l ] (8) where go = 2.0025, 2 the effective orbital angular momentum about the internuclear axis 2, E is the energy separating the states concerned in the Spin-orbit interaction, A = effective Spin-orbit Splitting, A = separation of the energy levels in- the 2pr state for two electron or one electron occupation. Thus for each radical, the xyz system is defined and the summetry operations deduced, which forces certain correct symmetry orbitals to be used for the description of the radical. Calculation of the energy separating the states between which there is spin-orbit interaction can then be made. The following rule has been found to hold (7): if rotation about an axis j belongs to that representation which is the product of the representation of the ground and excited states, then gj. will deviate from 2.0025 as a result of the Spin- orbit interaction between the two states. 45 606 6.66 6.66 6.66 6600.6 6600.6 6600.6 m02M 606 6.06 6.06 6.66 6600.6 6600.6 0600.6 6ox\mozx 606 0.6 0.6 0.6 660.6 660.6 600.6 60266 -moz 666 6.66 -- 6600.6 -- 6ox\mozx m 606 In II II 600.6 600.6 600.6 602% 066 6.6 6.6 6.6 6660.6 666066 6600.6 6026 666 - - - 6060.6 6660.6 6600.6 600666662600 ..”oz 606 6.66 6.66 6.66 600.6 600.6 6600.6 6om\mozx 606 0.66 0.66 0.66 600.6 600.6 600.6 60266 m-moz 606 0.6 0.6 0.6 660.6 606.6 666.6 0666.OZmAzovmmmmz -moNz 606 0.6 0.6 0.6 6660.6 6600.6 6600.6 60262 -6062 606 6.06 6.66 6.06 6600.6 0666.6 6600.6 6066 606 c6 6062 N02 606 6.06 6.66 6.66 6666.6 6666.6 6600.6 6026 moz 606 0.6 0.6 0.6 6600.6 6600.6 6600.6 mozmz 602 606 6.66 6.66 0.66 0666.6-06 6600.6"66 6600.6 "66 mozmz moz 606 6.66 6.6 6.6 6600.6- 6600.6 0600.6 6ox\mozx oz 606 0.66 0.6 6.6 600.6 060.6 600.6 602% oz .mmm musmumcou mc6mumm>m mm566> m 8:6Um2 Hmowpmm umoz cam 602 .-moz .moz .02 Mom mm566> m cam muamumcoo mC66666mm m26mummmm .ma magma THEORETICAL Spin Hamiltonians for Radicals in Single Crystals The treatment of the Spin Hamiltonian for S = 1/2 has been discussed many times (20,58,65,66,212-215) and a lucid discussion of the terms involved has been given by Slichter(22), the results of which will be summarized below. The Hamiltonian used is of the form. H=- §-=.fi+z§°z=x.°—f.-2 . .E-I. B 9 j JJngBJ 3 (9) +zf.-Q.-E.+z’f-.§-E.+z 3Z5 where the summation is over the jth nuclei coupled to the paramagnetic species, B is the Bohr magneton, 35 is the nuclear magneton and gj the gyromagnetic ratio. The term Tfi-E-Es is approximately 20 "kHz in.the solid state and is neglected. The last term involving coupling of the electron to nuclei in adjacent diamagnetic molecules amounts to approximately 10 .MHz; it is a dominant part of the line width and will be discussed later. The first term is the Zeeman term or the direct coupling of the electron with Spin E'to the magnetic field E through the Z tensor. The second term represents the coupling of the nuclei with spin E.to the electron Spin through the A tensor. The third term 44 45 is the coupling of the nuclei to the magnetic field and the fourth term is the effect of the magnetic field on the nuclear quadrupole interaction. The quadrupole tensor 5 must be included for any nucleus with nuclear Spin I._ 1. In these cases the energy levels are not expressible in algebraic form but are obtained numerically. Kohin has given a complete numerical treatment for the (I = %) chlorine case (168). Treatment of the 3 Tensor If the elements of the 3 tensor do not vary from the free spin value by more than 301 and the second term in the Hamiltonian is less than 1/25 of the first, then the approxi— mation that the components oflg perpendicular to the applied field have neglible effect on the solution of the Hamiltonian (first order theory), can be used. This approximation leads to resolved values of '§ of +% or ~% along the magnetic field direction. Equation 9 can be written as H = H1 + H2 where H1 is the first term and H2 the remaining terms. By using first—order perturbation theory for the solu— tion of H1 one obtains E1(MS) = MS g {:3 H (in MHz) (10) where E; is the energy level associated with a particular MS and g = (9:1: + gill: + gil:)% if the field E has direction cosines lx’ 1y, 12 with the principal axes. However in most applications a non-diagonal axis system such as the crystal 46 axes is chosen, so that (E)2 = 62 (E E2 (11) is the result (216) for H1. This equation is equated to an effective value of 9 defined as ge = Egg (12) where 98 is measured at a number of orientations in each rotation; Hois taken as the center line position for an odd number of hyperfine lines and one-half the distance between the two central lines for an even number of hyperfine lines. For a rotation about x, equations (11,12) reduce to 2 = 2 2 2 - 2 2 . 9e (9 )yy cos ¢x + gzz Sin ¢x + 2(g )yzcos ¢X81n ¢x where ¢ is measured from the y axis in the yz plane. The 2 2 values of gyy’ 922 the experimental data in the range of O0 < e < 1800. A right- and 932 are determined by the best fit to handed permutation of the axis gives about y g: = 9:2 COS2¢Y + gixsin2¢y + Zgixcos¢ysin¢y (14) about z 9: = gixcosa¢z + ggysin2¢z + Zgiycos¢zsin¢z (15) The complete tensor is obtained from the above equations and diagonalized in the usual manner. The results are the eigen- values (92) and the associated direction cosines. 47 A method by Schonland (217) fits the g value as a function of e to an expression of the form 92 = a + B c0326) + y sin29 where 2 a = g: + gf _ 2 _ 2 2 B — (9+ g_) cos 2 9+ (16) (g: - gf) Sin 2 9+ 2 7 9+ and g_ are the maximum and minimum g values in the plane and 9+ is the angle at which the maximum g value occurs. gXX=a+B . gyy = a - B (17) gyx = 7 Similar equations are found for the other planes. The derivation of the above expressions has been given (218). The method of Schonland is less tedious if the g tensor has nearly the same or the same principal axis as the hyper- fine tensor, since the directions of the hyperfine tensor are easily found (maximum and minimum Splittings occur) with an oscilloscope presentation and thus only 9 values near this direction need to be taken. Hyperfine Splitting Tensor to First Order Due to the separability of the nuclei in the above approximation, treatment (219) of H2 for the case I =.% results in two Simple equations,0ne corresponding to MS = +-% and the other MS = -'%. Thus 1 -= —-~— = — . '-F' o H2(:t) _+. 2 g: [(h A). xjh) Ij + HQ ] (18) 48 where equation 18 is in gauss, after dividing equation 9 through by gS l8 , and Xj = (ZgNjBNHo)/gS|BI , A]. (.