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Electron spin resonance of electrolytically generated nitro- and cyano anion radicals. Fischer, Peter Hans Herman 1963

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ELECTRON SPIN RESONANCE OP ELECTROLYTICALLY GENERATED NITRO- AND CYANO ANION RADICALS. by PETER HANS HERMAN FISCHER B.Sc., University of B r i t i s h Columbia, 1959 M.Sc, University of B r i t i s h Columbia, I96I A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of CHEMISTRY We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 1963 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that per-m i s s i o n f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i -c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date PUBLICATIONS The Infrared Spectra of Urea-Hydrocarbon Adducts P.H.H, Fischer and CA. McDowell, Can,J.Chem. 38, 187 (1960) E.S.R. of 7 , 7 1 ,8,8'-Tetracyanoquinodimethane Anion Radical. P.H.H. Fischer and C.A, McDowell, J.Am.Chem.Soc. September 1963 ( i n press) CHt'M/s -fJWSvCOri.. The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES • PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE.OF DOCTOR OF PHILOSOPHY of PETER HANS HERMAN FISCHER B.Sc, (Hon, Chem.), The U n i v e r s i t y of B r i t i s h Columbia, 1959 M.Sc, The University of B r i t i s h Columbia, 1961 FRIDAY, AUGUST 23, 1963, AT 9:30 A.M. IN ROOM 261, CHEMISTRY BUILDING COMMITTEE IN CHARGE Chairman: F.H. Soward N. B a r t l e t t L.D. Hayward W.A, Bryce F,A. Kaempffer J.B. Farmer L.W. Reeves External Examiner: A.H. Maki Harvard U n i v e r s i t y ELECTRON SPIN RESONANCE OF ELECTROLYTICALLY GENERATED NITRO AND CYANO ANION RADICALS ABSTRACT The r a d i c a l anions of 1,2-dinitrobenzene, 1,3-dini-trobenzene, 1,3=dinitrobenzene=d4, 1,4-dinitrobenzene, 1,4-dinitronaphthalene, 1,5-dinltronaphthalene, 1,8-dinitronaphthalene, 1,3,5-trinitrobanzene, 2,2',4,4', 6, 6' -hexanitrobiphenyl, 1, 2-dicyanobenzene, 1,4-dicya-?' nobenzene, 1,2,4,5-tetracyanobenzene, and 7,7',8,8'-= tetracyanoquinodimethane have been generated by e l e c t " r o l y t i c means, and the e l e c t r o n spin resonance spectra recorded. The spectra have been analyzed completely i n terms of the various coupling constants consistent with the symmetry of the. paramagnetic species, with the excep= t i o n of the hexanitrobiphenyl anion r a d i c a l spectrum. In the isomeric dinitrobenzenes, evidence i s presented which indicates that the spin density at the N ^ nuc-leus i s p o s i t i v e , i n agreement with findings by other workers on N-heterocyclic systems. A very large anomaly i n the E„S 0R o spectrum of 1,3-dinitrobenzene anion r a d i c a l i s explained by assumption of r o t a t i o n a l isomerism. A r e l a t i o n i s presented, expressing the nitrogen coupling constants of nitrogroup n u c l e i i n terms of the spin density d i s t r i b u t i o n of N ^ and contiguous atoms, calculated by simple Huckel M.O, theory. Anomalous behaviour of the 1,3,5-trinitrobenzene system can be explained i n terms of an e l e c t r o n donor-acceptor complex between a r a d i c a l anion acting as donor and a neutral molecule acting as acceptor. The r e s u l t s obtained for the cyano aromatic anion r a d i c a l s have been compared with those of Fraenkel et a l . , with the exception of 7,7',8,8'-tetracyanoquino-dimethane anion r a d i c a l , f o r which a more d e t a i l e d discussion i s presented. c!3 s p l i t t i n g s have been calculated t h e o r e t i c a l l y and found to agree reasonably well with experimentally determined values. For the TCNQ species, evidence i s also present which indicates a p o s i t i v e spin density at the N'i-A n u c l e i . GRADUATE STUDIES F i e l d of Study: Chemistry Topics i n Physical Chemistry J.A.R. Coope R.F. Snider Seminar i n Chemistry K.B. Harvey Quantum Chemistry J.A.R. Coope Topics i n Chemical Physics C.A. McDowell W.C. L i n B.A. Dunell Topics i n Inorganic Chemistry S t a f f Spectroscopy and Molecular Structure C, Reid R.M. Hochstrasser S t a t i s t i c a l Mechanics R.F. Snider C r y s t a l Structures K.B. Harvey Topics i n Organic Chemistry S t a f f Physical. Organic Chemistry R. Stewart Related Studies; Topics i n Algebra J.F. Scott-Thomas Elementary Quantum Mechanics F.A. Kaempffer Abstract The r a d i c a l anions of 1,2-dinitrobenzene, 1 , 3 - d i n i t r o -benzene, 1,3-dinitrobenzene-d^, 1,4-dinitronaphthalene, 1,5-dinitronaphthalene, 1 , 8-dinitronaphthalene, 1 ,3,5-trinitrobenzene, 2,2', 4,4',6,6'-hexanitrobiphenyl, 1,2-dicyanobenzene, 1,4-dicyanobenzene, 1,2,4,5-tetracyanobenzene, and 7,7' , 8 , 8 '-tetracyanoquinodi-methane have been generated by electrochemical means, and the electron spin resonance spectra recorded. The spectra have been analyzed completely i n terms of the various coupling constants consistent with the symmetry of the paramagnetic species. In the isomeric dinitrobenzenes, evidence i s presented which indicates that the spin density at the n u c l e i i s p o s i t i v e . A very large anomaly i n the ESR spectrum of 1 , 3 - d i n i t r o -benzene r a d i c a l anion i s explained by assumption of r o t a t i o n a l isomerism. A r e l a t i o n i s presented, expressing the nitrogen coupling constants of the n i t r o group nuc l e i i n terms of the spin densitjr d i s t r i b u t i o n of the r a d i c a l anion, calculated by the simple Hiickel M.O. method. Anomalous behaviour of the 1 , 3,5-trinitrobenzene system i s explained i n terms of an electron-donor-acceptor complex between r a d i c a l anion and neutral molecule. - i i i -The r e s u l t s obtained f o r the cyanoaromatic anions have been compared with those of Fraenkel et a l . with the exception of 7 ,7 ',8,8*-tetracyanoquinodimethane anion r a d i c a l , f o r which a more det a i l e d discussion 13 i s presented. C s p l i t t i n g s have been calculated t h e o r e t i c a l l y and found to agree reasonably well with experimentally determined values. For the TCNQ~ species, evidence i s also present which indicates a po s i t i v e spin density at the N-^ n u c l e i . - i -I wish to express my sincere gratitude to Professor C. A. McDowell f o r h i s continued i n t e r e s t and guidance during the course of thi s work, and to Professor G. Reid and Dr. R. M. Hochstrasser f o r many he l p f u l discuss-ions. Thanks are due to Mr. J . Sallos f o r his u n t i r i n g e f f o r t s i n keeping the ESR spectrometer at peak performance, and to Messrs. S. Rale and D. Bellamy f o r help i n designing and b u i l d i n g of ESR c e l l s . I., gr a t e f u l l y acknowledge receipt of two NRG studentships. i v -Contents Page Acknowledgement i Abstract i i L i s t of Figures v i i i L i s t of Plates x i i Chapter I. Theory of Electron Spin Resonance 1 A. Basic Theory 1 (1) Introduction 1 (2) Phenomenon of Resonance 3 a) Zeeman Levels 3 b) Isolated P a r t i c l e Approach 5 c) Bloch Equations 10 B. Theory of Hyperfine S p l i t t i n g 14 (1) Introduction 14 (2) Anisotropic Dipolar S p l i t t i n g 19 (3) Isotropic S p l i t t i n g 22 (4) Configurational Interaction 27 a) with Protons 27 b) with N 1 4, C 1 3 32 C. Relaxation and Linewidth 34 (1) Introduction 34 - v -Page (2) General Discussion, of Relaxation Phenomena 36 (3) Rotational Isomerism 41 (4) Motional Broadening 48 Chapter I I . Experimental Procedures 56 A. Introduction 56 B. Basic ESR Spectrometer 60 (1) Electronics 60 (2) Magnet System 62 G. Low Temperature Accessory 65 D. Electrochemical Methods 65 (1) Polarography 65 (2) Design of ESR E l e c t r o l y s i s C e l l s 66 (3) Design of Optical E l e c t r o l y s i s C e l l 69 E. Chemicals 69 (1) Solvents 69 (2) Supporting E l e c t r o l y t e 74 (3) Compounds Investigated 74 Chapter I I I . Nitroaromatic Compounds 77 A. Introduction 77 - v i -B. Isomeric Dinitrobenzenes 80 (1) 1,2-Dinitrobenzene 80 (2) 1,3-Dinitrobenzene and 1,3-dinitrobenzene-d^ 93 (3) 1,4-Dinitrobenzene 132 G. Isomeric Dinitronaphthalenes 138 (1) Introduction 138 (2) 1,4-Dinitronaphthalene 139 (3) 1,5-Dinitronaphthalene 143 (4) 1,8-Dinitronaphthalene 147 D. 1,3,5-Trinitrobenzene 151 E. General Results and Conclusions 174 Chapter IV. Cyanoaromatic Compounds 188 A. Introduction 188 B. Isomeric Dicyanobenzenes 189 (1) 1,2-Dicyanobenzene 189 (2) 1,4-Dicyanobenzene 194 C. Tetracyanobenzene 198 D. Tetracyanoquinodimethane 201 E. General Results and Conclusions 210 BIBLIOGRAPHY APPENDIX I APPENDIX II v i i -Page 215 221 223 - v i i i -L i s t of Figures Page F i g . 1. Precession of Spin Vector i n Magnetic F i e l d . 7 2. Energy Levels and Derivative Spectrum f o r System of 3 Equivalent Nuclei of Spin \. 20 3. Conformational Isomers of Tere-phthaldehyde. 43 4. Apparent Linewidth A l t e r n a t i o n (Ref. 74). 49 5. Block Diagram of 100 KC ESR Spectrometer. 63 6. AFC System. 64 7. ESR E l e c t r o l y s i s C e l l . 70 8. Observation C e l l with Calomel Reference Electrode. 71 9. C i r c u i t r y of E l e c t r o l y s i s Apparatus. 72 10. Optical E l e c t r o l y s i s C e l l 73 11. ESR Spectrum of 1,2-Dinitrobenzene Anion Radical. 82 12. Theoretical Spectrum of 1,2-Dinitrobenzene Anion Radical. 83 13. ESR Spectrum of 1,2-Dinitrobenzene Anion Radical at -30°C. 87 14. Theoretical Spectrum of 1,2-Dinitrobenzene Anion Radical at -30°C. 89 — i x -Page F i g . 15. ESR Spectrum of 1,3-Dirtitrobenzene Anion Radical i n 50% DME/50%DMF. 95 16. Theoretical Spectrum of 1,3-Dinitrobenzene Anion Radical. 97 17. ESR Spectrum of 1,3-Dinitrobenzene Anion Radical i n A c e t o n i t r i l e . 102 18. Theoretical Spectrum of 1,3-Dinitrobenzene Anion Radical. 104 19. Theoretical Spectrum of 1,3-Dinitrobenzene Anion Radical. 105 20. ESR Spectrum of 1,3-Dinitrobenzene Anion Radical i n CHoCN/DME. 107 21. Theoretical Spectrum of 1,3-Dinitrobenzene Anion Radical. 108 22. ESR Spectrum of 1,3-Dinitrobenzene Anion Radical i n 50%.CH3CN/50% DME. 109 23. ESR Spectrum of 1,3-Dinitrobenzene-d^ Anion Radical, low re s o l u t i o n . I l l 24. ESR Spectrum of 1,3-Dinitrobenzene-d Anion Radical high re s o l u t i o n . 112 4 25. Geometrical 1,3-Dinitrobenzene Isomers. 119 26. Theoretical Spectra Considering Variations i n a^ only. 121 27. Theoretical Spectra Considering Variations i n a^ only. 125 28. Theoretical Spectra Considering Variations i n both a N and a H . 127 29. ESR Spectrum of 1,4-Dinitrobenzene Anion Radical. 134 - x -Page F i g . 30. Theoretical Spectrum of 1,4-Dinitrobenzene Anion Radical. 135 31. ESR Spectrum of 1,4-Dinitro-naphthalene Anion Radical. 141 32. Theoretical Spectrum of 1,4-Dinitronaphthalene Anion Radical. 142a 33. ESR Spectrum of 1,5-Dinitro-naphthalene Anion Radical. 144 34. Theoretical Spectrum of 1,5-Dinitronaphthalene Anion Radical. 145 35. ESR Spectrum of 1,8-Dinitro-naphthalene Anion Radical. 148 36. Theoretical Spectrum of 1,8-Dinitronaphthalene Anion Radical. 149 37.. ESR Spectrum of TNB" — » TNB EDS Complex. 152 38. ESR Spectrum of 1,3,5-Trinitro-benzene Anion Radical. 154 39. Theoretical Spectrum of 1,3,5-Trinitrobenzene Anion Radical. 155 40. Optical Spectrum of TNB i n A c e t o n i t r i l e during E l e c t r o l y s i s at -0.48 v vs. S.C.E. 166 41. Optical Spectrum of TNB Anion Radical. 167a 42. ESR Spectrum During E l e c t r o l y s i s beyond -0.48 v vs. S.C.E. 171 43. F i n a l ESR Spectrum Obtained upon E l e c t r o l y s i s beyond -0.48 v vs. S.C.E. 172 - x i -Page F i g . 44. Optical Spectrum A f t e r E l e c t r o l y s i s beyond -0.48 v vs. S.C.E. 173 45. ESR Spectrum of 2,2 I4,4'6,6 ,-Hexa-nitrobiphenyl Anion Radical. 175a 46. Starring i n Nitroaraomatic Compounds. 176 47. ESR Spectrum of 1,2-Dicyanobenzene Anion Radical. 191 48. Theoretical Spectrum of 1,2-Dicyanobenzene Anion Radical. 193 49. ESR Spectrum of 1,4-Dicyanobenzene Anion Radical. 195 50. Theoretical Spectrum of 1,4-Dicyanobenzene Anion Radical. 197 51. ESR Spectrum of TCNB Anion Radical. 199 52. Theoretical Spectrum of TCNB Anion Radical. 200a 53. ESR Spectrum of TCNQ Anion Radical. 203 54. Theoretical Spectrum of TCNQ. Anion Radical. 204 - x i i L i s t of Tables Page Table I . Spin Densities and Coupling Constants i n 1,2-Dinitrobenzene Anion Radical. 85 I I . Spin Densities and Coupling Constants i n 1,3-Dinitrobenzene Anion Radical. 98 I I I . Spin Densities and Coupling Constants i n 1,4-Dinitrobenzene Anion Radical. 136 I V . Spin Densities and Coupling Constants i n 1,4-Dinitronaphthalene Anion Radical. 142 V . Spin Densities and Coupling Constants i n 1,5-Dinitronaphthalene Anion Radical. 146 V I . Spin Densities and Coupling Constants i n 1,8-Dinitronaphthalene Anion Radical. 150 V I I . Spin Densities and Coupling Constants i n 1,3,5-Trinitrobenzene Anion Radical. 155 V I I I . Q N ' s °f Nitroaromatic Anion - -. Radicals. 180 Spin Densities and Coupling Constants i n Nitrobenzene Anion Radical. 181 X . Experimental and Calculated Nitrogen Coupling Constants i n Nitroaromatic Anion Radicals. 185 X I . Spin Densities and Coupling Constants i n 1,2-Dicyanobenzene Anion Radical. 192 - x i i i Page Table XII. Spin Densities and Coupling Constants i n 1,4-Dicyanobenzene Anion Radical. 196 XIII. Spin Densities and Coupling Constants i n 1,2,4,5-Tetracyano-benzene Anion Radical. 200 XIV. Spin Densities and Coupling Constants i n TCNQ Anion Radical. 205 XV. C 1 3 S p l i t t i n g Constants i n TCNQ Anion Radical. 208 XVI. Nitrogen Coupling Constants i n Cyano-Anion Radicals. 212 - 1 -Chapter I. Theory of Electron Spin Resonance. A. Basic Theory. 1) Introduction. - I t was recognized at an early date, and amply v e r i f i e d by the experiments of Stern and Gerlach (1) and Uhlenbeck and Goudsmit (2,3), that the electron possesses an i n t r i n s i c property i n addition to i t s properties of mass, charge and o r b i t a l angular momentum. This i n t r i n s i c property of the electron has been c a l l e d i t s spin, and the associated mechanical and magnetic momenta are referred to as spin-angular momenta. I t i s a purely quantum-mechanical concept and i s characterized by a quantum number S, which i s found,by ex-perimental evidence, to have the value i - . The magnitude of the spin angular momentum S i s is I - Ls(s+ol"*t, (Al) while i t s projection along any a r b i t r a r y axis, z say, can be represented by the equation where mg i s c a l l e d the electron magnetic spin quantum number and can assume the values --§- only. - 2 -A s s o c i a t e d w i t h the above s p i n i s a magnetic moment JJS given by i / J - y * * ' ? ! •3/3[5($tifl"«- ( A 3 ) I n t h i s equation, y<i ^ s t n e magnetogyric r a t i o of the e l e c t r o n , g i s the Lande g - f a c t o r , and fb or i s the Bohr magneton where e and m are the charge and mass of the e l e c t r o n , c i s the v e l o c i t y of l i g h t , and h i s Planck's constant d i v i d e d by 2T . The component of ^ along any o r b i t r a r y a x i s assumes the values * . I t i s the above f a c t s which make the phenomenon of e l e c t r o n s p i n resonance (ESR) spectroscopy p o s s i b l e , s i n c e , upon immersion of any noncompensated s p i n i n a homogeneous s t a t i c magnetic f i e l d HQ , the degeneracy of the Zeeman l e v e l s , t h a t i s l e v e l s corresponding to d i f f e r e n t mg v a l u e s , i s removed, and t r a n s i t i o n s between these l e v e l s , v i a a s u i t a b l e experimental arrangement, may be observed. S t r i c t l y speaking, the term ESR i s somewhat of a misnomer, since o r b i t a l angular momentum a l s o c o n t r i b u t e s to the t o t a l e l e c t r o n i c d i p o l e moment. However, i n many f r e e r a d i c a l cases, the former i s very c l o s e to zero, and - 3 -hence neglected. Electron-paramagnetic resonance would per-haps be a more accurate, though less descriptive name. Experimentally, the f i r s t laboratory induced transitions among electronic Zeeman levels were observed by Zavoisky (4,5) i n 1945. Cu + + salts were investigated. Following in short order were the Mn + 2 resonance experiments of Gummerow and Halliday (6), and the C r + 3 experiments of Bagguley and Griffiths (7). A comprehensive survey of progress i n ESR up to 1955 i s given by Bleaney and Stevens (8) and by Bowers and Owen (9), since which time the f i e l d of ESR has blossomed to include not only the transition metal compounds, with which early investigators were mainly concerned, but also the study of conduction electron re-sonances in metals, studies of impurities i n solids, charge-transfer investigations, t r i p l e t states, odd electron molecules, and a large subclassification of the latter, the so-called a r t i f i c i a l l y produced free radicals. It i s with these, i n particular with free radicals in solution, that this thesis i s concerned. 2) The Resonance Phenomenon. (a) Zeeman Levels. - S t r i c t l y speaking, the Hamiltonian representing the various Zeeman level energies of any non-— ? compensated magnetic moment k in a static magnetic f i e l d H , takes the form y. * +6 H • 6* ? t (A4) where jf^ i s the t o t a l angular momentum operator and i s composed of the spin angular momentum operator and the o r b i t a l angular momentum operator L^ .. Thus Since however i n many r a d i c a l s the o r b i t a l angular momentum i s "quenched", equation (A4) takes the form Furthermore, when the system containing the noncompensated magnetic moment i s i n very rapid i s o t r o p i c motion (tumbling i n the gas or l i q u i d phase), the gyromagnetic r a t i o tensor —• has no d i r e c t i o n a l properties, that i s , i t i s a constant f o r a l l orientations, and equation (A5) i s reduced further. The Lande g-factor i s given, assuming LS coupling, by J 1 -2.3(3*1) so that f o r a free electron, g i s 2, a fa c t which also emerges d i r e c t l y from Dirac's theory of the electron. Experimentally, g has been determined as 2.00225. If we now imagine a p a r t i c l e of spin S=-§- and L=0, —> placed i n a s t a t i c magnetic f i e l d H q applied i n the Z-- 5 -d i r e c t i o n , then the Hamiltonian of the Zeeman l e v e l s i s Solving the eigenvalue problem using the above Hamiltonian, one obtains the eigenvalues where m i s the magnetic spin quantum number already described, s The energy l e v e l s can thus take the values ^$ftH9» An ab-sorption or emission of r a d i a t i o n , due to some t r a n s i t i o n between these l e v e l s , may now occur, i f the r a d i a t i o n f r e -quency i r , m u l t i p l i e d by Planck*s constant, equals the energy difference between the l e v e l s . Thus t h i s equation forming the basic formula of ESR spectroscopy. The above equation merely gives the energy difference between Zeeman l e v e l s corresponding to m =+-§- or m =--§-, but makes no statement regarding t r a n s i t i o n p r o b a b i l i t i e s or influences causing t r a n s i t i o n s to occur. b) Isolated P a r t i c l e Approach. - I t was f i r s t shown by Guttinger (10) that a p a r t i c l e i n i t i a l l y quantized with magnetic spin quantum number m, can be caused to undergo a t r a n s i t i o n to a state i n which the spin i s quantized with - 6 -magnetic spin quantum number m' * m, i f i t i s subjected to a f i e l d H , constant i n magnitude but ro t a t i n g with a f r e -quency oojzir about some d i r e c t i o n of H, and i f this frequency i s approximately equal to v0 (equation A 9 ) . If tlhie f i e l d were not rot a t i n g , the magnetic moment vector would merely precess about H with a frequency ( A 1 0 ) the so-called Larmor precession frequency. A r o t a t i n g f i e l d as described above i s very e a s i l y r e a l i z e d , and consists of a f i e l d H applied i n the z-— J > d i r e c t i o n , say, and a rota t i n g f i e l d Ht , angular frequency {jj , at r i g h t angles to i t . Generally i t i s stipulated that the magnitude of the ro t a t i n g f i e l d , |H,| , i s very much smaller than |H0| , that i s , i t may be considered as a weakly perturbing influence. The resultant f i e l d to which ju. i s subjected i s then H = HD X + Hjccoiui* fsin o +) ( A l l ) and i s i l l u s t r a t e d i n F i g . 1 . I f we r e s t r i c t ourselves to a p a r t i c l e of spin •§-, the time dependent Schrodinger equation i s given by m >/ r irc+) ( A 1 2 ) z 4 Fig. I. Precession of Spin Vector in Magnetic Field. - 8 -where i s given by a Linear superposition of eigenstates cf^ and of. , belonging to the eigenvalues rn^+i and m s=-i, respectively, Thus (A13) Taking the Hamiltonian as (A14) and employing (A13), equation (A12) can be rewritten i n the matrix form The above set of l i n e a r d i f f e r e n t i a l equations may, a f t e r transfer to polar coordinates and introduction of c e r t a i n i n i t i a l and normalization conditions, e a s i l y be solved , f o r the c o e f f i c i e n t s c,£V) and cx.O) • From t h i s , the t r a n s i -where uo and LO0 have been defined, and u>, i s a Larmor pre-cession frequency about U, . For a detailed discussion of the previous, Rabi (11), and f o r a derivation of (A16) through u t i l i z a t i o n of r o t a t i n g frames of reference, Schwinger (12), and Rabi, Ramsay, and Schwinger (13), should be consulted. (A15) t i o n p r o b a b i l i t y from a state of m. =+•§• to ms=~§- and v i c e versa, can be shown to take the form (A16) - 9 -Equation (A9) shows that an energy difference between m_ l e v e l s of a spin p a r t i c l e does e x i s t , while equation (A16) s shows the p r o b a b i l i t y with which tr a n s i t i o n s between these l e v e l s may occur. This l a t t e r p r o b a b i l i t y i s extremely small unless u>0-u> <z0 , t h i s being c a l l e d the resonance con-d i t i o n . Since f o r a free electron, = 17.6 x 10^(gauss sec) \ i^t>J2n i n a f i e l d of 3400 gauss w i l l be 0.95 x 1 6 1 0 sec, corresponding to 3.16 cm waves, i . e . i n the microwave range. These are the conditions employed i n the present investiga-tions . Since the p r o b a b i l i t y f o r an upward t r a n s i t i o n m =--§• to ms=+-§-, accompanied by an absorption of energy g(3H0 , i s equal to the p r o b a b i l i t y f o r a downward t r a n s i t i o n mg=+-§" to m =-r, i t appears obvious, that i f one i s to observe s any absorption or emission of energy experimentally, the population of one of the l e v e l s w i l l have to exceed that of the other. The population of l e v e l s i s approximately given by a Boltzman f a c t o r , so that the population r a t i o of lower to upper l e v e l w i l l be which, i n a f i e l d of 3400 gauss, and at room temperature, _ Q has the value 1 + 1.57 x 10 . - 10 -Again i t appears obvious that the net absorption of energy due to upward tr a n s i t i o n s w i l l tend to equalize the populations of l e v e l s , i f no mechanismXs) f o r d i s s i p a t i o n of energy other than stimulated emission, were a v a i l a b l e . These mechanisms, c a l l e d relaxation mechanisms, can e a s i l y be introduced by consideration of spin system/spin system, and spin system/surroundings i n t e r a c t i o n s . They are characterized by so-called relaxation times, and are introduced from macroscopic considerations i n the next subsection, and more f u l l y discussed i n section G. c) Bloch's Phenomenological Equations. - Whereas a l l previous r e s u l t s have been derived by a consideration of the microscopic properties of i n d i v i d u a l p a r t i c l e s , the so-called Bloch approach (14) attempts to describe the behaviour of a system of i n t e r a c t i n g magnetic species on a macroscopic scale. The treatment, although i n i t i a l l y developed f o r nuclear magnets, may with c e r t a i n changes of sign, due to the negative magnetic moment of the electron, be also applied to electron paramagnets. Let us define the magnetization of a system of para-magnets as fi'ZsZ (A17) «m~ ret • and l e t us assume that t h i s magnetization tends toward — ^ some equilibrium value M i n an applied s t a t i c magnetic - 11 -f i e l d H Q. Thus = ^0 (MS) where X e i s the s t a t i c s u s c e p t i b i l i t y f o r a system obeying the Curie Law, or y O J4LT Thus, i n a f i e l d applied i n the z d i r e c t i o n , say l£ i s the equilibrium value of M z. I f due to some per-turbation, Mi^^fg at any given time, i . e . i f we have a nonequilibrium orientation of M£ , the l a t t e r w i l l tend toward M Q with a c h a r a c t e r i s t i c time constant T^ , which Bloch c a l l s the thermal or longitudinal relaxation time, and which i n ESR i s commonly c a l l e d the s p i n - l a t t i c e r elaxation time, as i t requires a transfer of energy from the spin-system to the surroundings. Removal of the perturbation i s presupposed. The rate, f o r the above return of M z to M i s given as - - ^ (>U-M 0) CA19) A second process, c a l l e d transverse or spin-spin relaxation, and characterized by a time constant T 2, can destroy the x and y components M and M of the mag-net i z a t i o n M. I t may be v i s u a l i z e d as follows. The i n d i -vidual jut which comprise each see a l o c a l dipolar f i e l d due - 12 -the neighboringJu^fC » t h i s f i e l d either adding to or sub-t r a c t i n g from iT0 . The components ^ and ^ which are in-i t i a l l y i n phase to give;* an appreciable magnetization and M , w i l l progressively d i f f e r i n phase with time, due ^ —> to d i f f e r e n t precession frequencies ( i . e . d i f f e r e n t H), and thus cause and My to decay. The rate laws are again postulated to be of experi-mental nature and are given by N x = "4 M * (A20) and A7y " ~ 7 ^ rfy No energy transfer to the l a t t i c e i s required. If the above changes i n magnetization due to i n t e r n a l influences, as well as the change i n magnetization due to the external f i e l d , given by the c l a s s i c a l equation M = --y M*H = y^/xM (A2l) are considered c o l l e c t i v e l y , the following d i f f e r e n t i a l equations f o r the rate of change of the components Mx, M , and M are found: y' z y (A22) - 13 -Although the above equations are derived under the assumption that the small perturbation has been removed, a f t e r causing M* to deviate from MQ, i t has been shown that they also hold when a f i e l d W(£f) , small compared to —> Mo, i s present. They apply under experimental and Guttinger (10) conditions, and may be rewritten, using ( A l l ) , as and M ^ - y i ^ ^ c o s ^ - M ^ ^ i n i ^ i ) +j= (M^-M0) = Q (A23) Subject to c e r t a i n conditions, enumerated i n d e t a i l by Bloch (14), Pake (15), and others, the steady state solu-t i o n of (A23) gives the components of the complex suscepti-b i l i t y y.'-iy:" , as •X' -- 7 X„^0 7; Zfo0-u,)  and (A24) A p l o t of x"(which represents the absorption, whereas x' represents the dispersion mode) against the dimensionless quantity ^~z(u>o~u>) shows a Lorentzian or damped o s c i l l a t o r type curve of power absorption from H-^  f i e l d . The plot shows a maximum at CJ0-LO3the resonance condition, and a half-width at half-height of l / T 2 . Bloch's semimacroscopic approach, while broadly con-sis t e n t with the quantum-mechanical (microscopic) approach, - 14 -does i n addition y i e l d a d e f i n i t e l i n e shape f o r the en-countered absorption. Although deviations from t h i s shape are frequently found, and indeed expected, the Bloch approach i s a useful guide, p a r t i c u l a r l y when transient e f f e c t s are being studied. B. Theory of Hyperfine Interaction. 