+.) = h - (AjinU) (19) = _D_V__ ___ ‘ Ho gslBI A346) Mm) where Xj is the nuclear reSonance term, h a unit vector in the direction of the applied field, 8 a unit dyadic, :j is the Splitting tensor for the th-nucleus and v is the klystron frequency. Then equation 18 reduces to 1612(1) = :t 2 [3(1) 33. + HQ ] (20) J 3 j The original approximation separated the electron Spin wave function as a factor so no terms connect different nuclear spins. This means that the intensity patterns and Splitting values can be analyzed independently of the other nuclei, $33,, for several uncoupled nuclei with, I = %y the total energy would be equal to the sum of the individual energies and the total intensity equal to the product of the individual in- tensities. For I = %-, H is neglected, and the eigenvalues Q for one nucleus are (combining H1 in terms of gauss) E(MS)MI . = MsH + MS A (+) MIj (21) 3 Since K (+) and X (-) have different orientations in Space, the angle E is defined as the angle between the two axes of quantization so 49 cos E» = ‘A (+) ° A (-)/ |A+A_l (22) By proper matrix multiplication cos E. = E (Aii - X2) Ci / A+A_ (25) where the Ci. are the direction cosines of g_with respect to a principal axes system or _ 2 2 _ 2 2. and the‘ Cij are the direction cosines with respect to a non-diagonal axis system (usually the crystal axes). For one nucleus (I = %), 4 energy levels are possible. Using the selection rules AMI = O and AMS =.i 1, two transitions 1 1 . . _‘; H + §d+ and H - §d+ of intenSity Id+ result where d+ - 2 (A+ + A_) and Id = c052( E /2) . The forbidden transitions + correspond to the other 2 possible transitions. H + %d_ and H - 1d where d =‘; (A - A ) and I = Sin2( g /2). It is 2 - - 2 + - d_ noted that 2 2 A2 = Ax .+.x) o o cX id 2 2 o (A -+-x o c (25) Y ) Y 2 2 O O (Azzh x) CZ with reSpect to a principal axis system and 23. E Oll >H 2 _ Aij - where Z = (l m n) , A = A. :;x A. A A A ifix A XY YY yz A A A. $:X xz yz zz SO and l, m, n are the direction cosines with reSpect to non- diagonalized axes. The table of Rexroad, Hahn and Temple (219) has been ex- tended for the cases of two and three uncoupled nuclei with I =-% for each nucleus and are given in Table 20. In general the equations listed by Rexroad gt al. (219) for the case I 2,1, should only be used as an approximation and not at all in cases of large quadrupole coupling (168). The combination of Table 20 and the table by Rexroad gt 3;. (219) can be used to obtain the transition frequencies resulting from various combinations of interacting nuclei. These frequencies are ob- tained by adding the magnetic field at the center of the Spectrum to plus and minus one-half the various positive and negative combinations of the doublet Splittings, one doublet Splitting for each nucleus. For example, for two equally coupled nuclei plus one uncoupled nucleus, the transitions would be HO plus or minus one-half the positive and negative combinations in groups of two (ene term for the coupled nuclei and one term for the uncoupled nuclei) of the terms d+, d_ and (A+ + A_), zero, A A_, A - A_ + . In other words, the +I most intense transitions would be H.i'§ (d+ :t.(A+ + A_)) and H.i-% d+ with intensities-% coss(§’/2) and coss(§’/2) + c052( E /2) sin4(§ /2) , reSpectively. The forbidden transitions would result from the other possible combinations. ———- _...=.._. .._._ - _- ‘v uy‘n 9‘»; \- AN» 1 Pl. H(. A .u‘ .§ - - sauss . h... L.- nus . and t 51 Table 20. Anisotropic Splittings for Two and Three Unequally Coupled Nuclei No. of Transi- tions Doublet Splittings Relative Intensity Two nuclei I = 1/2, unequally coupled *d+(1) + d+(2) 2 cos4( E/Z) *d+(1) - d+(2) 2 cos4( 5/2) d_(1) + d_(2) 2 Sin4( E /2) d_(1) + d+(2) 4 sin2( E /2) c032( 3/2) d_(1) - d+(2) 4 Sin2( 3/2) cose( ‘E /2) d_(1) - d_(2) 2 sin4( E/z) Three nuclei I = 1/2, unequally coupled *d+(1) + d+(2) + d+(5) 2 cos5(E./2) *d+(1) + d+(2) - d+(5) 2 cos6(§ /2) *d+(1) - d+(2) + d+(5) 2 cose( E /2) *d+(1) - d+(2) - d+(5) 2 cos6(; /2) d_(1) + d_(2) + d_(3) 2 sin8( ‘3/2) d_(1) + d_(2) - d_(5) 2 sins“; /2) d_(1) - d_(2) + d_(5) 2 Sin6(‘£/2) d_(1) - d_(2) — d_(5) 2 sin6(‘§/2) d_(1) + d+(2) + d_(5) 6 sin4( g/z) cos2('; /2) d_(1) - d+(2) + d_(5) 6 sin4(E /2) cosa(5 /2) d_(1) + d+(2) - d_(5) 6 sin“( ~5/2) cose(’$ /2) d_(1) - d+(2) — d_(5) 6 Sin4( E/Z) c0820; /2) d_(1) + d+(2) + d+(5) 6 Sin2(‘§ /2) cos4(3/2) d_(1) - d+(2) - d+(5) 6 sir-2(3/2) cos4(‘;/2) d_(1) + d+(2) - d+(5) 6 sin2(‘; /2) cos4(} /2) d_(1) - d+(2) + d+(5) 6 sin2(; /2) cos4( E /2) The most intense lines (5 = o) are seen at X-hand, the re- mgining lines are forbidden transitions providing |A| >| xfiI-d (1) = 1/2 (A +A) and d (1) = 1/2 |A -A I for the nucleus Kumbered 1. + - - + - 52 Experimental Determination of Hyperfine SplittinggTensorS Experimentally, the angular variation of the hyperfine Splittings are obtained. Since in general a non-diagonal axis system will be used, the following function best fits the experimentally observed first order Splittings = .=2 0 AH ij (h A h)j where h is a unit vector in the direction of the applied field with respect to the non-diagonalized axes for the j nuclei. If the direction of uh is represented by the direction cosines (l, m, n) with respect to orthogbnal x; y, 2 crystal axes, then a rotation about the z axis will result in the following ._ = __ . l h - A2 - h = (l,m,O) (A2) (m) (27) O , = A2 12 + A2 m2 + 2A2 1m xx yy XY letA2=OL l = cos 9 m = sin 9 and on rearrangement “H ° A2 -'H = a cosze + a Sin29 + 2a sinecose, or xx yy xy -.=2._= _ h A h 1/2 (Qxx + 09y) + 1/2 (ka ny) c0529 . (28) + QkySanQ 7 a right-handed permutation of the axes yields the equations for rotation in the other planes. A best fit to the curve 55 with this function, Oxx and ny defined at 00 and 900, is obtained by fitting Qxy to the square of the splitting values between 00 and 1800. If two magnetically distinguishable sites are apparent when rotating in the xy plane, the two Sites correspond to the positive and negative signs of Qxy' For more than one off-diagonal element having a choice of + and - signs, the relative signs are found by comparing the observed spectrum for the (5‘5) 5‘5} 5-%) skew direction with the predicted Spectra obtained from the various Sign combi- nations for the off-diagonal elements. The tensor is then diagonalized by standard methods and the principal values obtained. In favorable monoclinic cases one of the two possible sets of eigenvalues obtained from the four possible undiagonalized tensorS(io&y,.i 0&2; I Qky,.i 0&2), has minimum eigenvalues which are much larger than the minimum Splittings found experimentally and can thus be disregarded. Forbidden Transitions Although four transitions are possible for each nucleus of Spin 1/2 as indicated above, only those for which AMI = 0 are sufficiently intense to be observed at all angles for a magnetic field of 5500 gauss. These are the transitions for which equations 15-15, 28 have been equated. The intensity of the lines for which AMI # 0 has been shown by various authors (82.19.66) to be dependent on the magnetic field strength; if higher magnetic fields (15,000 gauss) are used, the Sign of the hyperfine constants can be obtained from the 54 observation of these "forbidden" transitions. Only an X-band (9500 MHZX) Spectrometer was used throughout this study so calculations of the weaker lines were neglected. Second-Order Perturbation Theory For those splitting values greater than 200 gauss (at X—band frequency), second—order perturbation treatment is needed. Small deviations from the predicted first-order spectra can be found for Splitting values between 100-200 gauss near the direction perpendicular to the largest hyper- fine Splitting, reflecting the deletion of the SX and Sy components in the first-order approximations. The second- order perturbation treatment of Bleaney (220) retains the SX and Sy component, assumes cylindrical symmetry with 3 << A and that the A and S tensors possess the same principal axes. Even though the crystal will usually be described in a non-principal set of axes, the position of the maximum and minimum splitting can be found. Since these are the di- rections of the principal axis system, the formula 0f Bleaney 0 can be used by letting e = 00 and 90 . For 9 = o0 H = H + Am +-§3— [I(I+1) - m2 l (29) O m 2H0 For 9 = 900 (A2 + B2) [ ='H + H0 _ m + Bm 4H0 I(I + 1) - m2 } (50) where Hm is the field (gauss) at the particular line, H0 is the field (gauss) at the center of the Spectrum and A > B are the hyperfine Splittings (gauss). 