1) Introduction. - The Hamiltonian representing energy l e v e l s of a spin system, and excluding a l l the terms which are independent of spin, i s composed of several parts as follows. The Hamiltonian which describes the i n t e r a c t i o n of the elec t r o n i c spin with an applied magnetic f i e l d H i s given, as already stated, by * Z ? K V? (Bl) o where S^ . i s the spin operator of the k'th magnetic molecule and i s the gyromagnetic r a t i o tensor. One generally neglects a term f o r the nuclear Zeeman s p l i t t i n g , since energy l e v e l s corresponding to i d e n t i c a l nuclear magnetic spin quantum numbers m^ , but d i f f e r e n t m , are shi f t e d equally (at le a s t i n the high f i e l d s s commonly employed), and the appearance of the spectrum i s not a l t e r e d . - 15 -A f u r t h e r t e r m , t o be i n c l u d e d , r e p r e s e n t s t h e i n t e r a -c t i o n o f t h e e l e c t r o n s p i n w i t h t h e n u c l e a r s p i n o f n u c l e i h a v i n g 1*0 . I t i s w r i t t e n g e n e r a l l y as ^ZS^^/A-KXX, (B2) w h e r e A ^ i s t h e h y p e r f i n e i n t e r a c t i o n t e n s o r f o r t h e A ' t h g r o u p o f e q u i v a l e n t n u c l e i i n t h e k ' t h s p e c i e s , a n d J* i s t h e n u c l e a r s p i n o p e r a t o r f o r t h e X'th g r o u p o f n u c l e i i n t h a t k ' t h m o l e c u l e . I t i s e a s i l y s e e n t h a t J * * = £ -TaAj (B3) —» where I . . . i s t h e n u c l e a r s p i n o p e r a t o r f o r t h e A ' t h n u c l e u s i n t h e A ' t h s e t o f e q u i v a l e n t n u c l e i on m o l e c u l e k . I n s y s t e m s where t h e e l e c t r o n i c s p i n i s g r e a t e r t h a n f o r i n s t a n c e i n t r a n s i t i o n m e t a l i o n s , t r i p l e t s t a t e s o r b i r a d i c a l s , one h a s t o i n c l u d e a n a d d i t i o n a l t e r m t o r e p r e s e n t t h e e l e c t r o n i c s p i n - s p i n i n t e r a c t i o n . I t i s c a l l e d t h e f i n e - s t r u c t u r e t e r m and w r i t t e n as w h e r e D i s t h e f i n e s t r u c t u r e t e n s o r f o r t h e k ' t h m o l e c u l e , I n t h e c a s e o f o r g a n i c f r e e r a d i c a l s i n s o l u t i o n , t h i s e f f e c t i s a b s e n t and w i l l n o t be d i s c u s s e d f u r t h e r . - 16 -Another term which may be of importance when the system under consideration possesses n u c l e i of spin greater than \ i s the quadrupole i n t e r a c t i o n term No ef f e c t s due to i t have been observed i n organic r a d i c a l spectra i n solu t i o n . I t w i l l thus be neglected. Further terms to be included i n the Hamiltonian are the exchange term and the motional Hamiltonian. They w i l l be discussed i n the next section under the heading of relaxation mechanisms and l i n e shapes. The Hamiltonian has thusly been reduced to the form In the case of paramagnetic inorganic ions, the "g-value" may vary over a considerable range and thus give information regarding spin-orbit coupling, while the anisotropy of the g-factor i n c r y s t a l s may y i e l d informa-t i o n about c r y s t a l f i e l d s and environment of the para-magnetic species. In the case of organic free r a d i c a l s , the value of g i s in v a r i a b l y very close to the free spin value of 2.00225 and hence of l i t t l e use. The lack of spin-orbit coupling i s l a r g e l y due to the asymmetry i n t r o duced by the formation of bonds, and i n the case of very symmetrical systems, such as benzene negative ions, due (B5) (B6) - 17 -to Jahn-Teller d i s t o r t i o n s . The i n t e r p r e t a t i o n of ESR spectra of r a d i c a l s i n solution, apart from l i n e shape considerations to be discussed l a t e r , i s thus dependent on the hyperfine i n t e r a c t i o n term. E x p l i c i t l y , t h i s takes the form (B7) The above i s a generalization of the Hamiltonian f i r s t derived by Abragam and Pryce (16) f o r a single proton-electron i n t e r a c t i o n . In the above y and y £ are the ele c t r o n i c and nuclear gyromagnetic r a t i o s , S^ and T\ are the spin operators f o r the k*th electron and j T t h nucleus, i s the i n t e r p a r t i c l e distance, while i s a normalized Diras delta function. The f i r s t part of the above equation i s c a l l e d the anisotropic or dip o l a r hyperfine s p l i t t i n g term, as i t possesses d i r e c t i o n a l properties. The second part, c a l l e d a l t e r n a t e l y the con-tact term, the Eermi term (17), or the i s o t r o p i c hyperfine i n t e r a c t i o n term, possesses no d i r e c t i o n a l properties. I t i s i n f a c t the term which gives r i s e to the extremely r i c h hyperfine s p l i t t i n g s so frequently encountered i n spectra of r a d i c a l s i n solution. - 18 -Although quite elementary, the following i l l u s t r a t i v e example i s presented to show the dependence of the s p l i t t i n g observed, upon the number of n u c l e i as well as upon t h e i r spin. Consider a r a d i c a l i n solution, tumbling being rapid enough so that the anisotropic part of (B7) has been com-pl e t e l y averaged to zero, and assume that the high f i e l d approximation holds ( i . e . S*^  and are independently quantized i n the z - d i r e c t i o n ) . Then the Hamiltonian f o r one paramagnetic molecule may be written as If the further r e s t r i c t i o n , f o r s i m p l i c i t y of i l l u s t r a t i o n only, i s imposed that only one set of equivalent n u c l e i be present, that i s A = l , and that t h i s set contains 3, say, equivalent n u c l e i of spin -§-, then equation (B9) takes the form (B8) and, the energy l e v e l s are given by (B9) m.-r a m, m (BIO) I t i s e a s i l y v e r i f i e d that these energy l e v e l s are a jt - 19 -and •ft) T These energy l e v e l s are shown s c h e m a t i c a l l y i n F i g . 2, w i t h the d e r i v a t i v e of the abso r p t i o n spectrum to be ex-pected a l s o shown. The t r a n s i t i o n s which are allowed have to obey the s e l e c t i o n r u l e s w h i l e the i n t e n s i t i e s of the l i n e s are e a s i l y d e r i v e d from the degeneracies of the var i o u s l e v e l s . 2) A n i s o t r o p i c D i p o l a r S p l i t t i n g . - The a n i s o t r o p i c d i p o l a r s p l i t t i n g can, a t l e a s t f o r purposes of the present t h e s i s be dismissed w i t h a few words. The f i r s t term i n equation (B7) represents the magnetic d i p o l a r i n t e r a c t i o n of the unpaired electronC s) w i t h other magnetic systems, i n very many instances protons, on the same molecule or i o n . I t i s thus to be considered as an i n t r a m o l e c u l a r e f f e c t and to be d i s t i n g u i s h e d from the d i p o l a r i n t e r -a c t i o n s w i t h neighboring s p e c i e s , as discussed i n s e c t i o n and A "> 3 = 0 G. In c o n t r a s t to the Fermi term which always gives a hy p e r f i n e s p l i t t i n g , the a n i s o t r o p i c term does not always * a *—, .2. Energy Levels 8 Spectrum for System of 3 Equivalent Protons. - 21 -contribute. The l a t t e r , i f rewritten with scalar quantities, takes the form vector makes with the applied magnetic f i e l d d i r e c t i o n . For various numbers of nuclear magnets with which i n t e r a -c t i o n may take place, and f o r d i f f e r i n g orientations, s p l i t t i n g s and l i n e shapes of varying complicity have been calculated (18,19,20,21), which however, due to further interactions with the s o l i d , to which the present state-ments apply, cannot, with a few exceptions, be r e a l i z e d experimentally. An example where the l i n e shape and s p l i t t i n g to be expected (with additional broadening due to other sources) has been r e a l i z e d experimentally i s the g l y c y l g l y c i n e r a d i c a l (22,125-128), where the unpaired electron has been p a r t i a l l y l o c a l i z e d on an atom (oxygen i n t h i s case) which has a nuclear magnet. he-Id i n close proximity f o r s t e r i c reasons. A t y p i c a l value f o r t h i s anisotropic s p l i t t i n g i s approximately 20 gauss, a value which may however be considerably reduced due to motional e f f e c t s . ( B I D where 9^ i s the angle which the electron k-nucleus j - 22 -In d i l u t e solution the dipo l a r i n t e r a c t i o n gives a vanishing contribution to the hyperfine s p l i t t i n g , as was f i r s t shown by Weissman (23) and Weissman and B a n f i l l (24). The reason i s that the molecules or ions undergo normal Brownian motion and rapid tumbling, as a conse-quence of which the Hamiltonian ( B l l ) has to be averaged over a l l possible orientations. The thought of viscous phases at once occurs, that i s , solutions i n which tumbling, though at a les s e r speed, i s present. The c r i t e r i o n i s that an anisotropic hyperfine contribution may be present, generally not manifesting i t s e l f i n well-defined s p l i t t i n g s , but merely as a l i n e broadening e f f e c t on the i s o t r o p i c hyperfine s p l i t t i n g , i f the frequency of tumbling i s not very much smaller than the hyperfine s p l i t t i n g . I f the tumbling frequency i s con-siderably greater than the hyperfine s p l i t t i n g , only the Fermi type s p l i t t i n g w i l l be found. This i s d i s -cussed i n what follows, while further discussion of tumbling of the paramagnetic species i s found i n section C. 3) Isotropic Hyperfine S p l i t t i n g . - The second part of equation (B7) i s the one which describes the o r i g i n of the r i c h hyperfine s p l i t t i n g obtained experimentally from so many paramagnetic species. These spectra are re-produced t h e o r e t i c a l l y by constants a ^ , the so-called - 23 -"coupling" or s p l i t t i n g constants f o r n u c l e i . The re-l a t i o n s h i p between these a ^ and the spin density d i s t r i b u -t i o n i s the subject of t h i s and the following section. For s u f f i c i e n t l y large applied magnetic f i e l d s , the nuclear and e l e c t r o n i c spins w i l l be decoupled and w i l l be i n d i v i d u a l l y quantized. I f , furthermore, the f i e l d i s applied i n the z- d i r e c t i o n , say, then only the hyperfine interactions between z-components of the spins need be considered, and the Fermi contact Hamiltonian f o r the i n -teraction of a magnetic nucleus f< with the electron spin w i l l be given by vy- 9-r9«1r/ifr \ W»)SrtaJfW (Bi2) A l l symbols have been previously defined. The quantities of i n t e r e s t are of course the expecta-t i o n values of the operator ^ , and i f {({J i s the wave-function representing the ground state of the system, then the expectation value i s (B13) = See ft <*/< < ^ X V C « ) where a „ i s the above mentioned s p l i t t i n g constant ( i n - 24 -gauss) and i s given by a . <w»Jr> ^ fap < ^ ) < ^ f t j ) (B14) ' & W In equation (B14), ^C^) i s the spin density at nucleus and defined as ftfJO ^ <*\W¥)S*v\V7/<Sj <B15) while a ' - yfuParfs • One might mention at t h i s stage that the quantity i s i d e n t i c a l with the charge density i n one electron systems, while i n polyelectron systems, the charge and spin density must be c a r e f u l l y d i f f e r e n t i a t e d . C a l c u l a t i o n of a H f o r the hydrogen atom y i e l d s a value of 508 gauss, which compares ex c e l l e n t l y with the experi-mental value of 505 gauss (25). In the above, the s p l i t t i n g i s j u s t determined by the spin density of the Is o r b i t a l at the proton, i . e . " M ° > r The important term i n equation (B15) i s the Dirac delta function i ( ^ J and from well known properties of l a t t e r , - 25 -i t appears that the constants a ^ w i l l only show nonzero values i f the o r b i t a l containing the unpaired electron has a f i n i t e p r o b a b i l i t y amplitude at the nucleus ^ i n question. This c r i t e r i o n w i l l be f u l f i l l e d by single atoms where the unpaired electron i s i n an s-type o r b i t a l . When considering delocalized molecular o r b i t a l s , the same c r i t e r i a apply, and hyperfine s p l i t t i n g should only be observed from cr -type o r b i t a l s . As early as 1953 i t was noticed however, that r a d i c a l s , i n which the unpaired electron was not i n a ir -type o r b i t a l , but i n a r -type o r b i t a l having a node at the positions of the n u c l e i responsible f o r the s p l i t t i n g , do indeed show considerable hyperfine structure. Among these early findings, the r e s u l t s of Weissman (26), Weissman et a l (27), J a r r e t t and Sloan (28), and Ghu (29) should be men-tioned . To explain these phenomena, i t was f i r s t suggested by Weissman (27), that the zero-point out-of-plane vibrations of the protons attached to an aromatic r i n g , from which s p l i t t i n g was observed, would cause an appre-ci a b l e odd electron density at the protons due to overlap with the 7T-system. Venkatamaran and Fraenkel (30), and Anderson et a l (31) showed that such vibrations could not - 26 -account f o r the s p l i t t i n g . The former authors calculated the proton s p l i t t i n g i n p-benzosemiquinone r a d i c a l to be 0.053 gauss, assuming a v i b r a t i o n a l o r i g i n f o r the odd electron density, but found experimentally a value of 2.4 gauss. Furthermore, they f a i l e d to detect ESR spectra from r a d i c a l s i n various v i b r a t i o n a l l y excited states, and also succeeded i n showing that the spin densities i n deuterated and undetiterated r a d i c a l were the same. According to v i b r a t i o n a l theory, considerable differences should e x i s t . The theory was consequently discarded. Another early attempt to explain hyperfine s p l i t t i n g from such r a d i c a l s as triphenylmethyl (28) and di m e s i t y l -methyl, both due to J a r r e t t and Sloan, was the considera-t i o n of a coupling of the electronic and nuclear magnetic moments through a chemical bond, i n a manner si m i l a r to that postulated i n NMR spectroscopy (32,33). I t also had to be abandoned. Consideration of a so-called "pseudo contact" i n t e r a c t i o n , a combined i n t e r a c t i o n of electronic o r b i t a l and spin moments with the nuclear moments, by Anderson et a l (31), also gave s p l i t t i n g s which were orders of magnitude too small. The way out of thi s dilemma was shown by Altman (34), - 27 -who pointed out that the usual Huckel approach f o r c a l -c u lation of energy l e v e l s of conjugated If -systems, i n which tr- and TT-systems are considered independently, i s adequate f o r ground state energies, but that f o r excited state energies a tr-T i n t e r a c t i o n i s of great importance. This type of consideration was used i n an attempt to ex-p l a i n hyperfine s p l i t t i n g s , and order of magnitude c a l -culations by McGonnell (35), Bersohn (36), and Weissman (37), showed t h i s to be a reasonable approach. I t i s t h i s 0~-7T i n t e r a c t i o n , termed configurational i n t e r a c t i o n , which i s invoked to explain hyperfine s p l i t t i n g s . I t w i l l be considered i n the following section. 4) Configurational Interaction. The quantitative treatment of configurational i n t e r -action i s l a r g e l y due to Weissman (37), McGonnell (35,38); J a r r e t t (39), Bersohn (36), and Karplus and Fraenkel (40). These authors, with exception of the l a s t mentioned ones, have been mainly concerned with the c a l c u l a t i o n of proton s p l i t t i n g s , whereas the l a t t e r have extended the theory 14 to other types of magnetic nu c l e i such as N (1=1) and G L 3 ( I = i ) . a) Interaction with protons. - As shown i n equation (B15) the s p l i t t i n g constant due to a proton ^ i s given by the r e l a t i o n - 28 -and the problem i s to estimate the magnitude of This problem has been approached v i a valence-bond methods by McGonnell (35) and J a r r e t t (39), v i a simple molecular o r b i t a l theory by Weissman (37), and v i a the unrestricted Hartree-Fock method by McGonnell and Ghesnut (38). The general method of attacking the problem by a molecular o r b i t a l approach w i l l be i l l u s t r a t e d by consideration of a hypothetical GH fragment, containing 3 electrons. Let the ground state be represented by a normalized S l a t e r determinant where p i s the 2p o r b i t a l centered on the carbon atom, and cr i s the bonding o r b i t a l , that i s , a l i n e a r combina-t i o n of atomic hydrogen Is o r b i t a l , c a l l e d s, and carbon 2 sp hybridized o r b i t a l h, (B17) s i s the overlap i n t e g r a l <C^ |^ ) while & i s an antisymmetri-o zation operator. I t may be furthermore shown that (B18) - 29 -and ^ 2 ^ 0 . (r<r*p (*fi«-ft«*+) (B19) represent two doublet excited state configurations, cr* re-presenting a normalized antibonding <r o r b i t a l , The above functions (B17) to (B19) are now used as the basis of a v a r i a t i o n a l c a l c u l a t i o n f o r the mixing of the excited state functions with the ground state. Thus one represents the t o t a l wavefunction as ^ - + ^3*1 ( B 2 0 ) where and /X3I*«I. Employing (B20) and substituting into (B15"), we obtain Kt?H) •<iy0\zmjWAH)sMi)\&(szy' (B2D where Z^ZJC^S^ - b(?m)Sl(M .lftK)Sxla) .iftH)SlW This may be evaluated to be, expressing cr and rr*in terms of o r b i t a l s s and h, as - 30 -In the above equation terms h(0) have been neglected since h(0) S(0) T T. The c o e f f i c i e n t A , may be estimated H H from 1st order perturbation theory. Thus X - - ^xly'llT.y (B23) where yc i s the complete Hamiltonian f o r the three electron system. Evaluating (B23) one obtains -(B24) with Jps^Ofl^lf7*) aiid Jrh = (/j/'l^lfJl)-Substituting (B24) into (B22), and the r e s u l t into (B15), one obtains f o r the proton s p l i t t i n g from a GH fragment where ay i s the s p l i t t i n g from a hydrogen atom. Estimates of fyf/lph, *o , a n < i (E2-E-^) substituted into the above, give a^_jj= -20 to -200 Mc sec 1 , the best semiempirical value being -65.5 Mc sec"^ = -23.4 G (41). For further discussion of assumptions which need be made and f o r an evaluation of i n t e g r a l s , the reader i s referred to the o r i g i n a l papers. One has thus obtained a r e l a t i o n s h i p between the s p l i t t i n g constant ar^ of a proton and the spin density - 31 -^(~tjk) a t a carbon atom adjacent to i t , a r e l a t i o n f i r s t proposed by McGonnell i n the form (42): G^S <B25) The coupling constant f o r the proton i s thus negative, at le a s t when using the one electron approximation, a f a c t which -may be v i s u a l i z e d p h y s i c a l l y as an unpaired spin density at the nucleus (proton) being a n t i p a r a l l e l to the net spin p o l a r i z a t i o n ^S > . Without loss of generality, the above treatment can be extended to the case of polyatomic 7f - r a d i c a l s , i . e . planar aromatic systems. In that case one i s dealing with an unpaired spin d i s t r i b u t e d over a system of atoms, and the concept of an unpaired spin density fy< i s i n -troduced. I t i s considered to be the expectation value of a spin density operator ^ which i s defined as f > ^ S m = J ^ C S ) S m (B26) where A ^ ) i s a so-called atomic o r b i t a l d e l t a function (50). Also i t can be shown (38), that the expectation value of may at times be negative, a f a c t which im-p l i e s that the spin density at carbon atom /A may have a spin p o l a r i z a t i o n a n t i p a r a l l e l to the net spin p o l a r i -zation. The concept of negative spin densities was f i r s t - 32 -proposed on t h e o r e t i c a l grounds by Brovetto and Ferroni (77), and explains the very large o v e r a l l s p l i t t i n g s observ-ed f o r c e r t a i n r a d i c a l s (43). 13 1 A b) Interaction with C , N L . - The f i r s t attempt to calculate t h e o r e t i c a l l y C*-0 s p l i t t i n g s i s due to McLachlan, Dearman and Lefebvre (44), while a l a t e r , more complete 1 q G ° theory i s mainly due to Fraenkel and collaborators (40,41,45). The approach i s quite s i m i l a r to the one i l l u s t r a t e d above f o r the proton s p l i t t i n g i n a GH f r a g -ment, however the model commonly employed i s the seven electron planar GHG or also GH fragment. Let i s s u f f i c e to say that a rel a t i o n s h i p of the type can be derived, which explains many experimental r e s u l t s c 13 quite s a t i s f a c t o r i l y . In the above a i s the G s p l i t t i n g spin densities at atom G and atoms adjacent to G, re-spectively. S i s a parameter (-12.7 G) which represents c a contribution to a due to the Is electrons of the carbon atom i n question, t h i s contribution a r i s i n g primarily from ex c i t a t i o n of Is electrons to antibonding tr- o r b i t a l s . S i s expected to be reasonably constant f o r a l l hydrocarbon systems. &cxL i s the sigma-pi i n t e r a c t i o n parameter f o r nucleus G contribution, r e s u l t i n g from a p o l a r i z a t i o n of (B27) due to carbon atom G, and ^ c a n < i are the unpaired - 33 -the bonds CXL by the TT-electron spin density on atom C, while ^?x-c represents the F-W i n t e r a c t i o n parameter from p o l a r i z a t i o n of the bonds due to T -spin density on neighboring atoms XL . One r e a l i z e s immediately that a reasonably constant value a c , as f o r the proton s p l i t t i n g a c a n n o t be expected as the 6?\s , also the fx-jc } a r e quite se n s i t i v e to environment (bond lengths, bond angles, e t c . ) . Q'$ have been calculated f o r a v a r i e t y of hybridiza-t i o n combinations. For n u c l e i , s p l i t t i n g s have also been observed frequently, both i n heterocyclic systems, and i n systems where the nitrogen i s exocyclic to a r i n g system. A l -though i t has been found by Garrington and Santos-Veiga (49), Melchiar and Maki (130), and McDowell et a l . (129) that a simple equation of the type (B25) gives good agree-ment with c e r t a i n experimental r e s u l t s , t h e i r equation being (V (B28) other investigators, mainly Ward (46), and Henning and De Waard (47), also Rieger and Fraenkel (48), have postulated more complicated expressions. The formula given by Ward, and by Henning and De Waard i s - 34 -a " * * ? , ^ 1 - ^l 1, U (B29) while Rieger and Fraenkel's equation takes the form where a l l symbols have t h e i r usual meaning, the term r accounting f o r a l l the Is and contribution to the 2s p o l a r i z a t i o n of the unshared pair of electrons. G. Relaxation Mechanisms and Line Shapes. 1) Introduction. - As was previously mentioned, i t i s necessary, i f one i s to observe a steady state absorption of power from the microwave f i e l d , to have some sort of relaxation mechanism(s) which w i l l counteract the tendency of the spin l e v e l s to become equally populated. Also, one r e s u l t regarding l i n e shapes was derived, t h i s from Bloch's phenomenological treatment, and resulted i n a Lorentzian l i n e shape with half-width at h a l f - i n t e n s i t y of 7T 2 V ' i ?x 5' ( C D 'z since i n that case 1 JT « 1 (T> . The Lorentzian shape i s of course a r e s u l t of the postulated exponential decay of the nonequilibrium magnetization M. Although some l i n e shapes do agree with this Lorentz shape (see f o r instance Cummerow and Halliday ( 6 ) ) , many experimentally determined l i n e sHaapes are of a more general nature. Many l i n e s can however be approximated by a Lorentzian or Gaussian l i n e shape. I t i s a well known f a c t that the width of an absorp-t i o n l i n e cannot be smaller than the r e c i p r o c a l l i f e t i m e s of either of the states between which tra n s i t i o n s occur, i . e . A^> - T t = 2 j T < . (G2) where T i s the l i f e t i m e of the shorter l i v e d of the two quantum states and i s composed generally of various times Tr due to d i f f e r e n t relaxation mechanisms. These mechan-isms which influence Tr are generally divided into two classes; those processes which induce t r a n s i t i o n s between quantum l e v e l s , and those which actually a f f e c t the energy separation between l e v e l s ( i . e . produce a time-dependent f l u c t u a t i o n of energies). The former are commonly referred to as s p i n - l a t t i c e relaxation mechanisms since an energy transfer to the surroundings (or l a t t i c e ) i s involved. They are characterized by a l i f e t i m e 7~ . The second - 36 -type are c a l l e d spin-spin or transverse relaxation mechan-isms , and are characterized by a l i f e t i m e T . The l i f e -' J s times TL , T g ? and T^ may be i d e n t i f i e d with the l i f e t i m e s T l ' T2' L' a n d T2 ^ n e c l u a t : i - o n ( C D , respectively. There are a large v a r i e t y of mechanisms which con-t r i b u t e to either T 1 or T. , or both. A short discussion 2 1 of some of these mechanisms w i l l be given i n the following section. Only two mechanisms which a f f e c t the l i n e shape markedly w i l l be discussed i n d e t a i l , these being the phenomenon of r o t a t i o n a l isomerism, and the e f f e c t of tumbling upon paramagnetic species i n which the anisotropic hyperfine s p l i t t i n g i s not completely averaged to zero. The discussion of a l l other mechanisms i s only q u a l i t a t i v e i n nature, and consequently completely unsatisfactory. Since the present thesis i s however not concerned with l i n e shapes i n a major way, t h i s shortcoming can be over-looked. For detailed discussions on the subject of r e -laxation mechanisms and l i n e shapes, the reader i s referred to the following references: Pake (15), Abragam (51), Kubo and Tomita (52,53), Wangness and Bloch (54), Bloch (55), Redfield (56), Sher and Primakoff (57), Kivelson (58,59), Anderson (60), and others. 