55 The following equations (MHz) using perturbation theory have been derived assuming the absence of a quadrupole inter- action and that the A and E tensors have the same principal axes: _ Km I(I+1) - m2 A2 A2 Hm-Ho-ag ‘{ 49262-60 )Ai(§¥ + a?) m2 4. 2 AE-Bg 2 . 2 ‘ E3252§;'(H§g—) ( K ) cos 9 Sln 9 I I+1 -m2 2 _ (4:252H0 } (g§%¥%£9 $§K2 (A§ - Ai) coseesin2¥>coszw where g? = gicosap + g§sin2p B2 = A§g§c052¥> + A§g§sin2p g? 2 2 _ 2 2 2 2 2 - 2 9 K — Azgzcos e + B ngln 9 92 = gicos2e + gisinee Comparison of equations 29,50 (A = B) with Fessenden's (222) expansion of the exact Breit-Rabi solution shows that the perturbation equation differ by a factor of Hm/HO in the denominator. This results in a maximum error of 0.5 gauss for hyperfine Splittings of the order of 250 gauss. In the present study, the crystal could not be aligned to this accuracy so the perturbation results were used. In order to obtain a hyperfine splitting correct to second order without using the second-order equations, a measurement (225) is made of the separation between the lines (MS,.MI-+-MS-1, MI) and (-M + 1. -MI -+'-M -MI). This S S' procedure was used for fitting to equation 28. Thus the hyperfine constants obtained are correct to second order. 56 For radicals with several equivalent nuclei, second— order splittings are observed and have been treated by Fessenden (224). The above second—order formulas can be used if one uses an I representing the total Spin of the equivalent nuclei, with M being its component along H and I in addition using the I available to a particular M i,g,, I (using |I --1 ), [I - 2 I, ....). Electron Dipole-Nuclear Dipole Hyperfine Coupling It is observed that the ESR spectrum line width is dependent on the number of near neighbors. In the case of the radical°CH(SOS)2= (88), the presence of only two near neighbors(5.5 A distance) resulted in line widths as low as 1 gauss for the main line which permitted the appearance of a resolved triplet superhyperfine structure on the main lines with splittings of 2, -1 and -1 gauss. This superhyperfine‘ splitting is caused by-a pure nuclear spin-electron spin dipole interaction which can be calculated by the following equations derived by McConnell and Strathdee (160). It is assumed that an unpaired w-electron is localized on the carbon next to the nucleus causing the hyperfine interaction. “- 9 189 _ A(9- ¢) =‘%3(1-cos20){ 1d—32 + (a3+4a2+10a+17+—a+-§z)}e 2a 2 _9__ . 9 9 _ + (cos 9-1) c052§[2a2 -(a3+5a2+6a+9+a-+ 232)}8 2a R 3 (51) where a = ZR/2ao, R is the separation between the nucleus contributing to the hyperfine interaction and the carbon 57 nucleus and e and ¢ are the angles specifying the direction of the external field. The reverse process of calculating an R if the hyperfine Splittings are known can also be ob- tained. This same theory also explains the anisotropy present for the proton hyperfine splittings even though no p- character exists for the protons. In general this dipole- dipole contribution will always be present to some degree between the electron and any bonded nuclei present. The ef- fect will be reduced according to the electron density present in each configuration. Spin Flip Transitions The ESR absorption line is sometimes accompanied by satellite lines equally spaced on either Side of the main line. These occur when there is a change in the spin state of the diamagnetic nucleus concurrent with the change in the Spin state of the electron on the paramagnetic fragment and it represents a weak magnetic dipole-dipole interaction coupling the electron Spin to a neighboring nuclear spin. The detailed theory for this phenomena has been (225) worked out and is summarized below. When transitions are induced by an oscillating field along the applied magnetic field H) the transitions observed are for levels of different Me' When this occurs each vector 'ji = H + hei (Me) (where 2T1 is the direction of the total 58 field of the electron (e) at the iEQ-nucleus) changes directions and in turn allows changes in Mi' The transition probability from state Me,Mi > to Me', Mi' > equals Hw(; H) 2 S1 9262 Tags—L;- DMiMi' (592 (52) where DSi is the rotation matrix for a particle of Spin Si’ 81 is the angle between 2;: (Me) andFSE (Me') with Me # Me' and 2Hw(i H) is the sinusoidal (frequency w) magnetic field perpendicular to H. It can be shown (225) that if 8i or w-Bi is small (reflecting that ue°H > > Ui-(H + hei)) for hei < H, the most prominent transitions are ones in which changes occur in Spin orientation of these neighboring nuclei during the electron transition. For h > H the most ei prominent transitions are ones in which the nucleus does not reorient with the reorientation of the electron. An equation for héi obtained by calculating the electrostatic potential .due to the unpaired electron results in a large dependence of'hei on the probability of the electron in S or p states for nucleus(i). This dependence results in hei > > H for those atoms which share the electron and hei < < H for those nuclei which do not share the electron. The hei > > H case occurs for the normal hyperfine Spectrum while hei < < H results in the above mentioned satellite lines Spaced gNBNH from the main line. If 8i or (w-Bi) are large then the above results do not hold. By using the appropriate rotation matrix for protons in the transition probability equation, the ratio of 59 intensity of either proton satellite line T1 to that of the two superimposed central lines 2T2 equals 21:2 95.25.22 -2 2, 2T2 8 g H 71 Sin 91 cos 91 (53) where 91 is the angle between the §E- vector and H; 7i being the vector distance between the 1&2 nucleus and the nucleus containing the unpaired electron. For a poly- crystalline or glassy material containing protons 2 T = EL. +2T2 20 < 3 £536 > (54) 71 where the average is over the different environments of the hydrogen atoms. The above equationsC55,54) are valid for fields in excess of 8000 gauss but lead to an error of 10% in the transition rates for fields of'5000 gauSs. From equation 55,valid for protons, the proton distribution can be estimated from the change in intensity relative to the main peak. An extension to include interactions with other nuclei could be performed using the proper rotation matrix. If sufficient intensity can be obtained, a second set of satellites (l/y12 intensity dependence) can be observed corresponding to two neighboring protons changing state con— currently. 60 Optical Crystallography In general two waves of different velocity may be propagated through a crystal with a given wave normal and given refractive index.TL associated with each wave. The variation of the refractive index can be described with a three dimen- sional geometric figure called an indicatrix. The indicatrix is a function of the principal axes of the dielectric tensor which can be written in the form 81x? + 22X; + 83xg = 1 where the 8's are related to the refractive indices. This equation is generally known as a representation quadric. Neumann's principle (59) states that "the symmetry elements of any physical property of a crystal must include the symmetry ele- ments of the point group of the crystal." Since the quadric is thought to be fixed in orientation relative to the crystal, Neumann's principle states that the symmetry element of the crystal must also be shown by the representation quadric. Therefore the quadric takes on the following forms (59) for the various classes of crystals. Cubic: A quadric can only have four triad axes if it is a Sphere. Tetragonal, hexagonal and trigonal: Since a general quadric possesses three rotation diad axes at right angles, three planes of symmetry perpendicular to the diad axes and a center of symmetry, the only way for the quadric to have a 4-, 6— or 5-fold axis is by having this axis as its principal axis (known 61 as the optic axis). Thus the lengths ne and no of the major and minor axes respectively determine the quadric completely. Orthorhombic: Since a quadric contains three mutually perpendicular diad axes, the quadric is placed with its axes parallel to the diad axes of the orthorhombic system. In this way the quadric will have all the symmetry elements found in the orthor— hombic system with ne, ne' and no as the lengths of the principal axes. Monoclinic: If one of the diad axes of the general quadric is placed parallel to the crystallographic diad axes, then the quadric will contain ne, ne' and no with monoclinic symmetry. Triclinic: Imposes no restriction. In the direction of the optical axis, all light of a particular wavelength travels through the crystal as if the crystal were optically isotropic. Therefore light traveling through Nicol prisms. of a polarizing microscope will be extinct when the upper and lower Nicol prisms have their planes of vibration perpendicular to each other if the light has been directed down the optic axis of the crystal which is between the two prisms. w On the other hand light that has not been directed along the optic axis will be divided into two waves which will result in no extinction as seen in the microscope. 62 Therefore the optically isotropic cube will show extinc- tion at all angles. The uniaxial crystals (hexagonal, tetra- gonal and trigonal) where the refractive index fie (optic axis) lies along the c axis will show a dark image during the entire rotation of the microscope stage with the optic axis (c axis) placed parallel to the light beam. When the c axis of the uniaxial crystal is placed perpendicular to the light beam, extinction will result whenever the c axis is parallel or per— pendicular to the planes of the crossed Nicols. For biaxial crystals (orthorhombic, monoclinic and triclinic) the two optical axes lie along any two-fold axis which is present and extinction occurs whenever an optic axis is parallel or per- pendicular to the planes of the crossed Nicol. This provides a way of identifying the important crystal axes Since the c axis is parallel to the optic axis in uni- axial systems, while the optic axes are parallel to the diad axes in the orthorhombic case and parallel to the b axis in the monoclinic system. In addition, the crystal system can be identified by its extinction properties: total extinction for cubic systems, extinction in one plane for uniaxial sys— tems and extinction along an axis for biaxial systems. The distinction between orthorhombic, monoclinic and triclinic crystals depends on whether the crystal edges line up with the cross hairs at extinction in all planes, two planes or none, respectively. AS an example (58) for triclinic, orthorhombic and monoclinic systems the following results should be obtained at extinction: 65 (a) Triclinic (C) (b) Orthorhombic (c) 64 Monoclinic (C) Figure 2. Positions of extinction for triclinic, orthorhombic and monoclinic crystals. Crystals are resting on (a) the (001) face, (b) the (100) face, and (c) the (010) face, and the cross hairs of the microscope are parallel to the planes of polari- zation of the Nicol prisms. This provides an easy method for finding the b axis, when using many crystals grown from a common source, irg., some crystals will have the b axis parallel to the long crystal edge while for others the b axis may be parallel to the short edge or inclined 450 to an edge. Crystal Symmetry and Alignment It has been found that, in general, the radicals remain in approximately the same position as the parent molecules. Therefore the crystallographic symmetry of the molecules is assumed to be retained by the radicals (212,65). Since the magnetic field cannot distinguish molecular translation or complete inversion, these elements of the crystallographic 65 Symmetry are neglected. Each radical's position is determined by a set of direction cosines with respect to an orthogonal set of crystal axes. However, Since the direction cosines for each radical will retain the crystallographic symmetry certain special positions are of interest. Listed in Table 21 are the number of nonequivalent sites for the various special directions using the general position for each of the crystal classes. As an example the monoclinic Space group CC has the general positions (226) x,y.z;x+§. y+én z+§;x.§.é+z;x+§.§+ih z. Neglecting complete inversion (x -fi’-x, y-—+ -y, z-—+ -z) and molecular translation, x,y,z; xfy,z become the positions of interest. Now replacing these with direction cosines having the same symmetry, (1,m,n) and (1,—m,n) give the positions of the two nonequivalent molecules. At Special positions of the magnetic field only one nonequivalent radical will be present; at (1,0,0), (0,1,0), (0,0,1) and where m = 0, i,§,, (1,0,n). The presence of only one equivalent site permits an unambiguous assignment of the radical involved. It is apparent from Table 21 that if a radical occurs at a general position in a tetragonal, trigonal or hexagonal crystal system, the resulting ESR spectra will be very compli- cated. However, Spectra have been analyzed for radicals in crystals in these systems due to the fact that radicals occurred at Special positions in the crystal. As an example, 66 6 m m 6 6 m 6 N 6666 6 m m 6 6 6 6 6 $666 Hmcommxmm 6 m m 6 6 6 6 N mu66 6 m m m m m m 6 mu66 Hmsom6ua 6 N N 6 6 6 6 N m666 6 N N 6 6 N 6 6 $666 6msommuuue 6.6.6 “6.6.6. 