2) General Relaxation Phenomena. - Amongst the various mechanisms which a f f e c t l i n e shapes and provide relaxation - 37 -mechanisms, may be mentioned the dipolar i n t e r a c t i o n be-tween elec t r o n i c spins. This e f f e c t has been treated i n a c l a s s i c a l paper by Van VTeck (61), and by others, who considers the mutual i n t e r a c t i o n of a large number of paramagnetic species i n a c r y s t a l l i n e l a t t i c e . This re-s u l t shows, that i n addition to a resonance l i n e at k?0=y//o » a series of weaker l i n e s occur at 2^v)3^0l etc., and that the dipolar i n t e r a c t i o n does broaden the absorption l i n e s , which assume an approximately Gaussian shape. In very d i l u t e solutions, i n the present i n v e s t i -gations the r a d i c a l concentration was c e r t a i n l y much smaller than 10 t h i s e f f e c t does not play a large • r o l e , and other types of dipolar interactions w i l l pre-dominate. I t should be mentioned that at reasonable con-centrations of paramagnetic species t h i s i n t e r a c t i o n can-not be neglected, even i n the l i q u i d phase. As an example, the broadening e f f e c t which molecular oxygen (a ground state t r i p l e t ) i n s o l u t i o n has upon resonance l i n e s , i s mentioned C62,63). A dipolar i n t e r a c t i o n which i s of a d i f f e r e n t nature i s the i n t e r a c t i o n between elec t r o n i c and nuclear spins. This may of course be of an i n t r a - and of an intermolecular nature, and may also be between d i f f e r e n t species, such as - 38 -surrounding solvent molecules, f o r instance. In d i l u t e solution t h i s l a s t type of intermolecular i n t e r a c t i o n does indeed predominate. The form which the Hamiltonian re-presenting t h i s type of i n t e r a c t i o n takes has been ex-p l i c i t l y given i n equation (B7), and i t was stated that fo r a c e r t a i n tumbling frequency only the Fermi contact term remained, the anisotropic part of the Hamiltonian being completely averaged to zero, while i n the case of d e f i n i t e orientation of the -yy^ of the i n t e r a c t i n g species with respect to the applied magnetic f i e l d , c e r t a i n de-f i n i t e s p l i t t i n g s can be observed i n some cases, broadening i n many others. I t i s the intermediate cases which are of considerable i n t e r e s t , and which w i l l be discussed i n section ( 4 ) . The i n t e r a c t i o n between elec t r o n i c spin and nuclear spins of solvent molecules has also been shown to be an e f f e c t which can i n ce r t a i n instances not be ne-glected (64,65). Another type of phenomenon which often influences the l i f e t i m e s of states and hence the l i n e shape, i s the exchange i n t e r a c t i o n . I t i s represented by a Hamiltonian of the form - 39 -where S\ and are the electron spin operators f o r spins i and j , and 7.^  are exchange'integrals which are inde-pendent of both nuclear and electronic spin, but which are strongly dependent upon the s p a t i a l overlap of un-paired electron o r b i t a l s . J,^ i s thus a function of the interraolecular ( i n t e r - r a d i c a l ) distance -r,j , a function which i s not e a s i l y determined i n the s o l i d state, and which i s almost impossible to calculate i n l i q u i d or gaseous phases. I n t u i t i v e l y one does however expect to f a l l o ff very rapid with distance and as a consequence to observe a strong concentration dependence, which i s found experimentally. For the case of s o l i d substances, the exchange phenomenon has been considered i n considerable d e t a i l (58,66,60), while f o r l i q u i d s a greater number of approximations need be made, and the e f f e c t i s less well explained. Kivelson (58,59) and Kubo and Tomita (52,53), as well as Anderson (60) have contributed heavily i n t h i s f i e l d . The r e s u l t s are summarized as follows: In the-absence of any motional or dipolar i n t e r a c t i o n s , the spectrum from a c e r t a i n paramagnetic species appears as a "sharp" spectrum, with l i n e s at u>=fl(ZH +am > while i n the presence of exchange the l i n e s converge towards a central frequency co-^H a n d a t the same time become broader. As J,-, increases (stronger exchange), the - 40 -hyperfine s p l i t t i n g s tend to disappear, u n t i l a single broad l i n e i s observed, t h i s when J,^, has approximately the same magnitude as the hyperfine coupling. The l i n e shape i s approximately Gaussian. In the case of very strong exchange, i . e . J.j ^  & z , the linewidth decreases, giving r i s e to the so-called "exchange narrowed" l i n e s . This f a c t was f i r s t explained by Van Vleck (61) and i s well understood from considerations of the second and fourth moments of the l i n e shape function involved. Also, the e f f e c t of chemical relaxation upon l i n e -widths should be mentioned. This type of relaxation may involve several mechanisms, one of which i s intermolecular electron transfer between r a d i c a l and neutral molecule. Examples of thi s are the naphthalene system (67), the ben z o n i t r i l e system (68), and many others. In the benzo-n i t r i l e system, f o r instance, at concentrations 10 _ 3M i n neutral molecule, the complete 54 l i n e pattern which i s expected, i s observed, while at ^6.5 x 10 H i benzo-n i t r i l e , a single broad l i n e i s obtained. Almost any number of l i n e s between 1 and 54 may be observed, de-pending upon the intermediate concentrations employed. A second type of chemical relaxation i s the intramolecular electron exchange observed i n paracyclophanes (69). Another i n t e r e s t i n g e f f e c t has recently been observed by - 41 -De Boer and Mackor (70), who explain the linewidth anomalies i n pyracene by the time dependent modulation i n proton coupling constants, introduced by counter-ion (Na +) ex-changes between symmetrical positions i n the molecule. It i s e a s i l y seen from the previous, that the e f f e c t s which influence l i n e shapes and l i f e t i m e s of states, are numerous and diverse, and that a complete discussion of these i s c e r t a i n l y beyond the scope of t h i s t h e s i s . 3) Rotational Isomerism. - One of the phenomena which i s thought to a f f e c t the appearance of ESR spectra w i l l be discussed i n d e t a i l , since i t may well explain the r e s u l t s obtained i n some of the present work. I t i s the phenomenon of r o t a t i o n a l isomerism. I t had been observed i n various experiments, that an extraordinary l i n e width alt e r n a t i o n existed, which could not e a s i l y be explained i n the more conventional way of McGonnell (71), Stephen and Fraenkel (72), and Kivelson (59), to be discussed i n the following section, a treatment from which a more or less regular dependence of linewidth as a function of nuclear magnetic spin quantum number m-j-, emerges. The f i r s t concrete observations, due to Maki (73), are that the negative ions of both c i s and trans tere-phthaldehyde may be observed, that the equilibrium between - 42 -the two isomeric species i s temperature dependent, and that a simple r e l a t i o n s h i p exists between the coupling constants of the r i n g protons. These facts were u t i l i z e d by Garrington (74,75) i n explaining the linewidth alterna-t i o n observed i n durosemiquinone cation. In what follows, Garrington's approach i s c l o s e l y followed. Let us concentrate on a para-disubstituted benzene f o r s i m p l i c i t y , although a more general molecule i n which r o t a t i o n a l isomers are possible, could equally well be employed. For any given configuration of nuclear spins ( i n t h i s case protons), there e x i s t four d i s t i n c t mole-cular configurations, between which conformational changes without nuclear spin reorientation may occur. These four configurations are shown i n F i g . 3, and from the diagram i t i s obvious that 1 and 2 are c i s , 3 and 4 trans isomers. Although i t might appear that only two conformers are possible, i t i s r e a l i z e d on further thought that a r o t a t i o n about an axis perpendicular to the plane of the atoms by 180°, does not convert 3 into 4, say, while a r o t a t i o n by 180° about axes i n the plane of the atoms changes the nuclear configuration. + &co^  (y I s the contribution of the r i n g protons to the resonance frequency, the + sign r e f e r r i n g to <* , the - sign to spin. We w i l l also denote the l i f e t i m e s of the conformers by T-L and Fig. 3. Conformational Isomers of Terephth a ldehyde. - 44 -furthermore assume that conformational changes can only occur i n the indicated d i r e c t i o n s . Now i f the' magnetization of the electron f o r each conformer i s written as a complex quantity then the Bloch equations may be written as Gc= ~(iVo 'Ml) (G5) where with being the amplitude of the applied microwave f i e l d , M q i s the s t a t i c magnetization i n the di r e c t i o n of the applied f i e l d , and In (G6), i s the transverse relaxation time (under con-d i t i o n s of no isomerization ), ALO-U)v-UD} CJ0 being the Larmor frequency of the electron i n the applied f i e l d , and &-L i s the s h i f t i n resonance frequency due to hyper-f i n e interactions of conformer i . A solu t i o n of (G5) takes the form f>i- -^H/)J^^rH0 (C7) - 45 -where M° i s the value at a time t=0, when the molecule assumes the conformation i . Before the conformational change takes place, the average value of M. i s - -I&JML + Oil CG8) Now since the value vof M° depends upon the immediate past of the system, i . e . conformer 1 can r e s u l t from a con-formational change of either 3 or 4, one must average over a l l possible values of M°} so that the true average of RiF<Rj>(, say, i s given by <MT) - ~ - C ^ , M o T > t (G9) since x [ ( M > ( M , ) ] . ( G 1 0 ) Since r^T^TCli and 7} « one obtains,. <^>s-J**>Aya {*r«W** fc(r**Yi) } ( G i l ) where y , ^ / ^ a £ , and yJtf e ^ ^ ( consequently the net average electron magnetization<M> i s given by - 46 -where f-Cs and FH are the fractio n s of c i s and trans isomer, respectively with TCi and Tf being the l i f e t i m e s of the c i s and trans isomers. Equation (G12) i s the most general expression f o r the average electron magnetization, the exact form of which w i l l depend of course upon the l i f e t i m e s of the various states involved. The simplest case i s when Ta- T^= T and (G12) then takes the e x p l i c i t form ) In the above the contribution of the proton nuclear spins has not been considered. The contribution to resonance frequency of l a t t e r has been indicated i n F i g . 3, and i n what follows, use w i l l be made of Maki's observation (73) that & co, = <S *• £ ^ j i . e . that the ove r a l l s p l i t t -ing of the two isomers i s i d e n t i c a l . As a consequence, - » a n d (G13) can be s i m p l i f i e d to For Mj=2 states, of which there are si x , - 47 -< / ^ 7 -c^,M0 ^ ( G 1 5 ) the imaginary part of which represents a l i n e centered about co0 +Z$ to, +zbu>j_ , and whose width i s independent bf r . For M =0 states I <M >- - CO, M0{("<"lr+ } (G16) where -y'y" represents y-^ or which, f o r a given nuclear spin state, i s not equal to y2-. S p e c i f i c a l l y t h i s means that f o r states such as <x/3/?« and ^ <</?; ^ ^ " r ^ , 1 , but f o r states such as <xot.^/ y " ± z. . For states cx(3f2* and fie** ft» the imaginary part of (G16) describes a l i n e centered at u?o which i s independent of T. For other states such as txfttxft or (?«[I* , say, the imaginary part of (G16) does contain T . For very large T , three r e-sonance l i n e s centered at LJ0+$>} ^ 0 } and u)0- S are re-presented/^ ^ .2 <5w, n ^ t . ^ ) or -J&OjtlSoojjJ, while f o r very small T only one l i n e centered at u)g i s indicated. For i n t e r -mediate T , the l a t t e r obviously determines the linewidths. L a s t l y f o r M j = l states, of these four being present, a complex expression f o r <^ M) r e s u l t s , the f i n a l r e s u l t of which i s that the imaginary part of i t represents, f o r - 48 -very small T , four l i n e s which are a l l centered at The spectrum of terephthaldehyde r a d i c a l , say, i s thus seen to be dependent upon both the l i f e t i m e T of the isomers and the values of the hyperfine coupling constants. For small differences i n the coupling constants, and f o r four values of f , the expected spectra are shown i n F i g . 4. In t h i s case So^^j, hio^ IJf 6u)y <? f a n d <£^-/7 i n a r b i t r a r y u n i t s . For very large T~ , the spectrum i s jus t a superposition of spectra due to the isomers, f o r very small T the proton positions are equivalent and f i v e l i n e s i n the i n t e n s i t y r a t i o 1:4:6:4:1 appear, while f o r intermediate cases the o r i g i n of the observed alterna-t i o n of linewidths and i n t e n s i t i e s i s apparent. For a larger spread i n boo , the appearance of the spectra would be quite d i f f e r e n t . 4) Motional Broadening. - Another type of consideration, often used to explain a more regular v a r i a t i o n of l i n e -widths (71,73), i s that of the motional e f f e c t upon the anistropic hyperfine s p l i t t i n g and upon the anisotropy of the g-factor. F i r s t to examine the above e f f e c t t h e o r e t i c a l l y was McGonnell (71), who pointed out that the electron spin would be subject to a f l u c t u a t i n g force as LA LA T= 1/10 i J r= I/IOO —I r—« 1 i 1 1 1 1 T 80 40 0 -40 -80 A o o Fig. 4. Apparent Linewidth Alternation. (Reproduced from Ref. 74 ) V - 50 -the r a d i c a l underwent Brownian motion, i f an anisotropic i n t e r a c t i o n between electronic and nuclear spin were pre-sent. This time dependent perturbation would provide a relaxation mechanism by allowing the electron to a l t e r m^ , and i t would modulate the frequency of the various absorptions. Further extension and modification of McGonnell's theory i s due to Kivelson (59) and Stephen and Fraenkel (72). These workers always employed a Hamiltonian possessing a x i a l symmetry, and although many systems possess such a x i a l symmetry ( i . e . C^H^), i t i s not the most general case. As a consequence, the theory has recently been extended by Garrington and Longuet-Higgins (76) to be applicable to any r a d i c a l i r r e s p e c t i v e of symmetry, and i t i s t h e i r approach which w i l l be i l l u s t r a t e d . Let us r e s t r i c t ourselves to s=-| p a r t i c l e s , so that f i n e structure terms can be omitted. Let also quadrupole and nuclear Zeeman terms be neglected, so that i n e f f e c t we are dealing with a Hamiltonian of the form (B6), and we write f o r i n u c l e i (even i f equivalent) v • pttfi * 1%%,% (cl7) —> —"> where Sp i s the electron spin operator and i s the applied magnetic f i e l d , ^ i s the g-factor tensor, - 5 i -the hyperfine Interaction tensor, and J^' the nuclear spin operator. It should be mentioned that i f the p r i n c i p a l axes of a l l are p a r a l l e l , the Hamiltonian CC17; reduces to the one given i n p r i o r approaches to the problem. The Hamiltonian (G17) c a n D e divided into a part which i s independent of orientation, and one which through i t s orientation dependence acquires a random time dependence, i . e . In the above, the f i r s t two terms are the i s o t r o p i c terms, with J'$Utfi " ' ' t - r f a t j * ( C 1 9 ) while the terms i n the square bracket are the time de-pendent parts, with (C20) Let us focus our attention on one hyperfine l i n e , t h i s l i n e a r i s i n g from a t r a n s i t i o n between eigenstates of the i s o t r o p i c Hamiltonian and characterized by the quantum ( i ) -L numbers M g and , near eigenvalues of S z and I z . The - 52 -problem i s to determine what the anisotropic Hamiltonian (or more pr e c i s e l y the matrix elements of i t within the two s p e c i f i e d states giving r i s e to the hyperfine l i n e ) contributes to the linewidth. As a s i m p l i f i c a t i o n , no nuclear relaxation e f f e c t s are considered, that i s , matrix elements connecting states of d i f f e r e n t are neglected. If z i s the d i r e c t i o n of the applied magnetic f i e l d , the matrix elements of the anisotropic Hamiltonian within the t r a n s i t i o n a l states are the sum of the following terms: I! K'\~C.' (r?U,/. T< *r ~i * ff' \ ~? (G21) 1 i ' Since i n the above the factors g and A (g=x-y. z) & z g zg & are functions of time, a set of molecular coordinates i s chosen i n which ^ and are independent of the r o t a t i o n of the molecule. - a^o<, etc., the d i r e c t i o n cosines between molecular and laboratory coordinates are now the time dependent functions. At t h i s stage, a discussion of random functions and correlations would be appropriate. However, l e t i t s u f f i c e to say that the p r o b a b i l i t y of an x-induced t r a n s i t i o n - 53 -\k,"tJ -*\-k,tf)i> i s given by where 77w i s the energy of the t r a n s i t i o n , f i s the so-ca l l e d c o r r e l a t i o n time, a time i n t e r v a l i n which a cer-t a i n c o r r e l a t i o n exists between laboratory and molecular coordinates, and <(X(o)z^ i s defined i n terms of an ex-ponentially decaying auto c o r r e l a t i o n function-<x(o)X(+))*<X(o)*) e*p{- 'j1) ( C 2 3 ) where X(+) " <l, Mrl /-£ ,M£ > E x p l i c i t l y <^ X(/o)z >^ takes the form <*(<>?>'& (Pifify *ZM> fi^XpHjfjp +Zrtz'#Jp) (G24) For  <Cy(o) iy an i d e n t i c a l expression can be derived, t while f o r H , the l i n e breadth takes the form zz' t<IL> (C23) with <(zzy being equal to 16/3 times <(x(0)zy above. Gathering these contributions together, one obtains f o r the inverse of the transverse relaxation time (due to X(4) and y£+) ) - 54 -and f o r the Longitudinal contribution (due to 2 ( f ) ), r; - 17^ (G27) where P i s given by the product of the two bracketed terms i n equation (G24). The term P thus gives us the information we require about the v a r i a t i o n of linewidth. I f i t i s expanded, a term which'is independent of results and need not be considered further i n t h i s treatment. I t should be men-tioned however, that when nuclear relaxation e f f e c t s are included, the anisotropy of the g f a c t o r i s of importance, as the term containing i t i s also a function of M-j- (see Kivelson (59), equations 47 and 48. A second term i n the 2 expansion of P i s a function of M-j-, and both sides of the spectrum w i l l be affected i n a l i k e manner. Thus a v a r i a -t i o n of linewidth, symmetrical about the center, can be explained. The remaining or cross term can be written i n the form and since i t i s an odd function of M^, the l i n e s f o r p o s i t i v e or negative, and larger or smaller w i l l be affected i n opposite ways. The way i n which the linewidths (G28) i - 55 -are affected does of course not only depend on the M^ . value, but also on the sign of the inner product, $^ , the sign of which cannot be determined from experimental evidence. I t may be calculated using the method of McGonnell and Strathdee (78) f o r instance, and i n con-junction with the sign of the spin density at a given nucleus determines the trend i n linewidths. This i s , because the i s o t r o p i c term A 1 determines whether a l i n e corresponding to a c e r t a i n M^ value occurs at low or at high f i e l d . Also, i n the case of a completely i s o t r o p i c g-value, no linewidth dependence on M^ should be present. Summarizing, the assumption that a small anisotropy i n the g-factor and an anisotropy i n the hyperfine i n t e r a -c t i o n term cannot always be neglected, leads to a general expression f o r the linewidth of l i n e s corresponding to d i f f e r e n t values, namely A co = a -thmj- + c m^r. (C29) - 56 -Chapter I I . Experimental Procedures. A. Introduction Although a number of stable organic free r a d i c a l s exi s t and have been extensively investigated, the majority of ESR studies of organic compounds are concerned with s y n t h e t i c a l l y produced species. For t h i s purpose, several methods of producing r a d i c a l s are a v a i l a b l e . One of these methods, and u n t i l recently, the most common one, i s to reduce a neutral molecule, such as naphthalene f o r instance, by chemical means, using any one of the a l k a l i metals (or a l l o y s thereof) i n an i n e r t solvent (79). This conventional method does however possess several i n t r i n s i c d i f f i c u l t i e s . One of these i s that, quite apart from the laborious procedure involved, no control over the potential at which reduction occurs, i s present. Thus one may obtain negative ions, one may on the other hand obtain diamagnetic dinegative ions (80), mixtures of d i f f e r e n t species, and often i t i s apparent that actual chemical bond formation or breakage occurs to y i e l d species e n t i r e l y d i f f e r e n t from the ones desired (81). A second d i f f i c u l t y i s that one i s l i m i t e d i n the choice of solvent. In the non-polar and i n e r t solvents required, ion c l u s t e r i n g i s a p o s s i b i l i t y , not only among - 57 -paramagnetic species under inv e s t i g a t i o n , but with much higher p r o b a b i l i t y between paramagnetic negative ions and a l k a l i metal ions. I t i s a well established f a c t that t h i s l a t t e r type of association does indeed occur, as evidenced by the hyperfine s p l i t t i n g which one obtains from a l k a l i metal n u c l e i (82). In cases l i k e these, not only i s the i n t e r p r e t a t i o n of spectra rendered more d i f f i -c u l t , but one cannot even speak i n terms of an e s s e n t i a l l y "unperturbed" r a d i c a l anion. A second type of free r a d i c a l can be prepared when a neutral molecule, i n contrast to having an odd electron introduced into an empty o r b i t a l , has one electron re-moved from a f i l l e d o r b i t a l , to y i e l d a p o s i t i v e ion. This has been accomplished with several types of o x i d i z -ing agent, mainly concentrated s u l f u r i c acid (83,84), also antimony pentachloride (85), aluminum chloride (86), and other compounds such as hydrogen f l u o r i d e and t r i -f l u o r o a c e t i c acid/BFg,H 20 mixtures (87). Another method of r a d i c a l production i s that of i r r a d i a t i o n . Since the procedure i s almost always l i m i t e d to s o l i d phases, either c r y s t a l s or substances frozen i n glasses, nothing further w i l l be said about t h i s method. Recently, paramagnetism has been observed, when n i t r o -aromatics i n solution are i r r a d i a t e d with u l t r a v i o l e t - 58 -l i g h t (93,88,90). Since nothing i s yet known about the mechanism of r a d i c a l formation, or f o r that matter, about the nature of the species exhibiting the paramagnetism, nothing more regarding t h i s subject can be said. One of the most a t t r a c t i v e methods of preparing r a d i c a l s i n solution i s that of electrochemical reduction or oxida-t i o n . I t was f i r s t used i n conjunction with ESR by Galkin et a l (91), and by Austen et a l (92) to determine anion r a d i c a l s of anthracene, benzophenone, and anthraquinone, i n frozen solutions of N,N-dimethylformamide. The work of Maki and Geske (73,94,95,96,97, and others) i s responsible, however, f o r the wide use and popularity which the method now enjoys. The advantages of the method are many. The f i r s t and perhaps most important, i s , that the experimenter, with the aid of a previously determined polarogram, has a l -most complete control over the species to be generated. This involves simply an adjustment of the reducing or oxidizing potential to the required value. Second i s the absence of Na + ions, or more generally a l k a l i metal cations, which, as mentioned, complicate matters i n many instances. I t i s true that the p o s i t i v e tetra-n-propyl ammonium ion (from tetra-n-propyl ammonium perchlorate as supporting e l e c t r o l y t e ) may also associate with the generated negative ion, t h i s w i l l however, due to s i z e and charge d i s t r i b u t i o n - 59 -be of much les s e r influence. A further advantage i s that the only r e s t r i c t i o n s upon the choice of solvent are the s o l u b i l i t y of the substance to be investigated, and that of the supporting e l e c t r o l y t e . Most generally, a c e t o n i t r i l e and N,N-dimethylformamide are employed, however, aqueous studies have been undertaken (98,99) and well resolved hyperfine patterns f o r a v a r i e t y of compounds have been obtained. Dimethylsulfoxide, alcohols, and various solvent mixtures have also been employed. As to the actual design of e l e c t r o l y t i c c e l l s , the reader i s referred to papers by Fraenkel et a l (100), Maki and Geske (94), Hausser et a l (101), and P i e t t e and Ludwig (98), also to the following experimental part of the present thes i s . Two types of e l e c t r o l y t i c ESR c e l l are generally distinguished. One w i l l be used with the i n t r a muros tech-nique of Maki and Geske, i n which the r a d i c a l i s generated d i r e c t l y inside the ESR cavity. I t has the advantage of s i m p l i c i t y and ease of operation, i s also p a r t i c u l a r l y well suited to c e r t a i n types of inv e s t i g a t i o n , as f o r instance the study of d i f f u s i o n phenomena and reaction k i n e t i c s . I t does however have the disadvantage that the generated r a d i -c a l may be i n the presence of considerable amounts of non-r a d i c a l species, giving r i s e , i n c e r t a i n instances only, to electron exchange and consequent lack of re s o l u t i o n . - 60 -Furthermore, concentration gradients w i l l exist inside the cavity, as well as reaction products of the species generat-ed, i f simple donation by or acceptance from the counter-electrode i s not the only means of discharging the r a d i c a l . To counteract these e f f e c t s , and to make c e r t a i n that no unreduced substance remains present, the flow technique of Fraenkel et a l may be used. Here the e l e c t r o l y s i s c e l l i s situated outside the cavity, allowing use of larger electrodes as well as v i s u a l observation of the color changes taking place, and the generated species i s transferred to the cavity v i a a suitable flow system. Radical concentra-t i o n i n the cavity i s uniform, subsidiary species ( i f any) are constantly removed, and o v e r a l l control over the e l e c t r o -chemical reaction i s more precise. The present i n v e s t i g a t i o n employs the i n t r a muros technique, with, however, an externally placed e l e c t r o l y s i s c e l l i n p a r a l l e l , to observe v i s u a l l y any changes which may be taking place. Also a platinum cathode, i n preference to a mercury pool cathode, was employed, since i t was ob-served that during reduction of c e r t a i n nitrocompounds at the l a t t e r , p r e c i p i t a t i o n of unknown species occurred. B, Basic ESR Spectrometer. 1) E l e c t r o n i c s . - The X-band, 100 Kc/s spectrometer - 61 -employed i n the present investigations, i s i n almost a l l d e t a i l s i d e n t i c a l with the Varian V-4500 100 Kc ESR spectro-meter. The microwave power, from a Varian V153G klystron, de-l i v e r i n g ca. 300 mw over i t s tuning range of 8.6 to 10 kMc/ sec, i s fed d i r e c t l y into a wave guide run and v i a a magic tee and accessory equipment, to a Varian V-4531 M u l t i -purpose Cavity, operating i n the H mode. Accessory equipment includes Polytechnic Research and Development Company f e r r i t e i s o l a t o r , Model 1203, and a variable attenuator Model 159 A, a Hewlett Packard Model X870 A s l i d e screw tuner, as well as De Mornay/Bonardi terminating load and d i r e c t i o n a l couplers. The detection system employed i s as follows. The magnetic f i e l d i s modulated at 100 Kc/sec by a pair of sweep c o i l s surrounding the sample. The microwave f r e -quency i s held constant at exactly the resonant frequency of the cavity by means of automatic frequency control (AFC). When the p o l a r i z i n g f i e l d i s slowly swept through resonance, the bridge unbalance due to absorption of microwave power i n the cavity, i s detected by a s i l i c o n diode detector as an a.c. s i g n a l , controlled i n phase and amplitude by the slope of the resonance l i n e . The a.c. signal i s fed v i a the 100 Kc receiver to a phase sensitive detector, thence - 62 -to an integrator .