6 6 6 N N N 6 “N.>.x “N.%.x |.I. U6QEO£60£uHO 6 6 6 6 6 6 6 6.6.x 6.6.x I. l. 06:6600:02 6 6 6 6 6 6 6 N.%.x 06:660668 m6x< m6x< m6x<. m:66m_ msm6m mcm6m ms06u6mom m66m A6006 60606 AOO6V A: E 06 A: o 66 A0 E 66 ucm66>6sq®soz Hmu6vmm cam huumEE>m 6muwcmw 60 .oz mmwuumfifihm Hmumwuu mso6um> Mom mS6HHDUUO mmu6m usm6m>6560coz .6N mHQMB 67 the radical F2- occurring in a cubic lattice is oriented so that its axes are parallel to the face diagonals of the crystal; the field parallel to a face diagonal results in a Simplified pattern. EXPERIMENTAL ESR Spectrometer The ESR system which was used has been described in some detail (227) and only that part which was used in this re- search will be discusSed‘here. Use was made of a Varian Model 4500-10A Spectrometer with 100 kHz field modulation as previously modified so second-derivative presentation (resulting in better resolution but a decrease in gain of 1/16 from the first-derivative presentation) could be used. The magnetic field was measured by feeding the output of a proton marginal oscillator into the ESR system so that the proton Signals were superimposed on the second-derivative spectra. The proton frequency was measured with a Hewlett-Packard Electronic Counter, Model 524C, counting the frequency each time it appeared on the chart. A constant low field marker was placed on all rotation Spectra in order that a plot of angle versus magnetic field could be made without calculation. Since all the spectra from organic radicals had overlapping peaks, the second derivative was always used if sufficient concentration could be obtained. The Klystron frequency was measured with a TS-148/UP U. S. Navy Spectrum analyzer. The accuracy of the calibration was only d: 2 MHz; however, the precision was 68 69 1.0.5 men: so an initial calibration before a series of runs proved to be adequate. Also available were a Waveline 698 Wave Meter and a Micro-Now Model 101 frequency calibrator which was used for calibrating the Spectrum analyzer. The spectra were recorded on an Hewlett Packard x-y recorder with the x axis input fed from a Hall probe. It was thenneceSsary to calibrate only before andgafter a series of runs.' Accuracy was better than one part in 200. Crystal Holder The single crystal holder described before (227) was used for preliminary measurements. The final and most accurate measurements were taken on a 5600 2-circle‘Kel-F goniometer constructed according to the dimensions given in Figure 5. The entire crystal holder can be taken apart. The Kel-F rod (A) can be pulled up, thus disengaging the Teflon gear (C). The Kel-F support B, attached to the aluminum rod by a preSSrfit mount can then be removed by twisting the Kel-F support. If the small teeth of gear C are damaged then the Teflon pingE,held by a press fit to support13,can be removed and a new Teflon gear added. In this Same manner, a crystal-mounted on platform D can be re- moved from the crystal holder without damage to the crystal and a new gear added in order that the holder can be used for another crystal. The entire crystal holder fits in, and is supported by;a cylindrical Sleeve that screws on to the 7O ._ if I ,__._. " ”_ ‘~’ ”G *7 (6)223:- .4 I" ‘- i ' l y l ti {h ‘ i , (Kai-F) B-*» ~ Kel-F 'I C . ;‘ .240 6 ~--—- E / ' D - . l °° .I- l (- ‘1! ad“ ‘i Teflon L D Figure 5. Adjustable single crystal holder. 71 Varian cavity. Part G of the holder fits snugly in a pre- calibrated dial that measures 0 to 5600. One revolution of the Kel-F rod (A) turns the mounted crystal 900. This en- ables one to inSpect two planes with the same crystal mount- ing. If the crystal is to be mounted vertically, the inside of the gear provides an excellent vertical plane against which to mount the crystal. The outside diameter of the holder enables one to run variable temperature studies if a one-wall quartz dewar is used With‘the Varian variable temperature assembly. High vacuum greaSe is a good adhesive for mounting a crystal if the temperature of the ESR cavity does not exceed 500C. Using this adhesive prevents damage to the crystal when it is necessary to remount it. Standard Samples The following standard (227) samples were used occa- sionally to check the calibration of the xy recorder and the Klystron frequency readings. Varian standard pitch in KCl- 9 = 2.0028 Aqueous K2§r(CN)5NO g = 1.99454 i..00005, AN = 5.265.: .05 gauss Aqueous V0804 A = 116.15.: .2 gauss (between the fifth and fourth line) DPPH in KCl, g = 2.0056 72 Materials CCngCOONa-ZHZQ Two samples of chlorodifluoroacetic acid, one obtained from Columbia Chemicals Co., Columbia, South Carolina, and another sample from Procurement Laboratories Inc., College Point, New York, were neutralized in a hood (acid is very volatile) with sodium hydroxide to a pH = 6.5. CC 13CONH2, and CC lgCONDg A sample of 2,2,2-trichloroacetamide obtained from Eastman Organic Chemicals was exchanged with 99.7% D20 and crystals of CC13COND2 grown from D20. CF3§F2CF2COOAg A sample of perfluorobutyric acid was titrated at 50-600C in the hood (acid is very volatile and poisonous) with excess Silver oxide freshly prepared by dissolving silver nitrate in water and adding a sodium hydroxide solution. The unre- active Silver oxide was filtered off. NaOOCCEZCFQCOONa°6H20 Perfluorosuccinic acid from Peninsular Chemresearch Inc., was neutralized with sodium hydroxide. CF3CONH2 Two samples, one obtained from Pierce Chemical Co., and one obtained from the Peninsular Chemresearch Inc. were used. 75 NaOOCCHg ' SHZO Analytical reagent grade anhydrous sodium acetate was used° Na001300H3; NaOOClBCHg The 60% enriched samples obtained from Isomet Corp., Palisades Park, New Jersey, were recrystallized from water. Crystal Growing All single crystals except the trifluoroacetamide were grown from saturated water solutions by Slow evaporation in a desiccator at 25.i 20C. The trifluoroacetamide single crystals were grown by evaporation of a saturated water solution in a desiccator at 5°C. The temperature was maintained by placing the desiccator in a refrigerator regulated at 50C. Another batch of tri— fluoroacetamide Single crystals was grown by sublimation. A closed bottle containing a small amount of trifluoroacetamide powder was brought to equilibrium in a water bath at 500C. The bottle was then placed in the refrigerator at 5°C; crystals grew on the Side of the bottle. Irradiation Procedure Those crystals which did not react with oxygen, were sealed in polyethylene bags and could be irradiated at room temperature, dry ice or liquid nitrogen temperatures by plac- ing the bags horizontally on a conveyor belt 47 cm beneath the 1 m.e.v. electron beam (dosage, 1 min = 5 x 108 reps) 74 of a General Electric Resonant transformer, on top of a piece of dry ice in the conveyor (dosage, 1 min. = 2 x 108 reps) or 20 cm beneath the beam floating on liquid nitrogen (dosage, 15 sec. = 5 x 106 reps), respectively. The liquid nitrogen irradiation could also be done with crystals mounted on a copper disk, half covered with liquid nitrogen. Dosages of 5 x 106 reps were more than sufficient to produce the radicals. Longer irradiation periods than 15 seconds pro— duced severe crumbling of the crystals at 770K. For those radicals which react with air, two types of Specially evacuated Pyrex tubes were constructed. First, seal-off tubes 9 mm O.D. and 40 cm long were constructed with one end being as flat inside as possible. After one or more days of evacuation, the tubes containing a crystal were sealed off allowing 50 cm. for the length. This permitted a cork, flat on one end, to be turned on the glass tube after the crystal was irradiated which allowed the entire tube containing the crystal to be rotated when placed in the same calibrated-sleeve assembly as used for the crystal holder mounted on the ESR cavity. The second more useful type of tubes were constructed in a similar manner except a ball and socket joint was placed at the point of the seal-off in the first tubes above. Immediately above the ball, a valve followed by a 14/54 male joint was added. The distance from the ball and joint to the tip of the joint being 15 cm with a 45 cm overall length since only 48 cm clearance exists be- tween the top of the cavity and the ESR bridge. This 75 permitted various gases to be reacted with the crystals or various crystals to be added and removed from the tube. The flat portion was used as a platform to mount the crystal along an orthogonal axis system. This was accom— plished by cutting or using crystals which had a large flat area perpendicular to one of the axes. If this could not be done pieces of plastic were cut with the correct angles to permit mounting the crystals inside an evacuated tube. Crystals in the large Pyrex tubes could be irradiated at either room temperature or dry ice temperature by covering 10 centimeters of the flat end portion with lead foil on top of which was placed a one-half inch board. The pine stOpped the electrons while the lead stopped any X-rays which were generated from the pine. This procedure prevented boron centers from being produced in the Pyrex tubes. Since the crystals had coefficients of friction‘different from any inserted plastic pieces, the crystals could easily be shaken to the opposite unprotected end while the plastic pieces remained under lead covering. Following the irradiation the crystals could be shaken to the protected end where the ESR spectra were taken. For irradiation at 770K, thin wall glass seal seal-off Pyrex tubes,5.5 mm maximum outside diameter. were used. The tubes after seal-off could be no longer than 8.5 cm in length in order to allow them to float on liquid nitrogen contained in a stainless steel dewar while being irradiated. The quartz liquid nitrogen dewar finger is only 76 4 mm inside diameter preventing the use of any larger diameter tubes. The crystals were cut to fit along an axis inside the 5.0 mm tubing (each axis required a new crystal) with irradiation procedures Similar to the above, keeping 4 cm of the tubing free from boron centers. The tube with the crystal at the boron center free end was held firmly in place by a heavy copper wire in the quartz dewar,preventing any movement of the tube while the entire dewar was rotated in the cavity. The radicals which did not react with air were trans- ferred under liquid nitrogen and mounted on a brass clip attached to a 40 cm glass rod fitted with an oversize circle of Sponge. This entire assembly was quickly transferred to the quartz liquid nitrogen dewar, whereby the Sponge was squeezed into the top of the dewar while subsequently the evaporating nitrogen froze the sponge to the wall of the dewar and to the glass rod, preventing the rod and crystal from moving relative to the dewar. Use was made of crystals which had a long edge parallel to the crystal axis in order that better mounting could be achieved. A glass rod was attached to a plug machined to allow the passage of nitrogen. To the end of the glass rod a brass clip was attached and the entire assembly was fit into the top of the Teflon insulator used with the variable-tempera— ture dewar. In this way a crystal mounted at 770K could be placed in the variable‘temperature dewar at 1000K with the 77 magnetic field parallel to a crystal axis, so that the decay of the various radicals with temperature could be observed. Gas Reactions of Radicals in Crystals The irradiated crystals were mounted i§_yaggg so that the magnetic field was parallel to a crystal axis. The ESR spectrum at this position was observed before admitting an atmosphere of the reacting gas. After admitting each gas, airstopwatch was used to follow the change in the hyperfine pattern resulting from a gas-radical reaction. Matheson hydrogen, oxygen, carbon monoxide, carbon dioxide, nitric oxide and chlorine were used directly from the lecture bottles. The amount of oxygen present as an impurity in each gas was detected by the presence of a peroxide signal follow- ing the admission of each gas. Crystallography Only those Single crystals, 0.1 mm or less in diameter, were selected that showed total extinction at certain crystal mountings under a polarizing microscope. The crystals were mounted on a glass fiber with the long exterior direction of the crystal parallel to the fiber axis. This fiber had been previously mounted in clay on a small metal disk which mounts on a two-circle Weissenberg goniometer. After alignment of the crystal along a crystal axis, a zero layer-line Weissenberg photograph was obtained which produced a diffraction pattern 78 containing the crystal axes perpendicular to the alignment axis and the included angle. The alignment axis was measured by removing the goniometer from the Weissenberg camera to the Precession camera. Following this, the goni- ometer was returned to the Weissenberg for higher layerrline photographs. In this manner the three crystal axes could be obtained in addition to the Space group from the higher layer lines using only one crystal mount. Standard methods (41,42) for operating the Weissenberg and Precession camera were used. Use was also made of the method of Phillips (40) for identifying the crystal axes from the angles between the faces of the 5 mm x 5 mm x 2 mm crystals used in ESR work. Techniques for Obtaining Single Crystal ESR Spectra The following techniques were found valuable in the ESR study of irradiated single crystals. First,either the space group of the crystal was known or it was determined by the usual X-ray crystallographic methods (41,42). Although it was not absolutely necessary to know the space group, correct align— ment and assignment of the ESR lines could be made easier if it was known. The crystal axes for the 1.0 mm x 2.0 mm x 5.0 mm or larger crystals were identified by use of the polarizing microscope. What appeared to be single crystals (40) were examined