-to eliminate unwanted high-frequency noise, and to the recorder (Leeds and Northrup Speedomax H), where i t i s displayed as the f i r s t derivative of the absorption curve vs. magnetic f i e l d . The 100 Ke transmitter and receiver were b u i l t i n t h i s laboratory from Varian c i r c u i t s , but,,as opposed to the Varian u n i t , on separate copper-lined chassis. Further-more, the 100 Kc c r y s t a l was enclosed i n a heated shield f o r greater thermal s t a b i l i t y . ' The•unit, f o r equivalent gain, produced approximately 15 times less'noisei.' Figures (5) and (6) show block diagrams of the spectro-meter and the AFC systems. To monitor the microwave power, a Hewlett Packard Microwave Power Meter (Model 430G), i n conjunction with a thermistor (H/P Model X487B), was employed. 2) Magnet System. - The magnetic f i e l d i s supplied by a Varian #V 4012A 12" magnet, having a 2.5" pole gap. The f i e l d i s measured with a proton resonance magnetometer, consisting of a probe c o i l f i l l e d with g l y c e r o l , and i n -serted into the magnetic f i e l d beside the cavity, connected to a marginal o s c i l l a t o r , frequency modulated at 20 cps. The proton absorption l i n e i s displayed on an oscilloscope AFC Unit Terminal Load Reflector Power Supply Phase Shifter Klystron I s o l .11 or Attenuator — Magic Tee —. Crystal Detector 1 0 0 KC Receiver NMR Probe •• Modulation Coils Magnet Coils Magnet-ometer I 0 0 KC Oscillator C RO Signal Generator > Frequency Counter 1 0 0 KC Modulator Phase Shifter Recorder Ph as Detec e tor Integrator Rg. 5. 100 KC EPR Spectrometer. Reflector Klystron I 0 . 0 KC Oscillator M agic Tee Crystal Detector Pre amp-lifier 1 0 . 0 KC Amplif ie r Reflector Power Supply Phase Detector Fig. 6- AFC System - 65 -screen, and a loosely coupled signal generator (General Radio Go. Model 1001-A) i s tuned to zero-beat with the proton s i g n a l . The frequency of the generator i s measured with a Hewlett-Packard Counter, Model 524B. C. Low Temperature Accessory. For investigations below room temperature, a Varian V-4547 Variable.Temperature Accessory was employed. The unit consisted of a 4-| l i t e r open-top Dewar f o r storage of the coolant ( l i q u i d nitrogen or a dry ice-acetone mixture), a c o i l e d heat-exchanger, a so-called transfer-tube assembly (containing a heating element and iron-constantan thermo-couple) to connect the heat-exchanger and the quartz Dewar ESR cavity i n s e r t , as well as an adjustment cap f o r po s i -t i o n i n g of the cavity i n s e r t . The cap contained a copper-constantan thermocouple assembly. The cooling gas, depend-ing upon temperature desired, was either or bone dry CO^ The temperature was measured with a Rhodes potentiometer-voltmeter. D. Electrochemical Methods. 1) Polarography. - The reduction potentials of the sub-stances to be investigated were obtained on a Sargent Automatic Recording Polarograph, Model XXI. Solutions were - 66 -generally 10~%1 i n substance to be reduced and 10'^M i n tetra-n-propyl-ammonium perchlorate, the supporting e l e c t r o -lyte., Reductions were carried out i n solvents or solvent mixtures i d e n t i c a l to the ones used i n ESR observations, and i n a vessel with a sintered glass d i s c at i t s bottom to allow deaeration with suitable gases or CC^). A saturated calomel electrode, connected v i a an agar-agar salt-bridge, was used as reference electrode. 2) Design of ESR C e l l s . - The ESR c e l l , i n which e l e c t r o -l y t i c reduction of the compounds under i n v e s t i g a t i o n was carried out, i s shown i n F i g . ( 7 ) . I t e s s e n t i a l l y consists of two parts. The lower part, made e n t i r e l y of quartz, ends i n a piece of 2 mm I.D. V i t r e o s i l quartz tubing when employing reasonably non-polar solvents, but ends i n 1 mm I.D. tubing when using more polar solvents l i k e CH CN. Synthetic V i t r e o s i l type quartz tubing was chosen, since, among the various types investigated, i t showed the lea s t paramagnetic absorption. The upper part of the c e l l had a stopcock to allow evacuation of the c e l l and entry of the solvent, as well as two tungsten rods sealed into i t , electrodes being attached on the i n s i d e . The anode consisted either of a piece of platinum f o i l spotwelded onto the tungsten rod, or of a mercury - 67 -pool i n which the tungsten rod was immersed. To prevent any sort of contamination of the cavity with mercury, due to accidental breaking of the c e l l , the cathode consisted not of a mercury pool, as i s commonly employed, but of a 0.25 mm diameter platinum wire, also welded onto the tung-sten rod, and covered with a very f i n e Teflon sleeve with the exception of a 3 cm length exactly inside the cavity. This prevented reduction at places where the cathode would of necessity be i n close proximity with the anode. A further advantage of the 3 cm long platinum wire cathode i s that reduction i s carried out over the entire length of the cavity, and not only at the extreme lower end of the cavity as i s the case f o r a mercury pool cathode. This allows a good concentration of r a d i c a l to be b u i l t up within a r e l a t i v e l y short time, since the d i f f u s i o n con-t r o l l e d build-up from a mercury pool i s to a large extent eliminated, while at the same time eliminating or at l e a s t s u b s t a n t i a l l y minimizing concentration e f f e c t s . Also, no reaction was observed at the Pt cathode, while the Hg pool cathode frequently resulted i n p r e c i p i t a t e formation. Connected i n p a r a l l e l with the ESR c e l l shown i n F i g . (7), was another c e l l , shown i n F i g . (8), which, i n many d e t a i l s was i d e n t i c a l with the former. I t was incorporated - 68 -i n the c i r c u i t r y to aLlow v i s u a l observation of any color' changes or other processes which might occur. One d i f f -erence i s the attachment of a S.C.E. v i a an agar-agar s a l t bridge, as well as exposure of the Pt cathode, where flattened against the restraing sintered glass d i s c of the bridge. Measurement of the cathode potential was thus possible. The c i r c u i t r y employed i s shown i n F i g . (9) and i s i n most items self-explanatory. O.C. refers to the operating or ESR c e l l , while R.C. refers to the reference or observation c e l l . The variable resistances i n both anode connections were used to compensate f o r small d i f f -erences i n the in t e r n a l c e l l resistances, i . e . to have i d e n t i c a l currents flowing through both c e l l s . The E.M.F. across the anodes and cathodes of the two c e l l s w i l l of course be altered by t h i s . In most cases, however, only a very small adjustment was necessary, changing the E.M.F. by a small amount only. In any case, i f the electrode potential of the cathode having the lower E.M.F. across i t and corresponding anode, i s above the desired reduc-t i o n potential of the substance under investigation,' but the potential of the higher E.M.F. cathode i s below the next higher reduction p o t e n t i a l , the difference i n e l e c t -rode potentials should not a f f e c t the reduction process, whereas d i f f e r e n t current densities c e r t a i n l y would. - 69 -3) Design of Optical C e l l . - The c e l l f o r in v e s t i g a t i o n of the o p t i c a l spectrum during e l e c t r o l y s i s of a 1,3,5-trinitrobenzene solution consists of a 1 cm quartz c e l l , attached to which were two electrodes and stopcock f o r evacuation and solvent admittance. I t i s shown i n F i g . (10). The cathode again consisted of a 0.25 mm diameter platinum wire, covered, except f o r a 3 cm portion, with Teflon sleeving. E. Chemicals. 1) Solvents. - 1,2-Dimethoxyethane, EK #4639, was p u r i f i e d by f r a c t i o n a l d i s t i l l a t i o n , b.p. 84-85.5°C, dried over P o0_, and degassed by four to f i v e times freezing, £ 5 pumping, and melting. I t was stored on a vacuum system fo r d i r e c t d i s t i l l a t i o n into the ESR c e l l . A c e t o n i t r i l e , EK #S488, b.p. 81.5°C, was degassed by repeated freezing, pumping, and melting. Storage was on a vacuum system a l s o . N,N-Dimethylformamide, EK #S5870, was d i s t i l l e d , b.p. 149-150°C, and stored under N^. I t d i s t i l l e d only with considerable d i f f i c u l t y under vacuum, and was thus degassed by freezing, pumping, and melting, a f t e r having been placed d i r e c t l y into the ESR c e l l s . B 10 Socket Stopcock Tungsten Anode Connection B 10 Joint Tungsten Ca thode Connection B 2 4 Joint Hg Pool / Pt Foil Sintered Glass Disc Teflon S leev ing Vitreosil Tubing Bare Pt Wire Fig. 7. EPR Electrolysis Cell. Nitrogen reflon Sleeving Sintered Glass Discs Teflon Sleeving Bare Platinum Wire Tungsten Anode Connection B 10 Joint Tungsten Cathode Connection Agar Agar/Salt Bridge Sat'd. KCI Solution Hg 2 CI 2 /Hg Paste Hg Tungsten Connection Fig. 8. Observation Cell with Colomel Reference Electrode. OPDT Ref. SPDT Oper. O.C. R.C. S.C.E Fig. 9. Electrolysis Circuit. T u n g s t e n Anode C o n n e c t i o n B 10 S o c k e t B I O J o i n t S t o p c o c k S i n t e r e d G l a s s D i s c s T u n g s t e n C a t h o d e C o n n e c t i o n B 7 Jo int G r a d e d S e a l T e f l o n S l e e v i n g 0< I c m O p t i c a l C e l l Ba re Pt Wire Fig. 10. Optical Electrolysis Cell. - 74 -2) Supporting E l e c t r o l y t e . - Tetra-n-propyl ammonium perchlorate was prepared by tre a t i n g a 10% aqueous solution of tetra-n-propyl ammonium hydroxide (EK) with an equiva-le n t quantity of perchloric a c i d . The dLmost quantitative p r e c i p i t a t e of perchlorate was washed with l i b e r a l amounts of cold water, r e c r y s t a l l i z e d twice from an a c e t o n i t r i l e -water mixture, and dried over C a C l 2 (vacuum). White, well c r y s t a l l i z e d needles resulted. 3) Compounds Investigated. 1,2-Dicyanobenzene, EK # P7402, was r e c r y s t a l l i z e d from ethanol and vacuum sublimed. Colorless c r y s t a l s , m.p. 140-141°C. 1,4-Dicyanobenzene, EK # 6353, was r e c r y s t a l l i z e d from methanol and sublimed, colorless c r y s t a l s , m.p. 220-222°C. 2,3,5,6-Tetracyanobenzene, g i f t of Prof. C. Reid, previously p u r i f i e d , m.p. 267-269°C sublimes, colorless plates. 7,7,8,8-Tetracyanoquinodimethane, g i f t of Prof. C. Reid, previously p u r i f i e d , m.p. subl. 270°C, orange-yellow plates. 1,2-Dinitrobenzene, A l d r i c h Chem. Co., was r e c r y s t a l l i z e d from methanol and sublimed, m.p. 117-118°C. - 75 -1,3-Dinitrobenzene, Fisher # D-74, was r e c r y s t a l l i z e d from, methanol and sublimed, very pale yellow c r y s t a l s , m.p. 89-89.5°G. 1.3- Dinitrobenzene-d^, was synthesized by r e f l u x i n g a mixture of 2.84 ml. (0.032 moles) of Merck Canada Ltd. 99.9% C IK with 6.47 gms (0.064 moles) of reagent grade 6 6 KN0q and ca. 5 ml. of concentrated sulphuric acid at 130°C f o r 1 hour. The y i e l d was 2.8 gms (52%) of a f a i n t l y yellow powder a f t e r r e c r y s t a l l i z a t i o n from methanol, m.p. 89°C. NMR analysis showed no hydrogen sub s t i t u t i o n , and the com-pound was hence assumed to be C^D^-1 , S-dsK^^ • 1.4- Dinitrobenzene, EK // 1608, was r e c r y s t a l l i z e d from chloroform and sublimed, m.p. 173-4°C. 1,3,5-Trinitrobenzene, EK # 639, was r e c r y s t a l l i z e d 3 times from chloroform and twice sublimed under high vacuum. Be a u t i f u l l y c r y s t a l l i n e , almost colorless substance, m.p. 120.5-121.5°C was obtained. 1.4- Dinitronaphthalene, A l d r i c h Chem. Co. # D-19800, was r e c r y s t a l l i z e d from chloroform and sublimed, yellowish c r y s t a l s , m.p. 130.5-131.5°C. 1.5- Dinitronaphthalene, A l d r i c h Chem. Co. # D-19820, was r e c r y s t a l l i z e d from benzene and sublimed, yellowish plates, m.p. 217°C. - 76 -1,8-Dinitronaphthalene, Flucka AG. 80% technical grade, was f i r s t l y washed with hot water, dried, and then care-f u l l y sublimed, resubliming any residues, and r e c r y s t a l l i z -ing any sublimate and checking i t s m.p. A f t e r sublimation of the residue f o r a t h i r d time, and r e c r y s t a l l i z a t i o n from chloroform, yellowish plates of m.p. 173-175°G were obtained. This was considered to be pure 0^QH 6~1 jS-dSK^)^* 2,2',4,4',6,6'-Hexanitrobiphenyl, K & K Laboratories, sub-limed to give yellow c r y s t a l s , m.p. 237°G. - 77 -Chapter I I I . ESR Spectra of Nitroaromatics. A. Introduction. The n i t r o derivatives of various aromatic hydrocarbons generally e a s i l y y i e l d , upon reduction by either chemical;,i e l e c t r o l y t i c , or other means, one or several species which exhibit paramagnetic resonance spectra. They thus form a series of compounds which has been investigated by several researchers. The e a r l i e s t investigations are due to Chu et a l (29) and Ward and K l e i n (102), who prepared a paramagnetic species, by chemical reduction with sodium metal, from nitrobenzene, 1,3-dinitrobenzene, 1,3,5-trinitrobenzene, and 2,4,7-tri-nitrofluorenone. They obtained spectra of 10, 8, 8, and 1 peak(s) respectively, a l l showing an o v e r a l l s p l i t t i n g of approximately 25 gauss. This was followed by the i n -vestigation of the nitrobenzene r a d i c a l anion by Maki and Geske (94), who prepared the r a d i c a l by electrochemical reduction at a mercury pool cathode, and who were able to obtain a l l 54 of the t h e o r e t i c a l l y expected l i n e s , and were also able to assign, by means of is o t o p i c substitution, a l l four coupling constants unambiguously. The three isomeric dinitrobenzenes have also been reduced electrochemically by Maki and Geske (95). For 1,2-dinitrobenzene negative ion, they obtained 33 of the possible 45 l i n e s , f o r - 78 -1.3- dinitrobenzene anion 44 of 60 Lines, while f o r the 1.4- dinitrobenzene r a d i c a l 19 of 25 possible l i n e s were found. I t i s quite l i k e l y due to t h i s lack of perfect re-solution of a l l the l i n e s , that the coupling constants obtained i n the present investigations, d i f f e r somewhat from the ones due to Maki and Geske. The same compounds have been investigated by Ward (82, 103), however chemical reduction with various a l k a l i metals being employed to generate the paramagnetic species. The writer here used the phrasing "paramagnetic species", since a c e r t a i n uncertainty as to the exact i d e n t i t y of the species giving r i s e to the s i g n a l , i s present. To return to Ward's r e s u l t s , he obtained spectra consisting of 32, approxima-te l y 20, and 9 l i n e s respectively from the 1,2-, 1,3-, and 1,4-isomers. The spectra furthermore showed a v a r i a t i o n depending on which a l k a l i metal was employed as reducing agent. To explain the r e l a t i v e l y small number of absorp-t i o n l i n e s , i n t e r a c t i o n of the unpaired electron with only one nitrogen nucleus, seemingly corroborated by deuteration' studies, was postulated f o r the 1,3- and the 1,4-isomers. This one nitrogen i n t e r a c t i o n i s thought to be due to re-moval of the nitrogen equivalence by formation of a t i g h t -ion complex between negative aromatic ion and Na + ion. In - 79 -the case of the 1,2-isomer, the -NO^  groups are considered to be s u f f i c i e n t l y close to allow complexing of both -NO groups with one Na , ion. Even i f the above were the case, i t i s not at a l l apparent why no s p l i t t i n g from the second nitrogen, considerably smaller of course, should be present. Furthermore, the nitrogen s p l i t t i n g which was observed (7 to 16 gauss) i s approximately that commonly observed from r a d i c a l s containing one n i t r o group only. The trinitrobenzene molecule has also been investigated by Ward and the obtained 12 to 14 l i n e spectrum i s explained by arguments sim i l a r to those applying to the d i n i t r o -d e r i v a t i v e s . Again only one nitrogen i n t e r a c t i o n , but i n -tera c t i o n with three equivalent protons, i s invoked. In t h i s connection i t might be mentioned, that recent photo-induced paramagnetism by Lagercrantz and Yhland (89, 93) has been observed f o r 1,3,5-trinitrobenzene dissolved i n tetrahydrofuran, and that a 12 l i n e spectrum, less than the number of l i n e s t h e o r e t i c a l l y possible from i n t e r a c t i o n with sets of 3 equivalent nitrogen n u c l e i and protons, was obtained. I t appears, as a matter of f a c t , as i f only one nitrogen hyperfine i n t e r a c t i o n i s present. During a routine i n v e s t i g a t i o n of the ESR spectrum of the r a d i c a l anion of 1,3-dinitrobenzene, produced e l e c t r o -- 80 -chemically at a Pt wire cathode, a l i n e width and l i n e i n -tensity a l t e r n a t i o n was observed, which could not be re-conciled with the expected appearance of the spectra f o r various combinations of coupling constants. This f a c t l e d to a r e i n v e s t i g a t i o n of a l l three isomeric dinitrobenzenes, and resulted i n complete re s o l u t i o n of the spectra, 45, 25, and 60 l i n e s respectively being obtained f o r the 1,2-, 1,4-, and 1,3-isomers. A f t e r completion of the above investiga-tions, a note by Fraenkel et a l (104) has mentioned anoma-lous l i n e width behaviour i n the 1,3-dinitrobenzene anion, and a dependence of linewidth on the m^  value of the nitrogen nucleus. A complete description of re s u l t s and interpreta-t i o n thereof i s lacking. Anomalous linewidths have also been observed i n 1,4-dinitrodurene (105). An in v e s t i g a t i o n of various dinitronaphthalenes, mainly the 1,8-isomer, since i t possesses a nitro-group arrangement s i m i l a r to that of 1,3-dinitrobenzene, was also undertaken. Furthermore the symmetrical t r i n i t r o -benzene has also been reinvestigated, and the r e s u l t s ob-tained i n these experiments are presented i n what follows. B. Dinitrobenzenes. 1) 1,2-Dinitrobenzene. - A l o " 3 to 10~ 4 M solution of 1,2-dinitrobenzene i n 80% dimethoxyethane and ~ 20% - 81 -ac e t o r t i t r i l e , and using 10~ M tetra-n-propyl ammonium perchlorate (TPAP) as supporting e l e c t r o l y t e , was e l e c t -rolyzed i n previously described c e l l s . Reduction at the Pt wire cathode (at -0.75 v vs S.G.E.) yielded a brownish red solution which exhibited a well resolved hyperfine pattern of exactly 45 l i n e s , the exact number of l i n e s ex-pected on t h e o r e t i c a l grounds from an anion r a d i c a l of the above mentioned compound, and consistent with sym-metry, such that s p l i t t i n g from two equivalent nitrogen n u c l e i ( ^ - ^ A / * ^ ) a n<i 2 sets of 2 equivalent protons each CZXJH= l ) occurs. The spectrum which was obtained i s shown i n F i g . 11, while the calculated spectrum employing aN=2.82g, aHg=0.22g, and aH^=1.68g, i s reproduced i n F i g . 12. The agreement i s seen to be excellent, both i n l i n e p o s i t i o n and i n t e n s i t y , and leaves l i t t l e doubt as to the correctness of the in t e r p r e t a t i o n . The ov e r a l l experimental s p l i t t i n g i s 15.2 gauss, and the average linewidth between points of maximum slope i s ~110 mg. For the following discussions i t i s useful to i l l u -s trate the molecule i n the following manner. 0 O Fig. II. EPR Spectrum of 1,2- Dinitrobenzene Anion Radical, 2 0 ° C. Fig. 12. Theoretical Spectrum of 1,2-Dinitrobenzene Anion Radical, a N = 2.82 6, = 0.22 G, a H 4 = 1.68 G. - 84 -Using the l a b e l l i n g indicated, the subscripts on the above coupling constants a^. correspond to the positions 3/6 and 4/5. One cannot of course decide which of the coupling constants to assign to which r i n g p o s i t i o n , with-out further experimental work, deuterium substitution, say. As t h i s was performed by Maki and Geske (95), and since t h e i r spectrum and r e s u l t s agree approximately with the present, t h e i r assignment w i l l be followed. Thus the smaller proton s p l i t t i n g constants are assigned to protons 3 and 6. Also, the calculated electron spin densities at the various positions, using Huckel theory, indicates a smaller s p l i t t i n g constant from positions 3 and 6. In table I are presented the experimentally determined coupl-ing constants, as well as the r e s u l t s obtained by Maki and Geske (95), and by Ward (103). Also given are the calcu-lated spin d e n s i t i e s , using Huckel theory and employing the following Coulomb in t e g r a l s oLc and exchange integ r a l s a n d fi«o'l-l7pcc These integ r a l s were chosen as they give a reasonable agreement with experimentally determined spin density (using McConnell's r e l a t i o n ) f o r a large number of n i t r o compounds. The same constants were employed f o r a l l the - 85 -nitro-compounds investigated. P o s i t i o n Fischer (95) (103) fJCcalc.) f t r(expt.) L 0.07852 3 ( a H 3 ) 0.22 0.42 .03292 .0093 1.68 1.63 .05493 .0709 7(a N) 2.82 3.22 3.2 .10813 9 .11409 Table I. Spin Densities and Coupling Constants i n 1,2-Dinitrobenzene Anion Radical. Using McConnell's equation (C18) and a value of -23.7 g H f o r QCH , the experimental spin densities at positions 3 and 4 are \;c3= 0 . 0 0 ^ 3 and ^  = 0 .VIO^ » agreement with c a l -culated r e s u l t s leaving something to be desired. I t should however be remembered that the following assumptions are made, namely that Q.CH i n the compound i s taken the same as f o r a CHC2 fragment from which i s determined, and also that the Huckel parameters do represent a more or less a r b i t r a r y choice. Various authors have f o r various reasons employed Q. d i f f e r i n g considerably from -23.7 g, and employing d i f f e r e n t Q's , agreement could be improved considerably. The writer has some misgivings about using - 86 -the value -23.7 g f o r positions such as 3 or 6, where the hydrogen atoms are i n close proximity to one or more n i t r o -groups. Other factors which determine the spin density at such proton positions might conceivably be involved, a point which w i l l be discussed further at a l a t e r time. Also, from table I, i t can be seen that the values of the coupling constants, e s p e c i a l l y the nitrogen and posi t i o n 3 proton constants, d i f f e r from those obtained by Maki and Geske. As t h e i r r e s u l t s were obtained using pure a c e t o n i t r i l e as solvent, and since s i m i l a r coupling constants to th e i r s were obtained when using t h i s solvent, the e f f e c t i s ascribed to some sort of solvent i n t e r a c t i o n . A strong solvent e f f e c t has also been found i n investiga-tions of other compounds. I t should also be mentioned, that resolution, when employing a c e t o n i t r i l e as solvent, was poorer than when using the solvent mixture. A careful search of the spectrum at room temperature f a i l e d to y i e l d any gross linewidth ofC i n t e n s i t y anomalies. Since the l i m i t of resolution of the ESR spectrometer employed i s 70 mg, well below the 110-115 mg linewidths obtained at room temperature, experiments at a lower temperature were performed. F i g . 13 shows the spectrum which was obtained at -30°C from e l e c t r o l y s i s of an 80/20 Fig. 13. EPR Spectrum of 1,2-Dinitrobenzene Anion Radical at -30 ° C. - 88 -dimethoxyethane/acetonitrile s o l u t i o n , 5 x 10 Si i n 1,2-dinitrobenzene and 10~^M i n TPAP. The spectrum con-s i s t s of only 37 of the p o s s i b l e 45 l i n e s and does not show a decrease i n l i n e w i d t h , so that 110 mg appears to be the n a t u r a l l i n e w i d t h s under the c o n d i t i o n s employ-ed. The spectrum can be very a c c u r a t e l y reproduced t h e o r e t i c a l l y , u s i n g the f o l l o w i n g c o u p l i n g constants: aN=3.06 g, a H g=0.29 g, and ajj^=1.71 g. I t i s presented i n F i g . 14. A t very low scanning speed, e i g h t l i n e s , marked x i n F i g . 14, appear to be s l i g h t l y wider than 110 mg and show a c e r t a i n asymmetry. Since i t i s the exact e i g h t l i n e s which r e s u l t from overlap of two other s , and which alone show t h i s asymmetry, i t has been a s c r i b e d to inhomogeneous broadening and i s not a t t r i b u t e d to deeper l y i n g o r i g i n s . Upon c a r e f u l a n a l y s i s however, the f a c t emerges that a c e r t a i n systematic i n t e n s i t y v a r i a t i o n does e x i s t . This i s the f o l l o w i n g . The l i n e s which a r i s e from the n i t r o g e n mj=0 t r a n s i t i o n (the center l i n e of the spectrum) are very a c c u r a t e l y equal i n i n t e n s i t y to both the high and low f i e l d side of center. A l l other l i n e s , even those where overlap occurs, show a d i f f e r e n t i n t e n s i t y depending on whether the h i g h or low f i e l d l i n e i s observed. I n -v a r i a b l y the high f i e l d l i n e i s l e s s i n t e n s e , which could correspond to a l a r g e r l i n e w i d t h . X X X X < X X X Fig. 14. Theoretical Spectrum of 1,2-Dinitrobenzene Anion Radical, a N = 3.06 G, a H = 0.29 G, a H = 1.71 G. - 90 -To explain t h i s f a c t we revert to equation (C28) and see that the inner product {fjp &\ ) w i l l be negative =? i f f\ i s p o s i t i v e , i t has i n f a c t been calculated to be + 76 Mc sec ^ f o r a nitrogen 2p electron and nucleus (76), Z and i f <^ along the GN bond i s larger than the other components. Schreurs and Fraenkel (106) have indeed —g suggested the component of along the semiquinone cjne^ r a d i c a l ion GO bond to be much larger than the other two components. As a consequence, l i n e s of negative nitrogen m-j- should be broader, i . e . l e s s intense than those f o r posit i v e rrij, and as the high f i e l d mj(N) = ±1,-2 l i n e s show lower i n t e n s i t i e s consistently, i t i s stipulated that the nitrogen s p l i t t i n g constant, i . e . spin density at the nitrogen nucleus, be p o s i t i v e . This i s i n agreement with theore t i c a l considerations and with re s u l t s obtained by other investigators on heterocyclic system (47,49). I t may also be that further asymmetry (w.r.t. center) of the l i n e s due to protons i s present, the e f f e c t however would be quite small, and the writer prefers not to de-f i n i t e l y state that such an asymmetry has been observed. The second important f i n d i n g i n the spectrum obtained at -30°G, i s the change of the coupling constants, p a r t i -c u l a r l y a^ and ajj . Now i t has been shown by Kivelson - 91 -(59), that the motional term which leads to the dependence of the linewidths on the VCL^ value ( i f anisotropy i n g and /or A i s not completely averaged to zero), does also lead to a s h i f t of the hyperfine absorption l i n e s i f nonsecular contributions are included. For d i l u t e solutions of or-ganic free r a d i c a l s , t h i s s h i f t i s however n e g l i g i b l y small, so that another reason f o r the quite substantial change i n the coupling constants must be found. T u t t l e (107) has reported a temperature dependence of the coupling constants i n the spectrum of chemically generated toluenide r a d i c a l anion, which he attributes to the presence of a thermally accessible excited state, the change i n s p l i t t i n g constants r e s u l t i n g from the superposition of two spectra, the ground and excited state spectra. This view i s not unreasonable i f one considers the presence of the methyl group as a perturbation which l i f t s the degeneracy of the lowest antibonding o r b i t a l s of a benzene molecule, these l e v e l s being say 1-2 Kcal mole""*" apart. Huckel calculations show that the lowest and next to lowest u n f i l l e d o r b i t a l s i n 1,2-dinitrobenzene are however separated.by ca. 0.38 ft , which would correspond to approximately 8-10 Kcal mole \ depending upon the value of (3 chosen. I t seems u n l i k e l y that t r a n s i t i o n s occur between these states at a rate rapid enough to re-s u l t i n a weighted average of the spectra corresponding - 92 -to the two separate states, i f t h i s t r a n s i t i o n should occur at a l l . I f i t does, i t might very l i k e l y be at a frequency slow compared to the hyperfine in t e r a c t i o n s , i n which case a simple superposition of two spectra should r e s u l t . The Huckel c o e f f i c i e n t s given below f o r the two o r b i t a l s would indicate that the spectra of the two species • ^ ^ P o s i t i o n Energy ' ^ ^ ^ ^ 1 ; 3 4 7 9 -.2258 jS .07852 .03292 .05493 .10813 .11409 -.6055 .00004 .15927 .06178 .11684 .08102 should show observable differences. Only one spectrum i s found however. As mentioned previously, i t i s f e l t that the pre-sence of the nitro-group: adjacent to the r i n g protons, could a f f e c t the coupling constant ( i . e . spin density) of l a t t e r . Comparing coupling constants i n the species at 25°C and -30°C, i t 1 i s apparent that, although a^ . i s s l i g h t l y changed also, the predominant change i s i n the a^ and ajj constants, a f a c t which would further seem to indicate'a r e l a t i o n s h i p between the two constants. For instance, the CH bond length, more l i k e l y the CCH bond angle might be altered due to the proximity of the N0 2 groups, and one of these f a c t o r s , or both working simultaneously could r e s u l t i n the low value of a u . - 9 3 -I t i s also quite conceivable that a lowering of the temperature causes a s l i g h t geometrical rearrangement of the N0 2 groups, or that the solvation sheath surrounding the molecule, e s p e c i a l l y the NC^ groups, i s a l t e r e d , re-s u l t i n g i n a change of the nitrogen coupling constant. A dependence of a-^ upon the NO groups could then explain A ajj and A a ^ , or, i f no such dependence e x i s t s , the e f f e c t upon a N and ajj i n d i v i d u a l l y might s t i l l be larger than f o r the more distant p o s i t i o n 4 and 5 protons. Also, the above does not imply necessarily a large change i n the spin density at the nitrogen nucleus i t s e l f , but may perhaps be due to an e f f e c t primarily l o c a l i z e d on the oxygen atoms, as a N i s not only dependent on the spin density at the nitrogen atom, On the other hand, i t i s of course possible, that the Huckel density i s quite inaccurate i n the present case. 2) 1 , 3-Dinitrobenzene and 1,3-Dinitrobenzene-d4. - As mentioned previously, the spectrum of the anion r a d i c a l of 1 , 3-dinitrobenzene, unreconcilable with various com-binations of the four coupling constants, led to a re-i n v e s t i g a t i o n of a l l three dinitrobenzenes. Although a linewidth ( i n t e n s i t y ) e f f e c t has also been observed i n other compounds, as f o r instance i n the 1,2-isomer already - 94 -discussed, the anomaly i n the case of the 1,3-isomer i s very much more pronounced. Thus the i n t e n s i t y r a t i o of low f i e l d l i n e to corresponding high f i e l d l i n e i n the 1,2-anion i s approximately 1.08:1, whereas i n the 1,3-compound, l i n e s of at times h a l f the expected i n t e n s i t y are observed, a phenomenon not explicable i n terms of the McGonnell theory. The 1,3-dinitrobenzene negative ion was consequently more extensively studied than the other isomeric r a d i c a l s . The r e s u l t s are presented below. E l e c t r o l y s i s at -0.84 v vs. S.C.E. of a 10~ 4 M solution of 1,3-dinitrobenzene, the solvent being a 50/50 mixture of dimethoxyethane and dimethylformamide, yielded a brownish solution, the ESR spectrum of which i s shown i n F i g . 15. The spectrum consists of exactly sixty l i n e s which i s the number to be expected from a r a d i c a l i n which the electron spin i n t e r a c t s with two equivalent nitrogen n u c l e i (^-^--2.) ? o n e s e t o f 2 equivalent protons (ZXIH-1) s and 2 sets of one proton each . The assign-ment of the s p l i t t i n g due to the two nonequivalent protons i s once more ambiguous, and again Maki and Geske's deutera-t i o n r e s u l t s w i l l serve as a guide. I f the molecule i s l a b e l l e d as follows 3376 07 G 3373.13 G 3370 53 G 336855 G Fig.15. EPR Spectrum of 1,3-Dinitrobenzene Anion Radical in 50%DME/50%DMF . - 96 -then the spectrum can be analyzed i n terms of the follow-ing coupling constants (at l e a s t as f a r as l i n e positions are concerned): aN=3.99 g, aH^ .=1.08 g, an^=^'37 g, and aH^=2.81 g. In the wings of the spectrum, where l i t t l e or no overlap of l i n e s occurs, the "±2" l i n e s have a peak to peak width of ~115 mg, the M±l" l i n e s a peak to peak linewidth of ~ 145 mg. The t h e o r e t i c a l spectrum to be expected from th i s set of coupling constants i s shown i n F i g . 16, the numbering of the l i n e s i n d i c a t i n g t h e i r o r i g i n , that i s m^=-2,'tl, or 0 t r a n s i t i o n s . Presented i n Table II are the coupling constants from this i n v e s t i g a t i o n along with those of Maki and Geske and of Ward, and also the calculated and experimentally obtained spin densities (the l a t t e r using McConnell's Fig. 16. Theoretical Spectrum of 1,3- Dinitrobenzene Anion Radica l ,a N = 3.99 G,a H 2 =l .08 G,a H 4 =4.37 G , a H s =2.81 G. - 98 -r e l a t i o n and & = -23.7). I t i s seen that a gross d i s c r e -pancy exists between our re s u l t s and those obtained by Ward. I f the spectrum which Ward recorded was indeed that Table I I . Coupling Constants and Spin Densities i n 1,3-Dinitrobenzene Radical Anion. P o s i t i o n Fischer (95) (103) ( c a l c . ) £l" (obs.) 1 .02535 1.08 1.08 1*4.6, .00000 (-).0456 4 U H ; 4 ) 4.37 4.19 4.6 .19264 .1844 2.81 3.11 •1.2* .00000 (-0.1186 7(a N) 3.99 4.68 9.0 .10089 9 .09055 of the negative ion, then the discrepancy can be attributed to either the method of preparation of the r a d i c a l ( i . e . reduction with a l k a l i ) or to the use of non-polar solvents, or both. The discrepancy with Maki and Geske's constants i s not so d r a s t i c , and i s indeed' considerably improved i f CH GN i s used i n our inv e s t i g a t i o n as w i l l be seen l a t e r . However, complete agreement i s not observed. Another point need be made s p e c i f i c a l l y at t h i s stage. This i s , that the coupling constant a^=3.99 g - 99 -represents a value measured towards the edges of the spectrum, to obtain best (and exact) f i t to the experi-mentally obtained, and at the spectrum edge completely resolved l i n e s . I f the s p l i t t i n g of l i n e s representing m^ j l i n e s d i r e c t l y i s measured, the f i r s t s p l i t t i n g con-stant; m^ pO to m^=-1, i s s l i g h t l y smaller (3.88 g) than the mjq=-l to mN=-2 value of 3.99 g. A further point need be made. In the next to l a s t column of Table I I , the Huckel spin densities are given, and i t i s seen that f o r positions 2 and 5 zero density i s indicated. This would imply a zero s p l i t t i n g constant f o r these two positions and a 15 l i n e spectrum should r e s u l t . The fac t that 60 l i n e s are observed c l e a r l y i n -dicates that there i s spin density located at the carbon atoms contiguous to protons 2 and 5, and the spin density calculated from the coupling constants and employing &=-23.7 g i s given i n the l a s t column. I t i s one of the f a i l i n g s of the Huckel theory that i t does not y i e l d negative spin d e n s i t i e s , and i t has been found, that when Huckel spin densities are zero or very small, actual spin densities at those positions are often negative. I t i s f o r t h i s reason that the calculated spin densities f o r positions 2 and 5 are preceeded by a minus sign. The w r i t e r hastens to add that no experimental evidence - 100 -whatever exists f o r t h i s , and i n the absence of McLachlan type c a l c u l a t i o n s , the sign i s only speculative. In comparing F i g s . 15 and 16, i t i s at once apparent that the observed and calculated i n t e n s i t i e s disagree grossly. Towards the center of the spectrum one might be tempted to a t t r i b u t e the apparent anomaly to lack of perfect r e s o l u t i o n , however at l i n e s 7 and 8, also 9 and 10, f o r instance from each end, th i s can c e r t a i n l y not be the case. I t would furthermore be tempting to employ the theory discussed i n section (G4), and i t i s indeed found, as i n the case of the 1,2-isomer, that except f o r m^ =0 l i n e s , the high f i e l d l i n e s are somewhat less intense than t h e i r l o w - f i e l d counterparts, and following argu-ments as before, t h i s f a c t i s consistent with p o s i t i v e spin density at the nitrogen n u c l e i . The anomaly of the l i n e s mentioned previously i s however found on both the high and low f i e l d sides, and i t i s f e l t that the McGonnell approach ( i n t h i s case the terms b i l i n e a r i n mN being em-ployed) cannot explain the apparent discrepancy f o r two reasons. One i s that the e f f e c t would be smaller than that observed, and second i s the f a i l u r e to observe an 2 m^  dependence of the linewidth (at l e a s t one as large as here) i n both the 1,2- and 1,4-isomers. - 101 -To insure that the observed e f f e c t was not merely an e f f e c t p a r t i c u l a r to the solvent system employed, other solvents and solvent mixtures, as well as spectra at various temperatures, were studied. In 100% diraethylformamide, the spectrum obtained at room temperature consisted of 54 l i n e s and was i n a l l respects very s i m i l a r to the one shown i n F i g . 15. I t i s consequently not reproduced here. The coupling con-stants d i f f e r only s l i g h t l y from the previously given ones and are: a^r=4.02 g, a-jj =1.06 g, a-H^ 4 , 4? §» a n d -aH^=2.80 g. The linewidth and i n t e n s i t y anomaly i s again present, although i t does not appear to be as pronounced as i n the case discussed above. Lowering the temperature produced no observable e f f e c t . In 100% a c e t o n i t r i l e , a spectrum consisting of 50 l i n e s was obtained and i s shown i n F i g . 17, the fewer number of l i n e s obtained being due to a lack of resolution of nearly overlapping l i n e s , as shown i n the theoretical-spectra. The spectrum can a c t u a l l y be quite adequately described by two sets of coupling constants, namely aN=4.35 g, aEs=1.09 g, 3.^=4.17 g, and aHja=2.98 g, or aN=4.13 g, 3^=1.04 g, a H 4=4.48 g, and aH^=2.98 g. The spectra which would be obtained t h e o r e t i c a l l y from these 17 EPR Spectrum in CH 3 CN. 3-Dinitrobenzene Anion Rodi - 103 -constants are shown i n F i g s . 18 and 19. These figures are composed of two parts, the lower part showing the spectrum of a l l s i x t y possible l i n e s , while the upper part shows the spectrum when the sets of l i n e s marked x are not resolved. One f a c t becomes at once apparent, this being that i f the f i r s t mentioned set of constants i s used, the *1 l i n e s again appear to be much weaker than anticipated, while i f the second set of constants i s used, the -2 lines.'seem to show the larger anomaly. This, i n conjunction with deuteration r e s u l t s , seems to indicate that set 1 i s the preferred and correct one. The observed linewidth are as follows: -2 l i n e s ~ 120 mg, -1 l i n e s ~170 mg, 0 l i n e s ~ 135 mg. Again i t must be mentioned that the a^ quoted i s the one measured from well resolved l i n e s at the outside of the spectrum. Measurements of the m^  i n t e r v a l s d i r e c t l y again y i e l d s d i f f e r e n t constants, namely a^=4.25 g f o r f^j=0 to m^=-l, while aN=4.38 f o r ,mN=-r to ;mN=-2. Next, various solvent mixtures were employed. The spectra obtained from the-1,3-dinitrobenzene r a d i c a l s i n mixtures of a c e t o n i t r i l e and dimethoxyethane i n the proportions l8"/85, 30/70,' and 40/60 a l l showed 28 l i n e spectra over a temperature range from +20°G to -20°G, the linewidths being -~115 mg at 20°G and ~150 mg at • ft & * * « * % * * Fig.18. Theoretical Spectrum of L3-Dinitrobenzene Anion Radical in Cf-UCN, a N = 4.35 G, a H 2 = 1.04 G, a H 4 = 4.17 G, a H - 2.98 G. ° Fig. 19. Theoretical Spectrum of 1,3-Dinitrobenzene Anion Radical in CH^CN, a N = 4.13 G , a H - l . 0 4 G , a H 4 - 4.48 G , a H 5 = 2.986. - 106 -lower temperatures. A representative spectrum i s shown i n F i g . 20. In a l l the spectra, the coupling constants which would be unambiguously determined, namely a ^ and a H , showed great constancy and ranged only from 2.95 g 5 to 2.98 g and from 1.07 g to 1.09 g. A t h e o r e t i c a l spectrum consisting of 28 l i n e s only gives a reproduction of the observed spectrum quite accurately, i f i t i s assumed that the coupling constants a^ and a^j^ are equal. In that case the spectrum shown i n F i g . 21 i s predicted when using aN=aH^=4.30 g, a H j ^ 1.07 g, and ajj^=2.98 g. The o v e r a l l calculated s p l i t t i n g from these constants i s 29.85 gauss, which compares well with the measured o v e r a l l s p l i t t i n g of 29.83 g. Experi-mental findings to be discussed next, indicate however, that the apparently clear-cut case of accidental degener-acy of coupling constants which appears to e x i s t , i s not without ambiguity. The spectrum which was obtained when employing a 50/50 mixture of a c e t o n i t r i l e and dimethoxyethane, appears i n F i g . 22. This spectrum consists of 56 l i n e s , some of which are extremely weak i n i n t e n s i t y . These weak l i n e s , at l e a s t i n the positions which are completely without ambiguity, again towards the wings of the spectrum, are i n the exact spots i n which l i n e s when higher concentra-tions of a c e t o n i t r i l e and pure a c e t o n i t r i l e are used, Fig. 20. EPR Spectrum of 1,3-Dinitrobenzene Anion Radical in l57 0/85%, 30%/70%,and 40%/60 o/ o CH3CN/DME. Fig.21. Theoretical Spectrum of 1,3-Dinitrobenzene Anion Rad i ca l , a N = a,_,4 = 4 .30 G , Q H ^ 2 .98 G , aH^ s 1 0 7 G-Fig.22. EPR Spectrum of 1,3-Dinitrobenzene Anion Radical in 50%/50% CH3CN/DME. - 110 -are found,, and which appear to be due mainly to i % = - l t r a n s i t i o n s . The spectrum can be p e r f e c t l y explained i n terms of - the following coupling constants: ^=4.45 g, a^ =1.04 g, a^j =4.24 g, and'a^ =21.98 g. The f a c t that & 4 -2. these - I - l i n e s appear, though-weakly, at the positions to be expected, and do not gradually appear as a widen-ing i n the wings of already e x i s t i n g l i n e s and f i n a l l y a s p l i t t i n g into two d i s t i n c t l i n e s , seems' to indicate that these l i n e s , i n the more nonpolar solvents, are broadened completely out of existence. The spectrum shown i n F i g . 20 would i n that case represent a spectrum with c e r t a i n broadened l i n e s completely absent, and not a spectrum i n which fewer l i n e s due to degenerate coupl-ing constants are observed. Before making an attempt to explain the anomalous behaviour of the 1,3-dinitrobenzene r a d i c a l anion, re-sul t s which were obtained from the r a d i c a l anion of 1,3-dinitrobenzene-d^; w i l l be presented. Reduction of a 10~^M solution of th i s compound also yielded a reddish brown coloration and under low res o l u t i o n gave spectra resembling that shown i n F i g . 23, while at higher re-soluti o n deuterium s p l i t t i n g could be discerned and spectra resembling that shown i n F i g . 24, are obtained. In the low res o l u t i o n spectrum, the i n t e n s i t y of the 3380 95 G 3389 32 G Fig.23.EPR Spectrum of 1,3-Dinitrobenzene-CI4 ,low Resolution. . EPR Spectrum of 1,3-Dinitrobenzene- d 4 Radical,High Resolution. - 113 -l i n e s i s quite accurately i n the r a t i o of 1:2:3:2:1, exactly what one would expect from s p l i t t i n g due to two equivalent nitrogen n u c l e i . Nitrogen coupling con-stants determined from these spectra are: Solvent a N(gauss) DMF 3.98 CHgCN 4.28 CHgCN/DME (30/70) 4.22 and are seen to be consistent with coupling constants previously presented. No attempt has been made to analyze these spectra completely, as 225 l i n e s are theore-t i c a l l y possible, and the observed number, f a r below t h i s f i g u r e (approximately 60 to 70 l i n e s could be c l e a r l y distinguished although indications of many more are pre-sent), makes such an analysis most ambiguous. An attempt w i l l now be made to explain the anomalous l i n e i n t e n s i t y and linewidth behaviour. I t might be i n -s t r u c t i v e at t h i s stage to enumerate the experimental findings which a theory of this e f f e c t should i d e a l l y ex-p l a i n . F i r s t l y , there i s the large difference between the t h e o r e t i c a l l y calculated i n t e n s i t i e s and the observed - 114 -ones and also i n the linewidths, e s p e c i a l l y f o r l i n e s which appear to ar i s e from the ^ =-1 t r a n s i t i o n s . Se-condly the theory should explain why the anomalous be-haviour appears to be absent i n the deuterated 1,3-dinitrobenzene. One must of course state here that i t i s not absolutely c e r t a i n that the e f f e c t i s absent i n the deutero compound. This, one would only be able to decide upon complete resolution of the r e s u l t i n g spectra. I t i s however f e l t that an e f f e c t as large as that observed i n the undeuterated compound, should be observ-able even i n the absence of perfect r e s o l u t i o n . T h i r d l y , the theory should also, i f possible, explain why, although the o v e r a l l appearance of the spectrum i s explicable i n terms of two equivalent nitrogen coupling constants, a difference should e x i s t f o r the a^ for m^ =0 to m^='tl inte r v a l s and a N f o r l ^ = - l to itifl=:t:2 i n t e r v a l s . As already mentioned, an anomalous behaviour of linewidths and l i n e i n t e n s i t i e s has been observed i n several compounds, among theml,3-dinitrobenzene (104) and 1,4-dinitrodurene (105). The former of these ano-malous spectra has not been explained. I t has merely been stated that a time dependent f l u c t u a t i o n of nitrogen coupling constants can cause linewidth changes. In the - 115 -case of the dinitrodurene, the following sort of argument i s employed. I t i s assumed that the angle which the nitro-groups make with the plane of the r i n g v a r i e s , i . e . the nitrogen coupling constants are a function of that angle, a^((p) , say. Now t h i s r o t a t i o n a l modulation of ctN($) causes linewidth changes by inducing secular and nonsecular rela x a t i o n processes, andAdetermined by the Fourier spectrum of the deviation of the matrix elements from the average value <*„(*)> 15+1*1 1 In p a r t i c u l a r , Fraenkel and coworkers have stated that i f J ^ ( 0 ) i s the secular spectral density f o r motion of one NC>2 group r e l a t i v e to the plane of the r i n g (non-secular contributions w i l l be much les s important than secular ones), then the contribution to the linewidths f o r the various t r a n s i t i o n s shows the ^ = ± 2 t r a n s i t i o n s to be unaffected, i t shows a contribution of J^^(O) to the m^=-l t r a n s i t i o n linewidth, and a contribution of 0 and 4J|^(0) to the m^ =0 t r a n s i t i o n linewidth respectively, depending on whether s t a t i s t i c a l weights 1 or 2 are con-sidered. The end r e s u l t i s a spectrum i n which -2 tran-s i t i o n s appear normal, while ±1 and 0 t r a n s i t i o n s show anomalous broadening. The experimental findings of - 116 -Fraenkel et a l . are consequently s a t i s f a c t o r i l y explained. In the present investigations, further anomalous features are present and need be explained. To recapi-t u l a t e , these are the disappearance of the linewidth and i n t e n s i t y anomaly upon deuteration of the compound, as well as the apparent difference i n the nitrogen s p l i t t i n g s depending upon the i n t e r v a l observed. Let us begin by considering why such an anomalous behaviour should occur i n the 1,3-isomer of the d i n i t r o -benzenes only. Fraenkel (105) has calculated the e f f e c t upon the nitrogen s p l i t t i n g constants as the exchange i n t e g r a l ^ C f J i s altered, a decrease i n ficu corresponding to a ro t a t i o n of the N0 2 groups out of the plane of the r i n g , and of an a l t e r a t i o n of the Coulomb i n t e g r a l c<D of the oxygen atoms, due to varying solvation of the oxygen atoms. He shows that both these e f f e c t s w i l l be much more pronounced i n the 1,3- than i n the 1,4-isomer. In terms of valence bond theory one can v i s u a l i z e e a s i l y why r o t a t i o n of the N0 2 groups i n the 1,4-isomer should be much more d i f f i c u l t than i n the 1,3-isomer. Thus, quinonoid type resonance structures shown below, indicate why r o t a t i o n out of the plane of the r i n g should be i n h i b i t e d - 117 -i n the 1,4-isomer, but not i n the 1,3-dinitrobenzene anion, f o r which i t i s impossible to draw a structure of t h i s type. For the 1,2- anion, s i m i l a r considerations apply. Thus a structure of the type 0 0 -shows why r o t a t i o n about the CN bond should be hindered. I t might be argued that the proximity of the N0 2 groups would prevent coplanarity of former with the r i n g . This s t e r i c hindrance i n i t s e l f tends to prevent free r o t a t i o n of the N0 2 groups, and a compromise between the two types of e f f e c t i s most l i k e l y operative. - 1L8 -One can thus see q u a l i t a t i v e l y that the major difference between the three isomers i s the ease of r o t a t i o n of the nitro-groups, and t h i s f a c t does indeed indicate- rthat i t i s t h i s r o t a t i o n which leads to the anomalies observed. Then, to begin, l e t us assume that t h i s r o t a t i o n of nitro-groups occurs, and furthermore that i t must be the reason f o r the observed ESR anomalies. One can thus v i s u a l i z e four types of geometrical isomers f o r any p a r t i c u l a r nuclear spin configuration, as shown i n F i g . 25. Configuration I has both N0 2 groups i n the plane of the r i n g , while II and III have one nitro-group i n the plane of the r i n g and one out of i t , and configura-t i o n IV has both N0 2 groups perpendicular to the r i n g . If one neglects nuclear spin states, configurations II and I I I are equivalent. These structures as drawn, do of course represent extreme cases, I t i s now possible to calculate the average electron magnetization f o r each configuration, the net average magnetization of the system as a whole, and from the imaginary part of the l a t t e r , the absorption spectrum expected f o r a p a r t i -cular nuclear spin configuration. The mathematics i s tedious and. since a q u a l i t a t i v e discussion w i l l lead to Fig.25. Geometrical Isomers in 1,3- Dinitrobenzene. - 120 -i d e n t i c a l r e s u l t s , although the method may not appear as elegant, the l a t t e r course i s followed. From the appearance of the spectrum (see F i g . 15) i t i s seen that l i n e s a r i s i n g from i n t e r a c t i o n of the electron spin with protons 2 and 5, do not show any ano-molous behaviour, that i s , i n t e n s i t i e s as well as l i n e -widths f o r sets of l i n e s corresponding to such i n t e r a -ctions are i d e n t i c a l and considered normal. These protons w i l l be consequently neglected i n the following discussions. One may now consider three possible cases, f i r s t l y the case i n which the e f f e c t i s due to the nitrogen i n t e r a c t i o n alone, secondly the case where the e f f e c t i s due to the remaining r i n g protons alone, and t h i r d l y the e f f e c t i n which a combination of the above i s operative. In F i g . 26 are shown the i n d i v i d u a l spectra ( a r b i t r a r y coupling constants a^.) when a) both nitro rgroups are i n the plane of the r i n g and a a a N L = a N 3 » b) when both nitro-groups are perpendicular to the plane of the r i n g and b _ b a a a N l ~ a N 3 < a N L = a N 3 ' J2 J-2 b. c. d 1 1 1 Fig.26- Theoretical Spectra Considering Variation in a^ only. - 122 -and f i n a l l y c) when one of the nitro-groups i s i n the plane, the other perpendicular to the plane of the r i n g . Here c c a N L > a N 3 but also c c a a In the f i r s t and l a s t case the ov e r a l l s p l i t t i n g due to the nitrogen n u c l e i i s thus i d e n t i c a l , a reasonable assumption, while i n case b) a smaller o v e r a l l s p l i t t i n g i s necessarily present. The l a s t row i n F i g . 26 shows the sum spectrum of the above three, the t h i r d spectrum being used with a weighting fa c t o r of two. The spectrum which one w i l l observe experimentally w i l l depend on the res o l u t i o n of the spectrometer employed, and assuming that t h i s r e-solution i s perfect, the appearance w i l l be governed by the l i f e t i m e s C<- = I,JL,KtZZ) of the various isomers. If the l i f e t i m e should be much larger than the inverse of the hyperfine s p l i t t i n g , i . e . - 123 -then a superposition of the three spectra w i l l be observed. If the l i f e t i m e i s much smaller than the inverse hyper-f i n e s p l i t t i n g , that i s i f then a f i v e l i n e spectrum of normal i n t e n s i t y r a t i o and linewidth w i l l be observed, while i f the l i f e t i m e s and the rec i p r o c a l of the hyperfine s p l i t t i n g should be approximately the same, i . e . then a smeared out spectrum w i l l be observed. The m^p-2 tra n s i t i o n s w i l l appear as l i n e s of normal width, as the much smaller subsidiary l i n e towards center w i l l only a f f e c t the wings of the absorption l i n e s , and no ef f e c t due to i t w i l l be observed experimentally. Com-paring i n t e n s i t i e s , i t i s seen that t h i s l i n e i s not l/3 or l/2 the in t e n s i t y of the m-^ =0 and n ^ = ~ l l i n e s , respectively. The m^ =0 l i n e w i l l also be broadened somewhat beyond the T-t < ( A u ^ ) J linewidth, but by f a r the larg e s t observable e f f e c t w i l l be i n the mN=-l t r a n s i t i o n s , these l i n e s a c t u a l l y appearing s l i g h t l y l e s s intense and much wider than the mjq=-2 l i n e s . This i s the e f f e c t which on the surface appears to be observed, and which Fraenkel et a l . employ to explain t h e i r d i -nitrodurene r e s u l t s . - 124 -However, the spectral centers of the mjj=0, mN=-1, and mN='t2 l i n e s are equidistant from each other, and hence the above approach f a i l s to explain the apparent s p l i t t -ing constant anomaly. Also, the writer f a i l s to see why deuteration of the compound should remove the anomalous in t e n s i t y and linewidth behaviour. In the absence of deuterium s p l i t t i n g , a spectrum l i k e that shown l a s t i n F i g . 