under a polarizing microscope and those crystals whose entire structure did not reach extinction at 79 the same time were assumed to be twinned and were not used. In favorable cases, those pieces which adhere to an otherwise good cryStal could be removed by a sharp razor blade. Following irradiation by x— or y-rays or electrons, the crystals were mounted along a crystal axis on a goniometer. For triclinic symmetry, one of the crystal axes and the two orthogonal directions are used for the reference axes. If possible use is made of a traveling microscope in order to accurately align the crystal since the absence of nonequiva- lent positions make alignment difficult. For monoclinic symmetry (only type encountered), the crystal is precisely mounted if (for the case of two nonequivalent Sites) there exists one equivalent set of lines exactly every 90 degrees. For monoclinic symmetry with one nonequivalent Site, the maximum and minimum splitting for that plane must occur at the position parallel to one of the orthogonal crystal axes. Similar mounting is used for orthorhombic crystals. The radical, or radicals, present were identified from the spectra obtained with the magnetic field parallel to each of the three axes. Problems occurred when it was obvious that decay or radical-air reactions had taken place. In this case the ex- perimental set-up was modified. Following the radical identification, the spectra were taken every 100 if the pattern was easy to follow or every few degrees if the pattern was very complicated. Thehyper- fine splittings versus angle were measured and 80 fitted to equation 28 by a computer program. The hyperfine Splitting constants and their direction cosines were obtained from the diagonalization of the matrices generated by the above equation. More accurate hyperfine splitting values were obtained by mounting the crystal along one of the prin- cipal axes with small hyperfine splitting. This direction is found using the direction cosines from the diagonalization. A search was then made in the direction of the largest hyper- fine splitting value for the very largest splitting obtainable using the two-circle goniometer. This was followed by a 900 rotation to obtain the direction of the minimum splitting. Similarly, the other minimum splitting was obtained by remount- ing the crystal along the first minimum direction. RESULTS ESR Studyyof Irradiated Sodium Chlorodifluoroacetate Space Group Determination for Sodium Chlorodifluoroacetate X-ray analysis revealed that crystals of the form shown in Figure 4 were monoclinic with unit cell dimensions a = 24.48 X, b = 5.49 R, c = 10.42 R and 9 = 127° 5'. The ap- proximate density of 1.86 gm/cm3 measured by flotation in a mixture of methylene bromide (p = 2.495) and carbon tetra- chloride (p = 1.595) corresponds to four molecules of CCngCOONa-ZHZO per unit cell. Weissenberg and Precession photographs gave general reflections only when h + k = 2n: and l = 2n for(hol)reflections which is consistent with space group CC; Cg/C which has eight asymmetric molecules per unit cell was eliminated since it is not consistent with the ob- served number of molecules per unit cell. The crystals were plates with face perpendicular to the 0*(001) and are easily‘ cleaved by merely dropping the crystals or attempting to cut perpendicular to these faces. Identification and Angular Dependence ig_vacuo * With the c axis of the crystal vertical and the magnetic field along a, three sets of lines can be distinguished (Figure 5); for set (a) the outer lines are separated by 81 82 (1) 57 Figure 4. Definition of the orthogonal abc* reference axes and the monoclinic abc crystal axes with respect to the sodium chlorodifluoroacetate crystal morphology. The b-axis was found to be parallel to (1) a short edge, or (2) a long side of the crystal. 85 550 gauss, for set (b) the outer lines are separated by 210 gauss which, with a third central unresolved triplet, form a triplet of triplets, the smaller superhyperfine splitting equals 6.2 gauss;and for set (c) a pair of single lines separated by 252 gauss. Since all of the above hyper— fine splittings are larger than any fluorine hyperfine inter- action observed in fluorocarbon radicals (Table 12), it is presumed that all three sets are triplets with intensity 1:2:1 resulting from two equivalent orfluorines contained in a w-electron radical. Rotating the crystal about the b axis (Figure 7) results in a maximum and minimum Splitting for set (b), the triplet of triplets, of 182 and 11 gauss,respective1y. From Spectra at other orientations these prove to be very nearly principal components of the hyperfine splitting tensor for the radical giving these lines. The direction cosines are given in Table 22. In many orientations set (a) shows a doublet (Figure 6) superhyperfine Splitting,in addition to the regular hyperfine Splitting,with maximum and minimum of 182 and 19.5 gauss (Figure 7). These prove to be nearly principal com- ponents for the hyperfine splitting tensor for the radical giving rise to these lines and the directions of the maximum and minimum Splittings differ by about 500 from those for the radical of set (b) in the ac* plane. The principal axis for set (c) lies nearly in the (at>) plane and not the ac* plane. 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A sec- ond set of lines due to the same radical (set c) in a second orientation related by a two-fold axis is also seen (Figures 8 and 9). No 'CClFCOO- radical was present in any appreci- able concentration as has also been concluded independently (229) from Spectra of the irradiated powders. There are however additional lines one-tenth the intensity of the main line. Since no attempt was made to identify these lines, the presence of small amounts of °CC1FCOO- is not eliminated. Figures (7-9) show the variation of the ESR lines with orientation, for the crystals mounted ig_vacuo when the mag- netic field is parallel to the c*a plane, the be plane and the ba plane reSpectively. Assignment of the +a, +b, and +c* axes was made by obServing whether a minimum or maxi- mum splitting occurred in the positive quadrant of a right handed orthogonal axis system for each set. Comparison was made with Figures 7-9 and the assignment made.= By a least— SQuaresfit of equation 28 to one-half the separation between the high-and lowPfield fluorine lines versus theta, an un- diagonalized matrix was formed. The direction cosines listed in Table 22 are the eigenvectors resulting from the diagonali- zation of the above matrices where the off-diagonal elements are i 0% and'? 0&2 for set c. The eigenvectors obtained from the above choice of sign closely agreed with experiment. An additional set of eigenvalues resulting from the other choice of off-diagonal signs Liqu,.iq,z) gave eigenvalues of Y 181. 