26 should be observed and anomalies would be c l e a r l y d i s c e r n i b l e . The second p o s s i b i l i t y , although t h i s i s considered less l i k e l y than the one previously discussed, i s that the anomalies are due to the position 4 and 6 protons only. F i g . 27 shows the spectra which would be obtained f o r the three possible isomers, again keeping the over-a l l s p l i t t i n g due to the protons (ajj^ + a ^ ) constant whenever possible. Last i s shown the sum spectrum of the above three. As before, depending upon the r e l a t i o n of to d i f f e r e n t spectra w i l l be observed, a smeared out one, exhibiting linewidth and i n t e n s i t y anomalies f o r the case T~i = (Lo^cf]'' - t n that case the outside l i n e s a r i s i n g from the s p l i t t i n g of the l i n e marked g 2» would exhibit i d e n t i c a l linewidths and i n -t e n s i t i e s , although the i n t e n s i t y r a t i o of these lines, to the center l i n e N q , would be f a r from the expected H-H, N I "2 N HQ H. No H, N. HO H, H. N-2H-1 Fig. 27. Theoretical Spectra Considering Variation in a ^ only. - 126 -value of 1:6. The l i n e s marked H Q and would also show l i t t l e linewidth anomaly, although a gross d i s c r e -pancy i n the observed i n t e n s i t i e s would be present. The nitrogen l i n e s N Q, , and would show approximately s i m i l a r linewidths and i n t e n s i t i e s i n the correct r a t i o of lr2:3:2:1. The linewidths of a l l these l i n e s would how-ever be greater than f o r l i n e s such as H 2 say. While t h i s type of approach also shows oddities i n the appear-ance of the expected spectrum, these do i n no way re-semble those which are experimentally observed. Also, the spectral centers of the nitrogen m^=0,'tl,-2 l i n e s are equidistant from each other, f a i l i n g to explain the s p l i t t i n g constant differences. The e f f e c t of deuterium substitution might be explained on the basis of th i s approach, i n contrast to the one previously described. L a s t l y we s h a l l discuss an approach employing a v a r i a t i o n of nitrogen coupling constants a ^ and a^g, simultaneously with a v a r i a t i o n of the proton coupling constants ajj^ and aHg- Fig« 28 shows the spectrum to be expected from each type of isomer. The f i r s t one shown represents the case when both nitro-groups are i n the plane of the r i n g , with a _ a . a _ a a N i " aN3 X a H 4 ~ aH6' H-N, H, H,N 2 H. N 0 H, N -I H 0 N _ 2 H _ , H . Fig.28. Theoretical Spectra Considering Variation in Both a^ and a ^ . - 128 -the r a t i o of nitrogen coupling constant to proton coupling constant being chosen so as to be consistent with experi-mental s p l i t t i n g s . Secondly i s shown the type of spec-trum to be expected from a species having both n i t r o -groups at r i g h t angles to the plane of the r i n g , i . e . a ^ 3 a a H 6 • The nitrogen coupling constants are chosen smaller f o r th i s case, since a ro t a t i o n out of the plane of the r i n g w i l l decrease fiCA/ and as a consequence a N . The set of proton coupling constants i s chosen larger than a ajj^ , and i n such a way that the ov e r a l l s p l i t t i n g i n the two species w i l l be i d e n t i c a l , that i s . a a . a a b b D b 2 ( aN! + aN 3> + a H 4 + a H 6 = 2 ( a N L + aN 3> + a H 4 + aHg Thi r d l y i s shown the type of spectrum which one might expect when one nitro-groups i s perpendicular to the r i n g plane, and here c c In t h i s case several types" of very s i m i l a r spectra can be produced, but only the simplest of these i s shown. The one spectrum reproduced here i s the one f o r which the nitrogen coupling constants d i f f e r , but obey the a N L " < a N L ~ b b s a a H 4 = a H 6 > % = - 129 -r e l a t i o n c c a a ans also f o r which c c a a These constants can of course be randomly varied as long as the conditions of constant t o t a l s p l i t t i n g i s not v i o l a t e d . The sum spectrum of these above mentioned spectra i s shown l a s t l y . Again, i f the condition Ti = (Aooq)'1 i s obeyed, then a smeared out spectrum would be observed experimentally. In the f i r s t spect-rum shown, the l a s t spectrum would take t h i s form also i f the l i f e t i m e TL of the geometrical isomers were s u f f i c i e n t l y smaller than the r e c i p r o c a l hyperfine s p l i t t i n g , the l i n e s are l a b e l l e d according to the m^  t r a n s i t i o n from which they a r i s e . Thusly, a l i n e marked would a r i s e from the proton s p l i t t i n g of an m^ =+2 l i n e . I t can be seen, f i r s t l y , that a l l the l i n e s a r i s -ing from the outside t r a n s i t i o n s w i l l show the same in t e n s i t y and linewidth, and secondly, that the i n t e n s i t y of these l i n e s to the i n t e n s i t y of l i n e s a r i s i n g from the center N q l i n e , w i l l be i n the r a t i o of approximately 1:3, and not 1:6 as would be postulated normally. Both these observations are made experimentally. The - 130 -next two l i n e s towards center, l a b e l l e d H±^, and of course the l i n e s a r i s i n g from a s p l i t t i n g of former, w i l l appear to be wider than the outside l i n e s , and w i l l i n addition appear to be of approximately equal i n t e n s i t y , c e r t a i n l y not twice as intense, as expected. Again experimental evidence supports both these state-ments. Next, towards center are the nitrogen n^=-2 l i n e s , l a b e l l e d N + 2 » a n d although one would have a very s l i g h t broadening i n the wings of the l i n e s , t h i s would be impossible to observe experimentally. The l i n e s a r i s i n g from a s p l i t t i n g of N 2 l i n e s w i l l hence appear to have roughly the same linewidths as those a r i s i n g from H 2 l i n e s , and w i l l i n addition appear a l -most normal i n i n t e n s i t y , a r a t i o of ~ 1.75:1 to the outside l i n e s being expected, not very d i f f e r e n t from the normal 2:1 r a t i o . Again, these statements are corroborated by experimental findings. The only l i n e s f o r which evidence i s not without doubt, are the ones due to a s p l i t t i n g of the H-^  l i n e s . These l i n e s would appear le s s intense and also wider than expected. This seems to be the case, cannot however be stated with certainty due to i n s u f f i c i e n t r e solution. Next are the N^ l i n e s . These again should show an increase i n l i n e -width and an anomalous i n t e n s i t y , as observed, but more important, the spectral center of these l i n e s w i l l appear - 131 -to be s h i f t e d towards center, thus making the s p l i t t i n g AuoN(^-^f^ti) smaller than the s p l i t t i n g A (A/±, —>fiJtl) This i s one of the experimentally observed f a c t s , and one which the other two approaches had f a i l e d to ex-p l a i n . Next to t h i s l i n e , the l i n e s marked H ± would appear normal i n i n t e n s i t y and linewidth, as the small broadening i n the wings could again not be observed. At the center, the N Q l i n e would appear somewhat broader than expected, but with of course considerably l e s s e r i n t e n s i t y , as already mentioned. The H ± l i n e s next to N q w i l l appear broadened and somewhat more intense than the expected r a t i o NQ/H ^ = 3/1. Again experimental evidence supports t h i s . The previous discussion has thus explained the anomalous difference i n the nitrogen coupling constants depending upon the i n t e r v a l measured, and i t does on the surface appear as i f the l i n e s a r i s i n g from m ^ ^ l t r a n s i t i o n s are broadened. This i s the observation and statement made By Fraenkel et a l . , i s however due to a combination of the nitrogen and proton coupling constant v a r i a t i o n . If we assume that the condition f o r the observation of the anomalous e f f e c t s depends more or l e s s stringently upon the v a l i d i t y of the re-l a t i o n - 132 -Then this may be used to explain the disappearance of the anomalies upon deuteration. As deuteration w i l l a l t e r the hyperfine s p l i t t i n g from the r i n g positions i n the r a t i o ffH , that i s by a factor of almost 7, the above near equality w i l l no longer be v a l i d , and now would indicate a disappearance of the e f f e c t , perhaps only a considerable reduction i n the anomalous be-haviour, causing the deuterated compound spectra to appear normal or nearly normal. Furthermore, i f the explanation presented i s correct, then the above equality may be employed to calculate the frequency of r o t a t i o n of the n i t r o -groups. This, f o r a s p l i t t i n g of ~ 4 gauss, y i e l d s a value of 1.1 x 10 ' s e c - ^ . 3) 1,4-Dinitrobenzene. - A 10~3 M solution of 1,4-Dinitrobenzene, using an 85%/l5% mixture of dimethoxy-ethane/acetonitrile as solvent, and 10~-LM i n c a r r i e r e l e c t r o l y t e , was electrolyzed at -0.63 v vs. S.C.E. to y i e l d a reddish brown solution. This solution ex-h i b i t e d a well resolved hyperfine pattern consisting of 25 l i n e s , which number i s consistent with the - 133 -t h e o r e t i c a l l y expected s p l i t t i n g from a set of two equivalent nitrogen n u c l e i (^l^-i) and one set of four equivalent protons (T^Ih = JZ ) . The experimental spect-rum i s shown i n F i g . 29, while the calculated spectrum employing aN=1.56 g and aH=1.12 g, i s shown i n F i g . 30. Agreement i s seen to be excellent. The o v e r a l l theore-t i c a l s p l i t t i n g i s 10.72 g, compared with an experi-mental t o t a l s p l i t t i n g of 10.71 g; the linewidth of a l l the l i n e s i s ~ 130 mg. No anomalous patterns were observed, except that again l i n e s to the high f i e l d side of center and not a r i s i n g from m^ =0 t r a n s i t i o n s , appear s l i g h t l y l e s s intense than corresponding low f i e l d l i n e s . As i n the two previous cases, t h i s i s explained i f the spin density at the nitrogen nucleus i s p o s i t i v e . If the molecule i s l a b e l l e d as below then the following table gives the experimentally de-termined coupling constants, due to Fischer, Maki and Geske, and Ward, as well as the calculated Hiickel spin Fig.29. EPR Spectrum of 1,4-Dinitrobenzene Anion Radical. Fig. 30. Theoretical Spectrum of 1,4- Dinitrobenzene Anion Radical, o N = 1.56 G, a H = 1.12 G. - 136 -densities and the observed ones using = -23.7 g. Table I I I . Spin Densities and Coupling Constants i n 1,4-Dinitrobenzene Negative Ion. P o s i t i o n Fischer (95) (103) £ t" ( c a l c . ) £ r(expt.) 1 .07484 2(a H) 1.12 1.12 2.3 .05014 .0473 7(a N) 1.56 1.74 4.5 .10410 9 .11038 As i n previous cases, there exists a small discrepancy between the values of the coupling constants, as observed i n t h i s i n v e s t i g a t i o n and by Maki and Geske, th i s d i f f -erence being i n a l l p r o b a b i l i t y due to the d i f f e r e n t solvents being employed. The large discrepancy between both these r e s u l t s and Ward's, i s generally explained by the assumption of t i g h t ion-complex formation, an explanation which the writer f e e l s leaves something to be desired. The calculated spin density at the r i n g carbon atoms contiguous to protons i s 0.05014, a value which compares quite well with the experimental value of 0.0473. An attempt to observe any anomalous i n t e n s i t y and - 137 -linewidth behaviour at lower temperatures, as well as attempts to observe temperature dependence of the coupling constants, f a i l e d . Spectra, recorded at 0°G, -20°C, and -40°C, were i n almost a l l respects i d e n t i c a l with the one shown i n F i g . 29, and recorded at room tempera-ture. The coupling constants at -40°G were 1.54 g f o r a N , and 1.11 g f o r a H , almost equal to the ones at +20°C within experimental error. Linewidths at the lower temperatures were s l i g h t l y decreased, being ~105 mg. The f a i l u r e to observe any temperature e f f e c t i n the 1,4-isomer, as compared with the substantial a l t e r a -t i o n of coupling constants i n the 1,2-isomer, may throw some l i g h t onto the o r i g i n of l a t t e r . I f the change i n the coupling constants i n the 1,2-anion were merely the r e s u l t of a solvation difference, most l i k e l y re-s u l t i n g i n a change of the oxygen Coulomb in t e g r a l cxD, and hence i n a change of a^, then i t i s not easy to see, why other isomers should not show thi s e f f e c t at a l l . I f on the other hand a rearrangement of the N0 2 groups i s involved, then the e f f e c t would c e r t a i n l y be much more pronounced i n the molecule ion possessing two c l o s e l y spaced bulky groups such as N0 2, than i n the 1,4-isomer, there being perhaps no e f f e c t at a l l i n the l a t t e r case. - 138 -C. Isomeric Dinitronaphthalenes. 1) Introduction. - The ESR spectra of the 1,4-, 1,5-, and 1,8-dinitronaphthalene r a d i c a l anions, have to the writer's knowledge not been previously reported i n the l i t e r a t u r e . A l l three r a d i c a l s were very e a s i l y generated by e l e c t r o l y t i c means, as were a l l the species i n v e s t i -gated i n this thesis, and although, due to the larger number of hyperfine l i n e s which are t h e o r e t i c a l l y possible, a l l l i n e s could not be resolved, an analysis of the spectra i n terms of a nitrogen coupling constant and three proton s p l i t t i n g constants, was possible. I t appears furthermore, despite the lack of perfect resolu-t i o n , that no gross anomalies i n the linewidths and i n -t e n s i t i e s e x i s t , a search f o r these being the primary reason f o r investigation of the above compounds. Espe-c i a l l y the 1,8-isomer, also the 1,5-isomer, might be thought to possess such anomalies, since the n i t r o -groups are i n a r e l a t i v e l y s i m i l a r s t r u c t u r a l arrange-ment to the 1,3-dinitrobenzene, and since no quinonoid type structures can be drawn to indicate any i n h i b i t i o n of r o t a t i o n a l freedom of the nitro-groups. The oxygen atoms of adjacent nitro-groups i n the 1,8-dinitro-naphthalene, w i l l however be i n closer proximity than i n the benzene de r i v a t i v e . A s l i g h t s t e r i c e f f e c t i s thus presumably present. - L39 -As before, a variety of pure solvents, solvent mixtures, and spectra at varying temperatures, were i n -vestigated. In the case of dimethylformamide as solvent, resolution was generally quite good, followed c l o s e l y by a mixture of dimethoxyethane and a c e t o n i t r i l e i n the r a t i o of 85% to 15%. When employing pure a c e t o n i t r i l e , however, a remarkable drop i n the degree of res o l u t i o n which could be obtained, occurred, the res o l u t i o n being so poor as to make an analysis of the spectrum i n that solvent impossible. As f a r as i t was possible to t e l l , the coupling constants showed very l i t t l e influence 016 both solvent and temperature. 2) 1,4-Dinitronaphthalene. - When a 10~^M solution of 1,4-dinitronaphthalene was electrolyzed at " -0.5 v vs. S.G.E., a brownish solution resulted, which ex-hi b i t e d the hyperfine pattern shown i n F i g . 31. The spectrum, dimethylformamide i s the solvent, consists of ^60 l i n e s , t h e o r e t i c a l l y 135 l i n e s are possible, and has an o v e r a l l s p l i t t i n g of only 9.15 g. Line-widths of p e r f e c t l y resolved l i n e s towards the edge of the spectrum are approximately 80 mg between points of maximum slope. The spectrum can be quite well approximated by the following set of coupling constants: aN=0.97 g, a H l=1.69 g, a^O.53 g, and a H s=0.41 g, and - 140 -the t h e o r e t i c a l spectrum thus obtained i s shown i n F i g . 32. The o v e r a l l s p l i t t i n g of t h i s spectrum i s 9.14 g, i n excellent agreement with the experimentally deter-mined value. Since i n the present study, we have to deal with three sets of two equivalent protons i n addition to the two equivalent nitrogen n u c l e i , there exists an am-bi g u i t y as to which po s i t i o n the various proton coupling constants should be assigned. In the absence of deu-terium substitution t h i s ambiguity cannot be resolved. One may perhaps employ the calculated Huckel spin den-s i t i e s as a guide, and t h i s i s the only lead employed i n compiling the table which follows below. The v a l i d i t y of an assignment as presented there i s admittedly open to c r i t i c i s m . I f we l a b e l the molecule as follows '3 iH Fig. 31. EPR Spectrum of 1,4- Dinitronophtholene Anion Radical. - 142 -then the following table reproduces the calculated spin d e n s i t i e s , the experimentally determined spin densities subject to the statements above and using -23.7 g f o r the proportionality constants, as well as the experi-mentally observed coupling constants. As one of the proton coupling constants i s approximately 3 times larger than the remaining two, as i s the case f o r the spin densities of one set of carbon atoms contiguous to protons, one of the assignments can be made with reasonable certainty. This assignment places the 1.69 g constant as a r i s i n g from protons 2 and 3, the protons situated on the same r i n g as the NO^ groups. I n t u i t i v e l y t h i s assignment i s also correct. The other coupling constants remain ambiguous and are consequently bracketed. Table IV. S p l i t t i n g Constants and Spin Densities i n 1,4-Dinitronaphthalene Negative Ion. Pos i t i o n 1-c ( obs . ) ^ ( c a l c . ) f i " (obs.) 1 .09225 2 ( a H i ) 1.69 .07065 .0713 5< aH 2> (0.53) .02734 (.0224) 6< aH 3> (0.41) .02093 ( .0173) 9 ' .01466 l K a j j ) 0.97 .08198 13 .09607 Fig. 32. Theoretical Spectrum of 1,4-Dinitronaphthalene Anion Radical,a N = 0.97G, a H = l .69G,a H = 0 .53G,a H =0.41 G. - 143 -3) 1,5-Dinitronaphthalene. - E l e c t r o l y s i s at -0.62 v vs S.C.E. of a 10 - 4M solution of 1,5-dinitronaphthalene i n dimethylformamide, resulted i n a reddish brown solu-t i o n , which exhibits the spectrum shown i n F i g . 33. This spectrum, under very slow scanning conditions, ex-h i b i t s 111 l i n e s , and has an ov e r a l l s p l i t t i n g of 20.70 g. The linewidths of the well resolved l i n e s i s approxi-mately 70 mg, which i s very close to the l i m i t of reso-l u t i o n of the ESR spectrometer. I t i s as a consequence possible, that the res o l u t i o n of the spectrum i s i n thi s case being l i m i t e d by the machine employed, and not by some other phenomenon, such as chemical relaxation f o r instance. The spectrum again shows l i t t l e solvent and temperature dependence and can be analyzed i n terms of the following coupling constants: a^=2.30 g, aH_^=2.82 g, aH^=2.42 g, and a j j g = 0 * 4 4 §• ^ n e th e o r e t i c a l spectrum to be expected from such a set of coupling constants i s shown i n F i g . 34. Agreement between th e o r e t i c a l and experimental spectra i s good. The calculated spin d e n s i t i e s , as well as the observed ones, subject to of course s i m i l a r s t i p u l a t i o n s as i n the previous case, are presented i n Table V. The only set of protons from which the coupling constant i s not ambiguous, i s that comprising positions 3 and 7, 3374 82 G 3373 04 G 3380-II G 3385.39 G 3382.32 G Fig. 33. EPR Spectrum of 1,5-Dinitronaphthalene Anion Radical. p in iiiii iii 11 inn mill i i in i in nun inn in i in hi i i i i i Fig. 34. Theoretical Spectrum of 1,5 - Dinitronaphthalene Anion Radical, a N =2.30 G,a H x =2.82 6, a H = 2.42 G ,a H z = 0.44 G. - 146 -the following l a b e l l i n g of the molecule i s employed. Table V. Spin Densities and Coupling Constants i n 1,5-Dinitronaphthalene Negative Ion. Po s i t i o n a^Cobs.) ^ " ( c a l c . ) f ^ o b s . ) 1 .05402 2 ( a H i ) (2.42) .07566 ( .1021) 0.44 .02956 .0186 4 ( V (2.82) .09789 ( .1190) 9 .01069 l l ( a N ) 2.30 .07429 13 .07895 - 147 -4) 1,8-Dinitronaphthalene. - When a 5 x 10_Z|M solu-t i o n of 1,8-dinitronaphthalene was electrolyzed at -0.6 v vs. S.G.E., using dimethylformamide as solvent, a greenish yellow solution resulted which exhibited the hyperfine spectrum shown i n F i g . 35. The spectrum consists of 85 l i n e s out of the possible 135, and as f a r as could be discerned, no gross anomalies were present. The linewidths of well resolved l i n e s are approximately 140 mg. I t should be mentioned, that i n the present spectrum, as well as i n the spectra of the two previously discussed compounds, the l i n e s to high f i e l d of center appear somewhat less intense than t h e i r low f i e l d counterparts, except when l i n e s a r i s i n g d i r e c t l y from m^ =0 tran s i t i o n s are considered. This i s , as discussed i n the case of the 1,2-dinitrobenzene negative ion, consistent with p o s i t i v e spin density at the n u c l e i . The present spectrum can be analyzed i n terms of the following coupling constants: aN=3.03 g, aH = 3 « 7 3 g, a H =3.63g, and a H =0.95 g, the th e o r e t i c a l spectrum derived from such a set of constants being shown i n F i g . 36. Agreement i s considered s a t i s f a c t o r y . Employing the l a b e l l i n g 3371 9 IG 337 4 7 3 G Fig. 35. EPR Spectrum Fig. 36. Theoretical Spectrum of 1,8-Dinitronaphthalene Anion Radical ,a N =3.03G,a H =3.73 G , a H =3.636,a H =0.95 G. x y z - 150 -Table VI gives the calculated and experimental spin densities and coupling constants. Table VI. Spin Densities and Coupling Constants i n 1,8-Dinitronaphthalene Radical Anion. Po s i t i o n C?L(. obs.) p t 7 ( c a l c . ) (obs.) 1 .03557 2 ( a H i ) (3.63) .12280 (.1532) 3 ( aH 2> 0.95 .00952 .0401 « V (3.73) .14121 ( .1574) 9 .00000 10 .00000 3.03 .06310 13 .06388 - 151 -D. 1,3,5-Trinitrobenzene. During the e l e c t r o l y s i s of an approximately 10"%! solution of trinitrobenzene at the f i r s t polarographic reduction potential of -0.48 v vs. S.G.E., and using a c e t o n i t r i l e as solvent, some extremely i n t e r e s t i n g and at f i r s t completely unexplicable r e s u l t s were obtained. Shortly a f t e r the s t a r t of the e l e c t r o l y s i s , the solution turned a pale pink, and began exhi b i t i n g a weak ESR spectrum. The color would increase i n i n -t e n s i t y to a bright red, this change i n color being accompanied by a growth of the ESR spectrum, shown i n F i g . 37. This spectrum consists of approximately 23 to 24 l i n e s with an o v e r a l l s p l i t t i n g of approximately 10.3 gauss. The spectrum grows i n i n t e n s i t y , as does the color, to a l i m i t i n g value, and then decays gradually, without any changes i n the applied potential and current having taken place. As the spectrum decays, a series of l i n e s , superposed on the o r i g i n a l ones, and e s p e c i a l l y noticeable outside the extreme outside l i n e s of the old spectrum, begin to appear. Accompany-ing t h i s change i s a fading of the red c o l o r a t i o n and appearance of pale brown, then more intense brown colora-t i o n . Fig. 37 EPR Spectrum of TNB~->TNB Complex. - 153 -At this stage the narrow spectrum shown i n F i g . 37 has completely disappeared and a well resolved 28 l i n e spectrum, shown i n F i g . 38 can be observed. This spect-rum i s steady i n i n t e n s i t y a f t e r a c e r t a i n time has elapsed, 15 minutes, say, and can be monitored over long periods of time. The number of l i n e s to be ex-pected from the anion r a d i c a l of 1,3,5-trinitrobenzene i s 28, i f , as i s expected, i n t e r a c t i o n of the elec t r o n i c spin with three equivalent nitrogen n u c l e i (Z1^= S) and a set of three equivalent protons i s present. I t should be mentioned that Lagercrantz and Yhland (88,93) and Ward (90) have observed photo-induced paramagnetism i n solutions of s-trinitrobenzene i n donor solvents, that however only one dominant nitrogen s p l i t t i n g appears to be observed. S p l i t t i n g from 3 "equivalent" protons also appears to be present, an unexpected and unexplained behaviour. The 28 l i n e spectrum i s assigned to the 1,3,5-trinitrobensene anion r a d i c a l . I t can be perf e c t l y analyzed i n terms of the two coupling constants a-^ =2.48 gauss, and ajj=4.14 gauss. The th e o r e t i c a l spectrum to be expected from such a set of constants i s shown i n F i g . 39, and agreement between i t and the experi-mentally obtained hyperfine pattern i s seen to be excellent. The the o r e t i c a l o v e r a l l s p l i t t i n g s i s 3391 69 G Fig. 38. EPR Spectrum of 1,3,5-Trinitrobenzene Radical. i Fig. 39. Theoretical Spectrum of 1,3,5-Tri nitrobenzene Anion Radical, N = 2.48 G a H =4.14 G. - 156 -27.3 g, to be compared with 27.31 g f o r the experimental value. The r a d i c a l anion of s-trinitrobenzene, l a b e l l e d as follows possesses Dg^ symmetry, and possible molecular o r b i t a l s comprising the 18 electron, 15 center ~[f-electron t! " t system, may possess A^ , A 2 , or E" symmetry, the A^ , « t A 2 , and E l e v e l s being disallowed because of the re-quired antisymmetry with respect to the plane of the heavy atoms. A Huckel treatment of the above molecule shows that the f i r s t two u n f i l l e d o r b i t a l s are ener-ti g e t i c a l l y degenerate, that i s possessing E symmetry. The spin densities corresponding to the o r b i t a l s are given i n columns 2 and 3 of Table VII below. - 157 -Table VII. Spin Densities and Coupling Constants i n s-Trinitrobenzene Anion Radical. P o s i t i o n t r < B " > i ) 2 ^"(obs.) a^( obs.) a. (103) 1 .02972 .00408 .01690 2 .00722 .24965 .12843 .1747 4.14 4.1 3 .02004 .01376 .01690 4 .22580 .03106 .12843 5 .00095 .03285 .01690 6 .15228 .10459 .12843 7 .11826 .01627 .06726 2.48 7.0 8 .07975 .05477 .06726 9 .00378 .13074 .06726 10,11 .10614 .01460 .06037 12,13 .07158 .04916 .06037 14,15 .00339 . .11735 .06037 From t h i s table, i t can be seen that the spin densities f o r equivalent positions are not i d e n t i c a l within each o r b i t a l . The experimental spectrum does however i n -dicate that t h i s cannot be the case. One p o s s i b i l i t y i s that the degenerate o r b i t a l s are not a c t u a l l y de-generate, that i s Jahn-Teller d i s t o r t i o n s may have s p l i t the energies so subs t a n t i a l l y as to cause one of these - 153 -l e v e l s to be p r e f e r e n t i a l l y occupied by the unpaired electron. The second p o s s i b i l i t y i s to consider a l i n e a r combination of the degenerate e " molecular o r b i t a l s . Let us represent the f i r s t molecular o r b i t a l of the degenerate p a i r as where the <j>^ are the 15 atomic p o r b i t a l s centered on the heavy atoms, and the C^ are the c o e f f i c i e n t s , the squares of which are given i n Column 2 of Table VII. Let the second molecular o r b i t a l , i n terms of the same atomic o r b i t a l s but d i f f e r e n t c o e f f i c i e n t s C^', be represented by i-l 1 2 where (C^) i s given i n column 3. Now by d e f i n i t i o n , i f the degenerate molecular o r b i t a l s and ^ are solutions of the Schrodinger equation, so i s any l i n e a r combination thereof, namely ay+it/i-Z (aeries) "T3 - 159 -The c o e f f i c i e n t s should be such, that ( C ^ ) 2 = <C 3") 2 = C C / ) 2 ( G 2 ) 2 = ( G 4 r = (G 6 r ( G 7 " ) 2 = ( C 8 ' ) 2 = ( G 9 " ) 2 and ( G 1 0 " ) 2 = ( G n " ) 2 = ( G 1 2 " ) 2 = ( G 1 3 " ) 2 = ^ C \ ^ = ( G 1 5 The following c o e f f i c i e n t s a and b w i l l s a t i s f y this condition: The molecular o r b i t a l c^j w i l l thus take the form «-/ and the spin densities at positions i w i l l be given by Column 4 i n Table VII gives the spin densities calculated by t h i s method, and i t i s seen that f o r equivalent posi-t i o n s , i d e n t i c a l spin densities are present. This i s i n agreement with experimental facts of fi n d i n g only one nitrogen and one proton coupling constant. In the - 160 -same table, the observed coupling constants from th i s i n v e s t i g a t i o n and that of Ward (103) are presented, along with the experimental spin densities \^ h b Agreement i s not impressive. Upon increasing voltage and current beyond the f i r s t reduction p o t e n t i a l , further color and ESR changes are observed. These w i l l be described a f t e r an attempt has been made to interpret the already discussed spectra, more prec i s e l y t h e i r sequence of appearance. It i s a well known fac t that s-trinitrobenzene, along side many other compounds, i s capable, acting as an electron acceptor, to form an intermolecular compound, c a l l e d a charge transfer or electron-donor-acceptor (EDA) complex with a second molecule, which acts as the electron donor. Many s-trinitrobenzene complexes are known, an example i s naphthalene-trinitrobenzene, and f o r further discussion and many i l l u s t r a t i v e examples, the reader i s referred to Briegleb's monograph (108). Whereas the majority of these complexes are between neutral molecules, a class of compounds e x i s t s , i n which complexes between ions and neutral molecules are formed. Examples are, for instance, the s-trinitrobenzene/halogen ion complexes (108) and (109). More recently Le Goff and La Count (110) - 161 -have observed that a complex i s formed between 1,2,3,4,5-pentacarbomethoxycyclopentadienyl anion and t r i n i t r o -benzene. I t should also be mentioned that "self-complexes" between ions such as Wiirster's blue cations and between N-ethylphenazyl r a d i c a l s have been observed by Hausser and Murrell (111), and that these authors have also suggested the p o s s i b i l i t y of complex formation between aromatic ion r a d i c a l s and neutral aromatic molecules. The postulate i s thus put forward, that the present sequence of color changes, ESR changes, and o p t i c a l spectrum changes to be discussed l a t e r , can be explained i n terms of a complex, i n which a neutral molecule of 1,3,5-trinitrobenzene w i l l play the part of an electron acceptor, while an anion r a d i c a l of the same compound, formed by electrochemical reduction, acts as electron donor. The complex may be represented as TUB" — » TNB. Since a l l t h i s i s speculative to a c e r t a i n extent, not much more w i l l be said about the geometry of such a complex. Presumably the two rings of the constituent molecule and ion w i l l be superposed i n some manner, perhaps to give a staggered configuration, as below - 162 -0-... ...o 0 0 0 o with the 7T - o r b i t a l s of the two systems d i r e c t l y super-posed, perhaps with one r i n g somewhat displaced r e l a -t i v e to the other, as below r - 163 -i n which case IF -overlap, though to a les s e r degree i s s t i l l possible. Other configurations are of course also possible. In complexes made up of neutral mole-cules, the partners, i n the absence of dipole-induced dipolar i n t e r a c t i o n s , w i l l generally be positioned so as to give maximum overlap of wavefunctions, i f how-ever dipolar interactions are appreciable, a compro-mise between maximum overlap and dipolar interactions must be struck. In the case of neutral r a d i c a l s and ion r a d i c a l s , as i n t h i s case, simple considerations of overlap without the use of numerical evaluations, w i l l not determine the geometry of the complex formed. Consequently nothing more w i l l be said regarding the actual shape of the complex. The sequence of events which i s thought to occur and to be observed experimentally i s as follows. The r a d i c a l anion formed, brown i n color, i n the reaction TNB + e" — > t n b " i s complexed r a p i d l y by a neutral trinitrobenzene molecule to form the postulated complex, red i n color, v i a TNB" + TNB > TNB~ TNB - 164 -This process w i l l continue u n t i l a l l , at l e a s t a large majority, of the o r i g i n a l neutral compound i s i n the form of the complex, i . e . at t h i s stage approximately 50% of the s-trinitrobenzene has been reduced. A simple c a l c u l a t i o n shows, assuming 100% current e f f i -ciency, that t h i s would take ca. 1 minute. Due to the equilibrium d i s s o c i a t i o n of the complex k L _ TNB + TNB s==£ TNB -> TNB Z—^ TNB + TNB the reduction of neutral molecule w i l l proceed past the " a l l complex" stage i f k^/lc-, < 1. As the complex gradually disappears, the red color fades, as does the i n t e n s i t y of the narrow spectrum, and i s gradually replaced by the brown color and spectrum of the uncom-plexed r a d i c a l anion. I t should be mentioned here, that when using a mixture of 85% dimethoxyethane/l5% a c e t o n i t r i l e as solvent, the narrow spectrum could not be obtained. Rather a spectrum showing an o v e r a l l s p l i t t i n g of ca. 27 gauss over 24-25 l i n e s was obtained at -0.48 v vs. S.C.E. This spectrum i s thought to be due to the r a d i c a l anion, the s p l i t t i n g constants being d i f f e r e n t due to solvent e f f e c t s , not permitting complete resolution - 165 -of a l l 28 l i n e s . The f a c t that i n a non-polar solvent mixture the postulated complex i s not formed, i s con-s i s t e n t with the idea that complex formation involving i o n i c species i s hindered i n non-polar solvents. Additional support f o r the above postulated dimer and sequence of changes, are the changes observed i n the o p t i c a l spectrum during e l e c t r o l y s i s . Shortly a f t e r s t a r t of the e l e c t r o l y s i s , two peaks which are not observed i n the spectrum of s-trinitrobenzene solutions, using a c e t o n i t r i l e as solvent, made an appearance, one at 438 -w^, the other at 556 ^ nyu. These bands are found i n addition to trinitrobenzene bands at 290 "iy*, due to a TT—^ir t r a n s i t i o n . These tra n s i t i o n s have been i d e n t i f i e d by Abe (112,113), and Doub and Vandenbelt (114), and the 290 *y* band i s thought to correspond to the benzene 'fl,^ —-> ' 32u tran-s i t i o n at ca. 260 toy*. In the trinitrobenzene solution, t o t a l absorption i s observed below ~270 , probably due to further tt—^tt* t r a n s i t i o n s (benzene 180 -TJIand 200 <ryu t r a n s i t i o n s ) . Both of the new bands grow simul-taneously i n i n t e n s i t y with duration of e l e c t r o l y s i s , and a spectrum as shown i n F i g . 40 r e s u l t s . The short wavelength band i s more intense than the band at 556 -*y< and also possesses a much sharper appearance. The band Fig.40. Optical Spectrum of s-Trinitrobenzene in C H 3 C N During Electrolysis at -0.48V vs. S.C.E. - 167 -toward long wavelength i s much wider and more asymmetric, showing a smaller slope on the short wavelength than on the long wavelength side, o v e r a l l an appearance very c h a r a c t e r i s t i c of well known and i d e n t i f i e d charge transfer bands. This band has consequently, additional support f o r the assignment follows, been assigned to a t r a n s i t i o n of an electron from one constituent part of the complex to a l e v e l on the partner constituent. Upon prolonged e l e c t r o l y s i s , the solution, as before, changes color from red to brownish, t h i s stage coinciding with the appearance of the negative ion ESR spectrum, the change being accompanied by a d r a s t i c decrease i n i n t e n s i t y of the long wavelength band, and a s h i f t of the 438 ryt band to 465 *yt. The 438^ ?7^ < band i n the complexand the 465*yt i n the new spectrum (at which stage i t i s assumed that only anion, at lea s t a large excess over other species, i s present) are thought to be due to an electron t r a n s i t i o n of the r a d i c a l anion, the s h i f t of 27 ny* being due to the perturbing influence of the second trinitrobenzene r i n g . A c h a r a c t e r i s t i c spectrum observed at t h i s stage i s shown i n F i g . 41. 'The appearance of the 465 ^rryu-band i s such that a weak shoulder to the short wavelength side may be i n d i c a t i v e of a band. I t might be due to 3000 4000 5000\ 6000 7 0 0 0 A I I I 1 1 L Fig. 41. Optical Spectrum at Stage When T N B " is Largely Present. - L68 -the negative ion also, i s however more l i k e l y due to a small remnant concentration of complex. A shoulder at ~560'tf^ also remains. I t i s i n t e r e s t i n g to note here that Kemula and Sioda (115) have observed two peaks, at 435 <y and 465-^, during e l e c t r o l y s i s of a 10 M solution of nitrobenzene. Both bands are ascribed to r a d i c a l anion t r a n s i t i o n s . In F i g . 41, a new band at 355 <ryA can be observed. I t i s not known what the o r i g i n of t h i s band may be. If at any stage during the e l e c t r o l y s i s the current i s cut o f f , the 438 and 556 rji bands decrease i n i n -tensity and completely disappear. However, a comple-te l y c o l o r l e s s solution cannot be regenerated, rather a pale yellowish solution remains. Presumably the de-composition of the anion and the complex proceeds i n a fashion more complicated than a simple reversal to neutral molecule by l i b e r a t i o n of an electron to either electrodes or vessel walls etc. I t may thus be well true that the new band i s due to some decomposition product of the anion or complex, or both. To test whether a l l of the trinitrobenzene could be recovered a f t e r a c e r t a i n e l e c t r o l y s i s time, use was made of the charge transfer complex which s - t r i n i t r o -benzene forms with N,N-dimethylformamide. The GTG shows - 169 -bands at 445, 480, aid 520 -m^. A. plot of o p t i c a l density vs. concentration was prepared f o r a series of t r i n i t r o -benzene concentrations ranging from 10"^ to lO'^M, re-s u l t i n g i n an almost l i n e a r plot f o r a l l three peaks. Now an amount of trinitrobenzene, close to the quantity required to make an approximately 10~%1 solution, was placed into the e l e c t r o l y s i s c e l l , N,N-dimethylformamide added, and the o p t i c a l density of the charge-transfer bands measured to obtain the exact molarity of the solu-t i o n from the previously prepared c a l i b r a t i o n p l o t . The N,N-dimethylformamide was then boiled off under high vacuum, and an equivalent quantity of the e l e c t -r o l y s i s solvent, a c e t o n i t r i l e , was d i s t i l l e d into the c e l l . The e l e c t r o l y s i s and recording of o p t i c a l spectra was then car r i e d out, and a f t e r a c e r t a i n e l e c t r o l y s i s time, the a c e t o n i t r i l e again boiled o f f , N,N-dimethyl-formamide readded, and the residual trinitrobenzene concentration determined from the GTC band i n t e n s i t i e s . The t o t a l amount of TNB i n i t i a l introduced, could never, even a f t e r short e l e c t r o l y s i s time, be f u l l y recovered. Unfortunately time did not permit making a complete quantitative study. However, the above f a c t shows that the band appearing at 355 may e a s i l y be a decomposition product band. - 170 -I t has been mentioned, that a series of further changes i n the ESR spectrum, and also i n the color of the solution, may be observed, i f the potential i s increased to -0.72 v vs. S.G.E., the second polaro-graphic reduction p o t e n t i a l , and beyond. An increase i n potential to -0.72 v re s u l t s i n an i n t e n s i f i c a t i o n of the brown color, present from generation of the anion r a d i c a l , at times the solution appearing almost black. Further l i n e s can be observed, and a tr a n s i t o r y ESR spectrum, shown i n F i g . 42, can be isolated.' This spectrum however changes continuously u n t i l the spectrumylhown i n Fig.,- 43 i s observed. Accom-panying these changes i n the ESR spectrum are color changes brown to deep brown to black, and f i n a l l y yellow upon stoppage of the e l e c t r o l y s i s . Formation of a f i n e , f l o c c u l e n t , pale brown p r e c i p i t a t e i s also observ-ed. At t h i s stage the* sample exhibits the o p t i c a l spectrum shown i n F i g . 44, from which i t can be seen that the postulated "charge transfer" band has comple-t e l y disappeared, consistent with the idea-that no complex, or very l i t t l e , i s present by the time the negative ion ESR spectrum i s observed. A l so the 465 'ryu. band, thought to be due to the anion r a d i c a l has been very much weakened, while the 355 ^ band, possible due H -> Fig. 43. Final EPR Spectrum -from Electro-lysis Beyond -0.48 V vs. S.C.E. 3000 4000 5000 6000 7 0 0 0 A Fig. 44. Opticol Spectrum of Decomposition Products After Electrolysis Beyond -0.48V vs. S.C.E. - 174 -to a reaction product, has increased considerably i n i n t e n s i t y . The formation of a pr e c i p i t a t e i s also good i n d i c a t i o n of a subsidiary reaction. What these reaction products are i s not known at th i s time, and further work along these l i n e s seems desirable. One of the compounds which can be ruled out as a reaction product, perhaps more accurately, a r a d i c a l which does not occur during the observed sequence of events, i s the r a d i c a l anion of 2,2',4,4',6,6'-hexanitrobiphenyl. When a 10 solution of th i s com-pound i n a c e t o n i t r i l e i s electrolyzed, a brownish solu-t i o n r e s u l t s , which exhibits the ESR spectrum shown i n F i g . 45. This spectrum consists of ca. 90 l i n e s , does however not resemble any of the spectra obtained during the trinitrobenzene e l e c t r o l y s i s . The r a d i c a l anion of the hexanitrobiphenyl can t h e o r e t i c a l l y exhibit 225 l i n e s , and due to the considerably l e s s e r number of l i n e s observed, no attempt to analyze the spectrum was made. E. General Results and Conclusions. From the general appearance of the d i n i t r o - and t r i n i t r o - a n i o n r a d i c a l spectra, i t becomes apparent that the r a d i c a l s giving r i s e to them can be divided - 175 -into three classes, depending upon the o v e r a l l s p l i t t i n g found. Perhaps two major classes, and a subdivision of one of these into two subclasses, should be considered. One of these major classes has an o v e r a l l s p l i t t -ing of approximately 30 gauss, and comprises the r a d i -c a l anions of 1,3-dinitrobenzene, 1,3,5-trinitrobenzene, and 1,8-dinitronaphthalene. Examination of the corre-sponding tables giving the Hiickel spin density d i s t r i -bution, shows that these three compounds possess posi-tions at which the spin density i s zero or quite small, which as -.mentioned e a r l i e r , generally implies the presence of negative spin densities when more refined approaches f o r t h e i r c a l c u l a t i o n are employed. Another method of d i f f e r e n t i a t i o n employs the so-called " s t a r r i n g " procedure (116), the s t a r r i n g occurring i n such a way that at l e a s t one nitrogen atom i s starred. This s t a r r i n g procedure r e s u l t s i n the systems shown i n F i g . 46, f o r a l l the compounds investigated, also nitrobenzene. Now i t i s e a s i l y seen that a l l the -systems considered are analogous to hydrocarbon alternate systems, as a l l starred positions have unstarred neighbors only, and vice versa. I t i s furthermore noticed that i n any of the systems which FiQ.45.EPR Spectrum of 2 2 ' 4 4 ' 6 f i ' * ^ , ^ , 4 , 6 , 6 Hexanitrobiphenyl Anion Radical in C H 3 C N Fig.46. Starring in Nitroaromatic Compounds. - 177 -exhibit a wide hyperfine spectrum, none of the symmetry operations of the p a r t i c u l a r point group w i l l exchange a.'starred f o r a unstarred p o s i t i o n . Maki and Geske (95) f i r s t employed t h i s type of d i f f e r e n t i a t i o n , and stated that negative spin densities may occur i n the p o r b i t a l s of the unstarred atoms of such systems. Now, t h i s i s a concept which i s very f a m i l i a r f o r hydrocarbon r a d i c a l s (38,77) q u a l i t a t i v e l y , and which i s rigorously proved by McLachlan (117,118). I t must however be stated that the above i s only true for. neutral r a d i c a l s of alternant hydrocarbons, not f o r i o n i c species. Indeed, i f the above argument were true, i t would imply a negative spin density at the or Z QKn. 5 positions i n rn-dinitrobenzene anion, or at the 3, 6, and 10 positions i n the 1,8-dinitronaph-thalene anion, i t would imply the absence of negative spin densities i n such systems as naphthalene and pyrene negative ions, implications which, from SCF calculations (119), are known to be f a l s e . In Appendix I, some of these SCF.calculation r e s u l t s are presented f o r comparison purposes. In t h i s l i g h t , one should perhaps use the f a c t that wide spectra are obtained from r a d i c a l s i n which symmetry operations, do not exchange starred and unstarred positions, more as a rule of thumb, than as a rule with t h e o r e t i c a l foundation. - 178 -For the other molecular systems represented i n F i g . 46 some of the symmetry operations w i l l exchange starred f o r unstarred positions. I t i s f o r these compounds, as exemplified by 1,5-dinitronaphthalene anion, where the operations and d£. of the point group C 2 v exchange positions, that narrower spectra are observed. The above arguments and Appendix I w i l l again show that i t cannot be due to the absence of negative spin densities as implied by Maki and Geske. The second major c l a s s , as t y p i f i e d by 1,5-dinitronaphthalene anion, gives r i s e to spectra which are approximately 10 to 20 gauss i n o v e r a l l widths. This group contains the remaining n i t r o compounds investigated i n the present the s i s . I t w i l l however be noticed that two of the spectra, those of the 1,4-dinitrobenzene and 1,4-dinitronaphthalene r a d i c a l anions show a considerably smaller t o t a l s p l i t t i n g , 10.71 and 9.14 gauss, respectively, than the 1,2-dinitrobenzene and 1,5-dinitronaphthalene anion r a d i -c a l s . For both of these r a d i c a l s quinonoid type structures may be drawn, i . e . - 179 -and i t i s possible that a larger spin density than anticipated by Hiickel theory w i l l be situated on the oxygen atoms, or the carbon atoms to which the n i t r o -groups are attached, which w i l l not, of course, con-tribu t e to the o v e r a l l s p l i t t i n g , except f o r the spin p o l a r i z a t i o n contribution of the CN and ON bonds to a^. For 1,2-dinitrobenzene anion r a d i c a l , a quinonoid structure may also be drawn, but as t h i s type of s t a b i l i z a t i o n implies coplanarity of the nitro-groups and the r i n g system, s t e r i c reasons make such a structure very u n l i k e l y . Apart from the attempt to explain the anomalous l i n e width and i n t e n s i t y behaviour i n the 1,3-dinitro-benzene anion r a d i c a l , and of course a search f o r further such anomalies, the i n v e s t i g a t i o n of the - L80 -nitroaromatic derivatives was undertaken to see i f the coupling constant a^ of the nitrogen nucleus i n the nitro-group, can be related to the spin densities on the nitrogen atoms, and perhaps also to that of adjacent atoms. Since i t had been found by Garrington and Santos-Veiga (49) and others (129,130) that the r a t i o was nearly constant f o r a series of nitrogen hetero-c y c l i c s , i . e . that a re l a t i o n s h i p of the type e x i s t s , although Henning and De Waard (47) disagree with the v a l i d i t y of the r e s u l t s , an equation of this type was f i r s t tested. The r a t i o s °tNj^ f ° r the compounds investigated, along with ct^f^J" f o r nitrobenzene, are given i n Table VIII beloxv. Table VIII. Q.Js of Nitroaromatic Radical Anions. Compound a a/ Nitrobenzene 45.73 1,2-Dinitrobenzene 26.08 1,3-Dinitrobenzene 39.55 1,4-Dinitrobenzene 14.99 1,3,5-Trinitrobenzene 36.87 1,4-Dinitronaphthalene 11.83 1,5-Dinitronaphthalene 30.96 1,8-Dinitronaphthalene 47.43 - L81 -For nitrobenzene, the experimental r e s u l t s of Maki and Geske (94) have been employed along with the calculated Huckel spin densities shown i n Table IX. The l a b e l l i n g of the system i s while the coulomb and exchange in t e g r a l s previously quoted, were employed. Table IX. Spin Densities and Coupling Constants i n Nitrobenzene Anion Radicals. P o s i t i o n a ±( 79) ^ r ( c a l c . ) 1 .03979 2 3.39 .10546 .1430 3 1.09 .00492 (-).0460 4 3.97 .12439 .1675 7 10.32 .22568 8 .19467 - 182 -From Table VIII i t i s e a s i l y seen that a r e l a t i o n of the McGonnell type cannot exist f o r the n i t r o -d e r i v a t i v e s , a v a r i a t i o n i n from 11.83 to 47.43 being observed. Although i t may be argued that the Huckel spin densities do not represent a true picture of the spin d i s t r i b u t i o n i n the anions, they are nevertheless not so crude as to completely i n v a l i d a t e the range of djs observed. The next simplest type of equation to test would be of the type f o r which Henning and De Waard (47) and other workers culated and observed a^. The systems, however, were N-heterocyclics, and although the adjacent atoms i , over which the spin density i s summed, may be d i f f -erent i n that they may be ordinary r i n g carbons or bridge carbons, they are nevertheless carbon atoms, and a s i m i l a r f o r the two tjrpes may be expected. In the case of the NO^ grouping, the ^•T" would be extended over carbon and oxygen atoms, f o r which a s i m i l a r should not be very meaningful. As a consequence, the type of equation tested next, and have found quite acceptable agreement between c a l -- 183 -one which showed an acceptable f i t between calculated and experimental r e s u l t s , i s an intermediate between the above type and the more elaborate equation of Rieger and Fraenkel (48). The equation employed i s of the form In t h i s equation (x.0/j f 0 represents the contribution to the nitrogen s p l i t t i n g a^ of the spin p o l a r i z a t i o n of the NO bond by the spin density on the oxygen atom, QCKj ^ represents the contribution to a^ of the spin p o l a r i z a t i o n of the CN bond by the spin density at the r i n g carbon to which the n i t r o -group i s attached, and i s a "constant", which i n -cludes the spin p o l a r i z a t i o n of the NO and CN bonds by the nitrogen spin density, and terms representing the Is p o l a r i z a t i o n and contribution to the 2s p o l a r i -zation by the lone pair electrons. That i s , K N might be written in-analogy to Rieger and Fraenkel's t r e a t -ment of the cyano-group nitrogen, as A l e a s t squares treatment of the three d i n i t r o -benzene and the three dinitronaphthalene derivatives - 184 -simultaneously, yielded the following best constants: f and the calculated coupling constants using these, along with coupling constants f o r nitrobenzene and trinitrobenzene r a d i c a l s , and not used i n the c a l c u l a -t i o n of the constants, are given i n Table X, along with the experimental values of a^. I t was also found that a considerably better f i t between the experimental and calculated nitrogen coupling constants could be obtained, i f d i f f e r e n t values of are used, depending upon whether one or two aromatic rings are present i n the compound. For the isomeric dinitrobenzenes, the values of the "constant" which gave best agreement with experi-ment i s 172, while f o r the isomeric dinitronaphthalenes, a larger value of K^, namely 185, gives a better f i t . The calculated coupling constants using d i f f e r e n t K N are given i n the l a s t column of Table X. The i n -dependent nitrobenzene and trinitrobenzene constants show remarkably good agreement. - 185 -Table X. Experimental and Calculated Nitrogen Coupling Constants i n Nitroaromatic Anion Radicals. Compound a N(obs.) a N ( c a l c . ) a^j( calc.) Nitrobenzene 10.32 11.68 10.10 1,2-Dinitrobenzene 2.82 2.97 2.21 1, 3-Dinitrobenzene 3.99 4.75 4.04 1,4-Dinitrobenzene 1.56 2.76 2.03 1,3,5-Trinitrobenzene 2.48 3.17 2.70 1,4-Dinitronaphthalene .97 1.08 1.57 1,5-Dinitronaphthalene 2.30 1.96 2.40 1,8-Dinitronaphthalene 3.03 2.05 2.43 In obtaining the above constant, several assump-tions have to be made. The two most important are that the coupling constants a ^ ( i ) must a l l have the same sign, and furthermore that the spin densities employed are correct. The f i r s t i s questionable, the second i s almost c e r t a i n l y incorrect. Much could be said about corrections which have been introduced, as the McLachlan approach of considering atom-atom p o l a r i z a b i l i t i e s f o r instance, and also about the assumptions which are made i n regard to selection of the various parameters involved i n the c a l c u l a t i o n s . - 186 -For discussions of some of the d i f f i c u l t i e s to be en-countered, the reader i s referred to standard texts and Rieger and Fraenkel's paper on cyano derivatives (43). I t i s f e l t however that the relationships given i n the present work, namely f o r one-ring nitroaromatics, and f o r two-ring nitroaromatics, do present a guide as to the approximate nitrogen s p l i t t i n g to be expected from a p a r t i c u l a r n i t r o compound. The independent r e s u l t s seem to bear this out. To obtain any accurate c a l c u l a t i o n of the s p l i t t i n g constants i n terms of the various parameters, i t i s f e l t that a new theore-t i c a l approach, not an adjustment of various parameters ott ft, etc., and introduction of correction terms i s needed. Furthermore, i t can be seen from Table X, that i f we believe the Hiickel spin densities and proportion-a l i t y constants meaningful, and hence the calculated s p l i t t i n g constants, then the largest discrepancies are found i n r a d i c a l s i n which s t e r i c e f f e c t s may be - 187 t present, as i n 1,8-dinitronaphthalene anion, and i n 1,2-dinitrobenzene anion, i n which case they most ce r t a i n l y are present. The two compounds which show the next largest discrepancy are 1,4-dinitrobenzene and 1,4-dinitronaphthalene, f o r both of which quino-noid type resonance i s l i k e l y present. For a l l other compounds, the agreement i s remarkably good. A complete temperature e f f e c t , solvent effect,, and s t e r i c influence e f f e c t , study should be under-taken to elucidate what s p e c i f i c factors need be taken into account. 