75 and 62 gauss which are clearly not in agreement with 92 the experimental results (185.7, 14.5, 20.6 gauss). Since only one nonequivalent set occurred for sets (b) and (a), no choice in off-diagonal signs was possible. The principal valwesof the hyperfine splitting tensor listed in Table 22 were obtained by mounting the crystal on a two circle goniometer (227) in the principal axis system obtained by the above diagonalization. Since one principal axis is defined as that direction for which the largest hyper- fine Splitting is obtained (using oscilloscope presentation of the signal) a plane perpendicular to this direction is easily obtained. If the goniometer is able to rotate in this plane then the minimum and maximum splitting obtained in this plane equals the other two principal values of the hyper- fine tensor. Whenever it was possible to mount the irradiated crystal on the goniometer in Figure 3 (work at room tempera- ture), the above method was used to yield the best principal values. The 1?CF2000' Radicals The Aisc hyperfine Splitting was found for sets (a), (b) and (c) by assuming that the principal axes of the 13C tensor and the 19F tensor coincided. In the z principal axis direction, ESR lines 1/180 the intensity of the main fluorine lines were found equally Spaced (after second order correction) from the high and low field fluorine lines. Since these low intensity lines had the same fine Structure (Figure 10) as the main fluorine lines and the hyperfine Splittings measured (1) 1 9F- (b) (n) Figure 10 . 95 250 4 I l r 13C—radica1(b) -radical(a) 19 _ F >b) 13C 19F_(a) lac-(b) 13C-(a) (m) ac* plane ab plane The upfield 13C satellites for the 'CFZCOO- radicals (a) . (b). (c). The magnetic field is parallel to the principal zTaJCiS of each fluoring tensor for radicals (a), (b). (c) in fJSures 1, m, n at 500 K. 94 were dependent on angle, with the largest Splitting in the z direction, these ESR lines were assigned to the radical ls-cpzcoo— with 13C in natural abundance (1.1%). . . . 13c 130 An unambiguous determination of the AX and Ay hyper- fine Splittings was not possible due to the interference from forbidden transitions and other ~CF2COO- radicals. Irradiation and ESR Observation in vacuo at 77UK The 4.0 mm inside diameter of the quartz dewar used at 770K limited the crystals to 3.0 mm diameter.‘ Only naturally formed crystals of the above diameter were adequate for the experiment Since crystals which were cut usually Shattered or broke when irradiated. A typical spectrum obtained at 770K without warmup with the crystal mounted along the b axis can be seen in Figure 11-1. A complete analysis of the spectra of the radicals formed at 770K without warmup was not attempted due to the difficulty of accurately mounting the crystals and the complexity of the Spectra in the ac* plane. The triplet superhyperfine structure observed at room temperature at nearly all angles was not observed for the radicals initially formed at 770K; only nonequivalent triplets attributed to -CF2COO- radicals were observed. The predominant feature was a very strong center line of approximately 100 times the intensity of the remaining peaks. This may be attributable to a trapped electron orwa radical with the electrdn on a nucleus of zero spin. The center peak was not as easily saturated as the lines due to ~CF2COO- radicals. I30G Irradiated 770K —- Spectrum 770K (1) 13 db I50GI Irradiated 770K Spectrum 77 K o b (after warming to 300 K) a (2) W 1. .. BOG H——H Irradiated 7 0K ‘ Spectrum 500 K b r . 2db Figure 11. Temperature dependent superhyperfine Splittings 1n the °CF2COO' radicals. The magnetic field is parallel to the direction (cos 55°, 0, Sin 55°). 96 Temperature Dependent Fluorine Hyperfine Splitting Crystals cooled from room temperature to liquid nitrogen temperature Showed that the direction of the maxima and minima of the hyperfine Splitting for set (a) and (b) dif- fered by about 200 in the C*a plane occurring 10O closer to the 0* axis than those at room temperature. The triplet and single Superhyperfine Splitting occurring for sets (b) and (a) along the directions of maximum Splitting at room tempera- ture changed to two doublets of 8.4 gauss splitting as seen in Figure 11. In Figure 12 the temperature dependence of the maximum hyperfine Splitting for set (b) Shows a nearly linear dependence from 5000K to 770K. The temperature variation of the fluorine Splitting values was not measured when the crystal was warmed from 770K.to 3000K, however. The set of lines (D) in Figure 6 increases in intensity relative to set (b) and (a) from room temperature to 770K. The relative intensity ratio of set (D) to sets (a) and (b) was found to change from sample to sample and thus was at- tributed to impurities. However, the doublet-doublet fine structure of set (D), the variation in intensity and the retention of the same symmetry relative to sets (a) and (b) as the nonequivalent lines for set (c) in the ab plane, suggests that it may not be an impurity but radicals related geometrical- ly to sets (a) and*(b). 97 199'—— 191 F— ’0 m __ :5 6 3 6.6 ‘3 185 F— - L, ‘1 175 —- l I V l | l 115 195 275 T O K Figure 12. Temperature dependence of the A ahfluorine The crystal hyperfine Splitting for the oCF2COO' radical. was mounted ip_vacuo resulting in mounting errors. 98 Reactions of the CFZCOO- Radicals with Air When crystals which have been irradiated in vacuo are brought in contact with air or oxygen, the ESR Spectrum changes. The ESR lines from the radicals discussed above disappear over a period of one-half hour to eight hours depending on the amount of water vapor in the air and are replaced by a four-line spectrum (Figure 15). From the g value obtained for each line, they have been identified (165) as being due to a peroxide radical 'OOCF2COO- formed from the reaction of diffusing oxygen with each of the four mag- netically nonequivalent ~CF2COO- radicals. The most intense line (w) of the peroxide radical has a g tensor oriented nearly along the a, b, 0* crystal axes and its values are given in Table 22. Line (2) has a some- what different orientation and apparent 9 value, the reason for which is not understood. The other smaller lines Show angular dependenceand are Shown in Figure 14 in addition to lines (2) and (w). It is noted that the direction of the principal axes for the peroxide 9 values has changed from that of the hyperfine tensor. No change except an intensity increase occurred on varyingtthe temperature. 99 I | I g = 2.0546 9 2.0107 W z Y 6 156 . W alifi, ba plane X Z x bIIfi, ba plane Y Figure 15. ESR Spectra at 5000K of the peroxide radicals W, x, Y, Z in irradiated sodium chlorodifluoroacetate after one day in contact with air. 100 'E in ab plane IIIIIIIIIIIIIIIIIL b 120° a 50° * 60° _ r )— _ P P u. _ p. H in ac* plane I I I I I I I I I I I I I I I I I I a 1200 c 50° 600 (— I— — _ _ — 2.0540 9 2.0190 2.0040 2.0550 9 2.0180 2.0050 2.0560 g P2.021O 2.0060 Figure 14. Angular dependence of the peroxide lines for the radicals X, Y, Z, W of Figure 15. 101 ESR Study of Irradiated Trifluoroacetamide Assignment of the prstal Axes for Trifluoroacetamide The crystal morphology for the trifluoroacetamide crystals is Shown in Figure 1