9 - 188 -Chapter IV. ESR Spectra of Gyanoaromatics. A. Introduction. A system of compounds which had not been pre-viously investigated, and which, i t was hoped, would y i e l d information regarding the re l a t i o n s h i p of n i -trogen coupling constants to spin d e n s i t i e s , are the cyano-derivatives of benzene. To t h i s end we had hoped to investigate the three isomeric dicyano-benzenes, 1,2,4,5-tetracyanobenzene, 7,7'8,8'-tetracyanoquinodimethane, and several others. The singly substituted deri v a t i v e , b e n z o n i t r i l e , has a l -ready been investigated by Ward (120). For the above compounds, excepting the 1,3-dicyanobenzene system, f o r which only a weak and unresolved signal could be observed, complete experi-mental r e s u l t s had been obtained, when two very com-plete papers by Fraenkel et a l (48,100) were published, describing experimental r e s u l t s very s i m i l a r to ours, and also presenting calculations along l i n e s which we had hope to follow. In one compound however, Fraenkel et a l . observed only one broad l i n e , t h i s compound being 7,7'8,8'-tetracyanoquinodimethane anion r a d i c a l , while we were able to obtain a well resolved spectrum - 189 -of 45 major l i n e s , allowing a complete assignment of proton and nitrogen coupling constants to be made. A 13 large number of C l i n e s were also observed, and a complete assignment of the coupling constants was possible (121). Apparently a resolved spectrum of the TCN& anion r a d i c a l , produced by chemical reduction with lithiu m metal i n tetrahydrofuran, has been obtained by P h i l l i p s (122). As a consequence, only the l a s t -mentioned compound i s treated i n considerable d e t a i l , while a l l other r e s u l t s , agreeing c l o s e l y with those of Fraenkel et a l . , are presented shortly, and only f o r comparison purposes. S i m i l a r l y the molecular o r b i t a l calculations due to Fraenkel, as well as the derived spin density-coupling constant r e l a t i o n s , are employed. Since publication of Fraenkel et al.» s r e s u l t s , Nakamura and Deguchi (123) have published the spectrum of 1,2-dicyanobenzene anion r a d i c a l , while Garrington and Todd (124) have published spectra of the 1,2- and 1,4-isomers. B. Isomeric Dicyanobenzenes. 1) 1,2-Dicyanobenzene. - When a 10 solution of 1,2-dicyanobenzene i s reduced cathodically at ~1.1 v - 190 -vs. S.C.E., and using a mixture of ~ 75% dimethoxyethane and " 25% a c e t o n i t r i l e as solvent (lG'^M i n supporting e l e c t r o l y t e ) , a lemon-yellow solution i s obtained, which exhibits the ESR spectrum shown i n F i g . 47. The spec-trum consists of prec i s e l y 45 l i n e s , the number to be expected from an anion r a d i c a l i n which hyperfine s p l i t t i n g arises from a set of two equivalent nitrogen n u c l e i C£j,Tw= ^ ) and two sets of two equivalent protons each, (2XIH- I ) . The spectrum can be analyzed i n terms of the three coupling constants aN=1.80 g, an^= 0.45 g, and a =4..16 gauss, and i s consistent with a "4 r a d i c a l anion, as below: Here again ambiguity exists as to the assignment of the proton coupling constants, and, i n the absence of deuteration r e s u l t s , the calculated spin densities (48) are employed as a guide. The the o r e t i c a l spectrum to be expected from such a set of coupling constants 3401.29 G 3387.72 G 3395.00 G Fig.47. EPR Spectrum of 1,2-Dicyanobenzene Anion Radical. - 192 -i s shown i n F i g . 48, and agreement i s seen to be s a t i s -factory. In Table XI are presented the calculated and ex-perimentally obtained spin d e n s i t i e s , along with coupl-ing constants found: Table XI. Coupling Constants and Spin Densities i n 1,2-Dicyanobenzene Anion Radical. P o s i t i o n a^(Fischer) a^lOO) a i(123) a.(124) X ^ ( a ) "^( expt.) 1 .2006 .2417 3 ( a H ) 0.45 0.42 0.37 0.33 .0107 -.0467 ^0190 4 ( a H 4 ) 4.16 4.13 4.11 4.24 .1393 .1568 .1755 7(a N) 1.80 1.75 1.75 1.80 .0637 .0565 9 .0858 .0918 a - Hiickel M.O. Calculation, b - McLachlan Calculation. The analyses by the various experimenters are a l l i n agreement, leaving l i t t l e doubt as to the correct-ness of the i n t e r p r e t a t i o n . Agreement between calculated and observed spin densities i s quite poor. Fig.48. Theoretical Spectrum of 1,2- Dicyanobenzene Anion Radical, a^ =1.80 G, a H = 0.45 G, a H = 4-16 G. - 194 -2) 1,4-Dicyanobenzene. - When a 10' solution of 1,4-dicyanobenzene i s electrolyzed at * -1 v vs. S.C.E., and using approximately 75% dimethoxyethane and 25% a c e t o n i t r i l e as solvent, a lemon-yellow solution, as f o r the 1,2-isomer, i s obtained. A spectrum of 9, rather wide l i n e s i s observed. An increase of the potential to ~" -1.2 v vs. S.C.E. gives a spectrum showing additional l i n e s , and the spectrum obtained at t h i s p o t e n t i a l , and at -40°C, i s shown i n F i g . 49, This anomalous behaviour of observing a well resolved spectrum at the second reduction potential of tere-p h t h a l o n i t r i l e has also been observed by Rieger and Fraenkel, who explain t h i s phenomenon by assuming rapid intermolecular electron exchange between r a d i c a l anion and molecule to broaden the 25 l i n e anion spectrum to 9 l i n e s . Reduction at the higher potential y i e l d s the diamagnetic dinegative ion, and a reaction product of l a t t e r , b e n z o n i t r i l e , the anion of which acts as a scavenger to remove traces of neutral 1,4-dicyanobenzene. The resolved spectrum consists of 25 major l i n e s , the number to be expected from the anion r a d i c a l i f s p l i t t i n g from two equivalent nitrogen-14 n u c l e i and one set of four equivalent protons (ZT^-x.) occurs. The additional very weak indications of l i n e s may be Fig. 49. EPR Spectrum of 1,4-Dicyanobenzene Anion Radical. - 196 -due to C ^ s p l i t t i n g , they may be due to secondary species formed during the e l e c t r o l y s i s . Isotopic en-richment, by Rieger and Fraenkel, seems to suggest 1 q G s p l i t t i n g s , however our r e s u l t s are inadequate to make a d e f i n i t i v e assignment. The spectrum obtained can be analyzed i n terms of two coupling constants, aN='1.79 gauss and a H =1.61 gauss. The th e o r e t i c a l spectrum obtained from" a set of n u c l e i as described above, and employing the above coupling constants, i s shown i n F i g . 50. The calculated and the experimental spin d e n s i t i e s , as well as the coupling constants, are tabulated i n Table XII. Table XII. Coupling Constants and Spin Densities i n 1,4-Dicyanobenzene Anion Radical. Posit i o n a^CFischer) a ±(100) a ±(124) 0 > ) ^"(expt.) 1 .2088 .2545 1.61 1.59 1.67 .0727 .0506 .0679 7(a N) 1.79 1.80 1.87 .0609 .0530 9 .0848 .0914 The l a b e l l i n g of the molecule i s shown below 1 1 Fig. 50. Theoretical Spectrum of 1,4-Dicyanobenzene Anion Radical, a N = 1.79 G, a H =1.61 G. - 198 -The assignment again leaves l i t t l e doubt as to v a l i d i t y and the agreement between the o r e t i c a l and ex-perimental spin densities f o r the carbon atoms con-tiguous to protons, i s quite acceptable, at l e a s t i n the Huckel case. G. 1,2,4,5-Tetracyanobenzene. When a 5 x 10 - 4M solution of 1,2,4,5-tetracyano-benzene (TCNB) i s electrolyzed at -0.37 v vs. S.C.E., a lemon-yellow solution r e s u l t s , which exhibits a spectrum of eleven almost equidistantly spaced l i n e s at room temperature. This seemed to indicate that the proton s p l i t t i n g and nitrogen s p l i t t i n g were very nearly equal, since a very much smaller proton s p l i t t i n g should r e s u l t i n nine l i n e s , due to nitrogen s p l i t t i n g , only. The spectrum was consequently recorded at a lower temperature, -60°C, and resixlted i n a s p l i t t i n g of a l l but the two outside l i n e s . A t o t a l of 21 l i n e s was e a s i l y d i s t i n -guishable, a large number of further l i n e s , probably the missing 6 l i n e s of the 27 l i n e spectrum to be ex-pected, as well as C 1 3 s p l i t t i n g s , could be discerned, but no d e f i n i t e assignment could be made. The spectrum i s shown i n F i g . 51. T h e o r e t i c a l l y one would expect to observe 27 l i n e s — I Fig. 51. EPR Spectrum of 1,2,4,5-Tetracyanobenzene Anion Radical. - 200 -from s p l i t t i n g by a set of four equivalent nitrogen n u c l e i (T^I^-H) and a set of two equivalent protons (ZX!H= I ) .• A t h e o r e t i c a l spectrum based on s p l i t t i n g from such n u c l e i , and using a^=l .-21 g and a^=1.08 g, i s shown i n F i g . 52. The agreement i s quite good, and leaves no doubt as to the correctness of the analysis, although the maximum number of 27 l i n e s could not d e f i n i t e l y be observed.,. The calculated and experi-mental spin d e n s i t i e s , along with coupling constants, i s given i n Table XIII, employing the l a b e l l i n g given below; Table XIII,. Coupling Constants : and Spin Densities i n 1,2,4,5-Tetracyanobenzene Anion Radical. P o s i t i o n a^(Fischer) a.(100) ^ ( e x p t . ) 1 .1606 .1915 3(a H) 1.08 1.11 .0000 -.0572 .0456 7(a N) 1.21 1.15 .0344 .0277 11 .0550 .0594 Fig.52. Theoretical Spectrum of 1,2,4,5-Tetracyanobenzene Anion Radical, a N = 1.21 G , a H = 1.08 G. - 201 -From the above table, one sees that the coupling constants obtained by us and by Fraenkel et a l . are i n close agreement. The experimental spin density also agrees reasonably well with the theore t i c a l McLachlan spin density. However, Fraenkel et a l (100) have stated, that a spectrum consisting of nine t r i p l e t s had been obtained. This would be the case i f the proton coupling constant were considerably smaller than the nitrogen s p l i t t i n g constant. Two of these authors (48) also present an experimental spin density of 0.0018 at the carbon atoms contiguous to the proton positions, this value corresponding to a s p l i t t i n g of 0.04 gauss when using UCH - -237g . Both the quoted appearance of the spectrum, as well as the value of p" = 0 oo I 8 J though compatible with each other, are not i n accord with the proton coupling, constant quoted, i . e . 1.11 gauss. A spectrum consisting of at l e a s t 11 major l i n e s , even i f these are unresolved, must r e s u l t from a coupling corresponding to the con-stants quoted. D. 7,7'8,8'-Tetracyanoquinodimethane• E l e c t r o l y s i s at -0.1 v vs. S.C.E. of a 10 - 4M solu-t i o n of 7,7'8 ,8'-tetracyanoquinodimethane (TCNGL) , - 202 -using a mixture of 80% dimethoxyethane and 20% aceto-n i t r i l e , and 10~^ "M i n c a r r i e r e l e c t r o l y t e , resulted i n a pale yellow solution, the ESR spectrum of which i s shown i n F i g . 53. The spectrum i s seen to consist of 45 major l i n e s , the number to be expected from a species i n which hyperfine s p l i t t i n g from a set of 14 . /_ — four equivalent N n u c l e i ( Z v - i w = H) and one set of four equivalent protons F H *2) occurs. The t o t a l s p l i t t i n g i s 13.88 gauss, while linewidths between points of i n f l e c t i o n are ~ 70 mg, the l i m i t i n g l i n e -width of the spectrometer employed. The spectrum can be analyzed i n terms of the following coupling constants, aN=1.02 g and aH=1.44 a. The t h e o r e t i c a l spectrum thus obtained i s shown i n F i g . 54, agreement being excellent with the experimental spectrum. Calcula t i o n of the 7T -electron spin density d i s t r i b u t i o n f o r the TCN& r a d i c a l anion were ca r r i e d out using the Hiickel approximation with the Coulomb in t e g r a l cx^  varying from cxc + O.g ($cc to occ +- /. 2 (2Cc and the exchange i n t e g r a l ^>CN varying from i-O^^. to 2.i/ftcc. The values obtained f o r ^ (see following l a b e l l i n g ) varied from 0.0454 to 0.0560, which i s to be compared with an experimental value of 0.0608 when using 6l*H--23-14 Fig.53. EPR Spectrum of TCNQ Anion Radical Fig. 54. Theoretical Spectrum of 7,7',8,8'-Tetracyanoquino dimethane Anion Radical, a^ = 1.02 G, a H = 1.44 G. - 205 -gauss. Since no appreciably better agreement could be obtained, Rieger and Fraenkel's values (48), along with the coupling constants, are presented i n Table XIV. Table XIV. Coupling Constants and Spin Densities i n TCNQ. Anion Radical. P o s i t i o n a^(Fischer) a i ( P h i l l i p s ) ^ ( a ) (^(b) ^ T ( expt. ) 1 .0494 .0102 2(a H) 1.44 1.57 .0539 .0431 .0608 7 .2245 .0102 9 .0126 -.0005 13(a N) 1.02 1.10 .0465 .0537 The l a b e l l i n g employed f o r constructing the above table i s : Agreement with the Huckel spin density i s better than with the McLachlan density, even the former leaving something to be desired. - 206 -In the spectrum of the r a d i c a l anion, a large number of a d d i t i o n a l , though i n the majority of cases much les s intense, l i n e s , can be observed, these l i n e s being attributed to s p l i t t i n g from G n u c l e i (1=1") i n na-t u r a l abundance. I t i s known that the i n t e n s i t y of a 13 G l i n e , to be c a l l e d a s a t e l l i t e , i s , i n the absence of overlap, much less intense than the l i n e from which i t a r i s e s , c a l l e d the parent l i n e , more pr e c i s e l y , f o r a one-atom s i t e the i n t e n s i t y r a t i o of s a t e l l i t e to parent l i n e i s 0.005602 (45). Since there are two 13 sets of four equivalent G n u c l e i and 2 sets of -two 13 equivalent G n u c l e i , denoted by superscripts 4 and 2 respectively, a series of l i n e s with i n t e n s i t i e s 0.02408 and 0.011204 that of the respective parent l i n e s should be observed. In the present analysis only c l e a r l y resolved l i n e s were employed, thus making the use of any correction factors unneccessary. Lines 13 which overlapped with other G or with parent l i n e s were not used i n the analysis, though they do provide useful checks. I t was possible to d i s t i n g u i s h on the basis of i n t e n s i t y considerations between 4-atom and 2-atom s i t e s p l i t t i n g s , aid to assign coupling constants of 6.28 g and 0.62 g to 4-site positions, couplings of - 207 -7.18 g and 4.40 g to 2-site positions. In the absence of further r e s u l t s , i t i s of course evident, that no assignment within a set can be made. As shown by Fraenkel and collaborators, the s p l i t t i n g due to a C ^ nucleus can be expressed by an equation of the type (B27), so that e x p l i c i t ex-pressions f o r the coupling constants from the four 13 d i f f e r e n t G s i t e s take the form: <) - (fi-ty &. a*<, &, si*, p ; *% - [iC' rJ&Zc) {I r 2 <3^c, £ . & %c, f The following are,the values of the parameters estimated f o r a GHG? fragment with equivalent sp hybrid bond (40): SC=-12.7 gauss, & c* =19.5 gauss, &cc' =14.4 gauss, and 01°  ^c< =-13.9 gauss. For an sp hybridized atom £C> . has been given the value 13.63 gauss c (40), while f o r 6lc'c the value -13.9 gauss has been retained. This i s probably not quite connect, the error should however be small. To calculate the coupling - 208 -constants f o r the n i t r i l e carbon atoms, the a d d i t i o n a l parameters (2^j and $ C C are needed. These are given by Rieger and Fraenkel (48) and have the values 14.7-4.8 gauss f o r McLachian and 29.0-12.1 g f o r Huckel s p i n d e n s i t i e s , and -47.5-5.5 gauss f o r McLachian and -72.9-9.3 gauss f o r Huckel d e n s i t i e s , r e s p e c t i v e l y . Using these v a l u e s , the c o u p l i n g constants given i n Table XV have been c a l c u l a t e d . Table XV. G 1 3 S p l i t t i n g Constants i n TCNG Anion R a d i c a l . P o s i t i o n C a l c . a c Huckel C a l c . a^ McLachian a c (Expt.) C ( l ) 2 -3.11 -5.02 (-) 4.40 C ( 2 ) 4 + .48 + .79 .62 C ( 7 ) 2 + 5.23 + 8.49 7.18 C ( 9 ) 4 -7.17 -8.44 (-) 6.38 I n the above, the c o u p l i n g constants f o r the p o s i t i o n 1 and 9 carbon atoms have been c a l c u l a t e d to be nega-t i v e . Our experimental methods do not enable us to determine the absolute s i g n of the s p l i t t i n g constants. Furthermore the assignment of c o u p l i n g constants to a c e r t a i n p o s i t i o n w i t h i n a set of 2 - s i t e or 4 - s i t e s p l i t t i n g s has been guided only by the magnitude of - 209 -the calculated, s p l i t t i n g s . The agreement i s quite s a t i s f a c t o r y , when considered i n l i g h t of the approxi-mations involved. A further r e s u l t i s that the spin density at the nitrogen n u c l e i appears to be po s i t i v e i n the TCN& anion r a d i c a l . I t has been mentioned previously, that recent theories show that the linewidth of the ind i v i d u a l hyperfine components varies with the value of , the nuclear spin quantum numbers, the width depending on two terras which are proportional to M-j-2 and M-j., respectively. In accord with previous d i s -cussions, i f J ^ f l y y %•% ^z being perpendicular to the plane of the heavy atoms), then l i n e s on the low f i e l d side of center should be narrower and sharper (perhaps manifested i n a s l i g h t l y higher i n t e n s i t y i f the spectrometer resolution i s the linewidth determin-ing factor) than those on the h i g h . f i e l d side. Henning and de Waard (47) have found that t h i s requirement i s obeyed f o r several nitrogen heterocyclic aromatic anions. Careful i n v e s t i g a t i o n of the spectrum of TCNQ. also shows that the low f i e l d l i n e s are s l i g h t l y more intense and sharper than the high f i e l d l i n e s f o r M-j. # 0. This i s i n agreement with the view that a^ ( i . e . ^ ) i s p o s i t i v e . - 210 -E. General Results and Conclusions, The o v e r a l l s p l i t t i n g of the four compounds i n -vestigated ranges from 11.84 gauss f o r TCN6C to 16.42 gauss f o r p h t h a l o n i t r i l e r a d i c a l anion. I t may be possible to d i s t i n g u i s h between two types of compounds, as f o r the nitroaromatics, depending on whether a symmetry operation of the respective point group w i l l or w i l l not exchange a starred f o r an unstarred posi-t i o n . A l l of the compounds investigated by us f a l l i n to the category where exchange of such positions does occur, by analogy with the nitro-compounds suggesting narrow spectra. No compounds of the other type were investigated. Fraenkel et a l . (100) have investigated compounds of t h i s type, f o r instance b e n z o n i t r i l e , i s o p h t h a l o n i t r i l e , and 4-cyanopyridine, these systems showing an o v e r a l l s p l i t t i n g ranging from 20.58 g f o r benzonitrile anion to 24.04 gauss fo r 4-cyanopyridine anion. I t had been hoped to obtain a r e l a t i o n , expressing nitrogen coupling constants i n terms of spin d e n s i t i e s , but since such calculations have been reported by Rieger and Fraenkel (48), no calculations along these l i n e s have been performed by us. For a detailed d i s -cussion, the interested reader i s referred to above - 211 -author's paper. Here, Rieger and Fraenkel's r e s u l t s w i l l merely be employed to compare the calculated and experimental nitrogen coupling constants. The equation expressing the coupling constant i n terms of the spin densities on the nitrogen and surrounding atoms, has the form where a l l symbols have been previously described. The prime merely emphasizes the f a c t that the n i t r i l e carbon atom, sp hybridized, i s under consideration. The constants as determined by the previous authors are f o r spin densities using the McLachlan procedure, and f o r spin densities using Huckel c a l c u l a t i o n s . A second equation, of the McGonnell type - 212 -has also been shown to give reasonable agreement i f the values f o r K N are 18.9-.4 G and 19.8*.7 G, de-pending on whether a McLachian or simple Huckel approach i s used. Using both types of equation, the calculated coupling constants f o r the four compounds investigated, along with the experimental values, are given i n Table XVI. Table XVI. Nitrogen Coupling Constants i n Cyano-Anion Radicals. Compound a N(expt) a^ (Huckel) Fraenkel McConnell Rel. Rel. aftf( McLachian) Fraenkel. McConnell Rel. Rel. 1,2-Dicyanobenz. 1.80 1.70 1.70 1.74 1.74 1,4-Dicyanobenz. 1.79 1.71 . 1.68 1.80 1.73 TCNB 1.21 1.17 .92 1.18 1.12 TCNQ 1.02 1.21 1.09 1.24 1.01 From the above table, the agreement between ex-perimental and calculated a^ i s seen to be quite good, using both Huckel and McLachian approaches, although the McLachian procedure does y i e l d s l i g h t l y better r e s u l t s . Also the more complicated Fraenkel type equation gives better agreement than the simple McConnell equation, the difference being however not so large as - 213 -to enable one to state d e f i n i t e l y that CN bond p o l a r i z a -t i o n by the n i t r i l e carbon spin density contributes to the nitrogen coupling constant. For the TCNQ. anion, agreement i s s t i l l acceptable, though poorer than f o r the cyanobenzenes when the Fraenkel r e l a t i o n i s em-ployed. In t h i s case, the simple McConnell type equation y i e l d s very s a t i s f a c t o r y r e s u l t s . 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Miyagawa, Y. K u r i t a , and V/. Gordy, J . Chem. Phys. 33, 1599, (1960). 128. M. Katayama and W. Gordy, J . Chem. Phys. 35, 117, (1961). 129. C. A. McDowell, K. F. Paulus, and J . R. Rowlands, proc. Chem. Soc. 1962, 60. 130. M. I. Melchior and A. H. Maki, J . Chem. Phys. 34, 471, (1961). - 221 -Appendix I Spin Densities i n Nitroaromatic and Hydrocarbon Radicals. Atom 1 2 3 4 5 6 1 2 3 4 5 6 ? SCF + .203 -.079 + .172 + .296 + .145 + .023 + .091 -.010 + .088 + .058 -.093 + .180 \ " i HM—± X 7N 3> 0 N' 0 1 2 3 4 5 6 7 -.120 + .355 -.030 + .082 + .055 + .049 + .033 - 222 -- 223 -Appendix II Experimental g-Values of Nit r o - and Gyano Anion Radicals. Anion g-value 1,2-Dinitrobenzene 2 .0050 1,3-Dinitrobenzene 2 .0047 1,4-Dinitrobenzene 2 .0050 1,3,5-Trinitrobenzene 2 .0036 1,4-Dinitronaphthalene 2 .0053 1,5-Dinitronaphthalene 2 .0048 1,8-Dinitronaphthalene 2 .0070 1,2-Dicyanobenzene 2 .0030 1,4-Dicyanobenzene 2 .0029 Tetracyanobenzene 2 .0029 Tetracyanoquinodimethane 2 .0031 8 z X Y Fig. I. Precession of Spin Vector in Magnetic Field. .2. Energy Levels 8 Spectrum for System of 3 Equivalent Protons. Fig. 3. Conformational Isomers of Terephthaldehyde. 'I I I I I I I I I I I 80 40 0 -40 -80 ACA> Fig. 4. Apparent Linewidth Alternation. (Reproduced from Ref. 74 ) AFC Unit Terminal Loo d Reflector Power Supply I Phase Shifter Klystron Isolator — Attenuator — Magic Tee NMR Probe Modulation Coils Mognet Coils H Crystal Detector 100 KC Receiver Magnet-ometer I STB 1 0 0 KC Oscillator C RO TT" Signal Generator I Frequency Counter 100 KC Modulator Phase Shifter Phase Detector Recorder Integrator Rg. 5. 100 KC EPR Spectrometer. Reflector Klystron T I 0.0 KC Oscillator Reflector Power Supply Magic Tee Crystal Dete ctor Pre amp-lifier 10.0 KC Amplifier Phase Detector Fig. 6. AFC System. B 10 Socket Stopcock Tungsten Anode Connection B 10 Joint Tungsten Cathode Connection B24 Joint Hg Pool / Pt Foil Sintered Glass Oisc Teflon Sleeving Vitreosil Tubing Bare Pt Wire Fig.7 EPR Electrolysis Cell. Nitrogen Teflon Sleeving Sintered Glass Discs Teflon Sleeving Bare Platinum Wire Tungsten Anode Connection B 10 Joint Tungsten Cathode Connection Agar Agar/Salt Bridge Sat'd. KCI Solution Hg2CI2/Hg Paste Hg Tungsten Connection Fig. 8. Observation Cell with Calomel Reference Electrode. O.C. R.C. S.C.E Fig. 9. Electrolysis Circuit. Tungsten Anode Connection B 10 Socket B 10 Joint Stopcock Sintered Glass Discs Tungsten Cathode Connection B 7 Joint < Graded Seal Teflon Sleeving 0< :—I cm Optical Cell Bare Pt Wire Fig. 10. Optical Electrolysis Cell. 3392.04 G 3388.70 G 3376.87 G 3385.67 G 3381.24 G Fig. II. EPR Spectrum of 1,2- Dinitrobenzene Anion Radical, 2 0 ° C. Fig. 12. Theoretical Spectrum of 1,2-Dinitrobenzene Anion Radical, a N = 2.82 6, a H = 0.22 G, a H - 1.68 G. 3247.99 G Fig. 13. EPR Spectrum of 1,2-Dinitrobenzene Anion Radical at -30° C. Fig. 14. Theoretical Spectrum of 1,2-Dinitrobenzene Anion Radical, a N = 3.06 G, a H = 0.29 G, a H • 1.71 G. f 3 4 3376.07 G 3373.13 G 337053 G 3368.55 G Fig.15. EPR Spectrum of 1,3-Dinitrobenzene Anion Radical in 5 0 % D M E / 5 0 % D M F . X X X X o o o o o * o * 0 * 0 0 0 0 0 m = 0 m= I m= 2 0 * 0 * O • O H Fig. 16. Theoretical Spectrum of 1,3- Dinitrobenzene Anion Radical,a N=3.99 G, a H 2 = 1.08 G ,a H 4 = 4.37 G , a H 5 « 2 . 8 l G. 3386.40 G 3381.94 G Hg. 17. EPR Spectrum of CH5CN. 1,3-Dinitrobenzene Anion Radical Fig. 18. Theoretical Spectrum of 1,3-Dinitrobenzene Anion Radical in C H 3 C N , aN= 4.35 G, a H^= 1.04 G, a H 4 = 4.17 G, a H 5 = 2.98G. Fig. 19. Theoretical Spectrum of 1,3-Dinitrobenzene Anion Radical in C H 3 C N , a N = 4.!3 6 ,a H 2 =l .04G,a H 4 =4.48 G , a H s = 2.98G. - ' 5 % / 8 5 % , 3 o % / ; 0 b e n 2 e n e A n 4, and 40%/sooy ' ° n Rod/col C H 3 C N / 0 M E . Fig.21. Theoretical Spectrum of 1,3-Dinitrobenzene Anion Radical, a N = a H 4 = 4.30 6 , a H 5 = 2.98 6 , a H 2 = 1.07 G. Fig.22. EPR Spectrum of 1,3-Dinitrobenzene Anion Radical in 5 0 % / 5 0 % CH3CN/DME. 3380.95 G 3389.32 G Rg.23.EPR Spectrum of 1,3-Dinitrobenzene-d4,low Resolution. Fig. 24. EPR Spectrum of 1,3-Dinitrobenzene-d4 Anion Radical, High Resolution. I i t V Fig.25. Geometrical Isomers in 1,3- Dinitrobenzene. r a N 2 N 0 r r <-2 b. c. • d. i I i i i Rg.26. Theoretical Spectra Considering Variation in a N only. a. H 2 H , N 2 N l HQ H-, H, No H| N. HO H. N - 2 H - H_. b. I i Fig. 27. Theoretical Spectra Considering Variation in a ^ only. N i H. N 0 H, N . H. Fig.28. Theoretical Spectra Considering Variation in Both a^ and a ^ . Fig.30. Theoretical Spectrum of 1,4-Dinitrobenzene Anion Radical, a N * 1.56 G, a H = 1.12 G. Fig. 31. EPR Spectrum of 1,4- Dinitronaphtholene Anion Radical. Fig. 32. Theoretical Spectrum of 1,4- Dinitronaphthalene Anion Radical, a N = 0.97 G , a H = l .69G ,a H =0.53G,a H =0.416. X y Z 3374.82 G 3373.04 G 3385.39 G 3382.32 G Fig. 33. EPR Spectrum of 1,5-Dinitronaphthalene Anion Radical. Fig. 34. Theoretical Spectrum of 1,5-Dinitronaphthalene Anion Radical, a N =2.30 G , a H x = 2.826, a H y = 2.42 G , a H z * 0.44 G. 3371.91 G 3374.73 G 3396.17 G 3393.74 G Fig.35. EPR Spectrum of 1,8-Dinitronaphthalene Anion Radical. Fig. 36. Theoretical Spectrum of 1,8-Dinitronaphthalene Anion Radical, a N =3.03 G , a H =3.73 G , a H =3.63 G , a H =0.95 6. Fig.37 EPR Spectrum of TNB~-*TNB Complex. Fig. 38. EPR Spectrum of Radical. 339169 G 1,3,5- Trinitrobenzene Anion i Fig. 39. Theoretical Spectrum of 1,3,5-Tri nitrobenzene Anion Radical, N = 2.48 6, a H «4 . I4 G. I I I i L 3000 4000 5000 6000 7000 Fig.40. Optical Spectrum of s-Trinitrobenzene in CH3CN During Electrolysis at -0 .48 V vs. S.C.E. Fig. 41. Optical Spectrum at Stage When T N B " is Largely Present. H - > Fig. 42 . EPR Spectum During Electrolysis Beyond -0 .48 V vs. S.C.E. Fig. 43. Final EPR Spectrum from Electro-lysis Beyond -0.48 V vs. S.C.E. I 3000 i 4000 5000 6000 7 0 0 0 A Fig. 44. Opticol Spectrum of Decomposition Products After Electrolysis Beyond -0.48 V vs. S.C.E. Fig. 45. EPR Spectrum of 2 2'4 4'e A 1 - • ^ , 4 , 6 , 6 Hexanitrobiphenyl Anion Radical in CH5CN. Fig.46. Starring in Nitroaromatic Compounds. 3401.29 G 3387.72 G 3395.00 G Fig.47. EPR Spectrum of 1,2-Dicyanobenzene Anion Radical. Fig.48. Theoretical Spectrum of 1,2-Dicyanobenzene Anion Radical, a N =1.80 G, a H 3 = 0 . 4 5 G, -aH -4.16 G. Fig.49. EPR Spectrum of l£-Dicyanobenzene Anion Radical. Fig. 50. Theoretical Spectrum of 1,4-Dicyanobenzene Anion Radica l ,a N = 1.79 G,a H =l .6 l G. 3258.21 G 325229 G p,a. 51. EPR Spectrum of 1,2,4,5-Tetracyanobenzene Anion Radical. Fig.52. Theoretical Spectrum of 1,2,4,5-Tetracyanobenzene Anion Radical, a N = 1.21 G , a H = 1.08 G. 3 3 9 0 . 9 8 G Fig.53. EPR Spectrum of TCNQ Anion Radical.) i i I I II 1 Nil Illl.lllllllllll.llll 1111 I ill In—, Fig. 54. Theoretical Spectrum of 7,7',8,8'-Tetracyanoquino-dimethane Anion Radical, a N = 1.02 G, a H = 1.44 G. 

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